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3 years ago

What is the slope of the line defined by the equation y = 8?

Mathematics

2 answers:

Zielflug [23.3K]3 years ago

8 0

1 because its a straight line<span />

Harlamova29_29 [7]3 years ago

7 0

Y = 8 slope = 0

answer
slope = 0

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Y varies directly with x , and x=3 when y=16 . What is x when y=40

svetlana [45]

Answer:

X=7.5

Step-by-step explanation:

8 0

3 years ago

One ordered pair (a,b) satisfies the two equations ab^4 = 12 and a^5 b^5 = 7776. What is the value of 'a' in this ordered pair?

Ivan

Answer:

a = 4.762203156

Step-by-step explanation:

Given:

ab^4 = 12 and a^5b^5 = 7776

Making the equations a subject of a;

a = 12/b^4 and a^5 = 7776/b^5

Finding fifth root on both sides of equation two;

a = $\sqrt[5]{7776}$ /b

You will get a = 6/b

Equating the two equations;

12/b^4 = 6/b

Multiplying both sides by b^4 gives:

b = $\sqrt[3]{2}$ = 1.25992105

We had that a = 12/b^4 so;

a = 12/1.25992105^4 = 12/2.5198421 = 4.762203156

4 0

3 years ago

Use DeMoivre's Theorem to find the indicated power of the complex number. Write answers in rectangular form. [one half (cosine

Morgarella [4.7K]

Answer:

$(\, \cos(\frac{\pi}{16}) + i\sin(\frac{\pi}{16}) \,)^{1/2} = \cos(\frac{\pi}{32}) + i\sin(\frac{\pi}{32}) = 0.99 + i0.09$

Step-by-step explanation:

The complex number given is

$z = (\, \cos(\frac{\pi}{16}) + i\sin(\frac{\pi}{16}) \,)^{1/2}$

Now, remember that the DeMoivre's theorem states that

$( \cos(x) + i\sin(x) )^n = \cos(nx) + i\sin(nx)$

Then for this case we have that

$(\, \cos(\frac{\pi}{16}) + i\sin(\frac{\pi}{16}) \,)^{1/2} = \cos(\frac{\pi}{32}) + i\sin(\frac{\pi}{32}) = 0.99 + i0.09$

7 0

3 years ago

The length of a rectangle is 9 centimeters more than half

Sedaia [141]

Answer:

l = 16 cm

Step-by-step explanation:

Let's set the width of the rectangle as "w" and the length of the rectangle as "w/2 + 9".

The perimeter of a rectangle is calculated by adding up the value of all of its side lengths. Therefore, we can find the perimeter using 2l + 2w = P.

We can substitute 60 for P and w/2 + 9 for l.

2(w/2 + 9) + 2w = 60
2w/2 + 18 + 2w = 60
w + 18 + 2w = 60
3w + 18 = 60
3w = 42
w = 14

Substitute w = 14 into the equation for length l.

l = w/2 + 9
l = 14/2 + 9
l = 16

The length of the rectangle is 16 cm.

4 0

3 years ago

assume that women's heights are normally distributed with a mean of 63.6 inches and a standard deviation of 2.5 inches. find the

drek231 [11]

Answer:

65.3658 inches

Step-by-step explanation:

Let X be the height of a woman randomly choosen. We know tha X have a mean of 63.6 inches and a standard deviation of 2.5 inches. For an x value, the related z-score is given by z = (x-63.6)/2.5. We are looking for a value $x_{0}$ such that $P(X < x_{0}) = 0.76$ , but, $0.76 = P(X < x_{0}) = P((X-63.6)/2.5 < (x_{0}-63.6)/2.5) = P(Z < (x_{0}-63.6)/2.5)$ , i.e., $(x_{0}-63.6)/2.5$ is the 76th percentile of the standard normal distribution. So, $(x_{0}-63.6)/2.5 = 0.7063$ , $x_{0} =63.6+(2.5)(0.7063) = 65.3658$ . Therefore, the height of a woman who is at the 76th percentile is 65.3658 inches.

7 0

3 years ago