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
32 answers
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.
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.
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
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.
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.
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.
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
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.
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
6.8
6.9
7.0
7.1
To estimate √47 to the nearest tenth, we need to find a number whose square is closest to, but less than, 47.
The square of 6 is 36, and the square of 7 is 49. Since 47 is closer to 49, the best estimate of √47 is the square root of 49, which is 7.
Therefore, the best estimate of √47 to the nearest tenth is 7.0.
The square of 6 is 36, and the square of 7 is 49. Since 47 is closer to 49, the best estimate of √47 is the square root of 49, which is 7.
Therefore, the best estimate of √47 to the nearest tenth is 7.0.
Chelsea is making a kite in the shape of a triangle. To determine if the triangle is a right triangle, Chelsea completed the following steps.
Step 1:
Find the side lengths of the triangle: 30 inches, 24 inches, 18 inches.
Step 2:
Substitute the values into the Pythagorean theorem: 18 squared + 24 squared = 30 squared.
Step 3:
Combine like terms: (18 + 24) squared = 30 squared.
Step 4:
Evaluate each side: 1764 not-equals 900.
Chelsea says the triangle is not a right triangle. Which best describes the accuracy of her explanation?
The triangle is actually a right triangle. In step 2, Chelsea incorrectly substituted the values into the Pythagorean theorem.
The triangle is not a right triangle, but in step 2 Chelsea incorrectly substituted the values into the Pythagorean theorem.
The triangle is actually a right triangle. In step 3, Chelsea incorrectly rewrote the expression on the left side of the equation.
The triangle is not a right triangle, but in step 3, Chelsea incorrectly rewrote the expression on the left side of the equation.
Step 1:
Find the side lengths of the triangle: 30 inches, 24 inches, 18 inches.
Step 2:
Substitute the values into the Pythagorean theorem: 18 squared + 24 squared = 30 squared.
Step 3:
Combine like terms: (18 + 24) squared = 30 squared.
Step 4:
Evaluate each side: 1764 not-equals 900.
Chelsea says the triangle is not a right triangle. Which best describes the accuracy of her explanation?
The triangle is actually a right triangle. In step 2, Chelsea incorrectly substituted the values into the Pythagorean theorem.
The triangle is not a right triangle, but in step 2 Chelsea incorrectly substituted the values into the Pythagorean theorem.
The triangle is actually a right triangle. In step 3, Chelsea incorrectly rewrote the expression on the left side of the equation.
The triangle is not a right triangle, but in step 3, Chelsea incorrectly rewrote the expression on the left side of the equation.
The triangle is actually a right triangle. In step 3, Chelsea incorrectly rewrote the expression on the left side of the equation.
The correct step would be to square each side individually, rather than squaring the sum of 18 and 24. Therefore, Step 3 should be:
(18 squared) + (24 squared) = 30 squared
By correctly evaluating each side, Chelsea would find that 900 does equal 900, indicating that the triangle is indeed a right triangle.
The correct step would be to square each side individually, rather than squaring the sum of 18 and 24. Therefore, Step 3 should be:
(18 squared) + (24 squared) = 30 squared
By correctly evaluating each side, Chelsea would find that 900 does equal 900, indicating that the triangle is indeed a right triangle.
Jeremy is trying to explain why a triangle with side lengths 35, 30, 60 is not a right triangle. His explanation is shown below.
Step 1: 35 squared + 30 squared question mark equals 60 squared
Step 2: (35 + 30) squared question mark equals 60 squared
Step 3: 65 squared question mark equals 60 squared
Step 4: 4,225 not-equals 3,600
Which best describes Jeremy’s explanation?
Jeremy’s explanation is accurate.
Jeremy’s explanation is inaccurate. He wrote the leg lengths in the incorrect order in step 1.
Jeremy’s explanation is inaccurate. He incorrectly combined terms in step 2.
Jeremy’s explanation is inaccurate. He multiplied incorrectly in step 4.
