New SAT 2020 | Video Solns to 580 Official Study Guide Math

Walks through solving a non-calculator sat math question from 2016 test 1 section 3 #1 by substituting k=3 into (x-1)/3=3, clearing the denominator, and solving for x to get 10.

Group like terms to sum complex numbers, treating i as a variable. This SAT 2016 problem shows the real part -1 and imaginary part 12, giving -1 + 12i.

Compute Ahmed’s five hours at rate m and Tyrone’s four hours at rate p to yield 5m + 4p, confirming option c in this SAT math problem.

Use the equation P = 108 − 23d to find remaining phones after d days, with 23 fixed per day and 108 starting.

Distribute the negative through all terms in second polynomial, then combine like terms such as x^2 y and x y^2, and check the answer key to pick the correct option.

Apply the linear equation to interpret height growth; the slope is three inches per year and the y-intercept is 28.6 inches, showing yearly increase.

Learn to solve for p by cross-multiplying a fraction and isolating p, turning a complex expression into a clear, single-variable result.

Practice solving ratio problems by flipping fractions, cross-multiplying, and isolating B of A when A over B equals 2, leading to the answer C.

Practice solving a two-equation system by elimination or substitution, align coefficients to cancel x, obtain y = -8, then back-substitute to find x.

Explore evaluating the function g(x) = x^2 + 24 through substitution. Find g(4) and then determine g(-4) by applying the same formula with the corresponding input.

Set the beef price per pound equal to the chicken price per pound, solve for x, then substitute to find the beef price.

The lecture shows that a line through the origin with slope 1/7 keeps y/x constant; thus any point on the line satisfies y/x = 1/7, so the answer is D.

Master solving SAT algebra problems by finding a common denominator, combining fractions, and using reciprocal multiplication to simplify and identify the correct answer.

Learn to simplify 8^x / 2^y by rewriting 8 as 2^3, using common denominators to subtract exponents, and applying 3x - y = 12.

Factor and match coefficients to find ab = 15 and the x-term coefficients summing to 8; testing (a,b) = (3,5) or (5,3) yields c = 31 or 41.

solve sat 2016 test 1 sec 3 question 16 by factoring a difference of squares, rewriting as (c+2)(t-2)=0, and selecting the positive t, which gives t=2.

Demonstrates solving a SAT geometry problem by using similar triangles and proportional reasoning, cross-multiplication, and strategic simplification to find x quickly without heavy calculator use.

Solve a two-equation system using the substitution method by isolating y in the first equation and substituting into the second to find x equals 7.

This lecture explains how sine equals cosine of 90 minus angle, with examples like sin 30 equals cos 60 and sin 20 equals cos 70, and the answer is forfeits.

Substitute the given values into the equation, square both sides to eliminate the square root, and isolate x to find x equals 100.

Identify the interval where the function strictly increases then strictly decreases, from about 40 to just over 60, in SAT 2016 test 1, section 4 calculator; the answer is B.

Use the linear relation y = kx with a constant k. Solve k from y = 24 when x = 6, then compute y = 20 when x = 5.

Apply parallel line properties to determine the second angle: a 35-degree angle and vertical angle equality yield 145 degrees via a 180-degree straight line.

Solve a basic algebraic equation by combining like terms and isolating x, clarifying that 'more than' means plus. Substitute x into 8x to verify the final answer 16.

Explore how to identify slope types in graph questions, using the slope formula (y2 - y1) / (x2 - x1), including positive, negative, zero, and undefined slopes, with horizontal and vertical cases.

Explain converting deka grams to milligrams using grams as the reference: 1 deka gram equals 10 grams and 1 gram equals 1000 milligrams, so 2 deka grams equal 20000 milligrams.

Interpret a SAT data question using a table and histogram, identify the correct y-axis magnitude and label, and recognize that 27.5 corresponds to 27,500 when scaled by a thousand.

Test the answer choices A through D for the SAT 2016 problem |n-1|+1=0, show that none yield zero, and conclude there is no value of n.

solve for t by rearranging the equation that links temperature to the speed of sound waves, subtract 1052, and divide by 1.8 to isolate t; select option a.

Apply the temperature formula from question 9 to solve SAT 2016 test 1 section 4 question 10, using speed of sound and 1000 x 1000 to compute Fahrenheit.

Solve a linear inequality by moving terms and flipping the sign when multiplying by a negative to obtain x ≤ -2, then identify the option not in the solution set.

