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2 years ago

Solve the following equation

Mathematics

1 answer:

const2013 [10]2 years ago

4 0

Answer:

Write it down in comments i can barely see

Step-by-step explanation:

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Right triangle ABC and its image, triangle A'B'C' are shown in the image attached.

AlladinOne [14]

Answer:

See explanation

Step-by-step explanation:

Triangle ABC ha vertices at: A(-3,6), B(0,-4) and (2,6).

Let us apply 90 degrees clockwise about the origin twice to obtain 180 degrees clockwise rotation.

We apply the 90 degrees clockwise rotation rule.

$(x,y)\to (y,-x)$

$\implies A(-3,6)\to (6,3)$

$\implies B(0,4)\to (4,0)$

$\implies C(2,6)\to (6,-2)$

We apply the 90 degrees clockwise rotation rule again on the resulting points:

$\implies (6,3)\to A''(3,-6)$

$\implies (4,0)\to B''(0,-4)$

$\implies (6,-2)\to C''(-2,-6)$

Let us now apply 90 degrees counterclockwise rotation about the origin twice to obtain 180 degrees counterclockwise rotation.

We apply the 90 degrees counterclockwise rotation rule.

$(x,y)\to (-y,x)$

$\implies A(-3,6)\to (-6,-3)$

$\implies B(0,4)\to (-4,0)$

$\implies C(2,6)\to (-6,2)$

We apply the 90 degrees counterclockwise rotation rule again on the resulting points:

$\implies (-6,-3)\to A''(3,-6)$

$\implies (-4,0)\to B''(0,-4)$

$\implies (-6,2)\to C''(-2,-6)$

We can see that A''(3,-6), B''(0,-4) and C''(-2,-6) is the same for both the 180 degrees clockwise and counterclockwise rotations.

7 0

3 years ago

Assume that a computer was used to generate the given confidence interval for the population mean. Find the sample mean or margi

stealth61 [152]

Answer:

The sample mean is

b.3.55

The margin of error is

0.32

Step-by-step explanation:

Deep explanation about a confidence interval

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1-0.9}{2} = 0.05$

Now, we have to find z in the Ztable as such z has a pvalue of $1-\alpha$ .

So it is z with a pvalue of $1-0.05 = 0.95$ , so $z = 1.645$

Now, find M as such

$M = z*\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

$M = 1.645*215 = 353.675$

The lower end of the interval is the mean subtracted by M. So it is 6.4 - 0.3944 = 6.01 hours.

The upper end of the interval is the mean added to M. So it is 6.4 + 0.3944 = 6.74 hours.

In this problem:

The deep explanation is not that important.

We just have to recognize that the interval has a lower end and an upper end. The distance from both the upper and the lower end to the mean is M. This means that the sample mean is the halfway point between the lower end and the upper end.

The margin of error is the distance of these two points(lower and upper end) to the mean.

In our interval

Lower end: 3.23

Upper end: 3.87

Sample mean

$M = \frac{3.23 + 3.87}{2} = 3.55$

So the correct answer is:

b.3.55

The margin of error is

3.87 - 3.55 = 3.55 - 3.23 = 0.32

4 0

3 years ago

The Cobb family’s natural gas bill was 85.50 for 95 cubic feet of gas, What is the unit rate? (Cost per cubic foot of gas?)

Ratling [72]

Answer:

I believe it would cost 9 cents per cubic foot of gas.

Step-by-step explanation:

7 0

3 years ago

Kira has $40 to spend and used $20 to buy a new pair of jeans. Which integer best represents the situation of spending $20?

pishuonlain [190]

-20 because 40 is a positive and spent is negative

5 0

3 years ago

What is the simplest form of i^15

Korolek [52]

Answer: -iSimplify the expression using the definition of an imaginary number

i = √ − 1 . − i

Step-by-step explanation: Simplify the expression using the definition of an imaginary number i = √ − 1 . − i

4 0

3 years ago