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luda_lava [24]
3 years ago
14

What is an equation of the line that is perpendicular to y=−2/3x+5 and passes through the point (2, 11) ? Enter your equation in

the box.
Mathematics
1 answer:
barxatty [35]3 years ago
3 0

Answer:

y - 11 = \frac{3}{2}(x -2)

Step-by-step explanation:

A perpendicular line is a line whose slope is the negative reciprocal of the other line. The line y = -2/3x + 5 has slope -2/3. This means the line perpendicular will be 3/2.

Substitute 3/2 and (2,11) into the point slope form of a line.

y - y_1 = m(x-x_1)\\y - 11 = \frac{3}{2}(x -2)\\

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Find the radius and diameter of circle A, if the endpoints of the radius<br> are (-2, -1) and (6,4).
AleksandrR [38]

Step-by-step explanation:

length \: between \: ( - 2, - 1) \: and \: (6,4) \\  =  \sqrt{(x _{1} - x  _{2} )² + (y _{1}  - y _{2})²  }  \\  =  \sqrt{( -  2 - 6)²+ ( - 1 - 4)²}  \\  =   \sqrt{64 + 25}  \\  =  \sqrt{100}  \\  = 10 \: units \\ radius = 10 \: units \\ diameter = 2 \times radius \\ d = 2 \times 10 \\ d = 20 \: units

8 0
3 years ago
Distributions and Comparing Data Project
LenKa [72]

Answer:

1. The shape of the histogram created with MS Excel is approximately bell shaped and approximately evenly spread about the central (largest counts) values

The shape of the box plot created with MS Excel is approximately evenly distributed

2. The appropriate measure of central tendency for a bell shaped histogram is the mean and median, due to the approximately equal distribution about the highest frequency class

3. Part A

The 15 numbers between 1  and 20 generated by a random generator are;

1, 8, 8, 15, 4, 18, 11, 6, 17, 1, 18, 15, 10, 12, 11

The measure of center is the mean =  (1+8+8+15+4+18+11+6+17+1+18+15+10+12+11)/15 = 155/15 = 31/3

The measure of spread used is the variance, s² = 32.38

Where, \,s^2 =\dfrac{\sum \left (x_i-\bar x  \right )^{2} }{n - 1}

{\sum \left (x_i-\bar x  \right )^{2} } = 453.333

n = 15

s² = 453.\overline 3/(15 - 1) = 32.38

Part B

The measure of central tendency are the mean and the median because the size of the data (n = 15), is 75% of the population (N = 20) nd therefore the data is approximately normal and can be represented by the mean and the standard deviation

Step-by-step explanation:

4 0
3 years ago
Which phrase correctly represents the algebraic expression for 22-n?
Harrizon [31]

Answer:

D

Step-by-step explanation:

3 0
3 years ago
Lucas ate a fraction of a pizza. Hugo ate 5/8 of the same pizza. Now there is 1/8 of the pizza left what fraction of pizza did L
MatroZZZ [7]

Answer:

\frac{2}{8}

Step-by-step explanation:

In order to solve this equation we will need to use what we know in order to find the answer.

1=\frac{8}{8}

H=\frac{5}{8}

R = \frac{1}{8}

If Huge ate 5/8's of the pizza and 8/8's creates a whole pizza then the question is quite simple. There is only 1/8's remaining after the boys finish their meal but 5/8's of the pizza was already eaten by Hugo meaning Lucas has to eat 2/8's of the pizza in order for there to be only 1/8's of the pizza left which means 2/8's is your answer.

Hope this helps.

5 0
3 years ago
Given that Cosecant (t) = negative StartFraction 13 Over 5 EndFraction for Pi less-than t less-than StartFraction 3 pi Over 2 En
Sergio [31]

Answer:

\bold{cot(t) =\dfrac{12}{5}}

Step-by-step explanation:

Given that:

Cosec (t) = -\frac{13}5

for \pi < t < \frac{3 \pi}2

That means, angle t is in the 3rd quadrant.

To find:

Value of cot(t)

Solution:

First of all, let us recall what trigonometric ratios are positive and what trigonometric ratios are negative in 3rd quadrant.

In 3rd quadrant, tangent and cotangent are positive.

All other trigonometric ratios are negative.

Let us have a look at the following identity:

cosec^2\theta -cot^2\theta =1

here, \theta =t

So, cosec^2t-cot^2t=1

\Rightarrow (-\dfrac{13}{5})^2-cot^2t=1\\\Rightarrow (\dfrac{169}{25})-cot^2t=1\\\Rightarrow \dfrac{169}{25}-1=cot^2t\\\Rightarrow \dfrac{169-25}{25}=cot^2t\\\Rightarrow \dfrac{144}{25}=cot^2t\\\Rightarrow cot(t)=\pm\sqrt{\dfrac{144}{25}}\\\Rightarrow cot(t)=\pm\dfrac{12}{5}

But, angle t is in 3rd quadrant, so value of

\bold{cot(t) =\dfrac{12}{5}}

4 0
3 years ago
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