Answer:
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Step-by-step explanation:
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X^2 + 4x = 0
x^2 + 4x + 4 = 0 + 4
(x + 2)^2 = 4
Step-by-step explanation:
just see if this is right
f (x)+g (x)
f (x)= -3x^2 - 1---------(1)
g(x)= 4x - 2------------(2)
(1)+(2)
-3x^2 - 1+ 4x - 2
-3x^2+4x - 3
Answer:
1. ![m\angle EFO=62^{\circ}\\ \\m\angle EFD=76^{\circ}](https://tex.z-dn.net/?f=m%5Cangle%20EFO%3D62%5E%7B%5Ccirc%7D%5C%5C%20%5C%5Cm%5Cangle%20EFD%3D76%5E%7B%5Ccirc%7D)
2. ![m\angle RUS=65^{\circ}\\ \\m\angle UST=15^{\circ}](https://tex.z-dn.net/?f=m%5Cangle%20RUS%3D65%5E%7B%5Ccirc%7D%5C%5C%20%5C%5Cm%5Cangle%20UST%3D15%5E%7B%5Ccirc%7D)
Step-by-step explanation:
Q1. Given circle k(O).
The measure of the arc FE is 56°, this means the measure of the central angle FOE is 56° too.
Consider triangle FOE. This triangle is isosceles triangle with the base FE because FO = EO as radii of the circle.
Angles adjacent to the base of the isosceles triangle are congruent, so
![m\angle EFO=m\angle FEO](https://tex.z-dn.net/?f=m%5Cangle%20EFO%3Dm%5Cangle%20FEO)
The sum of the measures of all interior angles in the triangle FEO is always 180°, then
![2m\angle EFO+56^{\circ}=180^{\circ}\\ \\2m\angle EFO=124^{\circ}\\ \\m\angle EFO=62^{\circ}](https://tex.z-dn.net/?f=2m%5Cangle%20EFO%2B56%5E%7B%5Ccirc%7D%3D180%5E%7B%5Ccirc%7D%5C%5C%20%5C%5C2m%5Cangle%20EFO%3D124%5E%7B%5Ccirc%7D%5C%5C%20%5C%5Cm%5Cangle%20EFO%3D62%5E%7B%5Ccirc%7D)
Angle FDE is inscribed angle subtended on the arc FE, hence its measure is the half of the central angle FOE:
![m\angle FDE=\dfrac{1}{2}\cdot 56^{\circ}=28^{\circ}](https://tex.z-dn.net/?f=m%5Cangle%20FDE%3D%5Cdfrac%7B1%7D%7B2%7D%5Ccdot%2056%5E%7B%5Ccirc%7D%3D28%5E%7B%5Ccirc%7D)
Since FD = ED, thriangle FDE is isosceles triangle with congruent angles adjacent to the base FE. Then
![m\angle EFD=\dfrac{1}{2}(180^{\circ}-28^{\circ})=76^{\circ}](https://tex.z-dn.net/?f=m%5Cangle%20EFD%3D%5Cdfrac%7B1%7D%7B2%7D%28180%5E%7B%5Ccirc%7D-28%5E%7B%5Ccirc%7D%29%3D76%5E%7B%5Ccirc%7D)
Q2. If the measure of the arc RU is 50°, then the measure of the central angle ROU is 50° too.
If the measure of the arc UT is 30°, then the measure of the central angle TOU is 30° too.
Triangle ROU is isosceles triangle because RO = UO as radii of the circle. Angles adjacent to the base of the isosceles triangle are congruent, so
![m\angle ORU=m\angle OUR](https://tex.z-dn.net/?f=m%5Cangle%20ORU%3Dm%5Cangle%20OUR)
The sum of the measures of all interior angles in the triangle ROU is always 180°, then
![2m\angle RUO+50^{\circ}=180^{\circ}\\ \\2m\angle RUO=130^{\circ}\\ \\m\angle RUO=65^{\circ}\\ \\m\angle RUS=m\angle RUO=65^{\circ}](https://tex.z-dn.net/?f=2m%5Cangle%20RUO%2B50%5E%7B%5Ccirc%7D%3D180%5E%7B%5Ccirc%7D%5C%5C%20%5C%5C2m%5Cangle%20RUO%3D130%5E%7B%5Ccirc%7D%5C%5C%20%5C%5Cm%5Cangle%20RUO%3D65%5E%7B%5Ccirc%7D%5C%5C%20%5C%5Cm%5Cangle%20RUS%3Dm%5Cangle%20RUO%3D65%5E%7B%5Ccirc%7D)
Angle UST is inscribed angle subtended on the arc UT and has the measure that is half the measure of the central angle TOU:
![m\angle UST=\dfrac{1}{2}m\angle TOU=\dfrac{1}{2}\cdot 30^{\circ}=15^{\circ}](https://tex.z-dn.net/?f=m%5Cangle%20UST%3D%5Cdfrac%7B1%7D%7B2%7Dm%5Cangle%20TOU%3D%5Cdfrac%7B1%7D%7B2%7D%5Ccdot%2030%5E%7B%5Ccirc%7D%3D15%5E%7B%5Ccirc%7D)