Step 1: 35 squared + 30 squared question mark equals 60 squared
Step 2: (35 + 30) squared question mark equals 60 squared
Step 3: 65 squared question mark equals 60 squared
Step 4: 4,225 not-equals 3,600
Which best describes Jeremy’s explanation?
Jeremy’s explanation is accurate.
Jeremy’s explanation is inaccurate. He wrote the leg lengths in the incorrect order in step 1.
Jeremy’s explanation is inaccurate. He incorrectly combined terms in step 2.
Jeremy’s explanation is inaccurate. He multiplied incorrectly in step 4.
Jeremy’s explanation is inaccurate. He wrote the leg lengths in the incorrect order in step 1.
To use the Pythagorean theorem, the equation should be:
30 squared + 35 squared = 60 squared
By correcting the order of the leg lengths, Jeremy would have a more accurate explanation.
To use the Pythagorean theorem, the equation should be:
30 squared + 35 squared = 60 squared
By correcting the order of the leg lengths, Jeremy would have a more accurate explanation.
Which of these four sets of side lengths will form a right triangle?
Set 1
6 cm, 7 cm, StartRoot 12 EndRoot cm
Set 2
8 in., StartRoot 29 EndRoot in., StartRoot 35 EndRoot in.
Set 3
StartRoot 3 EndRoot mm, 4 mm, StartRoot 5 EndRoot mm
Set 4
9 ft, StartRoot 26 EndRoot ft, 6 ft
Set 1
Set 2
Set 3
Set 4
Set 1
6 cm, 7 cm, StartRoot 12 EndRoot cm
Set 2
8 in., StartRoot 29 EndRoot in., StartRoot 35 EndRoot in.
Set 3
StartRoot 3 EndRoot mm, 4 mm, StartRoot 5 EndRoot mm
Set 4
9 ft, StartRoot 26 EndRoot ft, 6 ft
Set 1
Set 2
Set 3
Set 4
Set 3 (√3 mm, 4 mm, √5 mm) will form a right triangle because it satisfies the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
For Set 3, (√3)^2 + (4)^2 = (√5)^2 simplifies to 3 + 16 = 5, which is true.
Therefore, the side lengths in Set 3 will form a right triangle.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
For Set 3, (√3)^2 + (4)^2 = (√5)^2 simplifies to 3 + 16 = 5, which is true.
Therefore, the side lengths in Set 3 will form a right triangle.
Which equation can be used to find the unknown length, b, in this triangle?
A right triangle has a side with length 4 inches and hypotenuse with length 5 inches. The other side is labeled b.
4 squared + b squared = 5 squared
4 squared minus b squared = 5 squared
5 squared + 4 squared = b squared
5 squared + b squared = 4 squared
A right triangle has a side with length 4 inches and hypotenuse with length 5 inches. The other side is labeled b.
4 squared + b squared = 5 squared
4 squared minus b squared = 5 squared
5 squared + 4 squared = b squared
5 squared + b squared = 4 squared
The equation that can be used to find the unknown length, b, in this triangle is:
4 squared + b squared = 5 squared
4 squared + b squared = 5 squared
What is the length of the missing leg in this right triangle?
A right triangle has a side with length 7 millimeters and hypotenuse with length 25 millimeters.
18 mm
24 mm
26 mm
32 mm
A right triangle has a side with length 7 millimeters and hypotenuse with length 25 millimeters.
18 mm
24 mm
26 mm
32 mm
To find the length of the missing leg in a right triangle, we can use the Pythagorean theorem. The theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
Let's call the missing leg length "b".
Using the Pythagorean theorem, we can set up the equation:
b^2 + 7^2 = 25^2.
Simplifying the equation, we have:
b^2 + 49 = 625.
Subtracting 49 from both sides:
b^2 = 576.
Taking the square root of both sides:
b = √576 = 24.
Therefore, the length of the missing leg in this right triangle is 24 mm.
