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3 years ago

8

Which values are equivalent to the fraction below 3^6/3^8

1 answer:

mestny [16]3 years ago

4 0

$\frac{3^{6}}{3^{8}} = 3^{6-8} = 3^{-2} = \frac{1}{ 3^{2} } = \frac{1}{9}$

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A dvd that originaly cost 30 dollars is on sale for 10 percent off. find the amount of the discount.

Dennis_Churaev [7]

The discounted price would be $27

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3 years ago

520% of 100<br> 20 1/4% of 3<br> 0.15% of 250<br> 200%of 79<br> 0.3% of 80<br> 0.28% of 50

Tema [17]

Since the word, 'of' means to multiply, whenever we see of multply the two numbers.
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2. 20.25x3=60.75/100=.6075
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8 0

3 years ago

Trapezoid MNPQ is similar to Trapezoid RSTU. What is the length of the "x" on the misside side NP ? Also, what is the length of

ivolga24 [154]

Answer:

$x = 15$

$y = 25$

Step-by-step explanation:

Given

See attachment for MNPQ and RSTU

Required

Find x and y

To solve this question, we make use of equivalent ratios of corresponding side lengths.

The ratio of corresponding sides are:

$MN : RS$

$NP : ST$

$PQ : TU$

$MQ : RU$

From the attachment, we have:

$MN : RS \to 18 : 30$

$NP : ST \to x : 25$

$PQ : TU \to 15 : y$

To solve for x, we equate $MN : RS$ and $NP : ST$

$18 : 30 = x : 25$

Express as fraction

$\frac{18 }{ 30 }= \frac{x }{ 25}$

Make x the subject

$x = 25 * \frac{18 }{ 30 }$

$x = \frac{25 * 18 }{ 30 }$

$x = \frac{450}{ 30 }$

$x = 15$

To solve for y, we equate $MN : RS$ and $PQ : TU$

$18 : 30 = 15 : y$

Express as fraction

$\frac{18 }{ 30 }= \frac{15 }{ y}$

Make y the subject

$y = 15 * \frac{30 }{ 18 }$

$y = \frac{15 *30}{ 18 }$

$y = \frac{450}{ 18 }$

$y = 25$

8 0

3 years ago

Marsha wants to determine the vertex of the quadratic function f(x) = x2 – x + 2. What is the function’s vertex?

BaLLatris [955]

Answer:

$Vertex = (\frac{1}{2},\frac{7}{4})$

Step-by-step explanation:

Given

$f(x) = x^2 - x +2$

Required

The vertex

We have:

$f(x) = x^2 - x +2$

First, we express the equation as:

$f(x) = a(x - h)^2 +k$

Where

$Vertex = (h,k)$

So, we have:

$f(x) = x^2 - x +2$

--------------------------------------------

Take the coefficient of x: -1

Divide by 2: (-1/2)

Square: (-1/2)^2

Add and subtract this to the equation

--------------------------------------------

$f(x) = x^2 - x +2$

$f(x) = x^2 - x + (-\frac{1}{2})^2+2 -(-\frac{1}{2})^2$

$f(x) = x^2 - x + \frac{1}{4}+2 -\frac{1}{4}$

Expand

$f(x) = x^2 - \frac{1}{2}x- \frac{1}{2}x + \frac{1}{4}+2 -\frac{1}{4}$

Factorize

$f(x) = x(x - \frac{1}{2})- \frac{1}{2}(x - \frac{1}{2})+2 -\frac{1}{4}$

Factor out x - 1/2

$f(x) = (x - \frac{1}{2})(x - \frac{1}{2})+2 -\frac{1}{4}$

$f(x) = (x - \frac{1}{2})^2+2 -\frac{1}{4}$

$f(x) = (x - \frac{1}{2})^2+ \frac{8 -1 }{4}$

$f(x) = (x - \frac{1}{2})^2+ \frac{7}{4}$

Compare to: $f(x) = a(x - h)^2 +k$

$h = \frac{1}{2}$

$k = \frac{7}{4}$

Hence:

$Vertex = (\frac{1}{2},\frac{7}{4})$

8 0

3 years ago

Read 2 more answers

I don't understand this.

sladkih [1.3K]

You mean the word or number

7 0

3 years ago