Please consider the graph of the sphere.
We know that the volume of sphere is equal to 
, where r represents radius of sphere.
We can see that diameter of sphere is 30 inches. We know that radius is half the diameter, so radius of the given sphere would be half of 30 inches that is 
inches.
Therefore, the volume of the given sphere is 
and option B is the correct choice.
Answer:
there is a 64% chance that the student got both problems wrong
a 32% chance that they got only 1 correct
and a 4% chance that they got both correct
Step-by-step explanation:
There are 25 total possible combinations of answers, with 8 possible combinations where the student would get 1 answer right, and 1 combination where the student would get both answers correct.
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B: (0, a)
C should have the same y value as B
D: (a,0)
C should have the same x value as D
So point C is (a,a)
Since point A is on the origin, its point is (0,0)
You use the slope formula and plug in point A and C:
m = 1
So the value that belongs in the green box is 1
Answer:
Horizontal shift of 4 units to the left.
Vertical translation of 8 units downward.
Step-by-step explanation:
Given the quadratic function, y = (x + 4)² - 8, which represents the horizontal and vertical translations of the parent graph, y = x²:
The vertex form of the quadratic function is y = a(x - h)² + k
Where:
The vertex is (h , k), which is either the <u>minimum</u> (upward facing graph) or <u>maximum</u> (downward-facing graph).
The axis of symmetry occurs at <em>x = h</em>.
<em>a</em> = determines whether the graph opens up or down, and makes the graph wider or narrower.
<em>h</em> = determines how far left or right the parent function is translated.
<em>k</em> = determines how far up or down the parent function is translated.
Going back to your quadratic function,
y = (x + 4)² - 8
- The vertex occrs at (-4, -8)
- a is assumed to have a value of 1.
- Given the value of <em>h</em> = -4, then it means that the graph shifted horizontally by <u>4 units to the left</u>.
- Since k = -8, then it implies that the graph translated vertically at <u>8 units downward</u>.
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