Answer:
Vertex form
y = -4(x + 3)^2 + 10
Standard form;
y = -4x^2-24x - 26
Step-by-step explanation:
Mathematically, we have the vertex form as
y = a(x-h)^2 + k
(h,k) represents the vertex
We have h as -3 and k as 10
y = a(x+3)^2 + 10
To get a, we substitute any of the points
Let us use (-1,-6)
-6 = a(-1+3)^2 + 10
-6-10 = 4a
4a = -16
a = -16/4
a = -4
So we have the equation as;
y = -4(x+3)^2 + 10
For the standard form;
We expand the vertex form;
y = -4(x + 3)(x + 3) + 10
y = -4(x^2 + 6x + 9) + 10
y = -4x^2 - 24x -36 + 10
y = -4x^2 -24x -26
Answer: 6.05 units
Step-by-step explanation:
<em>Correct question is:</em>
<em>A cone with radius 3 units is shown below. Its volume is 57 cubic units. Find the height of the cone. Use 3.14 for pi and round your final answer to the nearest hundredth.</em>
Hi, to answer this question we have to apply the next formula:
Volume of a cone = 1/3 x π x radius^2 x height
Replacing with the values given:
57 = 1/3x 3.14 x (3)^2 (h)
Solving for h
57 = 1/3 x 3.14 x 9 (h)
57 =9.42h
57/9.42 =h
h= 6.05 units
Feel free to ask for more if needed or if you did not understand something.
Let the number of raspberry bushes in one garden = x
And the number of raspberry bushes in second garden = y
Garden one has 5 times as many raspberry bushes as second garden,
So the equation will be,
x = 5y -------(1)
If 22 bushes were transplanted from garden one to the second, number of bushes in both the garden becomes same,
Therefore, (x - 22) = (y + 22)
x - y = 22 + 22
x - y = 44 ------(2)
Substitute the value of x from equation (1) to equation (2)
5y - y = 44
4y = 44
y = 11
Substitute the value of 'y' in equation (1),
x = 5(11)
x = 55
Therefore, Number of bushes in garden one were 55 and in second garden 11 originally.
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