Answer:
See Explanation
Step-by-step explanation:
According to the Question,
- Given That, ∠T and ∠S are complementary & ∠S and ∠U are complementary
Thus, m∠T + m∠S = 90 ------ Equation 1
& m∠S + m∠U = 90 ------- Equation 2
- Now, Subtract Equation 2 From Equation 1, we get
m∠T - m∠U = 0
Thus, m∠T = m∠U
The measure of angle T is equal to angle U.(∠U≅∠T).
Answer:
D. -2x - 8
Step-by-step explanation:
1) Simplify 1/3(6x+15) to 6x+15/3
-6x+15/3 - 3
2) Factor out the common term 3.
-3(2x+5)/3 - 3
3) Cancel 3.
-(2x+5)-3
4) Remove parentheses.
-2x-5-3
5) Collect like terms.
-2x+(-5-3)
6) Simplify
-2x-8
Answer:
9.12 + 9.12 = 18.24 inches
Step-by-step explanation:
Diameter = 23 inches (given)
Radius = 11.5 inches
2 Chords of length = 14 inches ( You didn't specify if the 14 inches is for both chords or for a single cord. I'll assume it's for two cords 14 and 14inches apart.
To clearly solve this, we'll make some mild assumptions.
Let the perpendicular distance of the chords from the center of the circle to represented as " x and y"
Therefore:
x^2 + 7^2 = 11.5 ^ 2
x^2 + 49 = 132.25
x^2 = 132.25 - 49
x^2 = 83.25
x = √ 83.25
x = 9.12 inches
Since the cords have thesame length (Assumed from the way the question was structured, the distance would still be thesame)
y^2 + 7^2 = 11.5 ^ 2
y^2 + 49 = 132.25
y^2 = 132.25 - 49
y^2 = 83.25
y = √ 83.25
y = 9.12 inches
Therefore, the distance will be :
9.12 + 9.12 = 18.24 inches
Have fun!
Answer:
y²=4√2.x
Step-by-step explanation:
The focus is at (0,4) and directrix is y=x or x-y =0, for a parabola P.
The distance between the focus and the directrix of the parabola P is
=
{Since the perpendicular distance of a point (x1, y1) from the straight line ax+by+c =0 is given by 
}
Let us assume that the equation of the parabola which is congruent with parabola P is y²=4ax
{Since the parabola has vertical directrix}
Hence, the distance between focus and the directrix is 2a = , {Two parabolas are congruent when the distances between their focus and the directrix are same}
⇒ a=√2
Therefore, the equation of the parabola is y²=4√2.x (Answer)
