Question

1. which could be the first step in solving the equation 0.05y - 3 - 0.02x = 4? a. add 3 to each side of the equation. b. divide each side of the equation by 100. c. multiply each side of the equation by 100. d. subtract 0.02x from each side of the equation. 12. solve the equation. check your solution. 1/3(x - 6) = 15 + 1/3(x - 24) x = 13. laurie earns $7.50 per hour at the fruit - stand plus an extra $2.00 per hour on sundays. one week in august, she worked on sunday, monday, and wednesday. she worked the same number of hours on monday and wednesday. on sunday she worked 4 hours. if she earned a total of $83.00 for the week, how many hours did laurie work on monday? write and solve an equation. 14. which equation has the solution x = 8? a. x + 2x - 4 = 1/4(3x + 4) b. x + 1/2(x + 8) = 4(1 + x) c. 2(x - 4) = 1/4(1 + 3) + x d. x + 4(1 + 3) = 1/2(2x + 4) 15. each year rolando saves 8% of his income. this year he saved $3000 and his salary was $2000 less than in the previous year. what was his salary in the previous year? write and solve an equation. spiral review 16. triangle abc is dilated by a scale factor of 1.5 to form triangle def. are triangles abc and def congruent? why or why not? 17. a triangle has angles measuring 45°, 55°, and 80°. it is dilated by a scale factor of 2. what are the angle measures of the dilated image?

Explanation:

11.

Step1: Analyze the equation 0.08y - 3 - 0.02x = 4

To get rid of the decimals, multiplying each side of the equation by 100 is a common first - step. This will convert the coefficients 0.08 and 0.02 into whole numbers.
$100(0.08y - 3 - 0.02x)=100\times4$

Step1: Distribute on both sides

$\frac{1}{3}(x - 6)=15+\frac{1}{2}(x - 24)$
$\frac{1}{3}x-2 = 15+\frac{1}{2}x-12$

Step2: Simplify the right - hand side

$\frac{1}{3}x-2=\frac{1}{2}x + 3$

Step3: Get the x terms on one side

Subtract $\frac{1}{3}x$ from both sides:
$-2=\frac{1}{2}x-\frac{1}{3}x + 3$

Step4: Combine x terms

$\frac{1}{2}x-\frac{1}{3}x=\frac{3x - 2x}{6}=\frac{1}{6}x$
$-2=\frac{1}{6}x + 3$

Step5: Isolate x

Subtract 3 from both sides: $-5=\frac{1}{6}x$
Multiply both sides by 6: $x=-30$

Step6: Check the solution

Substitute $x = - 30$ into the original equation:
Left - hand side: $\frac{1}{3}(-30 - 6)=\frac{1}{3}\times(-36)=-12$
Right - hand side: $15+\frac{1}{2}(-30 - 24)=15+\frac{1}{2}\times(-54)=15 - 27=-12$

Step1: Let the number of hours worked on Monday and Wednesday be $h$

On Sunday, she worked 4 hours. Her hourly rate on Sunday is $7.50 + 2=9.50$ dollars per hour, and on Monday and Wednesday, it is $7.50$ dollars per hour.
The total money she earned is given by the equation:
$9.50\times4+7.50h + 7.50h=83$

Step2: Simplify the left - hand side

$38+15h = 83$

Step3: Isolate h

Subtract 38 from both sides: $15h=83 - 38=45$
Divide both sides by 15: $h = 3$

Answer:

C. Multiply each side of the equation by 100

12.