1. if √16 = x, then x^2
1 answer:
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Answer:
See below.
Step-by-step explanation:
I'm assuming these questions are about the Midline Theorem (segment AL joins the midpoints of the non-parallel sides.
♦ The midline's length is the average of the lengths of the top and bottom parallel sides.
Use this equation and substitute values given in each problem, then solve for the missing information.
1. AL = x, CE = 9, OR = 5
2. AL = <em>m</em> - 4, CE = 15, OR = 17
3. OR = y + 5, AL = 15, CE = 18
Consecutive odd integers are 2 apart
they are x and x+2
the product (x times (x+2)) is 1 less than 4 times their sum
x(x+2)=-1+4(x+x+2)
![x^2+2x=8x+7 minus (8x+7) from both sides [tex]x^2-6x-7=0](https://tex.z-dn.net/?f=x%5E2%2B2x%3D8x%2B7%20minus%20%288x%2B7%29%20from%20both%20sides%20%5Btex%5Dx%5E2-6x-7%3D0)
factor
what numbers multliply to get -7 and add to get -6?
-7 and 1
(x-7)(x+1)=0
set equal to 0
x-7=0
x=7
x+1=0
x=-1
so the x can be 7 or -1
the other number (x+2) can be 7 or 1
test each
7 and 9
7(9)=-1+4(7+9)
63=-1+4(16)
63=-1+64
63=63
true
-1 and 1
-1(1)=-1+4(-1+1)
-1=-1+4(0)
-1=-1+0
-1=-1
true
the 2 integers can be 7 and 9 or -1 and 1 (both pairs of numbers work)
they are x and x+2
the product (x times (x+2)) is 1 less than 4 times their sum
x(x+2)=-1+4(x+x+2)
factor
what numbers multliply to get -7 and add to get -6?
-7 and 1
(x-7)(x+1)=0
set equal to 0
x-7=0
x=7
x+1=0
x=-1
so the x can be 7 or -1
the other number (x+2) can be 7 or 1
test each
7 and 9
7(9)=-1+4(7+9)
63=-1+4(16)
63=-1+64
63=63
true
-1 and 1
-1(1)=-1+4(-1+1)
-1=-1+4(0)
-1=-1+0
-1=-1
true
the 2 integers can be 7 and 9 or -1 and 1 (both pairs of numbers work)