Let's call the missing leg length "b".
Using the Pythagorean theorem, we can set up the equation:
b^2 + 7^2 = 25^2.
Simplifying the equation, we have:
b^2 + 49 = 625.
Subtracting 49 from both sides:
b^2 = 576.
Taking the square root of both sides:
b = √576 = 24.
Therefore, the length of the missing leg in this right triangle is 24 mm.
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.how many people participated in the walk
2.how many of the walkers traveled more than 14 kilometers
pleas explain
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.how many people participated in the walk
2.how many of the walkers traveled more than 14 kilometers
pleas explain
To find the number of participants in the walk, we need to count the number of entries in the given table for the different kilometers.
1. Counting the entries:
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
Counting the number of entries in each row:
12: 7 participants
13: 5 participants
14: 8 participants
15: 9 participants
16: 5 participants
17: 2 participants
Therefore, the total number of people who participated in the walk is:
7 + 5 + 8 + 9 + 5 + 2 = 36 people.
2. To find the number of walkers who traveled more than 14 kilometers, we need to count the number of entries for kilometers greater than 14.
Counting the number of entries greater than 14:
15: 9 participants
16: 5 participants
17: 2 participants
Adding up the number of participants:
9 + 5 + 2 = 16 walkers traveled more than 14 kilometers.
Therefore, there were 16 walkers who traveled more than 14 kilometers.
1. Counting the entries:
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
Counting the number of entries in each row:
12: 7 participants
13: 5 participants
14: 8 participants
15: 9 participants
16: 5 participants
17: 2 participants
Therefore, the total number of people who participated in the walk is:
7 + 5 + 8 + 9 + 5 + 2 = 36 people.
2. To find the number of walkers who traveled more than 14 kilometers, we need to count the number of entries for kilometers greater than 14.
Counting the number of entries greater than 14:
15: 9 participants
16: 5 participants
17: 2 participants
Adding up the number of participants:
9 + 5 + 2 = 16 walkers traveled more than 14 kilometers.
Therefore, there were 16 walkers who traveled more than 14 kilometers.
Stephanie collected data about the high temp in her city for 7 days in a row .the high temp for the 7 days were 70,78,85,73,78,89 she made the following graph to show her data she says the temp in in her city is pretty consistent how could she redraw the graph so that the daily temp doesn't seem quit so consistent
To redraw the graph so that the daily temperature doesn't seem as consistent, Stephanie can adjust the scale of the graph or use a different type of graph altogether. Here are a few suggestions:
1. Adjust the scale: Stephanie can change the vertical scale of the graph to exaggerate the differences in temperature. By expanding the range, even small variations in temperature will be magnified, giving the appearance of less consistency.
2. Use a line graph with data points: Instead of connecting the data points with straight lines, Stephanie can represent each data point as individual markers on the graph. This will show the distinct values for each day and highlight the variations.
3. Use a box plot: A box plot, also known as a box and whisker plot, displays the distribution of a dataset. Stephanie can create a box plot for the daily high temperatures, which will show the median, quartiles, and any outliers. This will provide a visual representation of the variability in the data.
By implementing these suggestions, Stephanie can accurately represent the variation in daily temperatures in her city, making the graph appear less consistent.
1. Adjust the scale: Stephanie can change the vertical scale of the graph to exaggerate the differences in temperature. By expanding the range, even small variations in temperature will be magnified, giving the appearance of less consistency.
2. Use a line graph with data points: Instead of connecting the data points with straight lines, Stephanie can represent each data point as individual markers on the graph. This will show the distinct values for each day and highlight the variations.
3. Use a box plot: A box plot, also known as a box and whisker plot, displays the distribution of a dataset. Stephanie can create a box plot for the daily high temperatures, which will show the median, quartiles, and any outliers. This will provide a visual representation of the variability in the data.
