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3 years ago

What's the solution to these questions?

Mathematics

1 answer:

Ann [662]3 years ago

6 0

√(X-2 )+1=5
√(X-2 )=5-1
√(X-2 )=4 <=== square the tow sides

X-2 =16
x=16+2
x=18
..................................................................
(4x+1)^1/4-4=-1
(4x+1)^1/4=-1+4
(4x+1)^1/4=3
4x+1=(3)^4
4x+1=81
4x=81-1
4x=80
x=80/4
x=20

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Type the correct answer for each.

xxTIMURxx [149]

If point $\left(x,\ \frac{\sqrt{7}}{3}\right)$ is on the unit ircle, then:

$x^2+\left( \frac{ \sqrt{7} }{3} \right)^2=1 \\ \\ \Rightarrow x^2+ \frac{7}{9} =1 \\ \\ \Rightarrow x^2=1- \frac{7}{9} = \frac{2}{9} \\ \\ \Rightarrow x= \sqrt{ \frac{2}{9} } = \frac{ \sqrt{2} }{3}$

Since, the point is in the second quadrant, x is negative.

Thus, $(x,\ y)=\left(x,\ \frac{\sqrt{7}}{3}\right)=\left(-\frac{ \sqrt{2} }{3},\ \frac{\sqrt{7}}{3}\right)$

Part A:

$3 \sqrt{7} =6\left( \frac{ \sqrt{7} }{2} \right) \\ \\ =6\left( \frac{ \sqrt{7} }{3} \cdot \frac{3}{ \sqrt{2} } \right) \\ \\ =6\left( \frac{ \frac{ \sqrt{7} }{3} }{ \frac{ \sqrt{2} }{3} } \right)=-6\left( \frac{ \frac{ \sqrt{7} }{3} }{ -\frac{ \sqrt{2} }{3} } \right) \\ \\ =-6\left( \frac{y}{x} \right)=-6\tan\theta$

Therefore, $-6\tan\theta=3\sqrt{7}$ .

Part B:

$- \frac{ \sqrt{7} }{2} =- \frac{ \sqrt{7} }{3} \cdot \frac{3}{ \sqrt{2} } \\ \\ =- \frac{ \frac{ \sqrt{7} }{3} }{ \frac{ \sqrt{2} }{3} } = \frac{ \frac{ \sqrt{7} }{3} }{ -\frac{ \sqrt{2} }{3} } = \frac{y}{x} \\ \\ =\tan\theta$

Therefore, $\tan\theta=- \frac{ \sqrt{7} }{2}$

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3 years ago

Complete the Table

nydimaria [60]

Answer:

N, which is the increment is 4

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3 years ago

One type of lightning bug glows once every 1 1/2 seconds. How many times can it glow in 1 minute?

KIM [24]

It can glow 40 times per minute

8 0

3 years ago

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A piece of paper is 11 inches long and 8.5 inches wide. What is the area of the paper in square centimeters? (Please show work!)

goldenfox [79]

If you would like to know what is the area of the paper in square centimeters, you can calculate this using the following steps:

1 inch equals to 2.54 centimeters.

11 inches = 11 * 2.54 = 27.94 centimeters long
8.5 inches = 8.5 * 2.54 = 21.59 centimeters wide

11 inches long * 8.5 inches wide = 27.94 centimeters long * 21.59 centimeters wide = 27.94 * 21.59 = 603.22 square centimeters

The correct result would be 603.22 square centimeters.

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3 years ago

canning operation is designed to fill cans with 14.5 oz of ingredients, on average, with a standard deviation of 0.1 oz. Nine ca

Pavlova-9 [17]

Answer:

SE = 0.025

Step-by-step explanation:

We are given;

Sample mean; x¯ = 14.52

Sample standard deviation; s = 0.075

Sample size; n = 9

Now,formula for standard error of sample mean is;

SE = s/√n

SE = 0.075/√9

SE = 0.075/3

SE = 0.025

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3 years ago