Use the histogram to compute the average seeds per apple by weighting each seed count by the number of apples, summing the products, and dividing by 12.

Calculate 19 percent of the total respondents (310) to get about 59. Identify that the closest category is male students in geometry (option C).

Analyze how removing the potential outlier 24 inches from a length data set alters the mean, median, and range, revealing the range changes the most.

Identify that the c intercept on a cost vs. time graph represents the initial cost at zero hours, i.e., the initial boat rental cost.

Derive a linear equation from the cost vs hours graph, identify the y-intercept 5 and slope 3, and express C = 3H + 5 to select option C.

Analyze the graph to locate the minimum point in the SAT 2016 test 1, section 4, problem 17. The x-value at this minimum is minus three.

Plug in 0,0 into the inequalities to test the system, infer a is positive and b is negative, and conclude that a is bigger than b, selecting option A.

Use a two-variable system to determine salads and drinks sold from prices 6.50 and 2, total items 209, and revenue 836.50, revealing 93 salads and 116 drinks.

solve a sat math problem involving a 20 percent discount and 8 percent sales tax to compute the original price from the amount paid, treating tax on the discounted amount.

Calculate probability among dream recallers by dividing group y's 79 by the total 164, illustrating probability as count over total.

Solve question 22 by evaluating the average rate of change of the annual budget from 2008 to 2010 using the table, yielding about 65 thousand dollars per year.

Apply rounding strategies to approximate two-thirds ratios using HR data from 2007–2010, then assess options A–D for SAT 2016 test 1 sec 4 problem 23.

derive an equation of a circle with center at (0,4) from a point on the circumference, using a right triangle and the Pythagorean theorem to find radius 5/3, so x^2+(y-4)^2=25/9.

Learn how to solve a projectile motion problem by setting height to zero and factoring the quadratic to find ground-contact times, yielding t = 0 and about five seconds.

Identify a proportional relationship where one type yields 20 percent more than the other by multiplying the base number by 1.2. Solving 1.2B = 144 gives B = 120.

Solve SAT problem 27 by estimating earthworms in a 10 by 10 field using ten 1-by-1 samples, average per square meter, and scale to the full area.

analyze two inequalities by graphing lines with y-intercepts 1 and -1 and slopes 2 and 1/2, identify their intersection, and determine the no-solution region in quadrant four, yielding answer c.

Examine how p(x) evaluated at 3 equals -2 reveals the remainder when dividing by x-3, illustrating the remainder theorem with a sample polynomial.

Explore transformation of the parabola y = x^2 by outside shifts (up or down) and inside shifts (left or right, opposite signs), with examples using plus three and minus five.

Analyze a rate problem where husking capacity ranges from 12 to 18 dozen ears per hour to complete 72 dozen, yielding a 4–6 hour range.

Determine how many 14-pound boxes the man can load on the truck without exceeding a 6000-pound bridge limit, given a 4500-pound base weight, yielding about 107 boxes.

Interpret a line graph to compare values from 2008 and 2011, determine the fraction of 2008 relative to 2011, and simplify to 5/8, reinforcing basic fraction concepts.

Calculate how many 30-minute ad slots fit in a 24-hour TV day and extend the reasoning to two days, yielding 96 slots.

Apply the cylinder volume formula V = π r^2 h with height eight and the given volume to get r^2 = 9, then diameter equals 6.

Identify when a fraction is undefined by setting the denominator to zero, then solve the quadratic by factoring to find x equals 3.

solve a compound interest problem: a $100 deposit grows at 2% annually, modeled by 100*(1.02)^t, yielding x = 1.2 for year-to-year growth.

Compare two 100-dollar investments under compound interest: 2% vs 2.5% over 10 years, using 100*(1.02)^t and 100*(1.025)^t to show a $6.11 difference.

learn to solve linear equations by recognizing that 10x is double 5x in 5x+6=10, deducing 5x=4 and 10x=8, then 10x+3=11, showing multiple ways to reach answer C.

Master solving simultaneous equations by substitution (or elimination), turning one equation into a single-variable expression, substituting into the other, and identifying the solution for x and y.

Interpret the landscaping price function: price equals 60 plus 12 per hour. The 12 represents the hourly rate, as price increases by $12 every hour.