By implementing these suggestions, Stephanie can accurately represent the variation in daily temperatures in her city, making the graph appear less consistent.
use the infromation from this table to answer the questions
year sales ($millions)
1998 45
1999 5
2000 15
2001 30
2002 50
which would be the best way the data---a bar graph, a histogram or a line graph justify your answer
year sales ($millions)
1998 45
1999 5
2000 15
2001 30
2002 50
which would be the best way the data---a bar graph, a histogram or a line graph justify your answer
Based on the given information in the table, the best way to represent the data would be a line graph.
A line graph is useful for displaying data that changes over time or in a sequence, which is the case in this table where the sales are recorded for different years.
Using a line graph, the x-axis can represent the years, and the y-axis can represent the sales in millions of dollars. By connecting the data points with a line, a line graph can show the trend or pattern of the sales over the years.
In this case, a line graph would effectively depict the sales progression from 1998 to 2002, and provide a clear visualization of any changes or fluctuations in the sales over time. A bar graph or histogram may not be as suitable, as they are typically used to represent discrete or categorical data, rather than a continuous progression as seen in this data set.
A line graph is useful for displaying data that changes over time or in a sequence, which is the case in this table where the sales are recorded for different years.
Using a line graph, the x-axis can represent the years, and the y-axis can represent the sales in millions of dollars. By connecting the data points with a line, a line graph can show the trend or pattern of the sales over the years.
In this case, a line graph would effectively depict the sales progression from 1998 to 2002, and provide a clear visualization of any changes or fluctuations in the sales over time. A bar graph or histogram may not be as suitable, as they are typically used to represent discrete or categorical data, rather than a continuous progression as seen in this data set.
Justine went swimming six days this week at her local pool use the following lengths of time spent at the pool to determine the mean absolute deviation
40,50,90,60,80,70,
40,50,90,60,80,70,
To find the mean absolute deviation (MAD), follow these steps:
1. Find the mean (average) of the set of lengths of time:
40 + 50 + 90 + 60 + 80 + 70 = 390
390 ÷ 6 = 65
2. Subtract the mean from each length of time to find the deviations from the mean:
40 - 65 = -25
50 - 65 = -15
90 - 65 = 25
60 - 65 = -5
80 - 65 = 15
70 - 65 = 5
3. Take the absolute value of each deviation (ignore the negative signs):
|-25| = 25
|-15| = 15
|25| = 25
|-5| = 5
|15| = 15
|5| = 5
4. Calculate the mean of the absolute deviations:
(25 + 15 + 25 + 5 + 15 + 5) ÷ 6 = 90 ÷ 6 = 15
The mean absolute deviation of the lengths of time spent at the pool is 15.
1. Find the mean (average) of the set of lengths of time:
40 + 50 + 90 + 60 + 80 + 70 = 390
390 ÷ 6 = 65
2. Subtract the mean from each length of time to find the deviations from the mean:
40 - 65 = -25
50 - 65 = -15
90 - 65 = 25
60 - 65 = -5
80 - 65 = 15
70 - 65 = 5
3. Take the absolute value of each deviation (ignore the negative signs):
|-25| = 25
|-15| = 15
|25| = 25
|-5| = 5
|15| = 15
|5| = 5
4. Calculate the mean of the absolute deviations:
(25 + 15 + 25 + 5 + 15 + 5) ÷ 6 = 90 ÷ 6 = 15
The mean absolute deviation of the lengths of time spent at the pool is 15.
what is the interquartile range for this set of numbers
18,19,22,22,25,25,26,31,32,34,37,37,37,
18,19,22,22,25,25,26,31,32,34,37,37,37,
To find the interquartile range (IQR) for the given
what is the interquartile range for this set of numbers
18,19,22,22,25,25,26,31,32,34,37,37,37
answer
a.12.5
b.13.3
c.19.0
d.26.0
18,19,22,22,25,25,26,31,32,34,37,37,37
answer
a.12.5
b.13.3
c.19.0
d.26.0
1 answer