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3 years ago

If DE = 7x + 3 and EF = 9x - 19, then EF = ?

Mathematics

1 answer:

ANEK [815]3 years ago

6 0

Answer:

Step-by-step explanation:

7x + 3 = 9x - 19

-2x + 3 = -19

-2x = -22

x = 11

DE= 7(11) + 3 = 77 + 3 = 80

EF = 9(11) - 19 = 99 - 19 = 80

80 + 80 = 160 for DF

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Anna007 [38]

Answer:

See below

Step-by-step explanation:

Do you mean -12(x+5)=-10?

Divide both sides by -12 -> x+5=10/12

Subtract 5 on both sides -> x=10/12-5 -> x=-4 1/6

So x=-4 1/6

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3 years ago

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(3-4i)(6i+7)-(2-3i)

Sergeu [11.5K]

Answer:

43-7i

Step-by-step explanation:

We are given the expression:

$\displaystyle \large{(3 - 4i)(6i + 7) - (2 - 3i)}$

First, expand 3-4i in 6i+7. To expand binomial with binomial, first we expand 3 in 6i+7 then expand -4i in 6i+7.

$\displaystyle \large{[(3 \cdot 6i) + (3 \cdot 7) + ( - 4i \cdot 6i) + ( - 4i \cdot 7)]- (2 - 3i)} \\ \displaystyle \large{[18i + 21 - 24 {i}^{2} - 28i]- (2 - 3i)}$

Now combine like terms.

$\displaystyle \large{[ - 10i+ 21 - 24 {i}^{2} ]- (2 - 3i)}$

Imaginary Unit

$\displaystyle \large{i = \sqrt{ - 1} } \\ \displaystyle \large{ {i}^{2} = - 1 }$

Therefore:-

$\displaystyle \large{[ - 10i+ 21 - 24 ( - 1) ]- (2 - 3i)} \\ \displaystyle \large{[ - 10i+ 21 + 24]- (2 - 3i)} \\ \displaystyle \large{[ - 10i+ 45]- (2 - 3i)}$

Then expand negative sign in 2-3i; remember that negative times negative is positive and negative times positive is negative.

$\displaystyle \large{- 10i+ 45 - (2 - 3i)} \\ \displaystyle \large{- 10i+ 45 - 2 + 3i}$

Combine like terms.

$\displaystyle \large{43 - 7i}$

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3 years ago

The diameter of the base of the cone measures 8 units. The height measures 6 units. What is the volume of the cone?

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