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Vilka [71]
3 years ago
7

If f(x) is a third degree polynomial function and g(x) = f(–2x), which of the following is NOT true?

Mathematics
1 answer:
valina [46]3 years ago
8 0

Answer:

f(x) and g(x) have the same x-intercepts (is <em>not true</em>)

Step-by-step explanation:

g(x) is a reflection across the y-axis and a horizontal compression of f(x). In general those transformations will move the x-intercepts. (The y-intercept and the number of x-intercepts will remain unchanged.)

_____

<em>Comment on the question/answer</em>

f(x) = x^3 is a 3rd degree polynomial. When transformed to g(x) = -8x^2, its only x-intercept (x=0) remains the same. The answer above will not apply in any instance where the only x-intercept is on the line of reflection. (The question is flawed in that it does not make any exception for such functions.)

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3 years ago
A pyramid has a regular hexagonal base with side lengths of 4 and a slant height of 6. Find the total area of the pyramid.
Tanzania [10]

The total area of pyramid is 113.569 square units

The equation to find the total area of the pyramid is Total area = base area + lateral area.

<u>Solution:</u>

Given, A pyramid has a regular hexagonal base with side lengths of 4 and a slant height of 6.

<em><u>The total area of pyramid is given by:</u></em>

A=A_{b}+A_{l}   ---- eqn 1

Where,

A_{b} \text { is the base area and } A_{l} \text { is the lateral area }

<em><u>The area of base is given as:</u></em>

A_{b}=\frac{3 \sqrt{3}}{2} l^{2}

Where "l" is the side of hexagon.

Substituting we get,

\begin{array}{l}{A_{b}=\frac{3 \sqrt{3}}{2}(4)^{2}} \\\\ {=\frac{3 \sqrt{3}}{2} \times 16=3 \sqrt{3} \times 8} \\\\ {A_{b}=24 \sqrt{3}}\end{array}

<em><u>The lateral area is given as:</u></em>

A_{l}=3 b h

Where,

b: base of the triangle

h: height of the triangle

Substituting we get,

\begin{array}{l}{A_{l}=3 \times(4) \times(6)} \\\\ {A_{l}=72}\end{array}

Plugging in the values we found in eqn 1 we get,

A=24 \sqrt{3}+72

A = 113.569 square units

<em><u>Summarizing the results:</u></em>

The total area of pyramid is 113.569 square units approximately

The equation used to find total area of pyramid is Total area = base area + lateral area.

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Answer:

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Step-by-step explanation:

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