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3 years ago

Please help, I think its D but I know that things are usually the opposite of what you think when doing these types of problems.

Mathematics

1 answer:

miskamm [114]3 years ago

4 0

Answer:

A. The graph of g(x) is the graph of f(x) vertically stretched by a factor of 5.

Step-by-step explanation:

The only thing that has changed is that x^2 is multiplied by 5.

If the x^2 is multiplied by a constant that has an absolute value less than 1, the parabola will undergo a vertical compression.

If the x^2 is multiplied by a constant that has an absolute value more than 1, the parabola will undergo a vertical stretch.

Since the absolute value of 5 is more than 1, A. The graph of g(x) is the graph of f(x) vertically stretched by a factor of 5.

Hope this helps!

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Which is true regarding the triangular frame? It is an acute triangle. About 0.8 foot needs to be removed from the 20-foot board

Ivanshal [37]

Question:

Arielle is building the wooden framework for the roof of a house. she needs the angle created by the vertical and horizontal boards of the frame to be a right angle. the height of the vertical board is 12 feet. the length of the horizontal board is 15 feet. the support beam that will connect the ends of the two boards measures 20 feet. which is true regarding the triangular frame? it is an acute triangle. about 0.8 foot needs to be removed from the 20-foot board to create a right triangle. it is an obtuse triangle. about 0.8 foot needs to be removed from the 20-foot board to create a right triangle. it is an acute triangle. about 7 feet need to be removed from the 20-foot board to create a right triangle. it is an obtuse triangle. about 7 feet need to be removed from the 20-foot board to create a right triangle.

Answer:

It is an obtuse triangle.About 0.8 foot needs to be removed from the 20 foot board to create a right triangle.

Explanation:

Let us use pythagorean theorem to check whether it is a right triangle.

The vertical board is 12 feet and the horizontal board is 15 feet.

By pythagoean theorem,

$\begin{aligned}c^{2} &=12^{2}+15^{2} \\&=144+225 \\c &=\sqrt{369} \\c &=19.2\end{aligned}$

Thus, we need to remove 0.8 foot from the 20 foot board to create a right triangle.

Now, we shall find the angle of the triangle.

Since, the vertical board is 12 and the horizontal board is 15 feet, the tangent ratio is given by opposite/adjacent.

$\begin{aligned}\tan x &=\frac{o p p}{a d j} \\&=\frac{15}{12}\end{aligned}$

To find the angle x, we shall take $tan^{-1}$ on both sides,

$\begin{aligned}\tan ^{-1}(\tan x) &=\tan ^{-1} \frac{15}{12} \\x &=51.34^{\circ}\end{aligned}$

The total angle of the triangle is $51.34+51.34=102.68$ which is an obtuse triangle.

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Answer:

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Step-by-step explanation:

From the given information:

Let's recall from our previous knowledge that the formula for finding the area of a rectangle = L × w

where;

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Suppose the Length L is twice the width w

Then L = 2w --- (1)

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A = L × w

A = 2w × w

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$\dfrac{dA}{dt }= 4w \times \dfrac{dw}{dt} --- (2)$

At the time t

$\dfrac{dw}{dt}= 34 m \ per \ year ; w = 450 \ m$

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$\dfrac{dA}{dt }= 4 \times 450 \times 34$

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Answer:

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Step-by-step explanation:

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Slav-nsk [51]

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grigory [225]

This is simple. Coordinate form is (x,y) so you would just plug in your values.

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