Recognize the expression 9a^4 + 12a^2b^2 + 4 as a perfect square trinomial, factor it to (3a^2 + 2b^2)^2, and select the correct option based on the square pattern.

solve a square root equation by isolating the radical, squaring both sides, and back-substituting to find k; with x = 7, derive k^2 = 16 and k = 4.

Identify that parallel lines have the same slope by comparing rise over run. Use cross-multiplication to solve for the missing segment and confirm the answer.

Learn to solve a SAT math fraction using the exponent rule for the same base, yielding a^2 - b^2, recognizing the difference of two squares, and with a+b=2, find a-b=8.

learn how to use the exterior angle sum, e = 360/n, to find the greatest polygon with exterior angle over 50 degrees, yielding n = 7.

Learn how to derive the line equation from a slope and a point, determine a second line from two points, and find their intersection by solving the equations.

Explore how to compare transformed graphs, the absolute value, x squared, and x cubed, to a horizontal line y = -1, and identify which equation lies above it, option c.

Rationalize the denominator of a complex-number division using the conjugate, apply FOIL, and simplify to reduced fractions.

Cross-multiply to gather f terms, factor out f, and divide by 1 - r to isolate f, yielding f = r/(1 - r).

Apply the quadratic formula to solve the quadratic equation. Find the roots 4 ± 2√3 and sum them to 8.

Learn to model radioactive decay from an initial 325 grams by applying yearly 15 percent decreases using sequential multipliers and recognizing the exponential pattern.

Use long division to simplify (5x-2)/(x+3), obtaining a quotient of 5 and remainder -17 over x+3, with the answer key guiding the solution toward option D.

Determine how many $250 bonuses were awarded given a total of $3000 and $750 bonuses. Reduce to x + 3y = 12 and find that x in {3, 6, 9}.

Learn to solve a quadratic by foiling and equating left and right sides, matching x-terms, x^2 terms, and constants to find B.

Apply the proportionality of similar triangles formed by parallel lines to resolve the missing length, using ratio and cross multiplication to find x = 4 and c = 12.

Identify a right triangle in the diagram, apply the 30-60-90 rule to determine the angles as 30 and 60 degrees, and convert to radians using pi/6 for 30 degrees.

the lesson shows that a system has infinitely many solutions when the equations are equivalent multiples, demonstrated by multiplying 2x+3y=10 to 8x+12y=40 and aligning x and y.

Compute the musician's revenue by multiplying download counts by the download price and streaming counts by the streaming price, then identify the correct option, which is option c.

Use ratio and proportion to scale from 7 of 400 to 350 inspections for 20000 bulbs, using cross-multiplication and a quick method.

Substitute L = 73 into the equation for the spring length, subtract 24 to get 49, then divide by 3.5 to find m = 14.

Apply direct proportion rules to money and people, identify a directly proportional relationship, and solve via cross-multiplication in a ratio problem, yielding 300.

Solve SAT 2016 question 5 by calculating profit from eight performers: subtract 43 percent expenses from 100 percent to get 57 percent, then multiply by 120 to obtain 68.40.

Solve a basic algebra problem by forming two equations, subtracting 12, dividing by 4 to get x = -1, then substitute into 2x+7 to get 5; the answer is B.

Solve a quadratic by factoring to find x-intercepts, using zero-product reasoning on x^2 - 6x + 8, which yields x = 2 and x = 4, matching the graph.

Explains a sat math problem: a player starts with k, loses two points per incomplete task, and 100 misses cost 200 points, solving for k and identifying answer is d.

Analyze a forklift problem by setting x and y as 40-pound and 65-pound boxes, forming x+y ≤ 45 and 40x+65y ≤ 2400, and selecting the correct option.

Solve by inside-out substitution: evaluate g(3)=2, substitute into f to get f(2)=3, and determine the answer is B.

Convert three hours to minutes and multiply by 250 words per minute to find Tony's daily reading output, then divide the book's total words by that rate to estimate days.

Set initial volume at 175,000 with annual increase of 7,500 to reach capacity of 325,000; form the inequality 175,000 + 7,500t ≥ 325,000 to identify years at or above capacity.

Explains how a sports-watching survey risks unreliable conclusions when data collection isn't random, especially when conducted at a single restaurant near a stadium.

Explore reading the line of best fit on a graph to estimate the year reaching 550 billion, using values around 2000–2005 to identify 2003 as the solution.

Learn to solve a distance per hour problem by converting years to hours and using a proportion to calculate the Earth's orbital miles per hour with clear unit handling.

