9514 1404 393
Answer:
p : q = 3 : 2
Step-by-step explanation:
You are given sufficient information to write two relations involving p and q. We presume these will be sufficient to find an answer to the question. We will be able to find p and q. Then we can find their ratio, as the problem asks.
(p-15)/(q-15) = 2/1
(p+30)/(q+30) = 5/4
__
From the first equation, we get ...
p -15 = 2(q -15)
p = 2q -15 . . . . . . . add 15, simplify
From the second equation, we get ...
4(p +30) = 5(q +30)
4p + 120 = 5q + 150
4p = 5q + 30
Using the first equation to substitute for p, we have ...
4(2q -15) = 5q +30
8q -60 = 5q +30 . . . eliminate parentheses
3q = 90 . . . . . . . . . . . add 60-5q to both sides
q = 30 . . . . . . . . . . . . divide by 3
p = 2q -15 = 2(30) -15 = 45
Then the desired ratio is ...
p : q = 45 : 30
p : q = 3 : 2
Answer:
The correct option is C.
Step-by-step explanation:
Two figures are congruent if their corresponding sides are congruent.
We know that, reflection, rotation and translation are rigid transformation. It means the size and shape of image and preimage are same. We can say that in rigid transformation, the image and preimage are congruent.
Dilation is not a rigid transformation. It represents enlargement and compression.
If scale factor |k|>1, then it represent enlargement. If scale factor |k|<1, then it represent compression.
In option C, the scale factor is 4. It means the sides of image are 4 times of the preimage.
Therefore option C is correct and the resultant figure of option C is not congruent to the original figure.
-11 is and Irrational number
Answer:
x=−y−1
Step-by-step explanation:
y=−x−1
Step 1: Flip the equation.
−x−1=y
Step 2: Add 1 to both sides.
−x−1+1=y+1
−x=y+1
Step 3: Divide both sides by -1.
−x
−1
=
y+1
−1
x=−y−1
Answer:
option 1
Step-by-step explanation: