<h3>
Answer: 126</h3>
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Work Shown:
Let x and y be the two numbers.
We're given x = 162 and the variable y is unknown.
We're also given LCM = 1134 and HCF = 18
So,
LCM = (x*y)/HCF
1134 = 162*y/18
1134 = (162/18)y
1134 = 9y
9y = 1134
y = 1134/9
y = 126
The other number is 126
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Notice that
showing that 18 is the highest common factor (HCF) of the numbers 162 and 126. This partially confirms the answer.
Now let,
- A = multiples of 162
- B = multiples of 126
So,
- A = 162, 324, 486, 648, 810, 972, 1134, 1296, ...
- B = 126, 252, 378, 504, 630, 756, 882, 1008, 1134, 1260, ...
We see that 1134 is in each list of multiples and the smallest such common item. So the lowest common multiple (LCM) of 162 and 126 is 1134. This helps fully confirm the answer.
Answer:
D. 4x-3
Step-by-step explanation:
First you subtract the 7x and 3x to get 4x.
Then you subtract the -5 and the -2 to get -3
Therfore, your answer is D
The perimeter of right isosceles ΔABC with midsegment DE is 16 + 8√2.
If right isosceles ΔABC has hypotenuse length h, then the two other sides are congruent.
side a = side b
Using Pythagorean theorem, c^2 = a^2 + b^2
h^2 = a^2 + b^2 a = b
h^2 = 2a^2
a = h/√2
If DE is a midsegment not parallel to the hypotenuse, then it is a segment that connects the midpoints of one side of a triangle and the hypotenuse. See photo for reference.
ΔABC and ΔADE are similar triangles.
a : b : h = a/2 : 4 : h/2
If a/2 = a/2, then b/2 = 4.
b/2 = 4
b = 8
If a = b, then a = 8.
If a = h/√2, then
8 = h/√2
h = 8√2
Solving for the perimeter,
P = a + b + h
P = 8 + 8 + 8√2
P = 16 + 8√2
P = 27.3137085
To learn more about midsegment: brainly.com/question/7423948
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Answer:
1. 128
2. 52
3. 47
4. 133
5. 81
Step-by-step explanation:
1. <1 and <52 are same side interior angles, therefore supplementary. So they should add up to equal 180, this means that <1 is 180 - 52. Solve to get <1 is 128
2. <2 is an alternate interior angle to <52, this means that they are congruent. Since they are congruent, they have the same value of 52.
3. <3 is an alternate interior angle to <47, so they are congruent, this means that they both have a value of 47
4. <4 is supplementary to <3 so you can say that <4 is equal to 180 - 47. Solve this to get <4 is 133
5. <5, <52, and <47 are supplementary when you combine all three. So you can create an equation that says <5 is equal to 180 - 52 + 47. This gives you that angle 5 is 81.
