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sesenic [268]
3 years ago
15

(0,4) (-1,01 Need help

Mathematics
1 answer:
storchak [24]3 years ago
5 0

Give me a graph

Step-by-step explanation:

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A rectangle is inscribed in a right isosceles triangle, such that two of its vertices lie on the hypotenuse, and two other on th
Ronch [10]
Refer to the attachment for the diagram of the problem.

Let us call the two identical sides of the isosceles triangle with s. Since we know that the hypotenuse measures 45 inches, we can find s by using the Pythagorean Theorem:
45^{2} = s^{2}+ s^{2}
45^{2} = 2s^{2}
45^{2} = 2s^{2}
1012.5 = s^{2}
s=31.82

We can notice that the figure will have similar triangles with the smaller triangle having one length equal to 5x. We then compute for the equivalent hypotenuse of the smaller triangle (denoted as y).
\frac{31.82}{5x} = \frac{45}{y}
y=7.07x

We can then solve for the value of x by applying the Pythagorean Theorem in the smaller triangle.
(7.07x)^{2} = (5x)^{2}+ (31.82-2x)^{2}
50x^{2} = 25x^{2}+ 1012.5-127.28x+4x^{2}
0= -21x^{2}-127.28x+1012.5
x=4.55,-10.61

We ignore the negative value since there is no negative side. x is therefore 4.55 thus the dimensions of the rectangle would be 22.75 and 9.1. For the other case, the dimensions would simply be inverted since we would be dealing with a rectangle with its width longer than its length.

6 0
3 years ago
Identify the sequence graphed below and the average rate of change from n = 1 to n = 3.
dsp73

Answer:

The required sequence is a_n=20(\frac{1}{2})^{n-1}. The average rate of change from n = 1 to n = 3 is -7.5.

Step-by-step explanation:

From the given graph it is clear that the sequence is a GP because the all terms are half of their previous terms.

Here, a_2=10,a_3=5,a_4=2.5,a_5=1.25

r=\frac{a_3}{a_2}=\frac{5}{10}=\frac{1}{2}

The common ratio of GP is 1/2.

r=\frac{a_2}{a_1}

\frac{1}{2}=\frac{10}{a_1}

a_1=20

The first term of the sequence is 20.

The formula for sequence is

a_n=a(r)^{n-1}

Where a is first term and r is common difference.

The required sequence is

a_n=20(\frac{1}{2})^{n-1}

The formula for rate of change is

m=\frac{f(x_2)-f(x_1)}{x_2-x_1}

The average rate of change from n = 1 to n = 3 is

m=\frac{f(3)-f(1)}{3-1}

m=\frac{5-20}{3-1}

m=\frac{-15}{2}=-7.5

Therefore the required sequence is a_n=20(\frac{1}{2})^{n-1}. The average rate of change from n = 1 to n = 3 is -7.5.

8 0
3 years ago
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Help! I can’t get this!
8_murik_8 [283]
If you haven’t tried this yet try typing the definitions into Google and it should give you the word.
6 0
3 years ago
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Can someone please help me i will give free 50 points
Grace [21]

Would it be 11 and 12?

6 0
2 years ago
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PLEASE PLEASE HELP ME, NO LINKS, I JUST NEED THIS DONE​
lianna [129]

Answer:

Here is your answer

Step-by-step explanation:

B) 2x + 5 = 7

vertical line

C) 2x - y = 6

oblique line

D) 3y + 9 = 0

horizontal line

6 0
3 years ago
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