An endurance athlete jogs at a rate of 5 miles per hour. How many minutes does it take for the athlete to jog 4.5 miles?

Can someone help me with 4 & 5 please :)

svp [43]

Hello there!

4).

125= total
77= constant (stays the same, doesn't change)
8= can change

So our equation will be 125= 77+8h

NOTE: The equal sign is actually a "greater than or equal to" symbol, which isn't a thing on phones lol.

Why? (Equation)

125 is our total. The money that Mrs. Byers pays will be exactly that or less than 125. Basically, it's her budget.

77 is a constant. It's a locked price. It doesn't change. But it's money she has to pay (not her budget). So it goes on the right side.

8h stands for 8 per hour, in this case. (Any letter/variable is fine, but h makes it easier to understand).

Why does 8 have an h? Because for every hour that passes by, Mrs. Byers has to pay 8 more dollars. So it goes on the right with the $77.

I hope this explanation helped! I don't want to solve it for you because I want you to understand WHY the equation is this way. As for solving for the answer, simply solve for h!
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Problem 5 is similar to 4. :)

I know these kinds of problems are challenging, and you probably hate them. Don't give up though! With practice and determination, these kinds of problems will be a piece of cake! :) I believe in you, and that you can do this assignment! Best of luck!

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DISCLAIMER: I am not a professional tutor or have any professional background in your subject. Please do not copy my work down, as that will only make things harder for you in the long run. Take the time to really understand this, and it'll make future problems easier. I am human, and may make mistakes, despite my best efforts. Again, I possess no professional background in your subject, so anything you do with my help will be your responsibility. Thank you for reading this, and have a wonderful day/night!

8 0

3 years ago

Lowering powers write in terms of first power of cosine. Cos^6

yaroslaw [1]

The main identity you need is the double angle one for cosine:

$\cos^2x=\dfrac{1+\cos2x}2$

We get

$\cos^6x=(\cos^2x)^3=\left(\dfrac{1+\cos2x}2\right)^3=\dfrac{(1+\cos2x)^3}8$

Expand the numerator to apply the identity again:

$\cos^6x=\dfrac{1+3\cos2x+3\cos^22x+\cos^32x}8$

$\cos^6x=\dfrac{1+3\cos2x+3\left(\frac{1+\cos2(2x)}2\right)+\cos2x\left(\frac{1+\cos2(2x)}2\right)}8$

$\cos^6x=\dfrac{1+3\cos2x+\frac32+\frac32\cos4x+\frac12\cos2x(1+\cos4x)}8$

$\cos^6x=\dfrac5{16}+\dfrac7{16}\cos2x+\dfrac3{16}\cos4x+\dfrac1{16}\cos2x\cos4x$

Finally, make use of the product identity for cosine:

$\cos2x\cos4x=\dfrac{\cos6x+\cos2x}2$

so that ultimately,

$\cos^6x=\dfrac5{16}+\dfrac7{16}\cos2x+\dfrac3{16}\cos4x+\dfrac1{32}\cos2x+\dfrac1{32}\cos6x$

$\cos^6x=\dfrac5{16}+\dfrac{15}{32}\cos2x+\dfrac3{16}\cos4x+\dfrac1{32}\cos6x$

4 0

3 years ago

The body of a great roadrunner is 16 in. Long and the tail is 8 in. Long. The total length of a great roadrunner is 4 times long

arlik [135]

Answer: Love bird is 4 inches long.

Step-by-step explanation:

Given: The body of a great roadrunner is 16 in. Long and the tail is 8 in.

Also, Total length of a great roadrunner is = 4 x (length of lovebird).

It implies, length of lovebird = $\dfrac{\text{length of lovebird}}{4}$

$=\dfrac{16}{4}=4\text{ inches}$

Hence, Love bird is 4 inches long.

8 0

2 years ago

What is the measure of EACH exterior angles t<br>of the polygon shown?

statuscvo [17]

Answer:

45 degrees

Step-by-step explanation:

The following shape is an octagon, having 8 sides and knowing that any regular polygon has an exterior angle value of 360 degrees, you can say 360/8 to find the measure of each exterior angle, leading to equal 45 degrees.

Hope it helped! (:

8 0

2 years ago

1/4 of febuary = ....... days

Alex Ar [27]

There are 28 days in February. Divide 28 by 4 and the answer is 7 days

8 0

3 years ago

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