Compute the probability that a randomly selected student who passed the bar exam did not take a review course, based on the table, yielding seven of twenty-five.

Learn how percent changes work by comparing an unknown element that is 20 percent less mass than calcium, and compute the new value by multiplying by 0.8 or 1.2.

Compare the median and mean using a five-home example to see how a few high values pull the mean upward while the median stays middle.

Apply the median formula for a large data set to two schools with 300 students each, total 600, using (N+1)/2 to locate the middle value, which is 1 sibling.

This lecture explains solving a racial proportion with data from Lincoln High and Washington High, using relative frequencies and cross-multiplication to scale from samples to totals.

Explain the SAT time-estimate problem using an inequality within 10 hours of the allowed time, with y minus x, and show how the answer key reveals the option that fits.

Cross-multiply the given equation to isolate r^2, expressing the square of the distance in terms of intensity and power. Divide by 4 pi to obtain r^2 = P/(4 pi I).

Solve for distance in intensity equations for two observers, cross-multiplying to compare the quantities a and b, showing that a is one fourth of b.

Learn to recognize circle equations and convert them to standard form using completing the square, identify the center and radius, and solve a SAT style circle problem.

Explore how the relation b equals the negative of a yields a positive slope for the line, using rise over run and example values to illustrate the graph.

Read the graph to identify inputs that yield an output of 1, tracing from x = -4, 1.5, and 3 to the graph and then to y = 1.

Compare insulated and non-insulated materials to understand rate of change in temperature. Read the data table and graph to see early drops and later declines.

Compute the line through (1,0) with slope -3, using the square's diagonals to relate slopes, yielding y = -3x + 3 and identifying option B.

Plug in the answer key values to test which option yields real solutions; only B works, since the square root of a negative is imaginary while A fails.

Demonstrates how to decompose a hexagon into two triangles and a rectangle, apply the sum of interior angles and 30-60-90 relationships, and solve for the square area as 256.

Solve a Richoux proportion from SAT 2016 test 2 sec 4 #31 by applying cross multiplication to a beach erosion setup, yielding 14 as the answer.

Convert hours to minutes by multiplying by 60, then add the 30 minutes to form a complete equation. Solve the equation to determine the age, which is seven.

In SAT 2016 test question 33, apply f(x) = 3x^2 − Bx + 12 with x = 3 and y = 6, and solve for B to get 11.

Solve a linear equation system by substitution: d = l + 40 and d + l = 250, giving Laura's hours equal to 105.

Apply a linear model y equals 18t plus 15 to deposits, showing initial deposit of 15 and a positive slope of 18 as the balance grows.

Identify that the ln minor arc corresponds to a 120-degree sector, making it one third of the circumference, then multiply 96 by 1/3 to obtain 32.

Apply the given growth formula with key 4000 to the initial 3000. End-of-year values grow to 3150 after year 1 and 3284 after year 2, showing compound-like growth.

Solve a linear equation to find the key, the number of plants an environment can support, using PEMDAS and cross-multiplication, and arrive at 7500 for question 38.

Identify how a more expensive paint brand affects cost: only the dollar per square foot changes, not the wall dimensions L and h.

Solve a sat math ratio problem by using given information, recognizing a doubling relationship from 3r = 18 to 6r = 36, and finding the answer as D.

Learn to interpret fractional powers as roots, break down exponents into two parts, and apply fourth and cube root concepts to determine equivalence to two thirds.

Analyze how to compare the ranges 1776–1849 and 1850–1900, using the fact that the larger number is twice the smaller to deduce 15 when the larger is 30.

Apply cross multiplication to a pair of fractions, isolate x to get x = 10, then compute x/5 to find 2, confirming option c.

Add 2x - 3y = -14 and 3x - 2y = -6, obtain 5x - 5y = -20, divide by five to reveal x - y = -4.

Learn how to factor a quadratic by testing zeros of f(x) and verifying that x-4 is a factor, with steps showing how f(3)=0 and f(4)=0.

Learn to find the slope of a line from a point using the equation y = kx + 4, substituting (c, d) to solve for k.

Find the value of k that makes the lines parallel, causing no solution; set slopes equal k/3 = 4/5, yielding k = 12/5.

Apply square roots to (x−11)^2=25, yielding x=6 or x=16, then interpret AB as the distance between intersection points, which is 10.

