Answer:
a. 4, 6
b. -72
c. (5, 3)
d. Graph A
Step-by-step explanation:
<h3>a.</h3>
To answer these questions, it is useful to start by factoring the equation.
y = -3x² +30x -72 . . . . given
y = -3(x² -10x +24) . . . . factor out leading coefficient
y = -3(x -4)(x -6)
The x-intercepts are the values of x that make the factors zero:
x = 4, 6
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<h3>b.</h3>
The y-intercept is the constant in the equation: -72.
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<h3>c.</h3>
We know the x-coordinate of the vertex is the midpoint between the x-intercepts: (4+6)/2 = 5. The y-coordinate can be found by evaluating y at that x-value.
y = -3(5 -4)(5 -6) = -3(1)(-1) = 3
The vertex is (5, 3).
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<h3>d.</h3>
The graph that has the correct vertex and x-intercepts is Graph A.
I believe the GCF of those two is 12.
Answer: radius of the largest circle is Zero.
Step-by-step explanation: A circle can't fit into an ellipse with such coordinate (3,0). What that coordinate means is that the ellipse lies along the x axis 3unit from the origin along the x axis and 0 unit from the origin along the y axis. At which no circle can fit in.
Moreso, the the coordinates at which the circle intercepts the ellipse as to be uniform not (3,0).
A circle as a constant radii coordinate on both axis.
I believe you can now see why my answer is Zero.
Your equation is gonna be a^2-24^2=25^2 and your answer is 7.
Answer:
34 degree
Step-by-step explanation:
we have a 90 degree angle height of 30ft
with a 20ft slope
We can confirm the 20ft slope with Pythagoras
30^2 - 20^2 = √900 - √400 = √500 = 22.36ft
Sin (x) = Opposite / Hypotenuse = 2.236 / 2 = 0.01951154282
sin (0.01951154282) = 3.405 = 34 degree
This makes the opposite angle 90- 34 = 56 degree as all add up to 180 degree.