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3 years ago

Where can you find the hypotenuse of a right triangle

Mathematics

2 answers:

galina1969 [7]3 years ago

7 0

Answer:

Opposite to the 90 degree angle.

Step-by-step explanation:

the hypotenuse is always the longest side with right triangles its always opposite of the right angle

goldenfox [79]3 years ago

6 0

Answer:

In geometry, a hypotenuse is the longest side of a right-angled triangle, the side opposite the right angle.

Step-by-step explanation:

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Normal Distribution

MariettaO [177]

Answer:

Step-by-step explanation:

<u>Explanation</u>:-

The graph of the normal distribution y = f(x) in the x y- plane is known as normal curve.The curve is bell shaped and symmetrical about the line x = μ

So The first statement is not true because symmetrical about the line x = μ not 'm'

Area under normal curve represents the total population

so the total area under the curve is 100 or one so The second statement is true

The normal distribution for mean is zero and standard deviation is one is known as standard normal distribution.

95 percentage within two standard deviations
99.7 percentage of the data are within three standard deviations of the mean.
68 percentage of the data are within one standard deviation

All above points are true so In given data the third statement is not true

95 percentage within two standard deviations not one

The fourth statement is false because 68 percentage of the data are within one standard deviation not 34 percentage.

All data sets are normally distributed its depend on given data

3 0

3 years ago

Read 2 more answers

Liz works at a movie theater. Her hourly wage increased from $14.50 to $18 and hour. What was the percent of increase in her hou

melomori [17]

I believe it is 124%

8 0

3 years ago

Read 2 more answers

A Norman window has the shape of a rectangle surmounted by a semicircle. Suppose the outer perimeter of such a window must

Feliz [49]

The base length that will maximize the area for such a window is 168.03 cm. The exact largest value of x when this occurs is 233.39 cm

Suppose we make an assumption that:

(x) should be the width of the rectangle base;
(h) should be the height of the rectangle

Also, provided that the diameter of the semi-circle appears to be the base of the rectangle, then;

the radius $\mathbf{r = \dfrac{x}{2}}$

and, the perimeter of the window can now be expressed as:

$\mathbf{x + 2h + \pi r = x + 2h + \dfrac{\pi x }{2}}$

$\mathbf{= \Big ( 1 + \dfrac{\pi}{2}\Big) x + 2h}$

Given that the perimeter = 600 cm

∴

$\mathbf{ \Big ( 1 + \dfrac{\pi}{2}\Big) x + 2h= 600}$

$\mathbf{ h = 300 - \Big( \dfrac{1}{2} + \dfrac{\pi}{4}\Big) x}$

Since h > 0, then:

$\mathbf{ h = 300 - \Big( \dfrac{1}{2} + \dfrac{\pi}{4}\Big) x>0}$

By rearrangement and using the inverse rule:

$\mathbf{ x< \dfrac{ 300}{\Big( \dfrac{1}{2} + \dfrac{\pi}{4}\Big) } }$

$\mathbf{ x= \dfrac{ 1200}{\Big( 2 +\pi \Big) } }$

$\mathbf{ x= 233.39 \ cm }$

Thus, the largest length x = 233.39 cm

However, the area of the window is given as:

$\mathbf{A(x) = xh + \dfrac{1}{2} \pi r^2}$

$\mathbf{A = x \Big [ 300 - \Big ( \dfrac{1}{2}+\dfrac{1}{4} \Big) x \Big ] +\dfrac{1}{2}\pi \Big(\dfrac{x}{2} \Big )^2}$

$\mathbf{A (x) = 300x - \Big( \dfrac{1}{2} + \dfrac{\pi}{8}\Big) x^2 \ cm^2}$

Now, at maximum, when the area A = 0. Taking the differentiation, we have:

$\mathbf{\dfrac{d}{dx} 300x - \dfrac{d}{dx} \Big( \dfrac{1}{2} + \dfrac{\pi}{8}\Big) x^2 \ =0}$

$\mathbf{ 300 - 2x \Big( \dfrac{1}{2} + \dfrac{\pi}{8}\Big) \ =0}$

Making x the subject of the formula, we have:

$\mathbf{x = \dfrac{1200}{4 +\pi}}$

x = 168.03 cm

Taking the second derivative:

$\mathbf{\dfrac{d}{dx} \Big [300 -2x \Big( \dfrac{1}{2} + \dfrac{\pi}{8}\Big) \Big]}$

$\mathbf{= -2 \Big( \dfrac{1}{2}+\dfrac{\pi}{8}\Big )$

Therefore, we can conclude that the maximum area that exists for such a window is 168.03 cm

Learn more about derivative here:

brainly.com/question/9964510?referrer=searchResults

6 0

3 years ago

Solve for x in the equation x² - 4x - 9 = 29.

alexandr1967 [171]

Answer: First option.

Step-by-step explanation:

1. To solve this problem you can applly the quadratic formula, which is shown below:

$x=\frac{-b+/-\sqrt{b^{2}-4ac}}{2a}$

2. The quadratic equation is:

$x^{2}-4x-9-29=0\\x^{2}-4x-38=0$

3. Then:

a=1

b=-4

c=-38

4. Therefore, when you substitute these values into the quadratic formula, you obtain the following result:

$x=\frac{-(-4)+/-\sqrt{(-4)^{2}-4(1)(-38)}}{2(1)}$

x=2±√42

7 0

3 years ago

Read 2 more answers

Find the GCF

Kaylis [27]

Greatest Common Factor. let's go over that. GCF of 6 and 12 would be 6 because 6 goes into 6, 1 times and 6 goes into 12, 2 times. . and it is the largest. so first you see if the lower number can go directly into the higher number. So 28a^2 b^2 c^2, is made of 14abc× 2abc. so you can say 14abc goes into 28a2b2c2, 2abc times. therefore 14abc is the largest factor.

7 0

3 years ago