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kkurt [141]
3 years ago
13

A sequence of two transformations that can be used to show that polygon ABCDE is congruent to polygon GFJIH

Mathematics
1 answer:
Ket [755]3 years ago
4 0

Answer:

Yes,they are congruent.

Step-by-step explanation:

We are required to make two transformations  and prove that they are congruent.

First Transformation:Now rotate the polygon FGHIJ by 90° about the axis parallel to x-axis and passinfg through the vertex I.You can observe that the sides are of same length AB=GF=2 units.

Second Transformation: Keeping the polygon ABCDE constant shift the centre of polygon FGHIJ to the centre of polygon ABCDE you will observe thta they exactly overlap on each other hence they are congruent with each other.

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If we assume that the annual rate of inflation were to remain steady at 3.4%, and particular item costs $45 now, what would this
Illusion [34]

Answer:

$46.53 and $49.75

Step-by-step explanation:

7 0
2 years ago
A piece of wire 30 m long is cut into two pieces. One piece is bent into a square and the other is bent into a circle.
antiseptic1488 [7]

Answer:

a) 0 m

b) 16.8 m

Step-by-step explanation:

A piece of wire, 30 m long, is cut in two sections: a and b. Then, the relation between a and b is:

a+b=30\\\\b=30-a

The section "a" is used to make a square and the section "b" is used to make a circle.

The section "a" will be the perimeter of the square, so the square side will be:

l=a/4

Then, the area of the square is:

A_s=l^2=(a/4)^2=a^2/16

The section "b" will be the perimeter of the circle. Then, the radius of the circle will be:

2\pi r=b=30-a\\\\r=\dfrac{30-a}{2\pi}

The area of the circle will be:

A_c=\pi r^2=\pi\left(\dfrac{30-a}{2\pi}\right)^2=\pi\left(\dfrac{900-60a+a^2}{4\pi^2}\right)=\dfrac{900-60a+a^2}{4\pi}

The total area enclosed in this two figures is:

A=A_s+A_c=\dfrac{a^2}{16}+\dfrac{900-60a+a^2}{4\pi}=\left(\dfrac{1}{16}+\dfrac{1}{4\pi}\right)a^2-\dfrac{60a}{4\pi}+\dfrac{900}{4\pi}

To calculate the extreme values of the total area, we derive and equal to 0:

\left(\dfrac{1}{16}+\dfrac{1}{4\pi}\right)a^2-\dfrac{60a}{4\pi}+\dfrac{900}{4\pi}\\\\\\\dfrac{dA}{da}=\left(\dfrac{1}{16}+\dfrac{1}{4\pi}\right)(2a)-\dfrac{60}{4\pi}+0=0\\\\\\\left(\dfrac{1}{8}+\dfrac{1}{2\pi}\right)a=\dfrac{15}{\pi}\\\\\\\dfrac{\pi+4}{8\pi}\cdot a=\dfrac{15}{\pi}\\\\\\\dfrac{\pi+4}{8}\cdot a=15\\\\\\a=15\cdot \dfrac{8}{\pi+4}\approx 16.8

We obtain one value for the extreme value, that is a=16.8.

We can derive again and calculate the value of the second derivative at a=16.8 in order to know if the extreme value is a minimum (the second derivative has a positive value) or is a maximum (the second derivative has a negative value):

\dfrac{d^2A}{da^2}=\left(\dfrac{1}{16}+\dfrac{1}{4\pi}\right)(2)-0=\dfrac{1}{8}+\dfrac{1}{2\pi}>0

As the second derivative is positive at a=16.8, this value is a minimum.

In order to find the maximum area, we analyze the function. It is a parabola, which decreases until a=16.8, and then increases.

Then, the maximum value has to be at a=0 or a=30, that are the extremes of the range of valid solutions.

When a=0 (and therefore, b=30), all the wire is used for the circle, so the total area is a circle, which surface is:

A=\pi r^2=\pi\left( \dfrac{30}{2\pi}\right)^2=\dfrac{900}{4\pi}\approx71.62

When a=30, all the wire is used for the square, so the total area is:

A=a^2/16=30^2/16=900/16=56.25

The maximum value happens for a=0.

3 0
3 years ago
What is 138.91 as a whole number ?
Nina [5.8K]

Answer: 139? Idek sorry

Step-by-step explanation:

8 0
3 years ago
Can a hexagon have angles that measures 85,62,135,173,and 160
Dvinal [7]

Answer:

If the sum of those angles adds up to 720 degrees, then they can be the angles of a hexagon. Your sum is 615.

Step-by-step explanation:

Hope that helps!

3 0
3 years ago
Given A = {1, 3, 5}, B = {2, 4, 6} and C={1, 2, 3, 4, 5, 6}, then A ∪ (B ∩ C)
Serggg [28]
B ∩ C is an intersection, which means only values that are present in both B and C are picked. So...
B ∩ C = {2, 4, 6}
A ∪ (B ∩ C) is a union, which means you combine all values, but discard duplicates. So...
A ∪ (B ∩ C) = {1, 2, 3, 4, 5, 6}
8 0
3 years ago
Read 2 more answers
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