Explore SAT geometry reasoning as we model a problem with intersecting lines, opposite angles, and variable equivalences to determine which statements about X, Y, Z, and W hold.

Learn how to find the vertex of a quadratic by expanding to x^2+2x-8 and applying x = -b/2a. Then evaluate the function at the vertex to obtain the D value.

Multiply through by the common denominator to clear the fractions, then compare and set like terms equal to solve for x. The result is -3 (choice b).

solve 3x^2+12x+6=0 by applying the quadratic formula, identify a=3, b=12, c=6, and obtain -2 ± sqrt(2).

Treat the fahrenheit-celsius relation as a straight line, with a y-intercept of 32 and a slope of about 1.8, showing that a 1-degree Celsius change corresponds to 1.8 degrees Fahrenheit.

solve a high-power polynomial by factoring into (x^2 − 1)(x^2 − 4), find x = ±1 or ±2, and select the positive solutions 1 or 2 due to grid constraints.

Solve a fraction equation by aligning denominators, combining like terms, and applying cross multiplication to find x, with x = 2.

Apply isosceles triangle angle rules to a SAT math problem, using given y=75 and derived z=30 to deduce x=105.

Solve a system of equations by substitution from the caption: 2h + 3f = 7500 and h = f + 50, yielding the hamburger calories at 370.

Two similar triangles with a one-third scale factor yield x = 12 via Pythagoras and a 3-4-5 pattern; then sin f = 3/5 using sohcahtoa.

Analyze distance-time graph in the calculator section to estimate when Marilyn finished lunch during a 30-minute stop, using the horizontal plateau for finish time between 1 and 2 pm.

Apply the probability formula to combine cases using the or rule, adding the probabilities of female under 40 and male 40 or older from a 25-person set.

Analyze a line graph of album sales from 1997 to 2009, noting an initial rise followed by a decline and selecting option C as the trend.

Test pairs of inputs in a table by substituting values into each equation to identify the one that matches the given data; the analysis shows the correct equation is C.

Convert percentages to decimals, multiply to find National Honor Society members among juniors and seniors, and approximate the total to solve the SAT math problem.

Learn how to add like terms from two quadratic expressions to produce 8x^2 - 7x - 4, illustrating a straightforward SAT math technique.

Learn to clear fractions by multiplying by the reciprocal on both sides, avoid cross-multiplication without an equals sign, and arrive at w = 20 (answer choice d).

Interpret the straight-line equation y = 0.56 x + 27.2, where slope 0.56 represents an annual increase in the average number of students per classroom.

Use a ratio-proportion to map 25 m at 13.7 s to four minutes by converting to seconds, cross-multiplying, and estimating the distance at about 437.95 meters.

Use the weight formula W = m × g to compute weight on Mercury, with mass 90 and g = 3.6, yielding 324.

Use W = m g to find mass from Earth weight, showing mass stays constant while weight changes with gravity; solve for a planet’s g to identify Saturn.

Analyze how to count five distinct zeros by examining where the graph crosses the x-axis, and note how tangential bounces still yield a single zero.

Isolate v by rearranging the equation, move h and k to the left, and divide by t to use the 16 t^2 term, guiding you to the correct choice.

Convert eight hours to minutes (8 × 60 = 480), then multiply by 0.20 dollars per minute to find the total call cost.

Analyze a randomized study on treatment X for people with poor eyesight. Use process of elimination to select the correct conclusion: treatment X likely improves eyesight for those with poor eyesight.

Learn to find where f(x) and g(x) equal zero by locating opposite-signed, equal magnitudes on the graphs. The example centers on minus two as the x-value where the zero occurs.

Explains how a $10 price increase affects quantity supplied by testing s(p)=0.5p+40 at p=2 and p=12, showing quantity rises from 41 to 46.

Solve for the price where supply equals demand by equating (1/2)p+40 to 220−p, and confirm p = 120.

Convert graphene quantities from ounces to football fields and then to acres, using one ounce equals seven fields and one field equals one third acre, yielding about 450 acres.

This lecture explains reading a scatterplot to compare the line of best fit with the actual heart rate at 34 minutes, showing a 2-point difference (150 vs 148).

Examine how compound interest grows money by applying interest to the current balance. Understand why this exponential growth differs from adding interest to the initial amount.

Solve a SAT math problem by modeling X, Y, Z with a total of 855, using X = 1.5(Y+Z) to find Y+Z = 342 and X = 513.

