Question

1. the graph shows a relationship between the cups of blue and yellow paint used to create green paint. what is the constant rate of change for the relationship? 5. find the area of the circle with a diameter of 22 cm, using the formula a = πr². 6. angle a and angle b are complementary. the measure of angle a is 25°. the measure of angle b is (x + 4)°. write an equation and solve it to find the measure of angle b.

Explanation:

4.

Step1: Recall slope formula

The slope (constant rate of change) formula for two - points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here, $(x_1,y_1)=(1,3)$ and $(x_2,y_2)=(2,5)$.

Step2: Substitute values

$m=\frac{5 - 3}{2 - 1}=\frac{2}{1}=2$.

Step1: Find the radius

The radius $r$ of a circle is half of the diameter. Given $d = 22$ cm, so $r=\frac{d}{2}=\frac{22}{2}=11$ cm.

Step2: Calculate the area

Using the formula $A=\pi r^{2}$, substitute $r = 11$ cm. Then $A=\pi\times(11)^{2}=121\pi$ $cm^{2}$. If we take $\pi\approx3.14$, then $A\approx121\times3.14 = 379.94$ $cm^{2}$.

Step1: Write the equation

Since complementary angles add up to $90^{\circ}$, the equation is $25+(x + 4)=90$.

Step2: Simplify the left - hand side

$25+x+4=29 + x$, so the equation becomes $29+x=90$.

Step3: Solve for $x$

Subtract 29 from both sides: $x=90 - 29=61$.

Step4: Find the measure of angle $B$

The measure of angle $B$ is $x + 4$. Substitute $x = 61$, so angle $B=61+4=65^{\circ}$.

Answer:

2

5.