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Sholpan [36]
3 years ago
14

-4(x - 2) - 3x = 2(5x - 7) + 6

Mathematics
1 answer:
Allisa [31]3 years ago
3 0

Answer: last option.

Step-by-step explanation:

To apply the Distributive property, remember that:

c(a-b)=ca-cb

Then, applying this, you get:

-4(x - 2) - 3x = 2(5x - 7) + 6\\\\(-4)(x)+(-4)(-2)-3x=(2)(5x)+(2)(-7)+6\\\\-4x+8-3x=10x-14+6

Combine like terms means that you need to add the like terms.

Therefore, you get:

-7x+8=10x-8

You can observe that the expression obtained matches with the expression provided in the last option.

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2 years ago
The area of a rectangular piece of cardboard is represented by
Liula [17]

This question is solved applying the formula of the area of the rectangle, and finding it's width. To do this, we solve a quadratic equation, and we get that the cardboard has a width of 1.5 feet.

Area of a rectangle:

The area of rectangle of length l and width w is given by:

A = wl

w(2w + 3) = 9

From this, we get that:

l = 2w + 3, A = 9

Solving a quadratic equation:

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{\Delta}}{2*a}

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

\Delta = b^{2} - 4ac

In this question:

w(2w+3) = 9

2w^2 + 3w - 9 = 0

Thus a quadratic equation with a = 2, b = 3, c = -9

Then

\Delta = 3^2 - 4(2)(-9) = 81

w_{1} = \frac{-3 + \sqrt{81}}{2*2} = 1.5

w_{2} = \frac{-3 - \sqrt{81}}{2*2} = -3

Width is a positive measure, thus, the width of the cardboard is of 1.5 feet.

Another similar problem can be found at brainly.com/question/16995958

5 0
2 years ago
What is m in the simultaneous equation <br> M -n=1<br><br> M+n=3
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The simultaneous equations is missing +8
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2 years ago
Read 2 more answers
Making an
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7 0
3 years ago
Consider the following problem: A farmer with 750 ft of fencing wants to enclose a rectangular area and then divide it into four
gregori [183]

Answer and step-by-step explanation:

For any rectangle, the one with the largest area will be the one whose dimensions are as close to a square as possible.

However, the dividers change the process to find this maximum somewhat.

Letting x represent two sides of the rectangle and the 3 parallel dividers, we have 2x+3x = 5x.

Letting y represent the other two sides of the rectangle, we have 2y.

We know that 2y + 5x = 750.

Solving for y, we first subtract 5x from each side:

2y + 5x - 5x = 750 - 5x

2y = -5x + 750

Next we divide both sides by 2:

2y/2 = -5x/2 + 750/2

y = -2.5x + 375

We know that the area of a rectangle is given by

A = lw, where l is the length and w is the width.  In this rectangle, one dimension is x and the other is y, making the area

A = xy

Substituting the expression for y we just found above, we have

A = x(-2.5x+375)

A = -2.5x² + 375x

This is a quadratic equation, with values a = -2.5, b = 375 and c = 0.

To find the maximum, we will find the vertex.  First we find the axis of symmetry, using the equation

x = -b/2a

x = -375/2(-2.5) = -375/-5 = 75

Substituting this back in place of every x in our area equation, we have

A = -2.5x² + 375x

A = -2.5(75)² + 375(75) = -2.5(5625) + 28125 = -14062.5 + 28125 = 14062.5

6 0
3 years ago
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