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3 years ago

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triangle RSt is similar to triangle xyz with rs= 3 inches and xy= 2 inches. Of the area of triangle RST is 27 in^2, determine an

d state the area of triangle XYZ in square inches.

1 answer:

Luden [163]3 years ago

7 0

Answer: The area of triangle ΔXYZ is 12 square inches.

Step-by-step explanation:

Since we have given that

RS = 3 inches

XY = 2 inches

Area of ΔRST = 27 in²

Since ΔRST is similar to ΔXYZ.

So, using the "Area similarity theorem":

$\dfrac{\Delta RST}{\Delta XYZ}=\dfrac{RS^2}{XY^2}\\\\\dfrac{27}{\Delta XYZ}=\dfrac{3^2}{2^2}\\\\\dfrac{27}{\Delta XYZ}=\dfrac{9}{4}\\\\\Delta XYZ=3\times 4=12\ in^2$

Hence, the area of triangle ΔXYZ is 12 square inches.

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Function f is an exponential function. It predicts the value of a famous painting, in thousands of dollars, as a function of the

nalin [4]

Answer:

$y=8 \cdot (\frac{5}{4})^x$

$f(x)=8 \cdot (\frac{5}{4})^x$

or

$f(x)=8 \cdot (1.25)^x$

Step-by-step explanation:

We are going to see if the exponential curve is of the form:

$y=a \cdot b^x$ , ( $b\neq 0$ ).

If you are given the $y-$ intercept, then $a$ is easy to find.

It is just the $y-$ coordinate of the $y-$ intercept is your value for $a$ .

(Why? The $y-$ intercept happens when $x=0$ . Replacing $x$ with 0 gives $y=a \cdot b^0=a \cdot 1=a$ . This says when $x=0 \text{ that} y=a$ .)

So $a=8$ .

So our function so far looks like this:

$y=8 \cdot b^x$

Now to find $b$ we need another point. We have two more points. So we will find $b$ using one of them and verify for our resulting equation works for the other.

Let's do this.

We are given $(1,10)$ is a point on our curve.

So when $x=1$ , $y=10$ .

$10=8 \cdot b^1$

$10=8 \cdot b$

Divide both sides by 8:

$\frac{10}{8}=b$

Reduce the fraction:

$\frac{5}{4}=b$

So the equation if it works out for the other point given is:

$y=8 \cdot (\frac{5}{4})^x$

Let's try it. So the last point given that we need to satisfy is $(2,12.5)$ .

This says when $x=2$ , $y=12.5$ .

Let's replace $x$ with 2 and see what we get for $y$ :

$y=8 \cdot (\frac{5}{4})^2$

$y=8 \cdot \frac{25}{16}$

$y=\frac{8}{16} \cdot 25$

$y=\frac{1}{2} \cdot 25}$

$y=\frac{25}{2}$

$y=12.5$

So we are good. We have found an equation satisfying all 3 points given.

The equation is $y=8 \cdot (\frac{5}{4})^x$ .

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3 years ago

Select all the expressions that have a value of 180 when b = 4. o 876 – 179 + 957 - 87 O 336 12 62 + 120 0 516 - 24 ( 115 + 187

BabaBlast [244]

Answer: miata

Step-by-step explanation:

6 0

3 years ago

Hey everyone I need help on the questions please!:)

Aneli [31]

Answer:

a. 1/2

b. 1 hair cut

c. 2.5

Step-by-step explanation:

4/8 divde by 4 to simplify and that gets you 1/2

8/4 is 2 so he does one hair cut every two hours

so you know how many he can do in 2 hours so add it up. It’s going to be 2 people in four hours so it will be half a hair cut in 5 hours

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2 years ago

Option 1:<br><br> Find x. Show all work.

Ronch [10]

Using law of cosines:

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Cos(22) = 12/x

Rewrite to get:

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Simplify:

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Round the answer as needed.

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2 years ago

Read 2 more answers

The following stem-and-leaf plot represents the test scores for

rewona [7]

Considering the given stem-and-leaf plot, the quartiles are given as follows:

The first quartile is of 67.5.

The second quartile, which is the median, is of 84.5.

The third quartile is of 91.5.

<h3>What are the median and the quartiles of a data-set?</h3>

The median of the data-set separates the bottom half from the upper half, that is, it is the 50th percentile.

The first quartile is the median of the first half of the data-set.

The third quartile is the median of the second half of the data-set.

There is an even number of elements(26), hence the median is the mean of the 13th and 14th elements, which are 83 and 86, hence:

Me = (83 + 86)/2 = 84.5.

The first half has 12 elements, hence the first quartile is the mean of the 6th and 7th elements, which are 67 and 68, hence:

Q1 = (67 + 68)/2 = 67.5.

The third half also has 12 elements, starting at the second 86, hence the third quartile is the mean of the 6th and 7th elements of this half, hence:

Q3 = (91 + 92)/2 = 91.5.

More can be learned about the quartiles of a data-set at brainly.com/question/28017610

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1 year ago