ged - math

First, find the coordinates of the points on the graph: when x = 5, y = 3→ (5, 3) when x = 9, y = 8→ (9, 8) The average rate of change is the slope of the line through these points: ave. rate of change = 8−3 / 9−5 = 5/4 = 1.25

A function is shown in the graph. What is the average rate of change of the function from x = 5 to x = 9? A. 0.8 B. 5 C. 1.25 D. 1.5

The top of the ladder is 8 feet up the side of the building. The ladder, the side of the building, and the wall form a right triangle. Using the formula for the Pythagorean relationship, a^2 + b^2 = c^2 , you can calculate how far up the building the top of the ladder is. The ladder forms the hypotenuse of the right triangle, c . a^2 + b^2 = c^2 6^2 + b^2 = 10^2 b^2 = 100 − 36 b2=64 b = 8

A ladder is leaning against a building as shown in the diagram. How many feet up the side of the building is the top of the ladder? _______ ft

This game involves independent probability. Multiply the probability for each event: P(blue then blue) = P(blue)P(blue) = (3/20)(3/20) = 9/400 = 2.25%

A new board game comes with a deck of 20 cards: 5 red, 3 blue, 2 orange, and 10 green. After the deck is shuffled, the player is to choose the top card and note its color, replace the card, shuffle the deck again, and then choose the top card again and note its color. What is the probability that both cards selected are blue? A. 6.25% B. 9% C. 3% D. 2.25%

A = lw lw = A The quadratic equation is (x + 20)(x−40) = 2700 x2 − 20x − 800 = 2700 x2 − 20x − 3500 = 0 (x − 70)(x + 50) = 0 x − 70 = 0 or x + 50 = 0 x = 70 or x = −50 You can't have negative measurements, so x = 70

A rectanglular building lot has the dimensions shown. If its area is 2,700 ft2, what is the value of x? (Do not include units when you type in your answer.) x =

Use the simple interest formula: I = Prt. P = $4,200 r = 12% = 0.12 t = 3/12 = 0.25 years $4,200 + $4,200(0.12)(0.25) = $4,326

A small business owner borrowed $4,200 at an annual simple interest rate of 12%. What is the total amount that must be repaid in 3 months?

Substitute p = 12 into the formula and solve for S: S(12) = 1.5 (−12^2 + 1600 ⋅ 12) = 1.5 (−144 + 19200) = 1.5 (19056) = 28,584 The total sales would be $28,584.

A small company markets a new multi-vitamin. The function S(p) = 1.5(−p^2 + 1600p) predicts the total sales S as a function of the price p of one jar of the the multi- vitamin. Predict the total sales if each jar of the multi-vitamin is priced at $12. A. $29,016 B. $2,184 C. $28,584 D. $2,616

Start by calculating the number of black and blue covers sold: 0.35(200) = 70 black covers 0.23(200) = 46 blue covers Subtract: 70 - 46 = 24 There were 24 more black covers that blue covers sold in April.

A store sold 200 cell phone covers in April. The circle graph shows the percent of each color sold in that month. How many more black covers were sold than blue covers? ____________ more black covers were sold than blue covers

The square markers are for English and the round markers are for Math. The first square marker at or above the 70 point line is at 3 hours. The first round marker at or above the 70 point line is at 5 hours. 3 hours for English, 5 hours for Math

A student wants to earn a final grade of at least 70 in English and Math. Based on the graph, what is the minimum amount of weekly study time the student should spend in each subject? A. 3 hours for English, 5 hours for Math B. 5 hours for English, 3 hours for Math C. 2 hours for English, 5 hours for Math D. 5 hours for English, 5 hours for Math

This question asks for the probability of rain on both days. This is solved using the multiplication rule for independent probability: P(rain on M and T) = (0.6)(0.3) = 0.18 There is an 18% chance or rain on both days.

A weather report said there is a 60% chance of rain on Monday, and a 30% chance of rain on Tuesday. Based on the report, what is the chance it will rain on both days?

