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Alisiya [41]
2 years ago
6

An arhitect wants to draw a rectangle with a diagonal of 20 inches. The length of the rectangle is to be 8 inches more than twic

e the width.what dimensions should she make the rectangle
Mathematics
1 answer:
kiruha [24]2 years ago
4 0

The diagonal of a rectangle = sqrt(w^2 + l^2)

w = width

l = length

In this problem,

The diagonal = 20 in

w = x

l = 2x + 8

Let's plug our numbers into the formula above.

20in = sqrt((x)^2 + (2x + 8)^2)

Let's simplify the inside of the sqrt

20 in = sqrt(5x^2 + 32x + 64)

Now, let's square both sides.

400 = 5x^2 + 32x + 64

Subtract 400 from both sides.

0 = 5x^2 + 32x - 336

Factor

0 = (5x - 28)(x + 12)

Set both terms equal to zero and solve.

x + 12 = 0

Subtract 12 from both sides.

x = -12

5x - 28 = 0

Add 28 to both sides.

5x = 28

Divide both sides by 5

x = 28/5

The width cant be a negative number so now we know that the only real solution is 28/5

Let's plug 28/5 into our length equation.

Length = 2(28/5) + 8 = 56/5 + 8 = 96/5

In conclusion,

Length = 96/5 inches

Width = 28/5

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Proof:
(-3 + 5 = 2)
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36x^6/y^10

Step-by-step explanation:

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final answer should be 36x^6/y^10

hope this helps :')

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Elliot has a total of 26 books. he has 12 more fiction books than nonfiction books. let x represent the number of fiction books
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Answer:

X+Y=26

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fiction books= X

non fiction books= Y

then,

fiction books= X

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6 0
2 years ago
877 to binary, octal, and hexadecimal
statuscvo [17]
Our number system is in base 10, which means that each digit has a value that is a multiple of 10.

For ex:
877 literally means
8  7  7   where each digit is multiplied by
10^ 2   10 ^1   10^0  respectively
which is 8 * 10^ 2 + 7 * 10^1 + 7 * 10^0 = 8 * 100 + 7 * 10 + 7 * 1 = 800 + 70 + 7 = 877

Binary is in base 2, so each of its digits (which can only be 0 or 1) are multiplied by multiples of 2 (2^0, 2^1, 2^2 ect.)

To find what 877 is in binary you can do the following:
the symbol : means divide and i'll write the quotient + the remainder

877 : 2 = 438 + 1  (438 is the quotient, 1 is the remainder)
438 : 2 = 219 + 0
219 : 2 = 109 + 1
109 : 2 = 54 + 1
54 : 2 = 27 + 0
27 : 2 = 13 + 1
13 : 2 = 6 + 1
6 : 2 = 3 + 0
3 : 2 = 1 + 1
1: 2 = 0 + 1

now write ALL off the remainders from BOTTOM to TOP:
1101101101

use a similar step for octal (use 8 instead of 2 as the divisor) and hexidecimal (use 16 instead of 2 as the divisor) 


6 0
2 years ago
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