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3 years ago

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Which equation is equivalent to 3[x + 3(4x – 5)] = 15x – 24?

2 answers:

makkiz [27]3 years ago

5 0

Hello from MrBillDoesMath!

Answer:

x = 7/8

Discussion:

3[x + 3(4x – 5)] = 15x – 24 =>

3x + (3*3)(4x-5) = 15x - 24 =>

3x + 9*(4x) - (3*3)*5 = 15x - 24 =>

3x + 36x - 45 = 15x - 24 => (add 24 to each side)

3x + 36x - 45 + 45 = 15x - 24 + 45 =>

39x = 15x + 21 => (as 45-24 = 21)

39x-15x = 21 => (subtract 15x from both sides)

24x = 21 =>

x = 21/24 = -7/8

Regards,

MrB

P.S. I'll be on vacation from Friday, Dec 22 to Jan 2, 2019. Have a Great New Year!

Anastaziya [24]3 years ago

4 0

I hope this will help

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There is a 72% chance that you will get an exam next week. What is the probability that you will NOT get an exam next week?

Yuliya22 [10]

100 minus 72 equals to 28. 28% of NOT getting an exam next week

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2 years ago

I know you want to answer this question.

Alik [6]

Answer:

D. x = 3

Step-by-step explanation:

$\frac{1}{2} ^{x-4}$ - 3 = $4^{x-3}$ - 2

First, convert $4^{x-3}$ to base 2:

$4^{x-3}$ = $(2^{2})^{x-3}$

$\frac{1}{2} ^{x-4}$ - 3 = $(2^{2})^{x-3}$ - 2

Next, convert $\frac{1}{2} ^{x-4}$ to base 2:

$\frac{1}{2} ^{x-4}$ = $(2^{-1})^{x-4}$

$(2^{-1})^{x-4}$ - 3 = $(2^{2})^{x-3}$ - 2

Apply exponent rule: $(a^{b})^{c}$ = $a^{bc}$ :

$(2^{-1})^{x-4}$ = $2^{-1*(x-4)}$

$2^{-1*(x-4)}$ - 3 = $(2^{2})^{x-3}$ - 2

Apply exponent rule: $(a^{b})^{c}$ = $a^{bc}$ :

$(2^{2})^{x-3}$ = $2^{2(x-3)}$

$2^{-1*(x-4)}$ - 3 = $2^{2(x-3)}$ - 2

Apply exponent rule: $a^{b+c}$ = $a^{b}$ $a^{c}$ :

$2^{-1(x-4)}$ = $2^{-1x}$ * $2^{4}$ , $2^{2(x-3)}$ = $2^{2x}$ * $2^{-6}$

$2^{-1 * x}$ * $2^{4}$ - 3 = $2^{2x}$ * $2^{-6}$ - 2

Apply exponent rule: $(a^{b})^{c}$ = $a^{bc}$ :

$2^{-1x}$ = $(2^{x})^{-1}$ , $2^{2x}$ = $(2^{x})^{2}$

$(2^{x})^{-1}$ * $2^{4}$ - 3 = $(2^{x})^{2}$ * $2^{-6}$ - 2

Rewrite the equation with $2^{x} = u$ :

$(u)^{-1}$ * $2^{4}$ - 3 = $(u)^{2}$ * $2^{-6}$ - 2

Solve $u^{-1}$ * $2^{4}$ - 3 = $u^{2}$ * $2^{-6}$ - 2:

$u^{-1}$ * $2^{4}$ - 3 = $u^{2}$ * $2^{-6}$ - 2

Refine:

$\frac{16}{u}$ - 3 = $\frac{1}{64}$ $u^{2}$ - 2

Add 3 to both sides:

$\frac{16}{u}$ - 3 + 3 = $\frac{1}{64}$ $u^{2}$ - 2 + 3

Simplify:

$\frac{16}{u}$ = $\frac{1}{64}$ $u^{2}$ + 1

Multiply by the Least Common Multiplier (64u):

$\frac{16}{u}$ * 64u = $\frac{1}{64}$ $u^{2}$ + 1 * 64u

Simplify:

$\frac{16}{u}$ * 64u = $\frac{1}{64}$ $u^{2}$ + 1 * 64u

Simplify $\frac{16}{u}$ * 64u:

1024

Simplify $\frac{1}{64}$ $u^{2}$ * 64u:

$u^{3}$

Substitute:

1024 = $u^{3}$ + 64u

Solve for u:

u = 8

Substitute back u = $2^{x}$ :

8 = $2^{x}$

Solve for x:

x = 3

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3 years ago

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Gennadij [26K]

5x^2
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3 years ago

What is the exact volume of the cylinder?

Mademuasel [1]

V=hpir^2
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v=5pi8^2
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3 years ago

Read 2 more answers

While shopping for a dress, mrs vargas found one that was in sale for 35% off. the original price was $40. how much will she sav

timurjin [86]

Answer: $14

Steps:
What if 35% of $40
35% of 40
35% * 40
0.35 * 40 = $14

She will save $14

Tips:
-The word “of” means multiply
-To change a percent to a decimal move the decimal 2 places to the left.

If this was helpful and correct I would appreciate the brainliest! :)

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2 years ago