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Ludmilka [50]
3 years ago
12

ABCD is a rectangle. Find the length of segment AC

Mathematics
1 answer:
Oksana_A [137]3 years ago
4 0

Answer:

52

Step-by-step explanation:

First, find x. As BE and DE will have the same measurements, you can set your formula up as

5x+11=3x+17

5x=3x+17-11

5x-2x=6

2x=6

x=6/2

x=3

CE and AE will also have the same value, now substitute 3 in place of x to get the value of segment BE

5x+11

5*3+11 = 26

This also means that CE = 26 and AE = 26

AC = CE + AE

AC = 52

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3) Midpoint is (-4,0.5)

Option A is correct.

4) Midpoint is (2.5,0)

Option B is correct.

5) The factors are (x+4)(x-7)

Option C is correct.

6) The factors are (x+4)(x+2)

Option A is correct.

Step-by-step explanation:

Question 3

Find midpoint of the following:

(2,-7), (-10,8)

The formula used to find midpoint is: Midpoint=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2} )

We have x_1=2, y_1=-7, x_2=-10,y_2=8

Putting values and finding midpoint

Midpoint=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2} )\\Midpoint=(\frac{2-10}{2},\frac{-7+8}{2} )\\Midpoint=(\frac{-8}{2},\frac{1}{2} )\\Midpoint=(-4,0.5 )

So, Midpoint is (-4,0.5)

Option A is correct.

Question 4

Find midpoint of the following:

(2,-10), (3,10)

The formula used to find midpoint is: Midpoint=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2} )

We have x_1=2, y_1=-10, x_2=3,y_2=10

Putting values and finding midpoint

Midpoint=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2} )\\Midpoint=(\frac{2+3}{2},\frac{-10+10}{2} )\\Midpoint=(\frac{5}{2},\frac{0}{2} )\\Midpoint=(2.5,0 )

So, Midpoint is (2.5,0)

Option B is correct.

Question 5

Factor each completely

x^2-3x-28

We will break the middle term and find factors

x^2-3x-28\\=x^2-7x+4x-28\\Taking\:common\\=x(x-7)+4(x-7)\\=(x+4)(x-7)

So, the factors are (x+4)(x-7)

Option C is correct.

Question 6

Factor each completely

x^2+6x+8

We will break the middle term and find factors

x^2+6x+8\\=x^2+4x+2x+8\\=x(x+4)+2(x+4)\\=(x+4)(x+2)

So, the factors are (x+4)(x+2)

Option A is correct.

7 0
3 years ago
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