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Sunny_sXe [5.5K]
3 years ago
11

What is the volume of a square pyramid with a base length of 4 cm and a height of 9 cm ​

Mathematics
1 answer:
galben [10]3 years ago
5 0
The volume is 48 cm
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Evaluate the expression for x=5, y=-3 and z=7<br> (x2 – z) (22+5)
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Answer:

81

Step-by-step explanation:

(Refer to image)

Plug in x and z and follow order of operations to simplify the expression

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Derive the equation of the parabola with a focus at (0, –4) and a directrix of y = 4. (2 points)
yan [13]
The vertex of the parabola is between the shortest line connecting its focus and directrix, so between (0, -4) and y = 4 is the point (0, 0), which is the vertex of the parabola. Also, this parabola faces downward.
The general formula for a parabola that faces downward is y = -4cx^2, where c is the distance from the vertex to either to focus or the parabola. Since c = 4, the equation is y = -16x^2, which is choice A.
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Natasha2012 [34]

Answer:

First question

a = 1 , h = 0 , k = 6 ⇒ third answer

Second question

y = 2x² + 4 ⇒ second answer

Third question

No of the choices correct ⇒ fourth answer

Step-by-step explanation:

First question

∵ f(x) = x² + 6

- It is a quadratic function with general form ax² + bx + c

- Its vertex is (h , k), where h = -b/2a and k = f(h)

∵ a = 1 , b = 0 , c = 6

∴ h = 0/2(1) = 0

∴ f(0) = 0² + 6 = 6

∴ a = 1 , h = 0 , k = 6 ⇒ third answer

Second question

- If the function f(x) translated vertically up  

 by k units, then the new function g(x) = f(x) + k

- If the function f(x) translated vertically down  

 by k units, then the new function g(x) = f(x) – k

∵ y = 2x²

∵ y is shifted 4 units up

∴ k = 4

∴ y + 4 = 2x² + 4

∴ y = 2x² + 4 ⇒ second answer

Third question

∵ y = -2x² + 3

- It is a quadratic equation with general form ax² + bx + c

- It represented graphically by parabola

- If a is positive the parabola opens upward

- If a is negative the parabola opens downward

∵ a = -2

∴ The parabola opens downward

∴ No of the choices correct ⇒ fourth answer

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3 years ago
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