Question

day 1

1. find the area. use 3.14 for pi. a = πr²
2. find the missing angle
3. does the table represent a function?
4. which expressions are equivalent to -9? select all that are correct.

a. 8 - 8 + 9
b. 3 - (-6) + (-18)
c. -1 + 7 - (-3)
d. 4 - 5 - 8

1. does the graph represent a function?

Explanation:

Step1: Calculate area of circle

Given radius $r = 6$ yd and formula $A=\pi r^{2}$, substitute $r = 6$ and $\pi=3.14$.
$A = 3.14\times6^{2}=3.14\times36 = 113.04$ yd$^{2}$

Step2: Find missing angle in right - triangle

In a right - triangle, one angle is $90^{\circ}$ and another is $27^{\circ}$. The sum of angles in a triangle is $180^{\circ}$. Let the missing angle be $x$. Then $x=180-(90 + 27)=63^{\circ}$

Step3: Check if table is a function

A function has one output ($y$ - value) for each input ($x$ - value). In the table, when $x = 4$, $y$ has two values ($- 20$ and $14$). So, it is not a function.

Step4: Simplify expressions

a.

$8-8 + 9=0 + 9=9
eq - 9$

b.

$3-(-6)+(-18)=3 + 6-18=9 - 18=-9$

c.

$-1 + 7-(-3)=-1 + 7 + 3=9
eq - 9$

d.

$4-5-8=-1-8=-9$

Step5: Check if graph is a function

Use the vertical - line test. If any vertical line intersects the graph at more than one point, it is not a function. Since no vertical line intersects the given graph at more than one point, it is a function.

Answer:

1. $113.04$ yd$^{2}$
2. $63^{\circ}$
3. No
4. b. $3-(-6)+(-18)$, d. $4 - 5-8$
5. Yes