Question

multiple choice practicealgebra regents reviewname:1. when factored, the expression $x^2 - 36$ is equivalent to(1) $(x + 6)(x - 6)$(2) $(x + 18)(x - 18)$(3) $x(x + 6)(x - 6)$(4) $x(x + 18)(x - 18)$2. what is the constant term of the polynomial $2x^3 - x + 3 + 4x^2$?(1) 5(2) 2(3) 3(4) 43. market street pizza kept a record of pizza sales for the month of february. the results are shown in the table below:| type | plain | veggie | meat only | the works || ---- | ---- | ---- | ---- | ---- || thin crust | 300 | 80 | 120 | 100 || deep-dish | 200 | 25 | 105 | 70 |of all the pizzas sold in february, what percent were plain, deep-dish pizzas?(1) 20%(2) 30%(3) 40%(4) 50%4. what is the sum of $8sqrt{3}$ and $sqrt{3}$?(1) $8sqrt{6}$(2) $9sqrt{6}$(3) $7sqrt{3}$(4) $9sqrt{3}$5. which graph is the solution to the inequality $6.4 - 4x geq -2.8$?(1) a number line graph with open circle at 2.3, arrow pointing right(2) a number line graph with closed circle at 2.3, arrow pointing right(3) a number line graph with open circle at 2.3, arrow pointing left(4) a number line graph with closed circle at 2.3, arrow pointing left

Explanation:

Step1: Factor first expression

First, factor out $x$ from $x^3 - 36x$:
$x^3 - 36x = x(x^2 - 36)$
Then factor the difference of squares:
$x(x^2 - 36) = x(x+6)(x-6)$

Step2: Identify constant term

A constant term has no variable. For $2x^3 - x + 3 + 4x^2$, the term without $x$ is $3$.

Step3: Calculate pizza percentage

First, find total pizza sales:
$300+80+120+100+200+25+105+70 = 1000$
Plain deep-dish sales = $200$.
Percentage: $\frac{200}{1000} \times 100 = 20\%$

Step4: Add radical terms

Combine like radicals:
$8\sqrt{3} + \sqrt{3} = (8+1)\sqrt{3} = 9\sqrt{3}$

Step5: Solve the inequality

Start with $6.4 - 4x \geq -2.8$
Subtract $6.4$ from both sides:
$-4x \geq -2.8 - 6.4$
$-4x \geq -9.2$
Divide by $-4$ (reverse inequality):
$x \leq 2.3$
This matches the graph with a closed dot at $2.3$ and arrow left.

Answer:

1. (3) $x(x + 6)(x - 6)$
2. (3) 3
3. (1) 20%
4. (4) $9\sqrt{3}$
5. (4) Graph with closed dot at 2.3, arrow left