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2 years ago

What single percentage change is equivalent to a 17% increase followed by a 8% decrease?

Mathematics

1 answer:

Ksju [112]2 years ago

8 0

Answer:

9% increase

Step-by-step explanation:

Given :

17% increase :

Let initial percentage = 100%

17% increase means :

100% + 17% = 117%

Followed by 8% decrease :

117% - 8% = 109%

Hence, the final percentage = 109%

To represent the total change as a single percentage change :

Change = final percentage - Initial percentage

Change = 109% - 100%

Change = 9%

This is a 9% increase

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Ava wants to figure out the average speed she is driving. She starts checking her car’s clock at mile marker 0. It takes her 4 m

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<h2>Answer:</h2>

The average speed of car is:

0.75 miles per minutes.

The equation of line is:

$n=\dfrac{3}{4}t$

<h2>Step-by-step solution:</h2>

The table that describes the time and number of miles marked is given by:

Time Miles

0 0

4 3

8 6

Clearly we could observe that with the increase in time by every 4 minutes the number of mile increases by 3.

i.e. the average speed is calculated as the ratio of change in miles to the change in time.

Hence,

$Average\ Speed=\dfrac{3-0}{4-0}\\\\\\i.e.\\\\\\Average\ Speed=\dfrac{3}{4}=0.75$

Hence, the average speed=0.75 miles per minutes.

Also we will find the equation of the lines that related the miles and time by using the two-point formula.

i.e. any line passing through (a,b) and (c,d) is calculated by using the formula:

$y-b=\dfrac{d-b}{c-a}\times (x-a)$

Here (a,b)=(0,0) and (c,d)=(4,3)

i.e. the equation is given by:

$n-0=\dfrac{3-0}{4-0}\times (t-0)\\\\i.e.\\\\n=\dfrac{3}{4}t$

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2 years ago

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Evaluate sin(Arcos(-9/√145)).

tino4ka555 [31]

Use the fact that $\sin x = \sqrt{1-\cos^2 x}$ to solve it.

$\sin(\arccos(-\frac{9}{\sqrt{145}}))=\sqrt{1-\cos^2(\arccos(-\frac{9}{\sqrt{145}}))} =\\= \sqrt{1-(-\frac{9}{\sqrt{145}})^2}=\frac{8}{\sqrt{145}}$

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1 year ago

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Which transformations have been applied to the graph of f(x) = x2 to produce the graph of g(x) = –5x2 + 100x – 450? Select three

RSB [31]

Answer:

The graph of f(x) is shifted up 50 units

The graph of f(x) is shifted right 10 units

The graph of f(x) is reflected over the x-axis

Step-by-step explanation:

we have

$f(x)=x^{2}$

This is a vertical parabola open upward

The vertex is a minimum

The vertex is the origin (0,0)

$g(x)=-5x^{2}+100x-450$

This is a vertical parabola open downward

The vertex is a maximum

The first thing to note is that fx) is a parabola that opens up and g(x) opens down, so a reflection across the x-axis must have been applied.

Find the vertex of g(x)

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$g(x)=-5x^{2}+100x-450$

Complete the square

$g(x)=-5(x^{2}-20x)-450$

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$g(x)=-5(x^{2}-20x+100)+50$

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The vertex is the point (10,50)

To translate the vertex of (0,0) to (10,50)

The rule of the translation is

(x,y) ------> (x+10,y+50)

That means ----> The translation is 10 units at right and 50 units up

therefore

The transformations are

The graph of f(x) is shifted up 50 units

The graph of f(x) is shifted right 10 units

The graph of f(x) is reflected over the x-axis

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Answer:

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Step-by-step explanation:

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