Answer:
In set-builder notation, the set of solutions is:
![\left \{u|-3](https://tex.z-dn.net/?f=%5Cleft%20%5C%7Bu%7C-3%3Cu%3C7%5Cright%5C%7D)
Step-by-step explanation:
Let's start by isolating the absolute value expression on one side of the inequality:
8 | u - 2 | - 7 < 33
add 7 on both sides:
8 | u - 2 | < 40
divide both sides by 8:
| u - 2 | < 5
Now, in order to remove the absolute value symbols, we need to consider two different cases:
1) what is inside the absolute value symbols is larger than or equal to zero, so in such case when we remove the absolute value we get exactly what was inside:
u - 2 < 5
u < 5 + 2
u < 7
Now the other case;
2) what is inside the absolute value is smaller than zero, then when removing the symbols we get:
2 - u < 5
2 - 5 < u
-3 < u
Then the set of solutions of this inequality are the set of u values such that u is larger than -3 (to the right of -3 on the number line, and smaller than 7 (to the left of the number 7 on the number line.
In graph form this should look like a highlighted segment on the number line that starts at -3 on the left, ends at 7 on the right, and doesn't include the endpoints -3 and 7.
in set builder notation, the set of solutions is given by:
![\left \{u|-3](https://tex.z-dn.net/?f=%5Cleft%20%5C%7Bu%7C-3%3Cu%3C7%5Cright%5C%7D)
Answer:
She will need 4 square and 8 triangular pieces.
Step-by-step explanation:
For every 6 pieces of cloth, 2 are squares.
So, for 12 pieces of cloth, the no. of square pieces would be,
![12 \times \frac {2}{6}](https://tex.z-dn.net/?f=12%20%5Ctimes%20%5Cfrac%20%7B2%7D%7B6%7D)
= ![2 \times 2](https://tex.z-dn.net/?f=2%20%5Ctimes%202)
= 4
As the remaining pieces will be triangles, so the no. of triangular pieces will be, equal to,
(12 - 4) = 8
Answer: The giraffe is 1.5 times tall as the zookeeper.
Step-by-step explanation:
Given: Height of Giraffe = ![9\dfrac38\ feet =\dfrac{72+3}{8}\ feet =\dfrac{75}{8}\ feet](https://tex.z-dn.net/?f=9%5Cdfrac38%5C%20feet%20%3D%5Cdfrac%7B72%2B3%7D%7B8%7D%5C%20feet%20%3D%5Cdfrac%7B75%7D%7B8%7D%5C%20feet)
Height of zookeeper= ![6\dfrac14\ feet =\dfrac{24+1}{4}\ feet =\dfrac{25}{4}\ feet](https://tex.z-dn.net/?f=6%5Cdfrac14%5C%20feet%20%3D%5Cdfrac%7B24%2B1%7D%7B4%7D%5C%20feet%20%3D%5Cdfrac%7B25%7D%7B4%7D%5C%20feet)
Let <em>n</em> = number of times the giraffe is tall as the zookeeper.
![n=\dfrac{\dfrac{75}{8}}{\dfrac{25}{4}}=\dfrac{75\times4}{25\times8} = 1.5](https://tex.z-dn.net/?f=n%3D%5Cdfrac%7B%5Cdfrac%7B75%7D%7B8%7D%7D%7B%5Cdfrac%7B25%7D%7B4%7D%7D%3D%5Cdfrac%7B75%5Ctimes4%7D%7B25%5Ctimes8%7D%20%3D%201.5)
Hence, the giraffe is 1.5 times tall as the zookeeper.
First step is to convert feet to kilometers. 2 kilometers is approximately equal to 6,560 ft.
Keeping that number in mind, we need to find the circumference of the circle. We need this number because that is the exact distance the wheel will travel in a single revolution. We can use the equation c=pi(d) to get it, or use the more commonly cited formula c=2pi(r), with a few added steps. Since we're given the diameter, not the radius, the first formula makes more sense.
The circumference is roughly equal to 6.28. That means the bike travels 6.28 feet for every complete revolution. Since that's 6.28 feet for every SINGLE revolution, we can simply divide the total distance the bike traveled (6560 ft) by the distance which it travels per revolution (6.28).
6560 ft divided by 6.28 ft/1 revolution = 1044.59 revolutions.