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2 years ago

– 36 – m = 8(4 + 2m)

Mathematics

2 answers:

valentina_108 [34]2 years ago

5 0

Answer:

m = -4

Step-by-step explanation:

- 36 - m = 8(4+2m)

- 36 - m = 32+16m (to remove m from the left side, we need to add m to both sides)

- 36 = 32+17m (subtract 32 from both sides)

- 68 = 17m (divide by 17 on both sides)

-4 = m

Marina86 [1]2 years ago

5 0

Answer:

-36-m=32+16m

-m-16m=32+36

-17m=68

m=68/-17

m=-4

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What is the value of f(g(1)

ladessa [460]

Composite functions is a way of substituting one function into another. The value of the composite function f(g(1)) is 1

<h3>Composite functions</h3>

Composite functions is a way of substituting one function into another.

Given the function expressed as:

y = 3√x + 1

g(1) from the mapping is 0

Substitute g(1) = 0 into the given function to have:

f(g(1)) = 3√0 .+ 1

f(g(1)) =0 + 1
f(g(1)) = 1

Hence the value of the composite function f(g(1)) is 1

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2 years ago

Cecilia bought 24 bottles of juice that each contained 12 fluid ounces of juice. How many pints of juice did she buy?

Nimfa-mama [501]

Answer:

it 288

Step-by-step explanation:

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2 years ago

Terry and Callie do word processing. For a certain prospectus Callie can prepare it two hours faster than Terry can. If they wor

Dahasolnce [82]

Time taken by jerry alone is 10.1 hours

Time taken by callie alone is 8.1 hours

<u>Solution:</u>

Given:- For a certain prospectus Callie can prepare it two hours faster than Terry can

Let the time taken by Terry be "a" hours

So, the time taken by Callie will be (a-2) hours

Hence, the efficiency of Callie and Terry per hour is $\frac{1}{a-2} \text { and } \frac{1}{a} \text { respectively }$

If they work together they can do the entire prospectus in five hours

$\text {So, } \frac{1}{a-2}+\frac{1}{a}=\frac{1}{5}$

On cross-multiplication we get,

$\frac{a+(a-2)}{(a-2) \times a}=\frac{1}{5}$

$\frac{2 a-2}{(a-2) \times a}=\frac{1}{5}$

On cross multiplication ,we get

$\begin{array}{l}{5 \times(2 a-2)=a \times(a-2)} \\\\ {10 a-10=a^{2}-2 a} \\\\ {a^{2}-2 a-10 a+10=0} \\\\ {a^{2}-12 a+10=0}\end{array}$

<em><u>using quadratic formula:-</u></em>

$x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$

$x=\frac{12 \pm \sqrt{144-40}}{2}$

$\begin{array}{l}{x=\frac{12 \pm \sqrt{144-40}}{2}} \\\\ {x=\frac{12 \pm \sqrt{104}}{2}} \\\\ {x=\frac{12 \pm 2 \sqrt{26}}{2}} \\\\ {x=6 \pm \sqrt{26}=6 \pm 5.1} \\\\ {x=10.1 \text { or } x=0.9}\end{array}$

If we take a = 0.9, then while calculating time taken by callie = a - 2 we will end up in negative value

Let us take a = 10.1

So time taken by jerry alone = a = 10.1 hours

Time taken by callie alone = a - 2 = 10.1 - 2 = 8.1 hours

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3 years ago

Andrew calculates that 40 % 40% of 50 % 50% of x x is equal to 20 % 20% of 30 % 30% of y y, where x ≠ 0 x≠0. Which of the follow

Shtirlitz [24]

Answer:

Step-by-step explanation:

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3 years ago

Prove that $5^{3^n} + 1$ is divisible by $3^{n + 1}$ for all nonnegative integers $n.$

Viktor [21]

When $n=0$ , we have

$5^{3^0} + 1 = 5^1 + 1 = 6$

$3^{0 + 1} = 3^1 = 3$

and of course 3 | 6. ("3 divides 6", in case the notation is unfamiliar.)

Suppose this is true for $n=k$ , that

$3^{k + 1} \mid 5^{3^k} + 1$

Now for $n=k+1$ , we have

$5^{3^{k+1}} + 1 = 5^{3^k \times 3} + 1 \\\\ ~~~~~~~~~~~~~ = \left(5^{3^k}\right)^3 + 1^3 \\\\ ~~~~~~~~~~~~~ = \left(5^{3^k} + 1\right) \left(\left(5^{3^k}\right)^2 - 5^{3^k} + 1\right)$