Answers JHS-Algebra 1A full yearZero and Negative Exponents

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A rectangle is shown on the coordinate grid. Which equation represents the side that is parallel to side d?

y = 2 x + 5

y = negative 2 x + 5

y = one-half x minus five-halves

y = negative one-half x minus seven-halves

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What is the slope, m, and the y-intercept of the line that is graphed below?

m = 1; (0, 3)

m = 1; (–3, 0)

m = –1; (0, 3)

m = –1; (–3, 0)

Which relationships could have a negative correlation? Select three options.number of hours worked and free timespeed of a car and minimum stopping distancethe speed of a train and the length of time to reach the destinationadult’s head circumference and agea tadpole’s age and the length of it’s tail

number of hours worked and free time

speed of a car and minimum stopping distance

the speed of a train and the length of time to reach the destination

adult’s head circumference and age

a tadpole’s age and the length of it’s tail

Line JK passes through points J(–3, 11) and K(1, –3). What is the equation of line JK in standard form?

7x + 2y = –1

7x + 2y = 1

14x + 4y = –1

14x + 4y = 1

The prime factorizations of 54 and 72 are shown below.Prime factorization of 54: 2, 3, 3, 3Prime factorization of 72: 2, 2, 2, 3, 3Using the prime factorizations, what is the greatest common factor of 54 and 72?

2 ´ 3

2 ´ 3 ´ 3

2 ´ 2 ´ 3 ´ 3

2 ´ 2 ´ 2 ´ 3 ´ 3 ´ 3

An auto mechanic charges $50 to diagnose a problem and $25 per hour to repair the problem. If x represents the total number of hours worked and y represents the total charges, which equation represents this situation?

y = 25x + 50

y = 50x + 25

y = 50x – 25

y = 25x – 50

Which is the simplified form of ?

StartFraction 1 Over m Superscript 8 Baseline p EndFraction

StartFraction 1 Over m Superscript 8 EndFraction

StartFraction p over m Superscript 8 EndFraction

m Superscript 8

The resale value of a textbook decreases by 25% with each previous owner. A new textbook is sold for $85. Which function represents the resale value of the textbook after x owners?

f(x) = 85(1 – 0.25)x

f(x) = 85(1 + 0.25)x

f(x) = 85(0.25)x

f(x) = (85 – 0.25)x

A line passes through the points (–1, –5) and (4, 5). The point (a, 1) is also on the line. What is the value of a?

–2

–1

What is the value of ?

Negative StartFraction 81 Over 16 EndFraction

Negative StartFraction 16 Over 81 EndFraction

StartFraction 16 Over 81 EndFraction

StartFraction 81 Over 16 EndFraction

The table shows the total cost of purchasing x same-priced items and a catalog.

$4, the cost per item

$4, the cost of the catalog

$6, the cost per item

$6, the cost of the catalog

Which graph represents the function y = 2x – 4?

Option

The table shows how an elevator 500 feet above the ground is descending at a steady rate.

h(t) = 5t + 500

h(t) = 5t – 500

h(t) = –5t + 500

h(t) = –5t – 500

A tree company charges a delivery fee for each tree purchased in addition to the cost of the tree. The delivery fee decreases as the number of trees purchased increases. The table below represents the total cost of x trees purchased, including delivery fees.

The rate of change between 1 and 2 trees is different than the rate of change between 2 and 3 trees.

The rate of change between 1 and 2 trees is different than the rate of change between 1 and 3 trees.

The rate of change between 2 and 3 trees is different than the rate of change between 3 and 4 trees.

The rate of change between 2 and 3 trees is different than the rate of change between 3 and 5 trees.

Gerri purchases a coupon book with discounts for her favorite coffee shop. Every coupon for the coffee shop offers the same discount. The table shows her total savings, y, based on the number of coupons, x, used from the book.

slope: 2, y-intercept: –20

slope: 2, y-intercept: 10

slope: 5, y-intercept: –20

slope: 5, y-intercept: 10

Which point represents the ordered pair ?

point Q

point R

point S

point T

Which best describes the range of the function f(x) = 2(3)x?

y > 0

y ≥ 0

y > 2

y ≥ 2

Manny has 48 feet of wood. He wants to use all of it to create a border around a garden. The equation can be used to find the length and width of the garden, where l is the length and w is the width of the garden. If Manny makes the garden 15 feet long, how wide should the garden be?

9 feet

18 feet

30 feet

33 feet

Use the graph below to answer the question. What is the slope of a line that is parallel to the line in the graph?

Answer not available

The graph below shows the number of cups of lemonade that Jermaine and Amelia sold using five different recipes.Lemonade Sold Using Different Recipes Which statement is supported by the graph?

