I NEED HELP PLEASEGeometry: Quadrilateral LMNO is reflected over the line as shown, resulting in quadrilateral CDAB. Given the congruency statement LMNO ≅ CDAB. What segment corresponds to ML? (Show your work or explain your reasoning).
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Answer: We are given Quadrilateral LMNO is reflected over a line.
Also given Quadrilateral LMNO is congruent Quadrilateral CDAB, that is
LMNO ≅ CDAB.
Note: Reflection over a line represents mirror images of the figures.
From the given image we can see
LM is congruent to CD.
ON is congruent to BA.
LO is congruent to BC.
MN is congruent to AD.
Therefore, DC segment corresponds to ML.
Hope i helped you out!
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We will see that the solution of the given inequality is:
How to solve the inequality?
Here we have the inequality:
To solve it, we need to isolate x on one side of the inequality.
First, we can multiply both sides for b:
Now we divide both sides by -a, because we are operating with a negative number, we need to change the direction of the greater than or equal to sign, so we will get:
That is the solution to the given inequality.
If you want to learn more about inequalities:
#SPJ2
What is the length of AB?
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1/x+3/8=1/4
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1/x+3/8-3/8=1/4-3/8
1/x=1/4-3/8
Step 2: Multiply 1/4 by 1/2
1/x=(1/4)(1/2)-3/8
1/x=2/8-3/8
Step 3: Subtract
1/x=-1/8
Step 5: Multiply by x on both sides
1/x(x)=-1/8(x)
1=-1/8x
Step 6: Divide -1/8
1/(-1/8)=-1/8x/(1/8)
*You can times flip
1(-8)=-1/8x(8)
-8=-x
*Divide by -1
-8/-1=-x/-1
8=x
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The product of two binomials is sometimes called FOIL.
It stands for ...
the product of the First terms (3j x 3j)
plus
the product of the Outside terms (3j x 5)
plus
the product of the Inside terms (-5 x 3j)
plus
the product of the Last terms (-5 x 5)
FOIL works for multiplying ANY two binomials (quantities with 2 terms).
Here's another tool that you can use for this particular problem (a).
It'll also be helpful when you get to part-c .
Notice that the terms are the same in both quantities ... 3j and 5 .
The only difference is they're added in the first one, and subtracted
in the other one.
Whenever you have
(the sum of two things) x (the difference of the same things)
the product is going to be
(the first thing)² minus (the second thing)² .
So in (a), that'll be (3j)² - (5)² = 9j² - 25 .
You could find the product with FOIL, or with this easier tool.
______________________________
(b).
This is the square of a binomial ... multiplying it by itself. So it's
another product of 2 binomials, that both happen to be the same:
(4h + 5) x (4h + 5) .
You can do the product with FOIL, or use another little tool:
The square of a binomial (4h + 5)² is ...
the square of the first term (4h)²
plus
the square of the last term (5)²
plus
double the product of the terms 2 · (4h · 5)
________________________________
(c).
Use the tool I gave you in part-a . . . twice .
The product of the first 2 binomials is (g² - 4) .
The product of the last 2 binomials is also (g² - 4) .
Now you can multiply these with FOIL,
or use the squaring tool I gave you in part-b .
3j(3j + 5) - 5(3j + 5)
3j(3j) + 3j(5) - 5(3j) - 5(5)
9j² + 15j - 15j - 25
9j² - 25
b. (4h + 5)²
(4h + 5)(4h + 5)
4h(4h + 5) + 5(4h + 5)
4h(4h) + 4h(5) + 5(4h) + 5(5)
16h² + 20h + 20h + 25
16h² + 40h + 25
c. (g - 2)²(g + 2)²
(g - 2)(g - 2)(g + 2)(g + 2)
(g(g - 2) - 2(g - 2))(g(g + 2) + 2(g + 2))
(g(g) - g(2) - 2(g) + 2(2))(g(g) + g(2) + 2(g) + 2(2))
(g² - 2g - 2g + 4)(g² + 2g + 2g + 4)
(g² - 4g + 4)(g² + 4g + 4)
g²(g² + 4g + 4) - 4g(g² + 4g + 4) + 4(g² + 4g + 4)
g²(g²) + g²(4g) + g²(4) - 4g(g²) - 4g(4g) - 4g(4) + 4(g²) + 4(4g) + 4(4)
g⁴ + 4g³ + 4g² - 4g³ - 16g² - 16g + 4g² + 16g + 16
g⁴ + 4g³ - 4g³ + 4g² - 16g² + 4g² - 16g + 16g + 16
g⁴ - 12g² + 4g² + 16
g⁴ - 8g² + 16
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Answer and work down below. Let me know if you have any questions