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3 years ago

6

Rate of change of y = –4.5x + 15

1 answer:

Minchanka [31]3 years ago

3 0

The rate of change would be -4.5, because no matter what the line is changing at a rate of -4.5

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A central angle of a circle measures 1.5 radians. If the radius of the circle is 3 cm, what is the area of the related sector?

soldi70 [24.7K]

Answer:

Option B. $6.75\ cm^{2}$

Step-by-step explanation:

we know that

The area of a circle is equal to

$A=\pi r^{2}$

we have

$r=3\ cm$

substitute

$A=\pi (3^{2})=9 \pi\ cm^{2}$

Remember that

$2\pi$ radians subtends the complete circle of area $9 \pi\ cm^{2}$

so

by proportion

Find the area of the related sector for a central angle of $1.5$ radians

Let

x------> the area of the related sector

$\frac{9 \pi}{2\pi}\frac{cm^{2}}{radians} =\frac{x}{1.5}\frac{cm^{2}}{radians}\\ \\x=9*1.5/2\\ \\x= 6.75\ cm^{2}$

7 0

3 years ago

On a coordinate plane, triangle A B C is shown. Point A is at (0, 0), point B is at (3, 4), and point C is at (3, 2). What is th

Elena L [17]

Answer:

The area of triangle for the given coordinates is 1.5 $\sqrt{4.6}$

Step-by-step explanation:

Given coordinates of triangles as

A = (0,0)

B = (3,4)

C = (3,2)

So, The measure of length AB = a = $\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2}}$

Or, a = $\sqrt{(3-0)^{2}+(4-0)^{2}}$

Or, a = $\sqrt{9+16}$

Or, a = $\sqrt{25}$

∴ a = 5 unit

Similarly

The measure of length BC = b = $\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2}}$

Or, b = $\sqrt{(3-3)^{2}+(2-4)^{2}}$

Or, a = $\sqrt{0+4}$

Or, b = $\sqrt{4}$

∴ b = 2 unit

And

So, The measure of length CA = c = $\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2}}$

Or, c = $\sqrt{(3-0)^{2}+(2-0)^{2}}$

Or, c = $\sqrt{9+4}$

Or, c = $\sqrt{13}$

∴ c = $\sqrt{13}$ unit

Now, area of Triangle written as , from Heron's formula

A = $\sqrt{s\times (s-a)\times (s-b)\times (s-c)}$

and s = $\frac{a+b+c}{2}$

I.e s = $\frac{5+2+\sqrt{13}}{2}$

Or. s = $\frac{7+\sqrt{13}}{2}$

So, A = $\sqrt{(\frac{(7+\sqrt{13})}{2})\times ((\frac{(7+\sqrt{13})}{2})-5)\times (\frac{7+\sqrt{13}}{2}-2)\times (\frac{7+\sqrt{13}}{2}-\sqrt{13})}$

Or, A = $\sqrt{(\frac{(7+\sqrt{13})}{2})\times (\frac{(\sqrt{13}-3)}{2})\times (\frac{4+\sqrt{13}}{2})\times (\frac{7-\sqrt{13}}{2})}$

Or, A = $\frac{3}{2}$ × $\sqrt{1+\sqrt{13} }$

∴ Area of triangle = 1.5 $\sqrt{4.6}$

Hence The area of triangle for the given coordinates is 1.5 $\sqrt{4.6}$ Answer

7 0

3 years ago

Read 2 more answers

Which of the following illustrates the truth value of the given conditional statement?

garri49 [273]

Answer:

TT➪T

Step-by-step explanation:

8 0

2 years ago

36.24 divided by 9.06 is equal to

dusya [7]

Answer:

4

Step-by-step explanation:

8 0

3 years ago

Which unit rate corresponds to the proportional relationship shown in the graph?

jeka57 [31]

Answer:

i think the answer is 1.33cm/s

Step-by-step explanation:

you have to use m=y2-y1/x2-x1

4 0

2 years ago