They sold the least lemonade with the recipe that used 3 lemons.

They sold the least lemonade with the recipe that used 7 lemons.

They sold the most lemonade with the recipe that used 3 lemons.

They sold the most lemonade with the recipe that used 7 lemons.

Alejandro bought $3.50 worth of pencils and erasers at the school store. Pencils cost $0.50 apiece, and erasers cost $0.75 apiece. Which equation written in standard form represents the number of pencils, p, and the number of erasers, e, that Alejandro bought?

0.75e = 3.50 – 0.50p

0.50p + 0.75e = 3.50

3e = 14 – 2p

2p + 3e = 14

Which linear function represents the line given by the point-slope equation y – 2 = 4(x – 3)?

f(x) = 6x – 1

f(x) = 8x – 6

f(x) = 4x – 14

f(x) = 4x – 10

A vertical line passes through the point (–3, 5). Which point is also on this line?

(0, 0)

(5, –3)

(–3, –4)

(–1, 5)

Sonji has $5.25 in nickels and dimes.The coin value can be modeled by the equation , where d represents the number of dimes and n represents the number of nickels. If Sonji has 21 dimes, how many nickels does she have?

105

Which expression has a value of ?

(StartFraction 1 Over 108 EndFraction) cubed

(StartFraction 1 Over 9 EndFraction) Superscript 4

(StartFraction 1 Over 6 EndFraction) squared

(one-half) Superscript 5

Which table represents viable solutions for y = 5x, where x is the number of tickets sold for the school play and y is the amount of money collected for the tickets?

A 2-column table with 4 rows titled School Play Tickets. The first column is labeled tickets (x) with entries negative 100, negative 25, 40, 600. The second column is labeled money collected (y) with entries negative 500, negative 125, 250, 3000.

A 2-column table with 4 rows titled School Play Tickets. The first column is labeled tickets (x) with entries negative 20, 20, 100, 109. The second column is labeled money collected (y) with entries negative 100, 100, 500, 545.

A 2-column table with 4 rows titled School Play Tickets. The first column is labeled tickets (x) with entries 0, 10, 51, 400. The second column is labeled money collected (y) with entries 0, 50, 255, 2000.

A 2-column table with 4 rows titled School Play Tickets. The first column is labeled tickets (x) with entries 5, 65, 80, 200. The second column is labeled money collected (y) with entries 25, 350, 400, 1000.

Which table shows no correlation?

A 2-row table with 7 columns. The first row is labeled x with entries 3, 5, 6, 8, 10, 14, 15. The second row is labeled y with entries negative 1, negative 2, negative 3, negative 2, negative 5, negative 4, negative 8.

A 2-row table with 7 columns. The first row is labeled x with entries 3, 5, 6, 8, 10, 14, 15. The second row is labeled y with entries negative 6, negative 7, negative 4, negative 2, 0, negative 1, positive 3.

A 2-row table with 7 columns. The first row is labeled x with entries 3, 5, 6, 8, 10, 14, 15. The second row is labeled y with entries negative 2, negative 4, positive 6, positive 8, positive 12, positive 10, negative 16.

A 2-row table with 7 columns. The first row is labeled x with entries 3, 5, 6, 8, 10, 14, 15. The second row is labeled y with entries negative 3, negative 5, negative 9, negative 11, negative 13, negative 15, negative 17.

Which is the graph of y – 3 = (x + 6)?

Option

Dwight creates a table of values for a function and plots the points. He finds that one y value divided by the next y value produces the same answer each time. What kind of function did he graph?

linear

quadratic

square root

exponential

A 2-column table has 4 rows. The first column is labeled x with entries 1, 2, 3, 4. The second column is labeled y with entries 4.5, 6.75, 10.125, 15.1875.

1.5

2.25

3.0

4.5

Yesterday, Selma read 75 pages of her book. If she reads at a pace of 2 pages per minute today, which table shows only viable solutions for the total number of pages she has read, y, after x minutes have elapsed?

A 2-column table with 4 rows titled Selma's Reading. The first column is labeled minutes of reading (x) with entries 2, 14, 39, 55. The second column is labeled total pages read (y) with entries 79, 101, 153, 185.

A 2-column table with 4 rows titled Selma's Reading. The first column is labeled minutes of reading (x) with entries negative 16, 6, 27, 52. The second column is labeled total pages read (y) with entries 43, 87, 129, 179.

A 2-column table with 4 rows titled Selma's Reading. The first column is labeled minutes of reading (x) with entries 0, 19, 32, 47. The second column is labeled total pages read (y) with entries 0, 113, 139, 169.

