Answer:
The last choice is the one you want
Step-by-step explanation:
First of all, a parabola has a minimum value if it is a positive parabola, one that opens upward. The first and the third parabolas are negative so they open upside down. That leaves us with choices 2 and 4. We find the side to side and up or down movement by finishing the completion of the square that has already been started for us. Do this by factoring what's inside the parenthesis into a perfect square binomial.
The second one factored becomes:
which reflects a shift to the right 3 and up 1. Not what we are asked to find.
The fourth one factored becomes:
which reflects a shift to the right 3 and down 5. That's what we want!
Answer:
- asymptotes: x = -4, x = 4
- zeros: x = 0
Step-by-step explanation:
The vertical asymptotes of the rational expression are the places where the denominator is zero:
x^2 -16 = 0
(x -4)(x +4) = 0 . . . . . true for x=4, x=-4
x = 4, x = -4 are the equations of the vertical asymptotes
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The zeros of a rational expression are the places where the numerator is zero:
4x = 0
x = 0 . . . . . . divide by 4
The two angles are vertical angles, which means they are the same.
Set the two equations to equal and solve:
2x +2 = 3x -52
Subtract 2x from each side:
2 = x -52
Add 52 to each side:
x = 54
Answer:
The answer will be 10
Step-by-step explanation:
15/3*4/2
5*2
=10
The interior angles of any triangle always sum to 180°.
In the triangle, angles C and D are labeled congruent, so the missing angle has measure
180° - 2 (6x - 5)°
This angle is supplementary to the one labeled (11x + 1)°, which means
180° = (11x + 1)° + (180° - 2 (6x - 5)°)
Solve for x :
180° = (11x + 1)° + 180° - 2 (6x - 5)°
0 = (11x + 1)° - 2 (6x - 5)°
0 = (11x)° + 1° - (12x)° + 10°
(12x - 11x)° = 1° + 10°
x° = 11°
x = 11
