Answer:
- B. Quadrilateral FLAG is a parallelogram because opposite sides are parallel.
Step-by-step explanation:
<em>Refer to attached.</em>
Plot the point and connect in order FLAG.
<u>We see </u>
- FL ║ GA
- GF ║ AL
- FA and GL are not perpendicular
<u>All the above can be confirmed by calculating the slopes:</u>
- m(FL) = (3 - 5)/(6 - 1) = -2/5
- m(GA) = (1 + 1)/(-2-3) = -2/5
- These are same.
- m(GF) = (5 - 1)/(1 + 2) = 4/3
- m(AL) = (3 + 1)/(6 - 3) = 4/3
- These are same
- m(FA) = (-1 - 5)/(3 - 1) = -3
- m(GL) = (3 - 1)/(6 +2) = -1/4
- These are negative but not reciprocal
The quadrilateral is a parallelogram.
Correct choice is B
Answer:
10.06 ft
Step-by-step explanation:
Maria's maximum height will occur when her velocity reaches zero (0). This means that she has stopped ascending and is about to begin descent.
The equation for the height reached by Maria on the trampoline is given as:
To find her maximum height, we first have to find the time it will take her to get to that height and corresponding velocity (zero).
Her velocity can be found by differentiating her height i.e. dh/dt:
Therefore, when v = 0:
It takes her 0.5625 seconds to get to her maximum height.
Therefore, her height at that time (0.5625 seconds) is:
Therefore, her maximum height is 10.06 ft.
Answer:
6.53
Step-by-step explanation:
Area of the square base = 5^2 = 25 cm^2
Area of one of the triangular side = 1/2 * 5 * 8 = 20 cm^2 and there are 4 sides
So the surface area of while pyramid = 4 * 20 + 25 = 105 cm^2
Volume of the cone = (1/3) pi r^2 h
= (1/3) pi * 5^2 * 8
= 209.44 ft^2
There are a few ways to solve this. The method I will use is the substitution method. Since they give us a "y = " statement, we can replace the y in the second equation with what it gives us to the right of the equal sign.
- 3x + 6(- 2x - 1) = 24
Simplify by using the distributive property.
- 3x + 6(- 2x) + 6(- 1) = 24
- 3x - 12x - 6 = 24.
Combine like terms
- 15x - 6 = 24
Add 6 to each side.
- 15x = 30
Divide both sides by - 15 to isolate variable X
x = 30 / - 15
x = - 2.
Now plug in the x-value we've found back into the first equation.
y = - 2( - 2) - 1
y = 4 - 1
y = 3
Your answer is (- 2, 3)