The slope of the wheelchair ramp can't exceed 1/12. Write this as an inequality and solve: 4/m ≤ 1/12 4(12) ≤ m (1) 48 ≤ m m ≥ 48

According to the National Building Code, the slope of a wheelchair ramp is not allowed to exceed 1/12. For the wheelchair ramp design shown, which inequality represents possible lengths for m? A. m ≥ 48 B. m > 48 C. m > 30 D. m ≤ 48

Start by writing a proportion, and let x equal the unknown height of the actual mall: 2cm/7.5m = 8.6cm/xm. Cross- multiply to solve for x: 2 ⋅ x = (7.5)(8.6) 2x = 64.5 x = 32.25 meters

An architect made a scale drawing of a mall she is designing using a scale of 2 centimeters = 7.5 meters. In the drawing, the mall is 8.6 centimeters tall. How tall is the actual mall? Enter your answer as a decimal. ________ meters

Find out how much each item costs in terms of b: 1 burrito: b 1 taco: b/2 1 chalupa: b + 0.75 Find out how much each item costs in terms of b: 2 burritos: 2b 8 tacos: 8 ⋅ b/2 4 chalupas: 4 (b + 0.75) Total cost: 2b + 8 ⋅ b/2 + 4 (b+0.75)

Arthur went to the local taqueria to buy lunch for his family. He can buy two tacos for the price of one burrito, and the chalupa is $0.75 more than a burrito. The cost of one burrito is b dollars. Which expression represents the cost of 2 burritos, 8 tacos and 4 chalupas? A. 2b + 8 ⋅ b2 + 4 (b−0.75) B. 2b + 8 ⋅ 2b + 4 (b−0.75) C. 2b + 8 ⋅ b2 + 4 (b+0.75) D. 2b + 8 ⋅ 2b + 4 (b+0.75)

To find the increase between two years, find the difference between the earnings in the first and second year. The smallest increase is between 1999 and 2000, an increase of 0.3 million, or 300,000 dollars.

Between what two consecutive years did the Buzby Corporation have the smallest increase in earnings? A. 1998 and 1999 B. 1996 and 1997 C. 1995 and 1996 D. 1999 and 2000

To find the answer, use the formula in the problem, d =(p−c) ÷ 2 . The problem gives the value of p , $120, and the value of c , $50. The discount will equal $120 minus $50, divided by two. The answer is $35.

Cece works at a dress shop and needs to calculate the discounts for dresses on sale using the formula d = (p − c) ÷ 2, where d is the discount, p is the original price, and c is the store's cost for the dress. If the store's cost for a dress is $50 and the original price of the dress is $120, what is the discount on the dress? A. $25 B. $40 C. $35 D. $50

Begin by placing a dot at 7. The first operation on the list was 7 − 11 = −4 , so place a dot on −4 The next operation is −4 + 4 = 0 so place a dot on 0.

Consider the sum: 7 + (−11) + 4 Place a dot on the number line at 7 to represent the first number in the expression. Then add the numbers. Place a dot on the number line for each resulting sum, as you add from left to right. To remove a dot you have already placed, click on it again.

100 times $10 equals $1,000, plus $130 equals $1,130. The total cost of the wind chimes is $1,130.

Eman is planning to sell wind chimes at a craft fair. The cost of her tools for building the wind chimes is $130. The costs of materials are $10 per wind chime. What is the total cost to make 100 wind chimes? A. $1,450 B. $1,260 C. $980 D. $1,130

The table represents a function when each x-value is paired with no more than one y-value. This only happens when a = 0 and b = 0.

For what values of a and b does the table represent a function? A. a = 0 and b = 0 B. a = 5 and b = 5 C. a = 4 and b = 7 D. a = 3 and b = 1

Find the time t it will take Gloria and Lynh to travel 12 miles using the distance formula, d = rt.The problem tells us that Lynh travels at a rate of 30 mph.Substitute d = 12 and r = 30 into the formula and solve for t: Find the time t it will take Gloria and Lynh to travel 12 miles using the distance formula, d = rt.The problem tells us that Lynh travels at a rate of 30 mph.Substitute d = 12 and r = 30 into the formula and solve for t: d = rt 12 = 30 t 12/30 = t t= 2/5 hr The line in the graph clearly passes through the point (20, 14). This means that Gloria travels 14 miles in 20 minutes, which is equivalent to travelling 42 miles in 60 minutes. So, Gloria's rate is 42 mph. Substitute d=12 and r=42 into the formula and solve for t:The line in the graph clearly passes through the point (20, 14). This means that Gloria travels 14 miles in 20 minutes, which is equivalent to travelling 42 miles in 60 minutes. So, Gloria's rate is 42 mph. Substitute d = 12 and r = 42 into the formula and solve for t: d = rt 12 = 42t 12 /42=t t = 2/7 hr Subtract the times: 2/5 − 2/7 = 14/35 − 10/35 = 4/35

Gloria and Lynh have each been travelling at constant speeds to arrive at the same destination 12 miles away. They departed from the same place at the same time. Gloria graphed her distance as a function of time, as shown in the graph. Lynh traveled 30 miles every 1 hour. How much sooner will Gloria reach their destination? A. 10 minutes B. 4/35 hour C. 2 minutes D. 2/7 hour

The formula for the volume of a cone is 1/3πr^2h. Substitute values into the formula and calculate the result. Notice that the radius is half the diameter, so 4.1 ft. 1/3 ⋅ π ⋅ 4.1 ^2 ⋅ 6 = 105.57 cubic feet.

