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timurjin [86]
3 years ago
6

A rectangle has a heigh if 4x^3 and a width of x^3+3x^2+2x

Mathematics
1 answer:
Andrews [41]3 years ago
8 0

Answer:

Area = 4x^6+12x^5+8x^4

Step-by-step explanation:

<u>The Complete Question:</u>

A rectangle has height  4x^3  and width  x^3+3x^2+2x. What is the area of the rectangle in terms of x?

<u>Solution:</u>

The formula for the area of a rectangle is:

Area = Height * Width

Both the expressions for height and width is given, so we just need to multiply both the expressions to get an expression, in x, for the area of the rectangle. The algebra is shown below:

A=(4x^3)(x^3+3x^2+2x)\\A=4x^6+12x^5+8x^4

This is the area of the rectangle.

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Find the product of all real values of r for which 1/2x=r-x/7
Dahasolnce [82]

Answer:

r = \±\sqrt{14

Product = -14

Step-by-step explanation:

Given

\frac{1}{2x} = \frac{r - x}{7}

Required

Find all product of real values that satisfy the equation

\frac{1}{2x} = \frac{r - x}{7}

Cross multiply:

2x(r - x) = 7 * 1

2xr - 2x^2 = 7

Subtract 7 from both sides

2xr - 2x^2 -7= 7 -7

2xr - 2x^2 -7= 0

Reorder

- 2x^2+ 2xr  -7= 0

Multiply through by -1

2x^2 - 2xr +7= 0

The above represents a quadratic equation and as such could take either of the following conditions.

(1) No real roots:

This possibility does not apply in this case as such, would not be considered.

(2) One real root

This is true if

b^2 - 4ac = 0

For a quadratic equation

ax^2 + bx + c = 0

By comparison with 2x^2 - 2xr +7= 0

a = 2

b = -2r

c =7

Substitute these values in b^2 - 4ac = 0

(-2r)^2 - 4 * 2 * 7 = 0

4r^2 - 56 = 0

Add 56 to both sides

4r^2 - 56 + 56= 0 + 56

4r^2 = 56

Divide through by 4

r^2 = 14

Take square roots

\sqrt{r^2} = \±\sqrt{14

r = \±\sqrt{14

Hence, the possible values of r are:

\sqrt{14 or -\sqrt{14

and the product is:

Product = \sqrt{14} * -\sqrt{14}

Product = -14

8 0
3 years ago
The sum of the measures of the interior angles in a polygon is 540 degrees. How many sides does the polygon have?
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I need this answer too
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erica [24]

Answer:

x=5

Step-by-step explanation:

3x+7-x+6=23

3x-x=23-6-7

3x-x=23-13

3x-x=10

2x=10

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3 years ago
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Are they the same or not
makkiz [27]

Answer:

yes

Step-by-step explanation:

They are corresponding angles in which they have the same angle measure

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3 years ago
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30 Points!!!!!! Help Pleaseee!!
WITCHER [35]

when you take the square root of a number  you get two answers

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you will also get

sqrt(x) = -6


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