HELP!

QUESTION 1.
What are two different ways 23x=10 could be solved for x?

a. Subtract 3/2 from both sides of the equation
b. Divide both sides of the equation by 3/2
c. Divide both sides of the equation by 2/3
d. Multiply both sides of the equation by 3/2
e. Multiply both sides of the equation by 2/3
f. Subtract 2/3 from both sides of the equation

QUESTION 2.
Shanice took a long bike ride today and is now 27.2 miles from home. She rides back home at an average of 9.8 miles per hour. This situation can be modeled with the equation d = 27.2 - 9.8t, where d represents the number of miles she is from home and t represents the number of hours she rides. How many hours will it take Shanice to ride home? Round your answer to the nearest hundredth.

a. 37.0 hours
b. 2.78 hours
c. 17.4 hours
d. 0.36 hours

QUESTION 3.
Suppose that in t months, the money you have saved, S, is given by the equation S=145t+85. What do the numbers in the equation represent?

a. 145 means you started with $145 and 85 means that you save $85 per month
b. 145 means that it will take you 145 months to save $85
c. 85 means you started with $85 and 145 means that you save $145 per month
d. 85 means that it will take you 85 months to save $145

QUESTION 4.
Suppose that in t months, the money you have saved is given by the equation S=145t+85. How many months will it take you to save $810?

a. 3 months
b. 4.5 months
c. 5 months
d. 5.5 months

QUESTION 5.
Your local volunteer group is making t-shirts. The shirt printers charge $35 to make the first t-shirt and $11 to make each additional shirt. What is the maximum number of shirts your group can buy for $250?

a. 15 shirts
b. 19 shirts
c. 17 shirts
d. 18 shirts
e. 20 shirts

Respuesta :

1) The way the equation could be solved for x is;

Option D; Multiply both sides of the equation by 3/2

2) The number of hours it will take Shanice to get home is;

Option B; 2.78 hours

3) The numbers in the equation represents;

Option C; 85 means you started with $85 and 145 means that you save $145 per month

4) The number of months it will it take you to save $810 is;

Option C; 5 months

5) The maximum number of shirts your group can buy for $250;

Option B; 19 Shirts

  • 1) [tex]\frac{2}{3}[/tex]x = 10

To solve for x, we need to first multiply both sides by the inverse of the coefficient of x since it is a fraction.

This means we multiply both sides by [tex]\frac{3}{2}[/tex].

Option D is correct

  • 2) We are given the equation;

d = 27.2 - 9.8t

where;

d represents the number of miles she is from home

t represents the number of hours she rides

We are told that she is now 27.2 miles from home.

Since she rides at an average of 9.8 mph, then formula for time is;

t = distance/speed = 27.2/9.8

t = 2.7755

To the nearest hundredth gives;

t = 2.78 hours

Option B is correct

  • 3)  S = 145t + 85.

t represents months you have saved

This means that the coefficient of t is the amount you saved monthly = $145

And 85 is the amount you started with.

Option C is correct

  • 4) From question 3 above, S represents the total amount saved after t months.

Thus, if you have saved  $810 after t months, then;

145t + 85 = 810

145t = 810 - 85

145t = 725

t = 725/145

t = 5 months

Option C is correct

  • 5) first shirt costs $35 and subsequent ones cost $11.

If the number you can buy is x and max amount to spend is $250, then;

35 + 11x [tex]\leq[/tex] 250

11x [tex]\leq[/tex] 250 - 35

11x [tex]\leq[/tex] 215

x [tex]\leq[/tex] 215/11

x [tex]\leq[/tex] 19.55

There is no decimal shirt and so we pick 19 shirts which is Option B.

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