Question

Jerald is having drain issues at his home and decides to call a plumber. The plumber charges $35 to come to his house and $60 for every hour they work. If the plumber charges Jerald a total of $305, how many hours did the plumber work? Write and solve an equation to determine the number of hours worked by the plumber. 35x + 60 = 305; x = 7 hours 35x − 60 = 305; x = 10.4 hours 60x + 35 = 305; x = 4.5 hours 60x − 35 = 305; x = 5.7 hours Question 4(Multiple Choice Worth 5 points) (Adding and Subtracting Linear Expressions MC) Which expression is equivalent to the expression quantity negative 10 over 9 times t plus 1 over 8 end quantity minus expression quantity negative 6 over 18 times t plus 3 over 4 end quantity? negative 14 over 18 times t minus 5 over 8 negative 14 over 18 times t plus 2 over 8 4 over 9 times t plus 2 over 4 16 over 18 times t plus negative 4 over 8 Question 5(Multiple Choice Worth 5 points) (One-Step Inequalities MC) Write an inequality for the statement: negative two sevenths is at most the product of a number and negative four fifths. negative 2 over 7 is less than or equal to negative 4 over 5 times w negative 4 over 5 is less than or equal to negative 2 over 7 times w negative 4 over 5 is greater than or equal to negative 2 over 7 times w negative 2 over 7 is greater than or equal to negative 4 over 5 times w Question 6(Multiple Choice Worth 5 points) (Solving Two-Step Equations MC) Solve the equation for w. w divided by 4.4 minus 2.8 equals 11.5 62.92 38.28 3.25 1.97 Question 7(Multiple Choice Worth 5 points) (Writing Two-Step Equations MC) Which equation represents the written description? Seven times the difference between 35.8 and a number is equal to 53.4 7(35.8) − m = 53.4 7(35.8 − m) = 53.4 7(m − 35.8) = 53.4 7m − 35.8 = 53.4 Question 8(Multiple Choice Worth 5 points) (Adding and Subtracting Linear Expressions MC) Subtract the expressions. (9.12n − 4.3) − (8 + 13.6n) −44.80n − 4.5 −4.48n − 12.3 13.42n − 21.6 22.72n + (−12.3) Question 9(Multiple

Answer 1

1.
`\(x = 4.5\)` hours.

4.
`\((-16t - 9)/(36)\).`

5.
`\(-(2)/(7) \leq -(4)/(5)w\).`

6.
`\(w \approx 62.92\).`

7.
`\(7(35.8 - m) = 53.4\).`

8.
`\(-4.48n - 12.3\).`

How did we get the values?

Let's go through each question one by one:

Question 1:

The correct equation is:

`\[35 + 60x = 305\]`

where
`\(x\)` is the number of hours worked.

Solving for
`\(x\)`:

`\[60x = 305 - 35\]`

`\[60x = 270\]`

`\[x = (270)/(60) = 4.5\]`

So, the correct answer is:
`\(x = 4.5\)` hours.

Question 4:

Which expression is equivalent to the expression
`\((-10)/(9)t + (1)/(8) - \left((-6)/(18)t + (3)/(4)\right)\)`?

Combine like terms:

`\[(-10)/(9)t + (1)/(8) + (6)/(18)t - (3)/(4)\]`

Find a common denominator for the fractions:

`\[(-80t + 9 + 48t - 27)/(72)\]`

Combine the numerators:

`\[(-32t - 18)/(72)\]`

Simplify by dividing both numerator and denominator by their greatest common factor (6):

`\[(-16t - 9)/(36)\]`

So, the correct answer is:
`\((-16t - 9)/(36)\).`

Question 5:

Write an inequality for the statement:
`\(-(2)/(7)\)` is at most the product of a number and
`\(-(4)/(5)\)`.

The correct inequality is:

`\[-(2)/(7) \leq -(4)/(5)w\]`

So, the correct answer is:
`\(-(2)/(7) \leq -(4)/(5)w\).`

Question 6:

Solve the equation for
`\(w\): \((w)/(4.4) - 2.8 = 11.5\)`

First, add 2.8 to both sides:

`\[(w)/(4.4) = 14.3\]`

Then, multiply both sides by 4.4:

`\[w = 4.4 * 14.3\]`

Calculating this gives:
`\(w \approx 62.92\)`

So, the correct answer is:
`\(w \approx 62.92\).`

Question 7:

Which equation represents the written description? "Seven times the difference between 35.8 and a number is equal to 53.4".

The correct equation is:
`\(7(35.8 - m) = 53.4\)`

So, the correct answer is:
`\(7(35.8 - m) = 53.4\).`

Question 8:

Subtract the expressions:
`\((9.12n - 4.3) - (8 + 13.6n)\)`

Combine like terms:

`\[9.12n - 4.3 - 8 - 13.6n\]`

Combine the
`\(n\)` terms:

`\[-4.48n - 12.3\]`

So, the correct answer is:
`\(-4.48n - 12.3\).`