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Juliette [100K]
3 years ago
9

Polygon C and polygon D are similar. The perimeter of polygon C is 192 inches, and the perimeter of polygon D is 48 inches. If o

ne side of polygon C is 8 inches, what is the length of the corresponding side in polygon D?
A. 64 in
B. 2 in
C. 8 in
D. 24 in
Mathematics
1 answer:
Marianna [84]3 years ago
3 0

Answer:

B. 2 in.

Step-by-step explanation:

First, put the two perimeters together to form a fraction.

192/48, which can simplify to 4/1

Now, following the order in which you put the perimeters (I used C/D,) set it equal to the sides.

\frac{4}{1}  =  \frac{8}{x}

Now, cross multiply. (multiply 1 and 8, 4 and x.)

4x = 8

Now, solve.

x=2 inches.

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Consider the function below. f(x) = ln(x4 + 27) (a) Find the interval of increase. (Enter your answer using interval notation.)
andrezito [222]

Answer:

a) The function is constantly increasing and is never decreasing

b) There is no local maximum or local minimum.

Step-by-step explanation:

To find the intervals of increasing and decreasing, we can start by finding the answers to part b, which is to find the local maximums and minimums. We do this by taking the derivatives of the equation.

f(x) = ln(x^4 + 27)

f'(x) = 1/(x^2 + 27)

Now we take the derivative and solve for zero to find the local max and mins.

f'(x) = 1/(x^2 + 27)

0 = 1/(x^2 + 27)

Since this function can never be equal to one, we know that there are no local maximums or minimums. This also lets us know that this function will constantly be increasing.

6 0
3 years ago
13. What is the result of adding 5.4a + 7.1 and -1.28 - 6.3?
den301095 [7]

Answer:

C. 4.2a + 0.8

Step-by-step explanation:

Given:

The two binomials given for addition are:

5.4a+7.1 and -1.2a-6.3

Now, adding both the binomials, we get:

5.4a+7.1+(-1.2a-6.3)

Distributing the positive sign inside the second binomial, we get:

5.4a+7.1-1.2a-6.3

Now, combining like terms using the commutative property of addition, we get:

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Simplifying the above expression, we get:

(5.4-1.2)a+0.8\\4.2a+0.8

Therefore, the resulting addition of the given binomials is 4.2a+0.8

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Answer:

The length of river frontage for each lot are 96.55 ft. 98.85 ft, 101.15 ft and 103.45 ft.

Step-by-step explanation:

See the attached diagram.

The river frontage of 400 ft will be divided into 84 : 86 : 88 : 90 for each lot as AP, BQ, CR, DS and ET all are parallel.

Therefore, PQ : QR : RS : ST = 84 : 86 : 88 : 90 = 42 : 43 : 44 : 45

Let, PQ = 42x, QR = 43x, RS = 44x and ST = 45x

So, (42x + 43x + 44x + 45x) = 400

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Answer:

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Step-by-step explanation:

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