Guanglei works in urban landscaping design. A delivery truck arrived, pouring a cone-shaped pile of gravel 6 feet high with a diameter at the base of 8.2 feet. How much gravel was delivered? (Use π=3.14) A. 105.57 cubic feet B. 215.9 cubic feet C. 33.62 cubic feet D. 422.48 cubic feet

Instead of using the ratio 2:3, use the ratio 2:5. This is useful because it tells us the ratio of grasshoppers with white markings to all grasshoppers. To find out how many grasshoppers have white markings on their backs, you can create a proportion: 2 out of 5 equals x out of 290. By cross-multiplying: 2/5 = x/290 2(290) = 5x 580 = 5x 116 = x About 116 of the photographs will show white markings.

In a population of grasshoppers, the ratio of grasshoppers with a white marking to those without a white marking is 2:3. An entomologist captures and photographs 290 grasshoppers. How many photographs are likely to show grasshoppers with a white marking? A. 193 B. 116 C. 58 D. 112

In order to solve the system of equations by substitution, the first step is to solve one of the equations for one variable so that the expression can be substituted into the other equation. Solve one of the equations for one variable.

In order to solve this system using the substitution method, what would be the first step? 2 + 2y = 10 7x - 2y = 12 A. Add the equations together. B. Solve one of the equations for one variable. C. Set the equations equal to each other. D. Draw the graph of the equations.

Change mixed numbers to improper fractions by multiplying the whole-number part by the denominator and adding the numerator. This is the new numerator. 2⋅4+3 /4 = 11/4. Triple means multiply by 3, which gives 33 / 4 . Convert 7 to a fraction with 4 in the denominator: 28 / 4 . The difference is 5/4 or 1 1/4 .

Javier is making a cake for a party. The recipe calls for 2 3/4 cups of flour, but he wants to triple the recipe. He guessed and put in 7 cups of flour. How many more cups of flour should he have used? A. 1 1/2 B. 3/4 C. 4 1/4 D. 1 1/4

To multiply decimals, multiply as you would if they were whole numbers. After multiplying, move the decimal 3 places to the left: The answer is: 0.729

Multiply without using a calculator. A. 7.209 B. 3.645 C. 0.729 D. 0.737

To locate the point (1, 3) on the coordinate plane, first find the 1 on the x-axis, then count up 3 vertically and place the dot. Similarly, to locate the point (4 ,−4) , find 4 on the x-axis and count down 4 vertically and place the point.

Plot the points (1,3) and (4,−4). Click on the coordinate plane to plot your points. To remove a point, click on it again.

First, substitute each value for x into the equation and solve for y. x = -2 y = 3 (-2) - 2 = -6 - 2 = -8 x = 0 y = 3 (0) - 2 = -2 x = 2 y = 3 (2) - 2 = 4 The ordered pairs are (−2,−8), (0,−2) and (2,4). Plot these on the plane. The graph looks like this.

Plot the points on the line y = 3x −2 that correspond with x = −2 , x = 0, and x = 2. Select your points by clicking on the coordinate plane. To remove a point you have already placed, click on it again.

Let x represent the value of the new home. 105000 + 2(110000) + 117000 + 125000 + 135000 + 138000 + x/8 = 122750 105000 + 2(110000) + 117000 + 125000 + 135000 + 138000 + x = 982000 x = 142000 The value of the new home is $142,000.

