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givi [52]
2 years ago
5

What is the value of x in the following equation? 5x−13=15+7x

Mathematics
1 answer:
Alex787 [66]2 years ago
7 0
5x-13=15+7x
-13=15+2x
-28=2x
-14=x
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Which of the following are square roots of —8 + 8i/3? Check all that apply.
8090 [49]

Answer:

Options (2) and (3)

Step-by-step explanation:

Let, \sqrt{-8+8i\sqrt{3}}=(a+bi)

(\sqrt{-8+8i\sqrt{3}})^2=(a+bi)^2

-8 + 8i√3 = a² + b²i² + 2abi

-8 + 8i√3 = a² - b² + 2abi

By comparing both the sides of the equation,

a² - b² = -8 -------(1)

2ab = 8√3

ab = 4√3 ----------(2)

a = \frac{4\sqrt{3}}{b}

By substituting the value of a in equation (1),

(\frac{4\sqrt{3}}{b})^2-b^2=-8

\frac{48}{b^2}-b^2=-8

48 - b⁴ = -8b²

b⁴ - 8b² - 48 = 0

b⁴ - 12b² + 4b² - 48 = 0

b²(b² - 12) + 4(b² - 12) = 0

(b² + 4)(b² - 12) = 0

b² + 4 = 0 ⇒ b = ±√-4

                     b = ± 2i

b² - 12 = 0 ⇒ b = ±2√3

Since, a = \frac{4\sqrt{3}}{b}

For b = ±2i,

a = \frac{4\sqrt{3}}{\pm2i}

  = \pm\frac{2i\sqrt{3}}{(-1)}

  = \mp 2i\sqrt{3}

But a is real therefore, a ≠ ±2i√3.

For b = ±2√3

a = \frac{4\sqrt{3}}{\pm 2\sqrt{3}}

a = ±2

Therefore, (a + bi) = (2 + 2i√3) and (-2 - 2i√3)

Options (2) and (3) are the correct options.

6 0
3 years ago
Decide if each pair of lines is parallel, perpendicular, or neither.
MA_775_DIABLO [31]

Answer:

Hi

Step-by-step explanation:

I feel like this question is hard to say but I will try my best. 1st one is pparallel, 2 is perpendicular, 3 is perpendicular and 4 is parallel.

#Im only in 15th grade

4 0
2 years ago
What is the value of y?
Pavel [41]
Y = (180-72)/2 = 54°
6 0
3 years ago
Read 2 more answers
Calculate the new balance of an account that has been sitting for three years with a 1.5% interest rate and had an initial depos
maksim [4K]

Answer:

$5225

Step-by-step explanation:

Use the formula for the amount after simple interest: A = P(1 + rt)

"A" is the final amount, or balance.

"P" is the principal, or the starting amount.

"r" is the rate of interest in decimal form.

"t" is the time.

What we know:

P = 5000

t = 3

r = 1.5%

Convert the rate to decimal form by dividing by 100, or moving the decimal place two places to the left.

1.5% => 0.015 = r

Substitute what we know into the formula:

A = P(1 + rt)

A = 5000(1 + (0.015)(3))     <=simplify

A = 5000(1 + 0.045)

A = 5000(1.045)

A = 5225     <= new balance

The new balance of an account is $5225.

4 0
3 years ago
5=4b-12 hurry and make sure you put how you got the answer
PIT_PIT [208]

Answer:

4.25

Process:

  • 5=4b-12
  • 4b=12+5
  • 4b=17
  • b=\frac{17}{4}
  • b= 4.25
5 0
2 years ago
Read 2 more answers
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