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3 years ago

Please answer!!! Will mark brainliest answer !!!

Mathematics

1 answer:

kenny6666 [7]3 years ago

3 0

Answer:

A, D

Step-by-step explanation:

When we multiply the fractions, we can get:

$\frac{1}{5^{4} }$

This is also equivalent to:

$5^{-4}$

When looking at the answer choices, the only ones that equal $5^{-4}$ are A and D because:

$(5^{-2})^{2} =5^{-4}$

$5^{2}*5^{-6} = 5^{-4}$

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I don't need you to work it out, just theorem(s) i need to reach the answer :)

VikaD [51]

Not sure why such an old question is showing up on my feed...

Anyway, let $x=\tan^{-1}\dfrac43$ and $y=\sin^{-1}\dfrac35$ . Then we want to find the exact value of $\cos(x-y)$ .

Use the angle difference identity:

$\cos(x-y)=\cos x\cos y+\sin x\sin y$

and right away we find $\sin y=\dfrac35$ . By the Pythagorean theorem, we also find $\cos y=\dfrac45$ . (Actually, this could potentially be negative, but let's assume all angles are in the first quadrant for convenience.)

Meanwhile, if $\tan x=\dfrac43$ , then (by Pythagorean theorem) $\sec x=\dfrac53$ , so $\cos x=\dfrac35$ . And from this, $\sin x=\dfrac45$ .

So,

$\cos\left(\tan^{-1}\dfrac43-\sin^{-1}\dfrac35\right)=\dfrac35\cdot\dfrac45+\dfrac45\cdot\dfrac35=\dfrac{24}{25}$

7 0

3 years ago

Identify the pattern then write the next three terms in each sequence 192,96,48,24,...

Karo-lina-s [1.5K]

1st. Find the pattern
Pattern is dividing by 2.
24/2=12
12/2=6
6/2=3

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3 years ago

Colin invests £1500 into a savings account. The bank gives 4% compound interest for the first 3 years and 5% thereafter. How muc

fomenos

1500(1+0.04)^3 = 1687.30

1687.30(1+0.05) = 1771.67 to the nearest pound: 1772

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2 years ago

Carly tried to solve an equation step by step. 7a=28 Step 1: 7a/a = 28/7 Step 2: 7 = 4 Find Carly's mistake A: Step 1 B: Step 2

Murrr4er [49]

This are the right steps

Step 1: first you divide the both size by 7 because there is 7 a's

7a/7 = 28/7

Step 2: You solve the equation

7a/7= a. 28/7 = 4

So, the answer is a = 4

not 7 = 4

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3 years ago

I think of a number and multiply it by 4. I then add 8 and I'm left with an answer of 30. What number did I think of? Form and s

postnew [5]

Answer: number= 5.5; equation: 4x+8=30

Step-by-step explanation:

Take x for the unknown number. Then just follow the words and turn them into mathematical symbols. Easy.

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3 years ago