Show that A and B are complementary because sin A equals cos B, with A = 4k-22 and B = 6k-13, then solve A+B=90 for k=12.5.

Solve a two-scenario distribution problem by setting equations for three millimeters per student with five leftovers and four millimeters per student needing twenty-one more to find the number of students.

Calculate the silo volume by adding the two cone volumes and the cylinder volume (r=5, h_cone=5, h_cyl=10) to get 1000/3 π ≈ 1047.

Solve a line through the origin by comparing slopes from two points, use rise over run to relate 32 and k, and conclude k = 8.

Solve a rectangle area problem with a 10 percent length increase and an unknown width decrease, finding P so area drops 12 percent, using decimals like 1.1 and 0.88.

Model a 10% population decline every 20 years by multiplying the starting 50,000 by 0.9, converting 100% to 1 and 10% to 0.9.

Use two simultaneous equations from the caption: F+M=18 and 5F+9M=122, apply elimination to find F=10 and 50 right-handed females, giving probability 50/122 ≈ 0.41.

Learn to solve a two-equation SAT problem via elimination. Use B−C=−1/2, subtract equations, and isolate x in terms of y.

Learn to solve a SAT math word problem: with one adult paying 3 and each student 2, find integer x where 11 ≤ 2x + 3 ≤ 14.

Compute the mean age of presidents at the start of their terms by summing the ages and dividing by the number of presidents, rounded to the nearest tenth.

Solve a system of quadratics by combining like terms to determine the coefficient of x in x^2 + Bx + C, with the solution showing B equals 9.

Translate the sector angle 5π/4 into a fraction of the full circle by dividing by 2π, yielding 5/8.

Apply average and total-sum reasoning to a 20-readings problem: with first 10 summing 750 and overall average 85, maximize 12–20 to minimize the 11th, yielding 50.

Solve a system of two linear inequalities by graphing y < 5x and y < -15x + 3000 to find the highest intersection at x = 150, y = 750.

solve a sat math quantity about shoppers and checkout time by converting hours to minutes and dividing 84 by 12 to yield 7 shoppers.

Compare the original store with 45 shoppers to the new store with 18 shoppers per hour, using the 60 to 12 minute relation. The percentage decrease is 60%.

Explore how shifting the absolute value graph changes where it hits the x-axis. Only the absolute value minus one crosses the x-axis, yielding a zero.

Determine the constant b in f(x)=3/2 x + b so that f(6)=7. Then evaluate f(-2) to get -5, illustrating substitution to compute function values.

Learn to solve a two-equation system by expressing x in terms of y, substituting into the other equation, and isolating y to obtain its value.

Compute f(-3x) for the linear function f(x) = -2x + 5 by substituting -3x for x to get 6x + 5.

Apply foil to expand (2x+1)(4x+1), collect like terms, and distribute the outer factor of 3 last to obtain 24x^2+18x+3.

the video solves an a over b expression from the sat math guide, using 7/7 to form a common denominator, showing a/b equals 3/7 and selecting b.

This lecture solves SAT question 7 by modeling Emilio's weekly miles as a straight line with constant increase, deriving a 1.5 miles per week slope from weeks 4 and 16.

Identify the slope of the given line and rewrite each option in slope-intercept form to find a parallel line with slope minus three; conclude that option A matches.

Explore solving a square-root equation by squaring both sides and expanding to a quadratic, then factor and test candidate roots in the original equation to verify x=6 is valid.

Learn how to apply cross multiplication, combine like terms, and isolate t to solve a SAT math problem, yielding t = 55/9.

Identify the number of ordered pairs by examining the equation's degree; in this example, two, since the highest term is x^2 and yields two solutions.

Calculate each of Ken and Paul's share of a sandwich order by summing x and x+1, applying a 20 percent tip (multiply by 1.2), then dividing the total by two.

Learn how to find the intersection of two graphs by setting f(x) equal to g(x) and solving for x. The example yields x = ±1/2.

Master how to simplify complex numbers by multiplying by the conjugate, using i^2 = -1, and rewriting fractions into a + bi form for SAT math problems.

Multiply through by two to clear the denominator, then use the quadratic formula with the identified A, B, and C to solve for x; the result matches option B.

Use ratio and proportion on a multi-level triangle with total height 18 to find the gap between the first and second levels, yielding 9.

Apply sohcahtoa to relate sine and cosine for angles x and y, showing sin x = 0.6 and cos y = 0.6 using opposite, adjacent, and the hypotenuse.

