A circle is cut from a square price of cloth, as shown

The sum of the angle measures of a triangle is 180°. Find the value of x. Then find the angle measures of the triangle.

MAXImum [283]

Answer:

x = 43
43°, 51°, 86°

Step-by-step explanation:

The sum of the angles is ...

x° + (x +8)° + 2x° = 180°

4x +8 = 180 . . . . . . . . . . . collect terms, divide by °

x +2 = 45 . . . . . . . . . . divide by 4

x = 43 . . . . . . . . . . subtract 2

x +8 = 51

2x = 86

The angles are 43°, 51°, 86°.

7 0

2 years ago

Find the interval in which f(x)=sinx−cosx is increasing or decreasing?

alisha [4.7K]

Answer:

There is no short answer.

Step-by-step explanation:

To find to intervals which f(x) increases or decreases, we first need to find it's derivative.

$f(x) = sinx - cosx\\f'(x) = cosx - (-sinx) = cosx + sinx$

The function is increasing when it's value is > 0 and decreasing when it's value is < 0.

If we take a look at this graph, cosx+sinx is positive when they are both positive or when cosx is greater then sinx on the negative part.

I hope this answer helps.

3 0

3 years ago

Suppose that the mean water hardness of lakes in Kansas is 425 mg/L and these values tend to follow a normal distribution. A lim

tino4ka555 [31]

Answer:

The mean water hardness of lakes in Kansas is 425 mg/L or greater.

Step-by-step explanation:

We are given the following data set:

346, 496, 352, 378, 315, 420, 485, 446, 479, 422, 494, 289, 436, 516, 615, 491, 360, 385, 500, 558, 381, 303, 434, 562, 496

Formula:

$\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}$

where $x_i$ are data points, $\bar{x}$ is the mean and n is the number of observations.

$Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}$

$Mean =\displaystyle\frac{10959}{25} =438.36$

Sum of squares of differences = 175413.76

$S.D = \sqrt{\dfrac{175413.76}{24}} = 85.49$

Population mean, μ = 425 mg/L

Sample mean, $\bar{x}$ = 438.36

Sample size, n = 25

Alpha, α = 0.05

Sample standard deviation, s = 85.49

First, we design the null and the alternate hypothesis

$H_{0}: \mu \geq 425\text{ mg per Litre}\\H_A: \mu < 425\text{ mg per Litre}$

We use one-tailed t test to perform this hypothesis.

Formula:

$t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}} }$

Putting all the values, we have

$t_{stat} = \displaystyle\frac{438.36 - 425}{\frac{85.49}{\sqrt{25}} } = 0.7813$

Now, $t_{critical} \text{ at 0.05 level of significance, 24 degree of freedom } = -1.7108$

Since,

The calculated t-statistic is greater than the critical value, we fail to reject the null hypothesis and accept it.

Thus, the mean water hardness of lakes in Kansas is 425 mg/L or greater.

6 0

3 years ago

- Draw a line AB 8 cm long. What is the locus of a point C such that the angle ACB is always a right angle?

bagirrra123 [75]

Answer:

1)Air transportation:Air Transportation

Transportation mode

Air transportation means the business of transporting natural persons, property, cargo and mail by aircraft. ... Air transportation means the operation of a transportation system by aircraft for the carriage of persons, property and mail, including activities reasonably necessary to such operation.

2)Road transportation:Road transport or road transportation is a type of transport using roads. Transport on roads can be roughly grouped into the transportation of goods and transportation of people. In many countries licensing requirements and safety regulations ensure a separation of the two industries

3)Rail transportation:Rail transport is a means of transferring passengers and goods on wheeled vehicles running on rails, which are located on tracks. In contrast to road transport, where the vehicles run on a prepared flat surface, rail vehicles are directionally guided by the tracks on which they run.

4)Water transportation:Water transportation is the intentional movement of water over large distances. Methods of transportation fall into three categories: Aqueducts, which include pipelines, canals, tunnels and bridges. ... Towing, where a tugboat is used to pull an iceberg or a large water bag along behind it.

5 0

2 years ago

Select one of the factors of 5x2 + 7x + 2. a. (5x − 2) b. (x + 2) c. (5x + 1) d. None of the above

Elan Coil [88]

$5x^{2}+7x+2=5x^{2}+5x+2x+2=5x(x+1)+2(x+1)= \\ \\ (5x+2)(x+1)$

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7 0

4 years ago

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