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Margarita [4]
3 years ago
12

4x + 3(4x + 7) = 4(7x + 3)​

Mathematics
1 answer:
Natasha2012 [34]3 years ago
5 0

Answer: 1

Step-by-step explanation:4x + 3(4x + 7) = 4(7x + 3) + -3

Reorder the terms:

4x + 3(7 + 4x) = 4(7x + 3) + -3

4x + (7 * 3 + 4x * 3) = 4(7x + 3) + -3

4x + (21 + 12x) = 4(7x + 3) + -3

Reorder the terms:

21 + 4x + 12x = 4(7x + 3) + -3

Combine like terms: 4x + 12x = 16x

21 + 16x = 4(7x + 3) + -3

Reorder the terms:

21 + 16x = 4(3 + 7x) + -3

21 + 16x = (3 * 4 + 7x * 4) + -3

21 + 16x = (12 + 28x) + -3

Reorder the terms:

21 + 16x = 12 + -3 + 28x

Combine like terms: 12 + -3 = 9

21 + 16x = 9 + 28x

Solving

21 + 16x = 9 + 28x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-28x' to each side of the equation.

21 + 16x + -28x = 9 + 28x + -28x

Combine like terms: 16x + -28x = -12x

21 + -12x = 9 + 28x + -28x

Combine like terms: 28x + -28x = 0

21 + -12x = 9 + 0

21 + -12x = 9

Add '-21' to each side of the equation.

21 + -21 + -12x = 9 + -21

Combine like terms: 21 + -21 = 0

0 + -12x = 9 + -21

-12x = 9 + -21

Combine like terms: 9 + -21 = -12

-12x = -12

Divide each side by -12.

x = 1

Simplifying

x = 1

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We are given degree of the polynomial function = 3.

Because degree is 3, there should be three x-intercepts of the given graph of the polynomial.

We also given roots of the equation f(x)=0 are −2 , 0, and 3.

Therefore, x intercepts should be at:

(0,0), (-2,0) and (3,0).

<h3>In the given options third option shows x-intercepts at 0, -2 and 3.</h3><h3>Therefore, correct option is 3rd option.</h3>

8 0
3 years ago
Write this ratio in simplest form: 72:9​
elena55 [62]

Answer:

12

Step-by-step explanation:12x9

3 0
3 years ago
Read 2 more answers
(-3)3 (26)
Lemur [1.5K]

<em><u>Question:</u></em>

Geoffrey is evaluating the expression (-3)^3(2^6)/(-3)^5(2^2) as shown below.

(-3)^3(2^6)/(-3)^5(2^2) = (2)^a/(-3)^b = c/d

What are the values of a, b, c, and d?

<em><u>Answer:</u></em>

<em><u>The values are a = 4, b = 2, c = 16, d = 9</u></em>

<em><u>Solution:</u></em>

Given that,

Geoffrey is evaluating the expression

\frac{(-3)^3 \times 2^6}{(-3)^5 \times 2^2}

He is evaluating as shown below:

\frac{(-3)^3 \times 2^6}{(-3)^5 \times 2^2} = \frac{2^a}{-3^b} = \frac{c}{d}

From given,

\frac{(-3)^3 \times 2^6}{(-3)^5 \times 2^2}

Use the law of exponent

\frac{a^m}{a^n} = a^{m - n}

Therefore,

\frac{(-3)^3 \times 2^6}{(-3)^5 \times 2^2} = \frac{2^{6-2}}{(-3)^{5-3}}\\\\Simplify\\\\\frac{(-3)^3 \times 2^6}{(-3)^5 \times 2^2} = \frac{2^4}{-3^2}

Thus,

a = 4

b = 2

Simplify further

\frac{(-3)^3 \times 2^6}{(-3)^5 \times 2^2} = \frac{2^4}{-3^2} = \frac{16}{9}

Thus,

c = 16

d = 9

Thus values are a = 4, b = 2, c = 16, d = 9

8 0
4 years ago
A computer that originally cost $500 is on sale for $350. What is the percent discount?
laiz [17]

Answer:

30%

Step-by-step explanation:

  1. 500 - 350 = 150
  2. Set up a proportion: \frac{150}{500} = \frac{x}{100}  
  3. Cross multiply, then divide: 150 × 100 = 15000, 15000 ÷ 500 = 30
  4. Write the completed fraction: \frac{30}{100}  
  5. \frac{30}{100} = 30%

I hope this helps!

8 0
3 years ago
Find the length of the arc to 2 decimals places
HACTEHA [7]

Answer:

Step-by-step explanation:

The formula for arc length is

AL=\frac{\theta}{360}*2\pi r where theta is the measure of the central angle and r is the radius. We have both of those pieces of info; filling in:

AL=\frac{30}{360}*2(3.14) (4) and simplifying a bit:

AL=\frac{1}{12}(8)(3.14) and a bit more:

AL=\frac{25.12}{12} and finally, to

AL = 2.09 m

7 0
3 years ago
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