Factor the cubic x^3 - 5x^2 + 2x - 10 by grouping to (x^2+2)(x-5). Solve for the real root x=5, since x^2 = -2 yields imaginary roots.

Use the elimination method on the linear system to create equal and opposite coefficients, cancel a variable, then substitute to obtain x=0 and y=5.

Compute the slope of the mesosphere temperature data to find the constant decrease per 10 kilometers, revealing a 25-degree drop between 50 and 80 kilometers.

Solve a linear equation to determine how many movies Jill rented given a $9.80 membership and $1.50 per movie, total spent $12.80, concluding two movies.

Calculate how many months Donald must improve from 180 wpm by five wpm each month to reach the requested speed, showing four months yields 200 wpm.

Solve a problem by taking a third of a half of three pounds, then convert to eight ounces, demonstrating how pounds relate to ounces through thirds in SAT math.

Apply ratio and proportion to a survey: from 90 surveyed, 25.6% prefer October, predicting about 57.6 (≈60) of 225 students. Cross-multiplication confirms the answer choice B.

Apply the density formula by cross-multiplying mass and volume with density; use mass 24 g and density 3 g/mL to find volume, giving v = 8 mL.

Set up an equation with Angelica’s hours a and Raul’s hours a+11, totaling 59, then solve for a to find Angelica works 24 hours (Raul 35 hours).

Compute the proportion of PG-13 movies in a 50-movie table, where four are PG-13, and simplify the fraction 4/50 to 2/25.

The line in the xy plane has a negative slope and passes through quadrants two, three, and four; the correct answer is D.

Calculate the probability of Midwest voters aged 18–44 by dividing the Midwest 18–44 counts by the total 18–44 voters, yielding about 0.22 (roughly 1 in 5).

Analyze the scatterplot to identify the data point with the longest gestation period and read its life expectancy from the y-axis.

Learn to identify the largest life expectancy to gestation period ratio by comparing fractions such as 7/23, 8/44, and 10/52, and determine that the largest ratio corresponds to option a.

Using the x-intercepts -3, -1, and 1, this lecture shows how to form the graph's equation by moving terms inside to x, identifying option C as the correct answer.

Analyze a time versus population graph to distinguish linear growth from exponential growth and identify the data as exponential, selecting option C.

Compare the future value of a $1,000 investment at 5% vs 3% with monthly compounding, and compute the difference by subtracting the two results.

This lecture explains how the exponent's sign in y = a x^b shapes the graph, guiding the choice of the correct option (B) for a falling curve.

Translate a construction-cost table into an inequality, combine like terms, and solve for x, yielding x ≤ 6 and the answer a.

We analyze the slope of the line for problem 17, showing the equation is y = 700 + 90x, so the slope reflects the wheelbarrow and concrete mixer rental.

Apply the cylinder volume formula with radius 1.5 in and height 6 in, then divide 231 by that volume to estimate about 5.4 glasses (five max).

Identify that 3p is at least 3, then the least value of 3p plus 2 is 5, shown by simple inequality reasoning and substitution.

Explore how biomass doubling each year demonstrates exponential growth and learn to identify the correct graph (option C) among linear and flat trends.

The lecture analyzes a 2000 vs 2010 energy consumption bar graph for biofuels, geothermal, wind, hydroelectric, and wood, showing 2010 data exceeds 2000 for three sources: biofuels, geothermal, and wind.

Determine the 2000 to 2010 consumption difference by reading the graph, compare 2.25 to 2.00, and apply the percentage decrease formula (decrease/original times 100) to get about 11 percent.

Compare the standard deviation of temperatures between two cities using the tables. City B shows a larger spread, while City A clusters around 79 degrees.

Identify that arc ADP equals half the circumference, apply c = 2 pi r with the given length 8 pi, and determine the radius as 8.

Discover how to make 2x+3 a factor by factoring x^2+3x+2 and combining f(x) with 3g(x), yielding the solution f(x) + 3g(x).

Explore testing inequalities with x and y using positive and negative examples, applying absolute value reasoning to determine which statements must hold for the setup, specifically statements 1 and 3.

Explore the equation of a straight line with y-intercept 61, explaining how even at near-zero population density the average housing cost remains at least 61 percent, based on the graph.

Convert the quadratic f(x) = x^2 + 2x - 24 to vertex form via completing the square, revealing the minimum value at x = -1 (−25) and the vertex.

