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2 years ago

If the area of the rectangle is given by the polynomial 2x^2-7x-15, what is the dimension of the reactangle in terms of x?

Mathematics

1 answer:

Irina18 [472]2 years ago

4 0

Answer:

x - 5 and 2x + 3

Step-by-step explanation:

<h3>Given</h3>

Area of rectangle = 2x^2 - 7x - 15

Dimensions of rectangle

<h3>Solution</h3>

Since the area is the product of the sides, let's try to factorize the given:

2x^2 - 7x - 15=
2x^2 - 10x + 3x - 15 =
2x(x - 5) + 3(x - 5) =
(x - 5)(2x + 3)

So the dimensions are:

x - 5 and 2x + 3

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9. The average diameter of an atom is 2 x 10-8 m. What if the average diameter of an atom was 1 cm? How tall would you be?

ozzi

Answer:

You'd be $2 * 10^{-6}$ times tall

Step-by-step explanation:

Given

Represent the previous and new diameter by D1 and D2;

$D_1 = 2 * 10^{-8}m$

$D_2 = 1\ cm$

To determine how tall you'd be, we need to divide D2 by D1;

$Ratio = \frac{D_2}{D_1}$

Substitute values for D2 and D1

$Ratio = \frac{2 * 10^{-8}m}{1\ cm}$

Convert cm to m

$Ratio = \frac{2 * 10^{-8}m}{1 * 0.01\ m}$

$Ratio = \frac{2 * 10^{-8}m}{0.01\ m}$

Convert denominator to exponents

$Ratio = \frac{2 * 10^{-8}m}{10^{-2}\ m}$

$Ratio = \frac{2 * 10^{-8}}{10^{-2}}$

Apply Law of indices

$Ratio = 2 * 10^{-8} * 10^2$

$Ratio = 2 * 10^{-8+2}$

$Ratio = 2 * 10^{-6}$

Hence;

You'd be $2 * 10^{-6}$ times tall

4 0

2 years ago

Jake made a total of 7 copies at a copy shop, with some being black-and-white copies and some being color copies. Black-and-whit

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Jake spent a total of 70 cents.
b = black-and-white = 8 cents
c = color = 15 cents

70 = 8b + 15c

he made a total of 7 copies
b + c = 7

system of equation:
70 = 8b + 15c
b + c = 7

--------------------------

b + c = 7
b + c (-c) = 7 (-c)
b = 7 - c

plug in 7 - c for b

70 = 8(7 - c) + 15c
Distribute the 8 to both 7 and - c (distributive property)

70 = 56 - 8c + 15c
Simplify like terms

70 = 56 - 8c + 15c
70 = 56 + 7c

Isolate the c, do the opposite of PEMDAS: Subtract 56 from both sides

70 (-56) = 56 (-56) + 7c
14 = 7c

divide 7 from both sides to isolate the c

14 = 7c
14/7 = 7c/7
c = 14/7
c = 2

c = 2
---------------

Now that you know what c equals (c = 2), plug in 2 for c in one of the equations.
b + c = 7
c = 2
b + (2) = 7
Find b by isolating it. subtract 2 from both sides
b + 2 = 7
b + 2 (-2) = 7 (-2)
b = 7 - 2
b = 5

Jake made 5 black-and-white copies, and 2 color copies

hope this helps

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Answer:

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Therefore, the right answer is A.

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Answer:

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2 years ago

If the area of the rectangle is given by the polynomial 2x^2-7x-15, what is the dimension of the reactangle in terms of x?​

If the area of the rectangle is given by the polynomial 2x^2-7x-15, what is the dimension of the reactangle in terms of x?