What is the length of the hypotenuse of the triangle?
Triangle A B C. Side A C is 7 feet and side C B is 4 feet. Hypotenuse A B is unknown.
StartRoot 22 EndRoot ft
StartRoot 33 EndRoot ft
StartRoot 57 EndRoot ft
StartRoot 65 EndRoot ft
The length of the hypotenuse of the triangle is √65 ft.
Lewis needed to find the difference in lengths between the hypotenuse and the longest leg of this triangle. His work is shown below.
Triangle A B C. Side B C is 16 and side A C is 12. Hypotenuse A B is labeled c.
12 squared + 16 squared = c squared. 144 + 256 = c squared. 400 = c squared. StartRoot 400 EndRoot = c. 200 = c. Difference: 200 minus 12 = 188.
What errors did Lewis make? Check all that apply.
He simplified StartRoot 400 EndRoot incorrectly. It should be 20 instead of 200.
He found the difference between the hypotenuse and the short leg instead of the long leg.
He evaluated 12 squared incorrectly. It should be 12 (2) = 24.
He evaluated 16 squared incorrectly. It should be 16 (2) = 32.
He should not have taken the square root of each side to get rid of the exponent.
The errors Lewis made are:
1. He simplified √400 incorrectly. It should be 20 instead of 200.
2. He found the difference between the hypotenuse and the shorter leg instead of the longer leg.
kilometers walked for charity
12|3,3,3,6,7,9,9
13|1,1,4,5,5
14|0,0,2,3,3,8,8,9
15|2,2,2,2,2,3,5,5,7
16|4,5,5,9,9
17|3,5
key 3 means 12.3
1.describe how to find the range of the data set
2.find the range
pleas explain
1. To find the range of a data set, you need to determine the difference between the largest and smallest values in the set. This provides a measure of the spread or variability in the data.
2. Let's find the range for the given data set:
12|3,3,3,6,7,9,9
13|1,1,4,5,5
14|0,0,2,3,3,8,8,9
15|2,2,2,2,2,3,5,5,7
16|4,5,5,9,9
17|3,5
The largest value in the data set is 17, and the smallest value is 0. To find the range, subtract the smallest value from the largest value:
Range = 17 - 0 = 17
Therefore, the range of the data set is 17 kilometers.
oseph and Isabelle left Omyra’s house at the same time. Joseph jogged north at 8 kilometers per hour, while Isabelle rode her bike west at 12 kilometers per hour. Omyra tried to figure out how far apart they were after 1.5 hours. Her work is shown below. Which statements describe her errors? Check all that apply.
A right triangle. The distance north from Omyra's House is 8 kilometers, and the distance west is 12 kilometers.
8 squared + 12 squared = d squared. 64 + 24 = d squared. 88 = d squared. StartRoot 88 EndRoot = d. 9.4 almost-equals d.
She did not find the full distance each traveled in 1.5 hours. She should have used 12 km for Joseph’s distance and 18 km for Isabelle’s distance.
She did not square the 12 in the problem. She should have used 12 squared = 144.
She did not evaluate 8 squared correctly. She should have used 8 squared = 8 (2) = 16.
She did not evaluate StartRoot 88 EndRoot correctly. She should have used StartRoot 88 EndRoot almost-equals 44.
She should not have taken the square root of each side when solving. She should have just divided each side by 2.
She should not have added the squares in the first step. She should have used 12 squared minus 8 squared = d squared.
The errors made by Omyra are:
1. She did not find the full distance each traveled in 1.5 hours. She should have used 12 km for Joseph’s distance and 18 km for Isabelle’s distance.
2. She did not square the 12 in the problem. She should have used 12 squared = 144.
3. She did not evaluate 8 squared correctly. She should have used 8 squared = 8 (2) = 16.
4. She did not evaluate √88 correctly. She should have used √88 ≈ 9.4
5. She should not have added the squares in the first step. She should have used 12 squared minus 8 squared = d squared.
The values StartRoot 12 EndRoot and StartRoot 15 EndRoot are plotted on the number line.
A number line going from 0 to 4. StartRoot 12 EndRoot is to the right of 3, and StartRoot 15 EndRoot is to the right of StartRoot 12 EndRoot.
What is the approximate difference in tenths between StartRoot 12 EndRoot and StartRoot 15 EndRoot?
0.2
0.4
1.5
1.7
To find the approximate difference in tenths between √12 and √15, we can subtract the value of √12 from the value of √15.
The value of √12 is approximately 3.46, and the value of √15 is approximately 3.87.
Subtracting 3.46 from 3.87 gives us approximately 0.41.
Since we are asked to approximate the difference in tenths, we can round 0.41 to the nearest tenth, which is 0.4.
Therefore, the approximate difference in tenths between √12 and √15 is 0.4.
Which is the best estimate of StartRoot 47 EndRoot to the nearest tenth?
6.8
6.9
7.0
7.1