Demonstrate how to correctly average X, Y, and Z using three items, avoid dividing by two, and derive the solution M plus seven for SAT 2016 test 4 question 29.

Explore how the horizontal line y equals minus three intersects the graph of f(x) to produce three real solutions, identifying the roots where f(x) equals minus three.

Calculate the pool's volume after 70 minutes at 8 gallons per minute, adding 560 gallons to the initial 600 for a final 1,160 gallons.

Explains modeling systolic blood pressure as a linear function of age, and identifies the slope as one half mmHg per year for age-related pressure increase.

Convert 75 Ruhlman digits to feet by relating 16 Ruhlman digits to 11.65 inches, yielding 54.6 inches or 4.55 feet.

Solve a ratio problem where male-to-total equals 3 to 5 after adding 100 tagged females and unknown extra males; the solution concludes the extra male count is 50.

Break down a fluid dynamics problem by comparing faster and slower fluids using q = 1/2 v^2, plug in 1.5 v for the fast case, and find the ratio 2.5.

Identify a circle of radius 10, where arc AB is a fraction of the circumference; (πx)/18 between 5 and 6 gives x between 28.65 and 34.37, so integers 29–34.

Apply exponential decay to model a stock value dropping 28 percent weekly, deriving the decay factor 0.72 and the formula V = 360*(0.72)^t.

Apply the general formula R^T, with R as the rate and t as time, to question 38 using R = 0.72 over three weeks and round to the nearest dollar.

Identify the slope and y-intercept from a graph to write line's equation in y = mx + b, using rise over run and example y = x + 1.

Determine the arc length by recognizing the 90-degree angle represents one fourth of the circle, then multiply the circumference 36 by 1/4 to find the arc length.

Solve a quadratic by factoring after simplifying with a common factor of four, reducing to (x+1)(x-3)=0 to obtain x = -1 and x = 3.

Identify the function with no x intercepts on the x-y plane by evaluating linear and quadratic options for real zeros, guiding you to the correct choice with no real zeros.

Plug in x = 9 to set up the radical equation, isolate the square root, square both sides to remove the radical, and solve to obtain 79.

Follow instructions to sum two expressions, cancel the -1 and +1, and obtain a^2 to identify the correct answer (A) quickly.

Set up equations and inequalities for Jackie's tutoring and lifeguarding hours, with 12 dollars per tutoring hour, a 50-hour lifeguard week, a 20-hour cap, and a 250-dollar minimum weekly earnings.

Explore interpreting a linear equation in slope-intercept form, identify slope and y-intercept, and apply t equals zero reasoning to answer a SAT official study guide math problem.

Learn to solve a system by substitution in a SAT-style question, using x^2 and y=x^2 to deduce x=1 and y=1. Then compute x times y equals 1 as the answer.

Explore substitution-based algebra in a new SAT problem, rewrite equations, foil squared terms, and select the correct answer (option B).

Apply the cylinder volume formula v = π r^2 h; doubling the radius and halving the height doubles the volume, giving a new volume of 44 from the initial 22.

Solve a fractional exponent problem by rewriting nine as three squared, converting to roots and powers, and recognizing that square roots require pairs to come out.

Learn to solve a SAT tea bags per cup problem by plugging in numbers and using cross-multiplication to determine tea bags per cup, concluding one tea bag per extra cup.

This lecture demonstrates transforming the exponential function 2^x with a vertical shift, compares it to the 2x+1 curve, and uses a negative to reflect about the x-axis.

Solve a SAT-style gasoline cost problem by converting dollars per gallon and miles per gallon into dollars per mile, then apply a linear setup to determine weekly mileage and savings.

Solve the inequality by combining the flat fee of 10 and the hourly rate of 60 to stay within a 280 budget. Determine that the maximum whole number of hours Maria can rent is four.

Solve a linear equation by distributing terms, combining like terms, and isolating p, then dividing by five to find its value.

Solve a pair of linear equations by substitution, using y = 2x to eliminate y and solve for x, yielding x = 21/4 (5.25) with alternative decimal or fraction forms.

Solve a rational equation by making every term have x^2 in the denominator, form a common denominator, distribute the negative sign carefully, and simplify the numerator to two.

Explore a geometry problem that uses the triangle angle-sum of 180 to solve for x, showing how 74 and 23 combine to yield x = 97.