Question

5 multiple choice 4 points solve: 3x + 7 > 19 x > -4 x < 4 x > 8\frac{2}{3} x > 4 6 multiple choice 4 points which equation is equivalent to \frac{y}{a}=b? y = a ÷ b y = a · b y = b ÷ a y = \frac{1}{2}a 7 multiple choice 4 points compared to its parent function f(x)=x², which of these best describes the function f(x)=2x² + 1? it is narrower and translated up it is wider and translated down it is wider and translated up it is narrower and translated down

Explanation:

Question 5

Step1: Isolate the term with x

Subtract 7 from both sides of $3x + 7>19$.
$3x+7 - 7>19 - 7$
$3x>12$

Step2: Solve for x

Divide both sides by 3.
$\frac{3x}{3}>\frac{12}{3}$
$x > 4$

Given $\frac{y}{a}=b$, multiply both sides by a to solve for y.
$\frac{y}{a}\times a=b\times a$
$y = a\cdot b$

For a quadratic function $y = ax^{2}+k$, compared to the parent - function $y=x^{2}$:

1. The coefficient a affects the width of the parabola. If $|a|>1$, the parabola is narrower than $y = x^{2}$. Since in $y = 2x^{2}+1$, $a = 2$ ($|2|>1$), the parabola is narrower.
2. The constant k affects the vertical translation. If $k>0$, the parabola is translated up. Since $k = 1>0$ in $y=2x^{2}+1$, the parabola is translated up.

Answer:

$x>4$

Question 6