Question

3.4 review & refresh (continued)
in exercises 7 and 8, find the value of x so that the function has the given value.

1. $f(x)=-3x;f(x)=33$
2. $h(x)=2x - 3;h(x)=5$
3. find the surface area of the square pyramid.
4. graph $f(x)=5x - 2$.

Explanation:

7.

Step1: Substitute given values

Substitute $f(x) = 33$ into $f(x)=-3x$. We get $33=-3x$.

Step2: Solve for $x$

Divide both sides by - 3. So, $x=\frac{33}{-3}=-11$.

Step1: Substitute given values

Substitute $h(x) = 5$ into $h(x)=2x - 3$. We get $5 = 2x-3$.

Step2: Isolate the term with $x$

Add 3 to both sides: $5 + 3=2x-3 + 3$, which simplifies to $8 = 2x$.

Step3: Solve for $x$

Divide both sides by 2. So, $x=\frac{8}{2}=4$.

Step1: Find the area of the base

The base is a square with side - length $s = 8$ in. The area of the base $B=s^{2}=8^{2}=64$ square inches.

Step2: Find the area of one triangular face

The base of each triangular face is $b = 8$ in and the height of each triangular face is $h = 6$ in. The area of a triangle is $A_{\triangle}=\frac{1}{2}bh$. So, $A_{\triangle}=\frac{1}{2}\times8\times6 = 24$ square inches.

Step3: Find the total surface area

There are 4 triangular faces and 1 base. The total surface area $SA=B + 4A_{\triangle}$. Substitute $B = 64$ and $A_{\triangle}=24$: $SA=64+4\times24=64 + 96=160$ square inches.

Answer:

$x = - 11$

8.