Seven houses on a block have values of $105,000, $110,000, $110,000, $117,000, $125,000, $135,000, and $138,000. When an eighth home is built on the block, the average home value for the block is $122,750. What is the value of the new home? A. $141,500 B. $138,000 C. $142,000 D. $144,000

Factor the radicands in √50 + √18. You get √25 ⋅ 2 + √9 ⋅ 2 . Pulling out the perfect squares gives 5√2 + 3√2 Because they are like radicals, you can add. The answer is 8√2

Simplify: √50 + √18 A. 34√2 B. 8√2 C. 5√2 + √18 D. 5√10 + 3

To solve this question, you must solve the equation for x. The first step is to simplify by distributing the −6 into the parentheses. The next step is to combine like terms. Finally, isolate x. 10x − 6 + 18x − 6(2x−4) = 2 10x − 6 + 18x − 12x + 24 = 2 (10x + 18x − 12x) +(−6 + 24) = 2 16x + 18 = 2 16x = −16 x = −1

Solve the equation for x: 10x − 6 + 18x − 6 (2x−4) = 2 A. x = −8/7 B. x = 1 C. x = −1 D. x = −7/8

This equation can be solved by factoring, however, the Quadratic Formula will be used here: x = 8 ± √64 − 4 ⋅ 3 ⋅ 5 / 2 ⋅ 3 = 8 ± 2 /6 = 1 ,5/3 .

Solve the following equation for x. 0 = 3x^2 − 8x + 5 A. x = 2, 2/3 B. x = 3/8, 3/5 C. x = 1, 5/3 D. There are no real solutions.

Start by writing 5y/2 as 2.5y. Next, subtract 1.5 from both sides of the inequality: 6.5 - 1.5 > 1.5 + 2.5y - 1.5 5 > 2.5y When each side of the inequality is divided by 2.5, the result is 2 > y, which is the same as y < 2.

Solve the inequality for y. A. y > 2 B. y < 2 C. y < −2.5 D. y > 1.6

In this question you are given the circumference of a circle and are asked to find the radius and then the area of the circle. The formula for circumference is C = 2πr . To find the radius you must solve for r . r = C/2πr = 188.4 / 2 ≈ 30 . Once you have found the length of the radius, you can calculate the area with the formula A = πr^2 = π ⋅ 30^2 = 2,826 .

The circus has several large circular tents. The floor of each tent has a circumference of 188.4 feet. The radius of the floor is _________ ft. The area of the the floor is _________ ft 2. (Use π = 3.14)

To find the right equation for Roberto's truck rental, start by looking at the information given. He is renting two things, a truck and a trailer. The cost of renting the trailer is 19.95 + 0.52m. The cost of renting the trailer is 24.95 + 0.24m. Add these equations together. c = (19.95 + 24.95) + (0.52 + 0.24) ⋅ m

The cost to rent a moving van is $19.95 per day plus $0.52 per mile. The cost of renting a car trailer to pull behind the van is $24.95 per day plus $0.24 per mile. Roberto is moving from Los Angeles to Denver, Colorado. Which equation can he use to find his daily rental costs c? (Use m for miles.) A. c = (19.95 + 24.95) ÷ m + (0.52 + 0.24) B. c = (19.95 + 0.52) + (24.95 + 0.24) ÷ m C. c = (19.95 + 24.95) + (0.52 + 0.24) ⋅ m D. c = (19.95 + 0.52) ⋅ m + (24.95 + 0.24)

Line 1 with equation y = − 2x + 7 has a slope of − 2. Line 2 passes through the points (2, 3) and (4, 4) has has a slope of: m = 4 − 3 /4 − 2 = 1/2 Line 1 and Line 2 are perpendicular because each slope is the negative reciprocal of the other.

The equation of Line 1 is y = −−2x + 7. Line 2 passes through the points (2, 3) and (4, 4). Which statement is true about Line 1 and Line 2? A. Line 1 is longer than Line 2 B. Line 1 has the same y-intercept as Line 2 C. Line 1 and Line 2 are perpendicular D. Line 1 and Line 2 are parallel

The formula is: V = s^3. Rewrite the formula so that V is on the right, and then take the cube root of both sides: s^3 = V 3^√8^3 = ^3√ V s = ^3 √ V

The formula for the volume of a cube is V = s^3, where V is the volume, and s is the length of a side. Solve the formula for s. A. s = V^3√ B. s = V√ C. s = V^3 D. s = V/3

There are three bars to the left of the bar that starts with heights of 170 cm or more. Subtract 215 from 288 to find the number of students that were less then 170 cm tall: 288 - 215 = 73 students

The graph shows the heights, in centimeters, of male students at a city college. Of the 288 male students shown in the graph, 215 of them had heights of 170 cm or more. How many of the male students were less than 170 cm tall? A. 73 students B. 65 students C. 45 students D. 118 students

Because the graph is strictly increasing, you can say that the price of bread increases with the cost of oil, so there is a relationship. However, the rate of increase (the slope) varies, so it is not a linear relationship, and therefore not proportional.

