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4 years ago

Given the following diagram, find the required measure.

Mathematics

1 answer:

Zielflug [23.3K]4 years ago

3 0

Answer:

∠ 5 = 40°

Step-by-step explanation:

∠ 1 and ∠ 2 are adjacent angles and supplementary, thus

∠ 2 = 180° - ∠ 1 = 180° - 140° = 40°

∠ 5 and ∠ 2 are alternate angles and congruent , thus

∠ 5 = 40°

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For the real-valued functions, find the composition and specify its domain using interval notation.

Helen [10]

Answer:

Composition: $f(x)\,^o\,h(x)=4\,\sqrt{x+4} -1$

Domain = { $x\,/\,x\geq \,-4$ }

Step-by-step explanation:

Given

$f(x)=4\,x-1\,\,\, and \,\,\, h(x)=\sqrt{x+4}$

The requested composition becomes:

$f(x)\,^o\,h(x)=f(h(x))\\f(x)\,^o\,h(x)=f(\sqrt{x+4} )\\f(x)\,^o\,h(x)=4\,\sqrt{x+4} -1$

Then the Domain consists of all Real x-values for which the function is defined. In this case, the function is defined for all x-values for which the square root is defined, that is all x values for which:

$x+4\geq \,0$ (so the square root is defined in the Real number system)

This means $x\geq \,-4$

The Domain is then all the Real x-values such that $x\geq \,-4$

6 0

3 years ago

QUICK PLS Your friend is able to invest $120 a month in a 401(k) with a predicted growth rate of 3%. Your friend's company will

Len [333]

The contribution of the friend's company is of: $60.

The account's balance after 20 years will be of: $130,694.36.

The total deposits after 20 years are given as follows: $28,800 by the friend and $14,400 by the company.

The interest earned during this entire period was of: $87,494.36.

<h3>How to obtain the balance?</h3>

The balance is obtained using the future value formula, which is presented as follows:

$B = \frac{P\left(\left(1 + \frac{r}{n}\right)^{nt}-1\right)}{\frac{r}{n}}$

The meaning of each parameter is explained as follows:

P is the total month deposit.

r is the interest rate.

n is the number of coupoundings per period, that is, compoundings per year.

t is the number of years.

The deposits will be of:

Friend: $120.

Company: $60, as it is half of the friend.

Then the parameter P is of:

P = 120 + 60 = 180.

The remaining parameters to obtain the balance after 20 years are given as follows:

r = 0.03, n = 12, t = 20.

Then the balance after 20 years is obtained as follows:

$B = \frac{P\left(\left(1 + \frac{r}{n}\right)^{nt}-1\right)}{\frac{r}{n}}$

$B = \frac{180\left(\left(1 + \frac{0.03}{12}\right)^{12 \times 20}-1\right)}{\frac{0.03}{12}}$

B = $130,694.36.

The total deposits will be of:

Friend: 120 x 20 x 12 = $28,800.

Company: half of friend -> $14,400.

The interest accrued is the balance subtracted by the total deposits, hence:

130694.36 - (28800 + 14400) = $87,494.36.

A similar problem, also featuring the future value formula, is presented at brainly.com/question/24703884

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2 years ago

Brainly trash finish your own homework by yourself

Gennadij [26K]

Answer:

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3 years ago

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Shannon test drives a car in Germany and drives 95 kilometers per hour. What is her speed in miles per hour?

kompoz [17]

Answer:59.03 miles

Step-by-step explanation:

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3 years ago

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Explain how you could use a number line to find the number that is 9 less than 1.

lara31 [8.8K]

The answer would be -8 because you would go 9 to the left in the number line

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3 years ago