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Rina8888 [55]
3 years ago
15

Given the prime factorisation of the each of

Mathematics
1 answer:
Zigmanuir [339]3 years ago
8 0
The cube root of 287496 is 66
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<img src="https://tex.z-dn.net/?f=%20%5Cfrac%7B%20%7B2%7D%5E%7Bx%20%2B%202%7D%20-%20%20%7B2%7D%5E%7B%20x%20%2B%203%7D%20%7D%7B%2
weeeeeb [17]

I suppose you just have to simplify this expression.

(2ˣ⁺² - 2ˣ⁺³) / (2ˣ⁺¹ - 2ˣ⁺²)

Divide through every term by the lowest power of 2, which would be <em>x</em> + 1 :

… = (2ˣ⁺²/2ˣ⁺¹ - 2ˣ⁺³/2ˣ⁺¹) / (2ˣ⁺¹/2ˣ⁺¹ - 2ˣ⁺²/2ˣ⁺¹)

Recall that <em>n</em>ª / <em>n</em>ᵇ = <em>n</em>ª⁻ᵇ, so that we have

… = (2⁽ˣ⁺²⁾ ⁻ ⁽ˣ⁺¹⁾ - 2⁽ˣ⁺³⁾ ⁻ ⁽ˣ⁺¹⁾) / (2⁽ˣ⁺¹⁾ ⁻ ⁽ˣ⁺¹⁾ - 2⁽ˣ⁺²⁾ ⁻ ⁽ˣ⁺¹⁾)

… = (2¹ - 2²) / (2⁰ - 2¹)

… = (2 - 4) / (1 - 2)

… = (-2) / (-1)

… = 2

Another way to get the same result: rewrite every term as a multiple of <em>y</em> = 2ˣ :

… = (2²×2ˣ - 2³×2ˣ) / (2×2ˣ - 2²×2ˣ)

… = (4×2ˣ - 8×2ˣ) / (2×2ˣ - 4×2ˣ)

… = (4<em>y</em> - 8<em>y</em>) / (2<em>y</em> - 4<em>y</em>)

… = (-4<em>y</em>) / (-2<em>y</em>)

… = 2

8 0
3 years ago
You spent $175 on a pair of shoes and three shirts. Each shirt cost the same amount. The shoes cost four times the amount of one
sergey [27]

Step-by-step explanation:

1. making the equation:

shoes = x

shirts = y

175 = x + 3y

x = 4y

2. graph it (I'm using desmos)

the green line is for 175 = x + 3y and the purple one is for x = 4y

3. find the price

x = 4y

175 = 4y + 3y

175 = 7y

y = 175/7 = $25

price of the shirt = $25

x = 4y = 4*25 = $100

price of a pair of shoes = $100

5 0
3 years ago
How do you solve (7-2)/5 step by step
gtnhenbr [62]
7 - 2 = 5

5 / 5 = 1

The answer would be 1.
3 0
3 years ago
Read 2 more answers
Determine whether test point (-6,4) is a solution to the linear inequality x+y_&lt;1
tamaranim1 [39]
\bf \begin{array}{llll}&#10;-6&,&4\\&#10;\uparrow &&\uparrow \\&#10;x&&y&#10;\end{array}\qquad x+y\le 1\implies -6+4\le 1\implies -2\le 1

now, is it true that -2 is lesser than 1? if it's true, is a solution, if is false, is not then
7 0
3 years ago
A rock show is being televised the lead singer who is 75 inches tall is 15 inches tall on a TV monitor the image of the bass pla
VladimirAG [237]
75 : 15 = x : 13
15 x = 75 · 13
15 x = 975
x = 975 : 15
x = 65
Answer:
The bass player is 65 inches tall.
6 0
3 years ago
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