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tensa zangetsu [6.8K]

3 years ago

5

The variables x and y vary directly. Use the values to find the constant of proportionality, k . Then write an equation that rel

ates x and y . Write any fractions in simplest form.

1 answer:

Vaselesa [24]3 years ago

7 0

Answer:

k = 9/8

y = 9/8x

Step-by-step explanation:

45/40 = 9/8

To check:

40 * 9/8 = 45

Hope this helps!

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Paul Havlik promised his grandson Jamie that he would give him $7,100 7 years from today for graduating from high school. Assume

Dominik [7]

Answer:

$\large \boxed{\$4100.07}$

Step-by-step explanation:

The formula for the future value (FV) of an investment earning compound interest is

$FV = PV \left (1 + \frac{r}{n} \right )^{nt}$

where

PV = the present value (PV) of the money invested

r = the annual interest rate expressed as a decimal fraction

t = the time in years

n = the number of compounding periods per year

Data:

FV = $7100

r = 8 % = 0.08

t = 7 yr

n = 2

Calculation:

$\begin{array}{rcl}\\7100& =& PV \left (1 + \dfrac{0.08}{2} \right )^{2 \times 7}\\\\& =& PV (1 + 0.04)^{14}\\\\& =&PV (1.04)^{14}\\& =& PV(1.731676)\\PV& =& \dfrac{7100}{1.731676}\\\\& =& \mathbf{4100.07}\\\end{array}\\\text{The present value of the money is $\large \boxed{\mathbf{\$4100.07}}$}$

4 0

3 years ago

Find the volume of the rectangular prism.<br> IN<br> in.<br> 4 in.<br> 9-in.<br> 2<br> I

prisoha [69]

Answer:

V = 36 in³

Step-by-step explanation:

The volume of a rectangular prism is given by the formula V = l × w × h

Here our length is $9\frac{1}{2}$ , our width is 4, and our height is $4\frac{1}{2}$

Plugging in these values to our formula give us $V=(9\frac{1}{2})(4)(4\frac{1}{2})= 36$

V = 36 in³

6 0

3 years ago

I'm genuinely lost in any problems like this and my teachers are no help, I need help doing exponents in general, everything to

Stolb23 [73]

Answer:

See below.

Step-by-step explanation:

4)

So we have the expression:

$(-6n^{-3})^2$

We can use the power of a product property, where:

$(ab)^n=a^n\cdot b^n$

So:

$=(-6)^2\cdot(n^{-3})^2$

For the left, -6 squared is the same as -6 times -6. This equals positive 36.

For the right, we can use the power of a power property. The property says that:

$(a^n)^k=a^{nk}$

So:

$(n^{-3})^2=n^{(-3)(2)}\\=n^{-6}$

So, all together, we have:

$=(-6)^2\cdot(n^{-3})^2\\=36n^{-6}$

6)

We have the expression:

$-\frac{3x^0}{x^4}$

First, note that anything to the zeroth power (except for 0) is 1, thus, x^0 is also 1. Simplify:

$=-\frac{3}{x^4}$

And that's the simplest we can do :)

Notes for 6)

We <em>can</em> put the x^4 to the numerator. Recall that when you put an exponent to opposite side, you put a negative. In other words:

$x^n=\frac{1}{x^{-n}}$

And vice versa:

$\frac{1}{x^{-n}}=x^n$

So, we can write the above as:

$=-\frac{3}{x^4}\\=-\frac{3}{x^{-(-4)}}\\=-3x^{-4}$

However, traditionally, we want only positive exponents, so this wouldn't be correct.

4 0

3 years ago

Read 2 more answers

In your own words,define a system of equations

lesya692 [45]

First you solve for X then substitute the number you got for X and then solve for Y.

8 0

3 years ago

Consider triangle GHJ.

bulgar [2K]

we know that

<u>Applying the Pythagorean Theorem</u>

$JG^{2} =HJ^{2}+HG^{2}$

solve for HJ

$HJ^{2}=JG^{2}-HG^{2}$

in this problem we have

$JG=10\ units\\ HG= 5\ units$

Substitute the values in the formula above

$HJ^{2}=10^{2}-5^{2}$

$HJ^{2}=100-25$

$HJ^{2}=75$

$HJ=\sqrt{75}=5\sqrt{3} \ units$

therefore

<u>the answer is the option</u>

B. 5 sq. root 3 units

5 0

3 years ago

Read 2 more answers