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3 years ago

Which equations are true?

Mathematics

1 answer:

liberstina [14]3 years ago

3 0

Answer:

B. D. E.

Step-by-step explanation:

A. False

${15}^{0} = 1$

B. True

$( {8}^{3} )( {8}^{6} ) = {8}^{(3 + 6)} = {8}^{9}$

C. False

${5}^{2} = 25$

D. True

$( {6}^{5} )^{3 } = {6}^{15}$

E. True

$\frac{ {3}^{7} }{ {3}^{9} } = {3}^{(7 - 9)} = {3}^{ - 2}$

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PLEASE HELP

Natalka [10]

Answer:

Step-by-step explanation:

the median is the number in the middle of a sorted array

here it has 10 numbers, so the median will be the average of the 5th and the 6th number

the 5th number is 7 and the 6th number is 7

the average is (7+7)/2 = 7

so the median is 7

4 0

2 years ago

Rob Herndon, an accountant with Southwest Airlines, wants to retire 50% of

valina [46]

To achieve his goal of paying off $430,000 in 10 years, Rob Herndon needs to make $34,186.97 at 5% compounded annually.

<h3>What is a future value?</h3>

A future value refers to a value on a future date based on an assumed growth rate of interest over time.

The future value can be determined using the FV formula or table.

We can also compute the future value using an online finance calculator as follows:

<h3>Data and Calculations:</h3>

N (# of periods) = 10 years

I/Y (Interest per year) = 5%

PV (Present Value) = $0

FV (Future Value) = $430,000

<u>Results:</u>

PMT = $34,186.97

Sum of all periodic payments = $341,869.70

Total Interest= $88,130.30

Thus, for Rob Herndon to achieve his goal of paying off $430,000 in 10 years, he needs to make $34,186.97 at 5% compounded annually.

Learn more about Calculating Future Values at brainly.com/question/24703884

#SPJ1

7 0

2 years ago

Write an equation in standard form of the hyperbola described.

marishachu [46]

Check the picture below, so the hyperbola looks more or less like so, so let's find the length of the conjugate axis, or namely let's find the "b" component.

$\textit{hyperbolas, horizontal traverse axis } \\\\ \cfrac{(x- h)^2}{ a^2}-\cfrac{(y- k)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h\pm a, k)\\ c=\textit{distance from}\\ \qquad \textit{center to foci}\\ \qquad \sqrt{ a ^2 + b ^2} \end{cases} \\\\[-0.35em] ~\dotfill$

$\begin{cases} h=0\\ k=0\\ a=2\\ c=4 \end{cases}\implies \cfrac{(x-0)^2}{2^2}-\cfrac{(y-0)^2}{b^2} \\\\\\ c^2=a^2+b^2\implies 4^2=2^2+b^2\implies 16=4+b^2\implies \underline{12=b^2} \\\\\\ \cfrac{(x-0)^2}{2^2}-\cfrac{(y-0)^2}{12}\implies \boxed{\cfrac{x^2}{4}-\cfrac{y^2}{12}}$