Answer: X = -4
Step-by-step explanation:
first you need to solve, so do what needs to be done in the equation, which is just multiply and add
147 = 5 - 35x + 2
147= 7 -35x
get rid of the numbers around x, which would be subtracting 7 from both sides
140 = -35x
x = -4
Step-by-step explanation:
The vertical angles are congruent. The right angles are congruent. There are 2 angles of a triangle congruent to 2 angles of anther triangle. By AA Similarity the triangles are similar.
Statement A. (vertical angles are congruent)
Statement D. (right angles are congruent)
Triangle AEC is similar to triangle BDC.
Statement E is true but does not help.
Correct statement of proportional side lengths:
BD/AE = CD/CE
x/150 = 200/50
x/150 = 4
x = 600
P.S. I think there is a mistake in the problem. I don't think that statement E is correct. It is a true statement, but it is useless. Statement F is false.
The length of AB is 9.
Solution:
Given data:
Radius OC = 8
Tangent AC = 15
The angle between the tangent and radius is always right angle.
∠C = 90°.
Hence OCA is a right triangle.
Using Pythagoras theorem,
<em>In a right triangle square of the hypotenuse is equal to the sum of the squares of the other two sides.</em>




Taking square root on both sides of the equation, we get
OA = 17
OB is the radius of the circle.
⇒ OB = 8
AB = OA – OB
= 17 – 8
= 9
AB = 9
Hence the length of AB is 9.
Answer: The required number of boys in the class is 18.
Step-by-step explanation: Given that in math class, the girl to boy ratio is 8 to 6 and there are 24 girls in the class.
We are to find the number of boys in the class.
Let 8x and 6x represents the number of girls and boys in the class.
Then, according to the given information, we have

Therefore, the number of boys in the class is given by

Thus, the required number of boys in the class is 18.