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3 years ago

What expression represents '' five times the quotient of some number and ten"? A.5(z/10) B.5(z-10) C.5(10/z) D.5(10-z)

Mathematics

2 answers:

harina [27]3 years ago

8 0

Let

z-------> the number

we know that

the expression ''the quotient of some number and ten'' is equal to

$(\frac{z}{10})$

and

the complete expression ''five times the quotient of some number and ten'' is equal to

$5(\frac{z}{10})$

therefore

the answer is the option A

$5(\frac{z}{10})$

maw [93]3 years ago

5 0

Answer:

Option A is correct

$5(\frac{z}{10})$

Step-by-step explanation:

Let the number be z.

Given the statement:

'' five times the quotient of some number and ten"

" quotient of some number and ten" translated to $\frac{z}{10}$

"five times the quotient of some number and ten" translated to $5 \times \frac{z}{10}$

Then, the expression we get,

$5(\frac{z}{10})$

Therefore, $5(\frac{z}{10})$ expression represents '' five times the quotient of some number and ten"

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BartSMP [9]

I am not sure is you are supposed to solve or rewrite but for solving its this picture, tell me if its rewriting the problem and ill give you that as well!

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2 years ago

Create the equation of a quadratic function with a vertex of (5,6) and a y-intercept of -69

Elena L [17]

If the y-intercept is at -69, meaning the point is (0, -69), thus x = 0, y = -69

$\bf ~~~~~~\textit{parabola vertex form}
\\\\
\begin{array}{llll}
\boxed{y=a(x- h)^2+ k}\\\\
x=a(y- k)^2+ h
\end{array}
\qquad\qquad
vertex~~(\stackrel{}{ h},\stackrel{}{ k})\\\\
-------------------------------\\\\
vertex~(5,6)\quad 
\begin{cases}
x=5\\
y=6
\end{cases}\implies y=a(x-5)^2+6
\\\\\\
\textit{we also know that }
\begin{cases}
x=0\\
y=-69
\end{cases}\implies -69=a(0-5)^2+6
\\\\\\
-75=25a\implies \cfrac{-75}{25}=a\implies a=-3
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3 years ago

Please solve, answer choices included.

qaws [65]

4. To solve this problem, we divide the two expressions step by step:

$\frac{x+2}{x-1}* \frac{x^{2}+4x-5 }{x+4}$
Here we have inverted the second term since division is just multiplying the inverse of the term.

$\frac{x+2}{x-1}* \frac{(x+5)(x-1)}{x+4}$
In this step we factor out the quadratic equation.

$\frac{x+2}{1}* \frac{(x+5)}{x+4}$
Then, we cancel out the like term which is x-1.

We then solve for the final combined expression:
$\frac{(x+2)(x+5)}{(x+4)}$

For the restrictions, we just need to prevent the denominators of the two original terms to reach zero since this would make the expression undefined:

$x-1\neq0$
$x+5\neq0$
$x+4\neq0$

Therefore, x should not be equal to 1, -5, or -4.

Comparing these to the choices, we can tell the correct answer.

ANSWER: $\frac{(x+2)(x+5)}{(x+4)}$ ; $x\neq1,-4,-5$

5. To get the ratio of the volume of the candle to its surface area, we simply divide the two terms with the volume on the numerator and the surface area on the denominator:

$\frac{ \frac{1}{3} \pi r^{2}h }{ \pi r^{2}+ \pi r \sqrt{ r^{2} +h^{2} } }$

We can simplify this expression by factoring out the denominator and cancelling like terms.

$\frac{ \frac{1}{3} \pi r^{2}h }{ \pi r(r+ \sqrt{ r^{2} +h^{2} } )}$
$\frac{ rh }{ 3(r+ \sqrt{ r^{2} +h^{2} } )}$
$\frac{ rh }{ 3r+ 3\sqrt{ r^{2} +h^{2} } }$

We then rationalize the denominator:

$\frac{rh}{3r+3 \sqrt{ r^{2} + h^{2} }} * \frac{3r-3 \sqrt{ r^{2} + h^{2} }}{3r-3 \sqrt{ r^{2} + h^{2} }}$
$\frac{rh(3r-3 \sqrt{ r^{2} + h^{2} })}{(3r)^{2}-(3 \sqrt{ r^{2} + h^{2} })^{2}}}=\frac{3 r^{2}h -3rh \sqrt{ r^{2} + h^{2} }}{9r^{2} -9 (r^{2} + h^{2} )}=\frac{3rh(r -\sqrt{ r^{2} + h^{2} })}{9[r^{2} -(r^{2} + h^{2} )]}=\frac{rh(r -\sqrt{ r^{2} + h^{2} })}{3[r^{2} -(r^{2} + h^{2} )]}$

Since the height is equal to the length of the radius, we can replace h with r and further simplify the expression:

$\frac{r*r(r -\sqrt{ r^{2} + r^{2} })}{3[r^{2} -(r^{2} + r^{2} )]}=\frac{ r^{2} (r -\sqrt{2 r^{2} })}{3[r^{2} -(2r^{2} )]}=\frac{ r^{2} (r -r\sqrt{2 })}{-3r^{2} }=\frac{r -r\sqrt{2 }}{-3 }=\frac{r(1 -\sqrt{2 })}{-3 }$

By examining the choices, we can see one option similar to the answer.

ANSWER: $\frac{r(1 -\sqrt{2 })}{-3 }$

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3 years ago

How are the graphs of f(x)=square foot 16^x and g(x)=3 square root 64^x related

FinnZ [79.3K]

Both functions can be expressed in the form of √2ˣ

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g(x)= √(2ˣ)⁶ = √64ˣ <-- these can be further broken down if required

Hope I helped :)

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Gnoma [55]

Answer:

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Step-by-step explanation:

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