Question

1)

Which of the following is a solution to the equation y=5x−3

(1 point)
Responses

a (−3,12)
b (4, 23)
c (1,−2)
d (−2,−13)

Answer 1

[AI-generated answer — Bot GPT 3.5]

To determine which of the given points is a solution to the equation y=5x-3, substitute the x-coordinate and y-coordinate values into the equation and check if the equation holds true.

For point (−3,12):
y = 5x - 3
12 = 5(-3) - 3
12 = -15 - 3
12 = -18

Clearly, this equation does not hold true. Therefore, point (−3,12) is not a solution to the equation.

For point (4, 23):
y = 5x - 3
23 = 5(4) - 3
23 = 20 - 3
23 = 17

Again, this equation does not hold true. Therefore, point (4, 23) is not a solution to the equation.

For point (1,−2):
y = 5x - 3
-2 = 5(1) - 3
-2 = 5 - 3
-2 = 2

Once again, this equation does not hold true. Therefore, point (1,−2) is not a solution to the equation.

For point (−2,−13):
y = 5x - 3
-13 = 5(-2) - 3
-13 = -10 - 3
-13 = -13

In this case, the equation holds true. Therefore, point (−2,−13) is a solution to the equation.

Answer:
d (−2,−13) is a solution to the equation y=5x−3.

Answer 2

2)

Which equation represents the pattern in the table below?

Noah's Ages 2 5 9 12 17
Sarah's Ages 8 11 15 18 23


(1 point)
Responses

a. s=n−6

b. n=s−6

c. s=3n

d. n=3s

Answer 3

[AI-generated answer — Bot GPT 3.5]

To determine the equation that represents the pattern in the given table, let's examine the relationship between Noah's and Sarah's ages.

Looking at the table, we can observe that Noah's ages (represented by n) are 2, 5, 9, 12, and 17. Sarah's ages (represented by s) are 8, 11, 15, 18, and 23.

Comparing the values of Noah's ages and Sarah's ages, we find that Sarah's ages are always 6 more than Noah's ages. Therefore, we can conclude that the equation that represents the pattern is:

s = n + 6

Answer:
a. s = n + 6 represents the pattern in the table.

Answer 4

3)

Which equation matches the statement: "The sum of −7x
and 3
is 9
"?

(1 point)
Responses

−7x+3=9
negative 7 x plus 3 is equal to 9

−7x+9=3
negative 7 x plus 9 is equal to 3

−7x−3=9
negative 7 x minus 3 is equal to 9

−7x(3)=9

Answer 5

[AI-generated answer — Bot GPT 3.5]

The statement "The sum of -7x and 3 is 9" can be represented as an equation by adding -7x and 3 and setting it equal to 9.

Therefore, the correct equation that matches the statement is:

-7x + 3 = 9

Answer:
a) -7x + 3 = 9 represents the statement "The sum of -7x and 3 is 9".

Answer 6

9)

Use the given equation to find the solution to the following problem.

The equation 2.85+ 0.40s=c
gives the cost c in dollars that a website charges for downloading songs. The variable s stands for the number of songs downloaded. Find the cost of downloading 36 songs.

(1 point)
Responses

c=$15.65
c is equal to 15 point 6 5 dollars

c=$28.05
c is equal to 28 point 0 5 dollars

c=$17.25
c is equal to 17 point 2 5 dollars

c=$16.45

Answer 7

[AI-generated answer — Bot GPT 3.5]

To find the cost of downloading 36 songs, we need to substitute s = 36 into the equation c = 2.85 + 0.40s and solve for c.

c = 2.85 + 0.40s
c = 2.85 + 0.40(36)
c = 2.85 + 14.4
c = 17.25

Therefore, the cost of downloading 36 songs is $17.25.

Answer:
c = $17.25

Answer 8

0)

Write an equation and solve to find the solution to the following problem.

You have $43 to spend at the mall and a coupon for $5 off at your favorite store. A t-shirt costs $12. How many t-shirts can you buy using your coupon and money?

(1 point)
Responses

1 shirt
1 shirt

2 shirts
2 shirts

3 shirts
3 shirts

4 shirts

Answer 9

[AI-generated answer — Bot GPT 3.5]

Let x represent the number of t-shirts you can buy. Each t-shirt costs $12, and you have a coupon for $5 off. This means the total cost of x t-shirts would be (12 * x) - 5, and this should be less than or equal to the $43 you have to spend.

Setting up the equation:

(12 * x) - 5 ≤ 43

Now, solve for x:

12x ≤ 48
x ≤ 48/12
x ≤ 4

The result shows that you can buy a maximum of 4 t-shirts with your coupon and money.

Answer:
4 shirts

Answer 10

[AI-generated answer — Explain Bot]

To determine which option is a solution to the equation y = 5x - 3, we need to substitute the x and y values from each option into the equation and check if the equation holds true.

Let's go through each option and check:

a) Option a: (-3,12)
Substituting x = -3 and y = 12 into the equation:
12 = 5(-3) - 3
12 = -15 - 3
12 = -18

The equation does not hold true for option a (-3,12).

b) Option b: (4,23)
Substituting x = 4 and y = 23 into the equation:
23 = 5(4) - 3
23 = 20 - 3
23 = 17

The equation does not hold true for option b (4,23).

c) Option c: (1,-2)
Substituting x = 1 and y = -2 into the equation:
-2 = 5(1) - 3
-2 = 5 - 3
-2 = 2

The equation does not hold true for option c (1,-2).

d) Option d: (-2,-13)
Substituting x = -2 and y = -13 into the equation:
-13 = 5(-2) - 3
-13 = -10 - 3
-13 = -13

The equation holds true for option d (-2,-13).

Therefore, the solution to the equation y = 5x - 3 is option d (−2,−13).