Question

1. what is the solution to the given equation?

for the function f the graph of y = f(x) in the xy - plane has a slope of 3 and passes through the point (0, - 8). which equation defines f?
a) f(x)=3x
b) f(x)=3x - 8
c) f(x)=3x + 3
d) f(x)=3x + 11
the triangle shown has a perimeter of 22 units. if x = 8 units and y = 7 units, what is the value of z, in units?
a) 6
b) 7
c) 9
d) 16

1. the function h is defined by h(x)=3x - 7. what is the value of h(-2)?

a) - 13
b) - 10
c) 10
d) 13

Explanation:

Step1: Solve the equation $\frac{24}{x}=6$

Multiply both sides by $x$: $24 = 6x$. Then divide both sides by 6, we get $x=\frac{24}{6}=4$.

Step2: Find the equation of the function $y = f(x)$

The slope - intercept form of a line is $y=mx + b$, where $m$ is the slope and $b$ is the y - intercept. Given $m = 3$ and the line passes through $(0,-8)$, so $b=-8$. Then $f(x)=3x - 8$, the answer is B.

Step3: Find the value of $z$ in the triangle

The perimeter of a triangle is the sum of its side - lengths. Given perimeter $P=x + y+z$, $P = 22$, $x = 5$, $y = 7$. Then $22=5 + 7+z$, $22=12 + z$, subtract 12 from both sides, $z=22 - 12=10$, the answer is C.

Step4: Find the value of $h(-2)$

Given $h(x)=3x - 7$, substitute $x=-2$ into the function: $h(-2)=3\times(-2)-7=-6 - 7=-13$, the answer is A.

Answer:

1. $x = 4$
2. B. $f(x)=3x - 8$
3. C. $10$
4. A. $-13$