Answer:
x = -8
Step-by-step explanation:
-8x + 3(x - 5) = 25
Distribute the 3 into the (x - 5).
-8x + 3x - 15 = 25
Combine like terms.
-5x - 15 = 25
Add 15 to both sides.
-5x = 40
Divide both sides by -5.
x = -8.
Proof:
-8x + 3(x - 5) = 25
Substitute variable.
-8(-8) + 3((-8) - 5) = 25
Subtract inside parenthesis.
-8(-8) + 3(-13) = 25
Multiply -8 and -8.
64 + 3(-13) = 25
Multiply 3 and -13.
64 + (-39) = 25
Add 64 and -39.
25 = 25
Answers:
x = 5
m∠C = m∠H = 38 degrees
WORKINGS
Given that ABCD ≅ FGHJ
We know that corresponding angles of two congruent
quadrilaterals are equal
Therefore,
m∠A = m∠F
m∠B = m∠G
m∠C = m∠H
m∠D = m∠I
Given,
m∠C = 9x – 7
m∠H = 5x + 13
Since m∠C = m∠H
9x – 7 = 5x + 13
Add 7 to both sides of the equation
9x – 7 + 7 = 5x + 13 + 7
9x = 5x + 20
Subtract 5x from both sides of the equation
9x – 5x = 5x – 5x + 20
4x = 20
Divide both sides of the equation by 4
4x/4 = 20/4
x = 5
To determine the measures of angle C and angle H
m∠C = m∠H
We know that m∠C = 9x – 7
Since x = 5
m∠C = 9(5) – 7
m∠C = 45 – 7
m∠C = 38
Therefore, m∠C = m∠H = 38 degrees
You have to find first the discriminant
∆=8^2-4*(-1) *(-7) =36
x=(-8±√36) /-2=(-8±6)/-2=4±3=1 or 7
So x(1)=1 or x(2)=7
-x^2+8x-7=[x-x(1) ][x-x(2) ]=(x-1) (x-7)
Answer: Angle bisectors
Step-by-step explanation:
The incenter is the point forming the origin of a circle inscribed inside the triangle. Like the centroid, the incenter is always inside the triangle. It is constructed by taking the intersection of the angle bisectors of the three vertices of the triangle.
