Two parallelograms are similar. The base of the first is 12cm, and its height is 8 cm. Find the base of the second parallelogram
1 answer:
Answer:
The base of the second parallelogram is 51cm.
Step-by-step explanation:
If the parallelograms are similar, it means by applying the same scale factor to all the sides in one gives you the other. The question tells us the height of the first shape is 8cm and the height of the second shape is 34cm. That means the scale factor is:
Apply this same scale factor to the base of the first shape to find the base of the second:
You might be interested in
Answer:
The conclusion is invalid.
The required diagram is shown below:
Step-by-step explanation:
Consider the provided statement.
Great tennis players use Hexrackets. Therefore, if you use a Hexracket, you are a great tennis player.
From the above statement we can concluded that Great tennis players use Hexrackets. But it may be possible that some people who use a haxracket are not great tennis player.
Therefore, the conclusion is invalid.
The required diagram is shown below:
Problem 18
Answers:
~P -> Q: "if it is not fall, then the leaves change colors"
~P -> ~Q: "if it is not fall, then the leaves don't change colors"
P -> ~Q: "If it is fall, then the leaves don't change colors"
Q -> ~P: "If the leaves change colors, then it is not fall"
----------
Explanation:
Simply replace each letter with the corresponding definition. We replace each P with "it is fall" and each ~P with "it is not fall". The squiggly line means "not". The same idea applies with Q and ~Q.
==========================================
Problem 19
Answer: Choice A) 134
----------
Explanation:
AB = CD
8x = 4x+24
8x-4x = 24
4x = 24
x = 6
BC = 18x+26
BC = 18*6+26
BC = 134
==========================================
Problem 20
Answer: Choice C) x = 5 and y = 11
----------
Explanation:
(anglePQR)+(angleRQS) = 90
(12x-2)+(6x+2) = 90
18x = 90
x = 5
angle TQU = 90
10y-20 = 90
10y = 110
y = 11
==========================================
Problem 21
Answer: 99
----------
Explanation:
The remote interior angles add to the exterior angle (remote interior angle theorem)
(angle RPQ) + (angle PQR) = angle PRS
(3x-29) + (7x-42) = 6x-3
10x-71 = 6x-3
10x-6x = -3+71
4x = 68
x = 68/4
x = 17
angle PRS = 6x-3
angle PRS = 6*17-3
angle PRS = 99
==========================================
Problem 22
Answer: 116
----------
Explanation:
Refer to the diagram below.
Solve 105+x = 180 to get x = 75
Solve 135+y = 180 to get y = 45
Solve x+y+z = 180 to get z = 60
Solve z+82+p = 180 to get p = 38
Solve p+78+q = 180 to get q = 64
Solve q+r = 180 to get r = 116
==========================================
Problem 23
Answer: B) between 4 and 44 inches
----------
Explanation:
We use a variation of the triangle inequality theorem here.
If p is the missing side length, then
24-20 < p < 24+20
4 < p < 44
So,
4 < XY < 44
The side XY cannot be 4 inches and it cannot be 44 inches either.
==========================================
Problem 24
4 Answers: A, B, C, D
----------
Explanation:
Same idea as problem 23
24-10 < x < 24+10
14 < x < 34
So we'll select values between 14 and 34, excluding each endpoint. Those values are x = 16, 18, 24, 26
In other words, only 12 and 34 are non-answers.
==========================================
Problem 25
Answer: C) 84 degrees
----------
Explanation:
The given exterior angle is 152 degrees
Subtract that from 180 to get the adjacent interior angle 180-152 = 28
Now let's find the missing angle of triangle DEB
D+E+B = 180
28+68+B = 180
96+B = 180
B = 180-96
B = 84
This is the measure of angle DBE
This is also the measure of angle ABC because the two angles are vertical angles.
Vertical angles are always congruent.
Hello!
You can use the Pythagorean Theorem to solve this
c is the hypotenuse
a and b are the legs
Put in the values you know
Square the numbers
Subtract 2.25 from both sides
Take the square root of both sides
b = 0.8
The answer is 0.8km
Hope this helps!
You can use the Pythagorean Theorem to solve this
c is the hypotenuse
a and b are the legs
Put in the values you know
Square the numbers
Subtract 2.25 from both sides
Take the square root of both sides
b = 0.8
The answer is 0.8km
Hope this helps!