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3 years ago

Factor 8a^2+8ab+8ac+3a+3b+3c

Mathematics

1 answer:

nalin [4]3 years ago

5 0

Answer:

(8a + 3)(a + b + c)

Step-by-step explanation:

8a^2 + 8ab + 8ac + 3a + 3b + 3c =

= 8a(a + b + c) + 3(a + b + c)

= (8a + 3)(a + b + c)

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One serving of the food product contains 1g total saturated fat or 5% daily value (DV) for saturated fat. What is the daily valu

Leona [35]

Answer:

The daily value for saturated fat is 20g.

Step-by-step explanation:

Percentage problems can be solved by rule of three

In a rule of three problem, the first step is identifying the measures and how they are related, if their relationship is direct of inverse.

When the relationship between the measures is direct, as the value of one measure increases, the value of the other measure is going to increase too. In this case, the rule of three is a cross multiplication.

When the relationship between the measures is inverse, as the value of one measure increases, the value of the other measure will decrease. In this case, the rule of three is a line multiplication.

A percentage problem is an example where the relationship between the measures is direct.

The problem states that 1g is 5% of the daily value for saturated fat. The daily value(100%) for saturated fat is x, so:

1g - 5%

xg - 100%

5x = 100

$x = \frac{100}{5}$

x = 20g

The daily value for saturated fat is 20g.

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3 years ago

Fill in the missing portions of the function to rewrite g(x) = 3a^2 − 42a + 135 to reveal the zeros of the function. What are th

mariarad [96]

Answer:

g(x) = 3(x-9)(x-5)

Zeros: x = 9 and x = 5.

Step-by-step explanation:

Given a second order polynomial expressed by the following equation:

$ax^{2} + bx + c, a\neq0$ .

This polynomial has roots $x_{1}, x_{2}$ such that $ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})$ , given by the following formulas:

$x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}$

$x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}$

$\bigtriangleup = b^{2} - 4ac$

In this question:

$g(x) = 3x^{2} - 42a + 135$

$a = 3, b = -42, c = 135$

$\bigtriangleup = (-42)^{2} - 4*3*135 = 144$

$x_{1} = \frac{-(-42) + \sqrt{144}}{2*3} = 9$

$x_{2} = \frac{-(42) - \sqrt{144}}{2*3} = 5$

g(x) = 3(x-9)(x-5)

Zeros: x = 9 and x = 5.

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3 years ago

1. Gabriella had a piece of ribbon that was 3į yards long. She used this ribbon to make bows. Each

Kobotan [32]

Answer:

Step-by-step explanation:

When Gabriella finish her bows she had 4 extra.

Hope this helps ;)

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2 years ago

What are the solutions of the inequality? -2(3x + 2) ≥ -6x - 4 Question 2 options: all real numbers x ≤ 6 no solution x ≥ 0

Tju [1.3M]

$Solution, -2\left(3x+2\right)\ge \:-6x-4\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:True\quad \forall \:x\in \mathbb{R}\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:\infty \:\right)\end{bmatrix}$

$Steps:$

$-2\left(3x+2\right)\ge \:-6x-4$

$\mathrm{Expand\:}-2\left(3x+2\right),\\\mathrm{Apply\:the\:distributive\:law}:\quad \:a\left(b+c\right)=ab+ac,\\a=-2,\:b=3x,\:c=2,\\-2\cdot \:3x+\left(-2\right)\cdot \:2,\\\mathrm{Apply\:minus-plus\:rules},\\+\left(-a\right)=-a,\\-2\cdot \:3x-2\cdot \:2,\\\mathrm{Simplify}\:-2\cdot \:3x-2\cdot \:2,\\\mathrm{Multiply\:the\:numbers:}\:2\cdot \:3=6,\\-6x-2\cdot \:2,\\\mathrm{Multiply\:the\:numbers:}\:2\cdot \:2=4,\\-6x-4,\\-6x-4\ge \:-6x-4$

$\mathrm{Add\:}4\mathrm{\:to\:both\:sides},\\-6x-4+4\ge \:-6x-4+4$

$\mathrm{Simplify},\\-6x\ge \:-6x$

$\mathrm{Add\:}6x\mathrm{\:to\:both\:sides},\\-6x+6x\ge \:-6x+6x$

$\mathrm{Simplify},\\0\ge \:0$

$\mathrm{Therefore,\:the\:final\:solution\:is},\\True\quad \forall \:x\in \mathbb{R}$

$Or\:No\:Solution\:x\geq 0$

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