Question

1. you buy 135 pieces of candy to fill piñatas. write and solve an equation to find how many piñatas you can fill when each piñata must have 45 pieces. 21. find the perimeter and area of the composite figure.

Explanation:

20.

Step1: Set up the equation

Let $x$ be the number of piñatas. The equation is $45x = 135$ since each piñata has 45 pieces of candy and there are a total of 135 pieces of candy.

Step2: Solve the equation

Divide both sides of the equation $45x = 135$ by 45. So $x=\frac{135}{45}$.

Step3: Calculate the result

$x = 3$.

Step1: Analyze the perimeter

The perimeter of the composite - figure consists of two lengths of 4 cm and the circumferences of two semi - circles which together form a full circle. The diameter of the circle is 2 cm, so the circumference of the circle $C=\pi d=\pi\times2 = 2\pi$ cm, and the two lengths contribute $2\times4 = 8$ cm. The perimeter $P=8 + 2\pi$ cm.

Step2: Analyze the area

The area of the composite - figure is the area of the rectangle plus the area of the semi - circle minus the area of the semi - circle (the two semi - circles cancel out in terms of area calculation). The area of the rectangle $A_{rect}=4\times2=8$ $cm^{2}$.

Answer:

3

21.