A 2-column table with 4 rows titled Selma's Reading. The first column is labeled minutes of reading (x) with entries 0, 11, 20.25, 58. The second column is labeled total pages read (y) with entries 75, 97, 115.5, 191.

Which is the best description of the graph of the function f(x) = 60()x?

The graph has an initial value of 20, and each successive term is determined by subtracting .

The graph has an initial value of 20, and each successive term is determined by multiplying by .

The graph has an initial value of 60, and each successive term is determined by subtracting .

The graph has an initial value of 60, and each successive term is determined by multiplying by .

The graphs of y = 3x and y = 3x are shown below. In general, how does the growth of y = 3x compare to the growth of y = 3x?

The function y = 3x is growing slower than y = 3x.

The function y = 3x is growing faster than y = 3x.

The functions y = 3x and y = 3x are growing at the same rate.

The function y = 3x is growing slower than y = 3x.

The least common multiple of two numbers is 24. Which could be the two numbers?

6 and 8

4 and 6

8 and 16

4 and 12

In the table, x represents the age in years of a collectible baseball card, and y represents its value in dollars. Cost of a Pack of Baseball CardsAge in years, xValue in dollars, y50.75105.751510.752015.75Which statement is correct about the slope of the linear function that the table represents?

The slope is positive because as the age decreases, the value increases.

The slope is positive because as the age increases, the value increases.

The slope is negative because as the age decreases, the value decreases.

The slope is negative because as the age increases, the value decreases.

The 10th-grade class officers ordered t-shirts and sweatshirts to sell as a fundraiser. Each t-shirt weighed of a pound, and each sweatshirt weighed of a pound. The total weight of the contents of the box was pounds. Which equation written in standard form represents the number of t-shirts, t, and the number of sweatshirts, s, that were ordered?

StartFraction one-half EndFraction t plus StartFraction 3 Over 4 EndFraction s equals 43 and StartFraction 3 Over 4 EndFraction

StartFraction 3 Over 4 EndFraction s equals negative StartFraction one-half EndFraction s plus 43 and StartFraction 3 Over 4 EndFraction.

2t + 3s = 175

3s = –2t + 175

The graph represents the function where electricity usage in kilowatts per hour of a clock radio varies directly with the number of days it is plugged into the wall current.

0.25 kWh per day

0.50 kWh per day

2.40 kWh per day

4.00 kWh per day

Which expression is equivalent to ?

10 Superscript 12

11 Superscript 12

12 Superscript 10

12 Superscript 11

A team is selling discount cards as a fundraiser. The table shows the number of cards sold and the remaining amount of money needed.

zero

undefined

negative

positive

What is the slope of the line that passes through the points (–20, 18) and (30, 14)?

Negative StartFraction 25 Over 2 EndFraction

Negative five-halves

Negative two-fifths

Negative StartFraction 2 Over 25 EndFraction

Which table represents a direct variation function?

A table with 6 columns and 2 rows. The first row, x, has the entries, negative 3, negative 1, 2, 5, 10. The second row, y, has the entries, negative 4.5, negative 3.0, negative 1.5, 0.0, 1.5.

A table with 6 columns and 2 rows. The first row, x, has the entries, negative 5.5, negative 4.5, negative 3.5, negative 2.5, negative 1.5. The second row, y, has the entries, 10, 8, 6, 4, 2.

A table with 6 columns and 2 rows. The first row, x, has the entries, negative 5.5, negative 5.5, negative 5.5, negative 5.5, negative 5.5. The second row, y, has the entries, negative 3, negative 1, 2, 5, 10.

A table with 6 columns and 2 rows. The first row, x, has the entries, negative 3, negative 1, 2, 5, 10. The second row, y, has the entries, negative 7.5, negative 2.5, 5.0, 12.5, 25.0.

Wren recorded an outside temperature of –2°F at 8 a.m. When she checked the temperature again, it was 4°F at 12:00 p.m. If x represents the time and y represents the temperature in degrees Fahrenheit, what is the slope of the line through these two data points?

–1.5

–0.5

0.5

1.5

Which linear function has the greatest y-intercept?

y + 6 y = 36

y = 15 x + 5

3 x + 8 y = 24

y = 4 x + 7

What are the slope and the y-intercept of the linear function that is represented by the equation ?

The slope is , and the y-intercept is 4.

The slope is 4, and the y-intercept is .

Raquel throws darts at a coordinate grid centered at the origin. Her goal is to create a line of darts. Her darts actually hit the coordinate grid at (–5, 0), (1, –3), (4, 5), (–8, –6), (0, 2), and (9, 6). Which equation best approximates the line of best fit of the darts?

y = 0.6x + 0.6

y = 0.1x + 0.8

y = 0.8x + 0.1

y = 0.5x + 0.6

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