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3 years ago

Solve 2(x - 5) = 6(x - 1)

Mathematics

2 answers:

Svetlanka [38]3 years ago

5 0

Answer:

x=-1

Step-by-step explanation:

2(x-5)=6(x-1)

2x-10=6x-6

-4x-10=-6

-4x=4

x=-1

9966 [12]3 years ago

4 0

Answer:

Step-by-step explanation:

so first you multiply 2 times 5 =15 and the we do 15 times six which is 90 and then subtract one and keep subtracting util you get to 60

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timurjin [86]

Answer:

Proved

Step-by-step explanation:

$cos^4\alpha +sin^4\alpha =\frac{1}{4}(3+cos4\alpha )\\\\$

Take the Left Hand Side:

$cos^4\alpha +sin^4\alpha\\\\(cos^2\alpha )^2+(sin^2\alpha )^2\\\\(\frac{1+cos2\alpha }{2})^2+(\frac{1-cos2\alpha }{2})^2 \\\\\frac{1+2cos2\alpha +cos^22\alpha }{4}+\frac{1-2cos2\alpha +cos^22\alpha }{4} \\\\$

$\frac{1+2cos2\alpha +cos^22\alpha +1-2cos2\alpha +cos^22\alpha }{4} \\\\\frac{2+2cos^22\alpha }{4} \\\\\frac{1+cos^22\alpha }{2} \\\\\frac{1}{2}(1+cos^22\alpha )\\\\$

$\frac{1}{2}(1+\frac{1+cos4\alpha }{2})$

$\frac{1}{2}(\frac{2+1+cos4\alpha }{2})\\\\\frac{1}{4}(3+cos4\alpha )\\\\$

Hence Proved!

The following identities were used are attached in an image

3 0

3 years ago

∠85° is supplementary to which of the following angles?

Illusion [34]

Answer:

∠95

Step-by-step explanation:

Hello There!

the measure of supplementary angles add up to equal 180

so to find an angle that is supplementary to angle 85 we subtract it from 180

180-85-95

so an angle that is supplementary to angle 85 would have a measure of 95 degrees

5 0

3 years ago

The average waiting time for a drive-in window at a local bank is 9.2 minutes, with a standard deviation of 2.6 minutes. When a

Lady bird [3.3K]

Answer:

a) 56.91% probability that the customer will have to wait between 5 and 10 minutes.

b) 65.49% probability that the client will have to wait less than 6 minutes of more than 9 minutes.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 9.2, \sigma = 2.6$

(a) Between 5 and 10 minutes

This is the pvalue of Z when X = 10 subtracted by the pvalue of Z when X = 5. So

X = 10

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{10 - 9.2}{2.6}$

$Z = 0.31$

$Z = 0.31$ has a pvalue of 0.6217

X = 5

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{5 - 9.2}{2.6}$

$Z = -1.62$

$Z = -1.62$ has a pvalue of 0.0526

0.6217 - 0.0526 = 0.5691

56.91% probability that the customer will have to wait between 5 and 10 minutes.

(b) Less than 6 minutes or more than 9 minutes

Less than 6

pvalue of Z when X = 6

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{6 - 9.2}{2.6}$

$Z = -1.23$

$Z = -1.23$ has a pvalue of 0.1230

12.30% probability that the client will have to wait less than 6 minutes

More than 9

1 subtracted by the pvalue of Z when X = 9.

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{9 - 9.2}{2.6}$

$Z = -0.08$

$Z = -0.08$ has a pvalue of 0.4681

1 - 0.4681 = 0.5319

53.19% probability that the client will have to wait more than 9 minutes

Less than 6 or more than 9

12.30 + 53.19 = 65.49% probability that the client will have to wait less than 6 minutes of more than 9 minutes.

5 0

3 years ago

A cylinder has a height of 9 centimeters and a radius of 13 centimeters. What is its volume? Use ≈ 3.14 and round your answer

mash [69]

Step-by-step explanation:

as any other fully symmetric 3D object, the volume is

base area × height.

the area of a circle is

pi×r²

so, we have in our case

pi×13²×9 = 3.14×169×9 = 4,775.94 cm³

5 0

3 years ago

Plzzzzz help 3 9/10 is the same as the sum of 3 1/3 and half of a number what is the number

kirill [66]

Answer:

9/10 = 1/3 + 1/2x

9/10 - 1/3 = 1/2x

LCM of 10 and 3 is 30

( 27 - 10)/30 = 1/2x

17/30 = 1/2x

17 * 2 = 30x

34=30x

34/30= 30x/30

x = 17/15

6 0

3 years ago