Answer:
mZR = (4x + 160)°
Step-by-step explanation:
cause, mZR = mZN
;-))
(x + 7)/2 - (x + 4)/2 = (x + 7 - (x + 4)/2 = (x + 7 - x - 4)/2 = 3/2
................................................
The answer is 15.
Answer:
Pears: 30
Step-by-step explanation:
Constant:
3x + 5x + 2x = 150
10x = 150
x = 15
Multiply ratio with constant from above:
oranges : apples
3 * 15 : 5 * 15
45 : 75 ==> 45 oranges: 75 apples
pears : apples
2 * 15 : 5 * 15
30 : 75 ==> 30 pears: 75 apples
Check:
45 oranges + 75 apples + 30 pears = 150 fruits
The given equation of the ellipse is x^2
+ y^2 = 2 x + 2 y
At tangent line, the point is horizontal with the x-axis
therefore slope = dy / dx = 0
<span>So we have to take the 1st derivative of the equation
then equate dy / dx to zero.</span>
x^2 + y^2 = 2 x + 2 y
x^2 – 2 x = 2 y – y^2
(2x – 2) dx = (2 – 2y) dy
(2x – 2) / (2 – 2y) = 0
2x – 2 = 0
x = 1
To find for y, we go back to the original equation then substitute
the value of x.
x^2 + y^2 = 2 x + 2 y
1^2 + y^2 = 2 * 1 + 2 y
y^2 – 2y + 1 – 2 = 0
y^2 – 2y – 1 = 0
Finding the roots using the quadratic formula:
y = [-(- 2) ± sqrt ( (-2)^2 – 4*1*-1)] / 2*1
y = 1 ± 2.828
y = -1.828 , 3.828
<span>Therefore the tangents are parallel to the x-axis at points (1, -1.828)
and (1, 3.828).</span>
