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3 years ago

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Gretchen is using an overhead projector to enlarge a drawing so she can make a poster. The original drawing measures 60 mm wide

by 80 mm high. She moves the projector so that the width of the projected image is 300 mm. If the original drawing and the projected image are similar figures, what will be the height of the projected image? A. 225 mm B. 180 mm C. 400 mm D. 440 mm

1 answer:

inn [45]3 years ago

4 0

The height should be C.) 400 mm. Hope this helps!! <3

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Using the factorised trinomial <img src="https://tex.z-dn.net/?f=%28n-2%29%284n-7%29" id="TexFormula1" title="(n-2)(4n-7)" alt="

andrew-mc [135]

4n² - 15n + 14<span> is always the product of two numbers, for it to be prime number, one of these factors must be either 1 or -1.

Case n - 2 = 1
That would be n = 3
Then </span>4n² - 15n + 14<span> = 5 , which is prime.

Case n - 2 = -1
That would be n = 1
Then </span>4n<span>² - 15n + 14 = 3, which is also prime.

Case 4n - 7 = 1
That would be n = 2 and that makes other factor (n-2) zero so it's not prime

Case 4n-7 = -1
That would be n = 3/2 which is not integer, so </span>4n<span>² - 15n + 14 will not be interger.

For any other n values, </span>4n<span>² - 15n + 14 will be composite number since it is product of two factors.

Therefore we are left with n = 1 and n = 3; only two values of n.</span>

5 0

3 years ago

Solve #2 with an explanation please

KatRina [158]

The fence is 210 ft long.
There is a post every 3.5 ft.
If you divide 210 ft by 3.5 ft, you get the number of spaces between posts.
(210 ft)/(3.5 ft) = 60
The fence starts with a post. Then there is 3.5 ft of fencing. Then there is another post. Then there is another 3.5 ft of fencing followed by a post. In total there are 61 posts.

Here's another way of thinking of why you end up with 60 posts.
For each 3.5 ft of fencing, you place a post at the end of the fencing.
Since there are 60 3.5-ft-long pieces of fencing, there will be 60 posts, one at the end of each piece of fencing. The first thing that is done is to put the initial post before any fencing is put up. The first post plus 60 more posts add up to 61 posts.

Now that you see why there are 61 posts, we can calculate their cost.
61 * $8.50 = $518.50

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3 years ago

How do I work this problem-×+6×=10

timofeeve [1]

Answer:

add -x to 6x to get 5x then divide by 5 to get 2 x is 2

Step-by-step explanation:hope this helps god bless

4 0

3 years ago

Read 2 more answers

The area of a cross section through the center of a sphere is 46 square inches. Find the surface area of the sphere.

gavmur [86]

Answer:

184 in.^2

Step-by-step explanation:

The cross section through the center of a sphere is a circle whose radius is equal to the radius of the sphere.

area of circle

$A_{circle} = \pi r^2$

$\pi r^2 = 46$

$r^2 = \dfrac{46}{\pi}$

$r = \sqrt{\dfrac{46}{\pi}}$

$r = 3.83 ~in.$

surface area of sphere

$SA = 4 \pi r^2$

$SA = 4 \times \pi \times (3.83)^2$

$SA = 184~in.^2$

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3 years ago

Use the power series for 1 1−x to find a power series representation of f(x) = ln(1−x). What is the radius of convergence? (Note

Viktor [21]

a. Recall that

$\displaystyle\int\frac{\mathrm dx}{1-x}=-\ln|1-x|+C$

For $|x|$ , we have

$\displaystyle\frac1{1-x}=\sum_{n=0}^\infty x^n$

By integrating both sides, we get

$\displaystyle-\ln(1-x)=C+\sum_{n=0}^\infty\frac{x^{n+1}}{n+1}$

If $x=0$ , then

$\displaystyle-\ln1=C+\sum_{n=0}^\infty\frac{0^{n+1}}{n+1}\implies 0=C+0\implies C=0$

so that

$\displaystyle\ln(1-x)=-\sum_{n=0}^\infty\frac{x^{n+1}}{n+1}$

We can shift the index to simplify the sum slightly.

$\displaystyle\ln(1-x)=-\sum_{n=1}^\infty\frac{x^n}n$

b. The power series for $x\ln(1-x)$ can be obtained simply by multiplying both sides of the series above by $x$ .

$\displaystyle x\ln(1-x)=-\sum_{n=1}^\infty\frac{x^{n+1}}n$

c. We have

$\ln2=-\dfrac\ln12=-\ln\left(1-\dfrac12\right)$

$\displaystyle\implies\ln2=\sum_{n=1}^\infty\frac1{n2^n}$

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3 years ago