The graph shows the relationship between the price of oil and the price of bread in the United States. What can be said about this relationship? A. The quantities do not have a relationship. B. The price of bread increases with the cost of oil, but the relationship is not proportional. C. The price of bread is inversely proportional to the cost of oil. D. The price of bread increases proportionally to the cost of oil.

Half of 32,404 is 16,202. So, the population of Baker is at least 16,202. " At least" uses the symbol ≥, because the population P of Baker can equal 16,202 or it can be greater than 16,202. So P ≥ 16,202.

The population of Sherwood is 32,404. The population of Baker (P) is at least half the population of Sherwood. Which inequality represents the population of Baker? A. P ≥ 64,808 B. P ≥ 16,202 C. P > 16,202 D. P < 16,202

The total earnings will be base salary plus commission. The base salary is $10,000. The commission is 15% of $90,000, or $13,500. The total base salary plus commission is $23,500.

This table is used to calculate annual commissions and salaries for car salespeople. What would the total yearly earnings of a sales assistant be who has $90,000 in sales? A. $15,750 B. $24,675 C. $23,500 D. $29,400

To find the average dice roll, multiply each result by the number of rolls, and divide by 100, the total number of rolls. 15(1)+18(2)+14(3)+16(4)+19(5)+18(6) /100 = 360/100 = 3.6 The answer is 3.6.

To find the average result of rolling a six-sided dice, Josh rolls a dice 100 times. The table shows how many times Josh rolled each number. What is the mean, or average, of the dice rolls? A. 4.2 B. 3 C. 2.9 D. 3.6

To find the solution to a system of linear equations graphically, you must find where the two lines intersect.

To the right is a graph of a system of two linear equations. Click on the graph to identify the solution of this system of equations. {y = 2x + 2 y = 8x − 4

To find the line between two points, first find the slope of the line between the two points. The slope is the difference in the y values divided by the difference in the x values, or 6 − 2/10 − 2 = 4/8 = 1/2 Substitute the value for slope and one of the points into the point-slope form of an equation for a line, y − y1 = m(x−x1) y − 2 = 1/2(x−2) y − 2 =1/2x − 1 y = 1/2x + 1

What is the equation of the line that passes through points (10,6) and (2,2)? A. y = 1/2x + 1 B. y = 2x + 7 C. y = 2x − 2 D. y = 1/2x + 7

To find the slope of a line, pick two points on the line. Subtract the y's of the two points, and subtract the x's of the two points. Then divide the difference between the y's by the difference between the x's. If the line slopes up to the right, the slope is positive. If the line slopes up to the left, the slope is negative. The slope of this line is 3 divided by 1, which is 3.

What is the slope of the line? A. 1/3 B. −1/3 C. 3 D. 2/3

Solve for m: 2 (m+3) < −5 + 3m 2m + 6 < −5 + 3m −m + 6 < −5 −m < −11 m > 11

What is the solution of the inequality? 2 (m + 3) < −5 + 3m A. m > 11 B. m > 2 C. m < 11 D. m < −8

4+(−2) / −3+3 = 2/0 = undefined

What is the value of the expression?

To find the equation for the line in the graph, first look at the y-intercept. This is 3, so the equation will be y = mx + 3 . Next look at the slope and count how much the graph goes up or down for each step to the right. This graph goes down 2 for every step to the right, so the slope is negative 2. Therefore, the equation for the line is y = −2x + 3 .

Which equation represents the line shown in the graph? A. y = −0.5x + 3 B. y = −2x + 1.5 C. y = −2x + 3 D. y = 2x + 3

Slope is defined as change in y divided by the change in x, or m = y2 − y1/ x2 − x1 So, the calculation m = 2 − 4 /8 − 3 is the first step in finding the slope.

Which expression can be used to find the slope of the line that contains the points (8, 2) and (3,4)? A. 8−3/4−2 B. 4−2/8−3 C. 8−2/3−4 D. 2−4/8−3

In order for the table to represent a function, Each number in the x-column should be paired with no more than one number in the y-column. From the answer choices listed, this can only happen when N = 8.

Which number could replace N so that the table represents a function? A. 4 B. 12 C. 8 D. 11

This question asks you to compare fractions, decimals, and percents. In order to directly compare the numbers, convert each of them to a decimal. Comparing the numbers in decimal form, 0.153 is the largest.

Which of the following numbers is largest? A. 1/12 B. 0.153 C. 1/7 D. 15%