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Llana [10]
3 years ago
11

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.

6 0
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

So

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

So

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

Zeros: x = 9 and x = 5.

8 0
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:

B

Step-by-step explanation:

When Gabriella finish her bows she had 4 extra.

Hope this helps ;)

5 0
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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2 years ago
Use a protractor to draw a pentagon so that the bottom side is horizontal and the left and right sides are perpendicular to the
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5 0
2 years ago
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