Answer:
175 feet
Step-by-step explanation:
In 1 full revolution, the bike will travel 42 inches because the diameter of the tire is 21 inches. Any point on the tire will have to go through a whole revolution to be back at the original point which means 21 inches times 2.
So the bike travels 42 inches in 1 revolution then in 50 revolutions it will travel 2100 inches (42 times 50). Now if your convert 2100 inches to feet, you get 175 feet.
Answer:
9984 cm³
Step-by-step explanation:
2496 ÷ 1/4
The image shows how to divide, but we get 9984 cm³
This question is solved applying the formula of the area of the rectangle, and finding it's width. To do this, we solve a quadratic equation, and we get that the cardboard has a width of 1.5 feet.
Area of a rectangle:
The area of rectangle of length l and width w is given by:

w(2w + 3) = 9
From this, we get that:

Solving a quadratic equation:
Given a second order polynomial expressed by the following equation:
.
This polynomial has roots
such that
, given by the following formulas:
In this question:


Thus a quadratic equation with 
Then


Width is a positive measure, thus, the width of the cardboard is of 1.5 feet.
Another similar problem can be found at brainly.com/question/16995958
Step-by-step explanation:
5.
angle STQ is the supplementary angle (together they are 180° below line MQ) to 2x + 8.
above ST we have a group of 3 angles that combine to 180° :
2x + 8
90°
71 - x
so, to get x first :
2x + 8 + 90 + 71 - x = 180
x + 169 = 180
x = 11
so, the angle MTS =
2x + 8 = 2×11 + 8 = 22 + 8 = 30°.
6.
therefore, the angle STQ is
180 - angle MTS = 180 - 30 = 150°.
<h2>
Answer with explanation:</h2>
We are asked to prove by the method of mathematical induction that:

where n is a positive integer.
then we have:

Hence, the result is true for n=1.
- Let us assume that the result is true for n=k
i.e.

- Now, we have to prove the result for n=k+1
i.e.
<u>To prove:</u> 
Let us take n=k+1
Hence, we have:

( Since, the result was true for n=k )
Hence, we have:

Also, we know that:

(
Since, for n=k+1 being a positive integer we have:
)
Hence, we have finally,

Hence, the result holds true for n=k+1
Hence, we may infer that the result is true for all n belonging to positive integer.
i.e.
where n is a positive integer.