Question

1. the lengths of two sides of a triangle are 4 centimeters and 6 centimeters. if the perimeter of the triangle is 18 centimeters, what is the length, in centimeters, of the third side of this triangle? a) 2 b) 8 c) 10 d) 24 2. 16x + 30 = 190. which equation has the same solution as the given equation? a) 16x = 30 b) 16x = 130 c) 16x = 160 d) 16x = 190 4. the function g is defined by g(x)=x² + 9. for which value of x is g(x)=25? a) 4 b) 5 c) 9 d) 13 5. which expression is equivalent to 9x²+5x? a) x(9x + 5) b) 5x(9x + 1) c) 9x(x + 5) d) x²(9x + 5)

Explanation:

1.

Step1: Recall perimeter formula

The perimeter $P$ of a triangle is $P=a + b + c$, where $a$, $b$, and $c$ are the side - lengths. Given $a = 4$, $b = 6$, and $P=18$.

Step2: Solve for the third side

We substitute the known values into the formula: $18=4 + 6 + c$. Then we simplify the right - hand side: $4+6 = 10$, so the equation becomes $18=10 + c$. Subtracting 10 from both sides gives $c=18 - 10=8$.

Step1: Isolate the term with $x$

Given the equation $16x+30 = 190$. We want to get $16x$ alone on one side. We subtract 30 from both sides of the equation.

Step2: Simplify the equation

$16x+30-30=190 - 30$. This simplifies to $16x=160$.

Step1: Set up the equation

We are given $g(x)=x^{2}+9$ and $g(x) = 25$. So we set up the equation $x^{2}+9 = 25$.

Step2: Isolate the $x^{2}$ term

Subtract 9 from both sides: $x^{2}=25 - 9=16$.

Step3: Solve for $x$

Taking the square root of both sides, we get $x=\pm4$. Since 4 is one of the options, the answer is 4.

Answer:

B. 8

2.