Answer:
Option D is correct.
Length of PQ is 36 unit.
Explanation:
If the measures of two sides in one triangle are proportional to the corresponding sides in the another triangle and their including angles are congruent, then the triangles are similar.
Given: Right angle triangle ABC at B , Length of AB = 12 unit and length of BC = 11.5 unit and in right angle triangle PQR at Q , length of QR = 34.5 unit.
Also it is given that Angle A is congruent to angle P and angle C is congruent to angle R.
To find the length of QR:
It is given that ΔABC and ΔPQR are Similar triangle
then, by the definition of similar triangle:
![\frac{PQ}{AB} = \frac{QR}{BC}](https://tex.z-dn.net/?f=%5Cfrac%7BPQ%7D%7BAB%7D%20%3D%20%5Cfrac%7BQR%7D%7BBC%7D)
Substitute the value of AB, QR and BC to solve for PQ;
or
![PQ = \frac{34.5 \times 12}{11.5}](https://tex.z-dn.net/?f=PQ%20%3D%20%5Cfrac%7B34.5%20%5Ctimes%2012%7D%7B11.5%7D)
On simplify:
![PQ = 3 \times 12 = 36](https://tex.z-dn.net/?f=PQ%20%3D%203%20%5Ctimes%2012%20%3D%2036)
Therefore, the length of side PQ is 36 units.
Answer-
The number is 5
Explanation-
let the number be x
according to the condition
2x-(x-7)= 12
2x-x+7=12
x+7=12
x+7-7=12-7
x=5
therefore the required number is 5
Answer: 1 unit
Step-by-step explanation:
The formula for calculating the distance between two points is given as :
D = ![\sqrt{(x_{2}-x_{1}) ^{2}+(y_{2}-y_{1}) ^{2}}](https://tex.z-dn.net/?f=%5Csqrt%7B%28x_%7B2%7D-x_%7B1%7D%29%20%5E%7B2%7D%2B%28y_%7B2%7D-y_%7B1%7D%29%20%5E%7B2%7D%7D)
= - 7
= - 7
= 7
= 8
substituting into the formula , we have
![\sqrt{(-7-(-7))^{2}+ (8-7)^{2}}](https://tex.z-dn.net/?f=%5Csqrt%7B%28-7-%28-7%29%29%5E%7B2%7D%2B%20%288-7%29%5E%7B2%7D%7D)
D = ![\sqrt{1}](https://tex.z-dn.net/?f=%5Csqrt%7B1%7D)
D = 1 unit
A)
x = # of students in math class
2x+7=40
B)
2x+7=40
-7
------------
2x = 33
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2 2
x = 76 students
Sorry if it's hard to read. I tried my best. Hope I helped.