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3 years ago

Pentagon ABCDE is rotated 180° clockwise about the origin to form pentagon A'B'C'D'E.

Mathematics

1 answer:

alexandr1967 [171]3 years ago

4 0

Answer:

Statement A is true

Step-by-step explanation:

Here, we want to select the correct statement

the correct answer here is that pentagon ABCDE is congruent to A’B’C’D’E

A 180 degrees counterclockwise rotation will only turn (x,y) to (-x,-y)

It doesn’t change the distance between the points which corresponds to the length of the sides of the pentagon

This means that the side lengths will be exactly the same and so, the two pentagons are congruent

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The equation $a^7xy-a^6y-a^5x=a^4(b^4-1)$ is equivalent to the equation $(a^mx-a^n)(a^py-a^2)=a^4b^4$ for some integers $m$, $n$

Ksivusya [100]

Let simplify the equations $a^7xy-a^6y-a^5x=a^4(b^4-1)$ and $(a^mx-a^n)(a^py-a^2)=a^4b^4$ :

1) $a^7xy-a^6y-a^5x+a^4=a^4b^4$

and

2) $a^{m+p}xy-a^{n+p}y-a^{m+2}x+a^{n+2}=a^4b^4$ .

Equate the coefficients:

 $xy: m+p=7 \\ y: n+p=6 \\ x: m+2=5 \\ 1: n+2=4$ .
Then $n=2 \\ p=4 \\ m=3$ and mnp=24.

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3 years ago

Light travels 186,282 miles per second. How many miles will light travel in one year? (Use 365 days in a year) This unit ofdista

Phantasy [73]

Answer:

5,874,589,152,000 mi.

Step-by-step explanation:

3 0

3 years ago

(3x/5-7)+7 is equal to what

Elena L [17]

(3x/5-7)+7

= (3x/-2) + 7

= -3x/2 + 7

5 0

3 years ago

The figures are similar. The area of one figure is given. Find the area of the other figure to the nearest whole number.

Akimi4 [234]

Answer: Option b.

Step-by-step explanation:

First, you need to calculate the ratio of the area. This is:

$ratio=(\frac{64}{28})^2\\\\ratio=\frac{256}{49}$

You know that the area of the smaller trapezoid is 771 m², then you can set up the following proportion, where "x" is the area of the larger trapezoid. Then you have:

$\frac{256}{49}=\frac{x}{771}$

Now you must solve for "x". Therefore, you get that the area of the larger trapezoid is:

$x=(771)(\frac{256}{49})\\\\x=4,028m^2$

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4 years ago

A store is having a sale on liquid soap and sponges. The cost of 6 bottles of soap is $9.12. The cost of 4 sponges is $5.00 what

Alenkinab [10]

Answer:

$6.79

Step-by-step explanation:

We need to find the cost of a bottle of soap. We divide the cost by the number of bottles

$9.12/6 = $1.52 per bottle

We also need to find the cost for a sponge

$5.00/4 = $1.25 per sponge

We want to find the total cost of 2 bottles of soap and 3 sponges

cost = 2 * 1.52 + 3 * 1.25

= 3.04 + 3.75

= 6.79

7 0

3 years ago