The statements that are true about the unknown side length in this right triangle are:
- The equation a squared + (StartRoot 13 EndRoot) squared = 6 squared can be used to find the unknown length.
- The equation (StartRoot 13 EndRoot) squared + 6 squared = c squared can be used to find the unknown length.
Which statements are true about the unknown side length in this right triangle? Check all that apply.
A triangle with side StartRoot 13 EndRoot meters and hypotenuse of 6 meters.
The equation a squared + (StartRoot 13 EndRoot) squared = 6 squared can be used to find the unknown length.
The equation (StartRoot 13 EndRoot) squared + b squared + 6 squared can be used to find the unknown length.
The equation (StartRoot 13 EndRoot) squared + 6 squared = c squared can be used to find the unknown length.
The length of the unknown leg is StartRoot 23 EndRoot meters.
The length of the unknown leg is 7 meters.
22 answers
Nadine is making a quilt. She can use a rectangle of any length and width, as long as the angles in the shape are right angles. Which pieces of fabric can Nadine use in the quilt? Check all that apply.
Fabric 1
length: 5 cm
width: 12 cm
diagonal: 13 cm
Fabric 2
length: 8 cm
width: 6 cm
diagonal: 10 cm
Fabric 3
length: 4 cm
width: 5 cm
diagonal: 6 cm
Fabric 4
length: 10 cm
width: 8 cm
diagonal: 12 cm
Fabric 5
length: 6 cm
width: 4 cm
diagonal: 8 cm
Fabric 6
length: 8 cm
width: 15 cm
diagonal: 17 cm
Fabric 1
Fabric 2
Fabric 3
Fabric 4
Fabric 5
Fabric 6
Fabric 1
length: 5 cm
width: 12 cm
diagonal: 13 cm
Fabric 2
length: 8 cm
width: 6 cm
diagonal: 10 cm
Fabric 3
length: 4 cm
width: 5 cm
diagonal: 6 cm
Fabric 4
length: 10 cm
width: 8 cm
diagonal: 12 cm
Fabric 5
length: 6 cm
width: 4 cm
diagonal: 8 cm
Fabric 6
length: 8 cm
width: 15 cm
diagonal: 17 cm
Fabric 1
Fabric 2
Fabric 3
Fabric 4
Fabric 5
Fabric 6
The pieces of fabric that Nadine can use in the quilt are:
- Fabric 1
- Fabric 2
- Fabric 3
- Fabric 4
- Fabric 5
- Fabric 6
- Fabric 1
- Fabric 2
- Fabric 3
- Fabric 4
- Fabric 5
- Fabric 6
Jesse and Mark are jogging along the route shown at a rate of 12 miles per hour. They start by jogging south along Capitol Street for 1 mile, then turn east on H Street and jog for 1.75 miles. At that point, Jesse is tired and decides to walk home along Florida Avenue at a rate of 5 miles per hour. Mark plans to jog back the way they came. Jesse wants to find out who will arrive home first and by how much time. Which statements should he consider when solving the problem? Check all that apply.
A triangle. The sides are Capitol Street, H Street, and they hypotenuse is Florida Avenue.
Jesse will walk home a distance of approximately 2.0 miles as found by evaluating 1 squared + 1.75 squared = d squared and then 1 + 3.0625 = d squared.
Jesse will take about 0.4 hours to walk the rest of the way home as found by 2.0 = 5 (t).
Jesse will walk home a distance of approximately 2.25 miles as found by 1 squared + 1.75 squared = d squared and then 2 + 3.0625 = d squared.
Mark will jog home a distance of 2.75 miles.
It will take Mark about 0.23 hours to jog home as found by 2.75 = 12 (t).
Mark will jog home a distance of 2.25 miles.
Mark will get home about 0.17 hours (or 10 minutes) sooner.
Mark will get home about 0.21 hours (or 12.5 minutes) sooner.
A triangle. The sides are Capitol Street, H Street, and they hypotenuse is Florida Avenue.
Jesse will walk home a distance of approximately 2.0 miles as found by evaluating 1 squared + 1.75 squared = d squared and then 1 + 3.0625 = d squared.
Jesse will take about 0.4 hours to walk the rest of the way home as found by 2.0 = 5 (t).
Jesse will walk home a distance of approximately 2.25 miles as found by 1 squared + 1.75 squared = d squared and then 2 + 3.0625 = d squared.
Mark will jog home a distance of 2.75 miles.
It will take Mark about 0.23 hours to jog home as found by 2.75 = 12 (t).
Mark will jog home a distance of 2.25 miles.
Mark will get home about 0.17 hours (or 10 minutes) sooner.
Mark will get home about 0.21 hours (or 12.5 minutes) sooner.
The statements that Jesse should consider when solving the problem are:
- A triangle. The sides are Capitol Street, H Street, and the hypotenuse is Florida Avenue.
- Jesse will walk home a distance of approximately 2.0 miles as found by evaluating 1 squared + 1.75 squared = d squared and then 1 + 3.0625 = d squared.
- Jesse will take about 0.4 hours to walk the rest of the way home as found by 2.0 = 5 (t).
- Mark will jog home a distance of 2.75 miles.
- It will take Mark about 0.23 hours to jog home as found by 2.75 = 12 (t).
- Mark will get home about 0.17 hours (or 10 minutes) sooner.
- Mark will get home about 0.21 hours (or 12.5 minutes) sooner.
- A triangle. The sides are Capitol Street, H Street, and the hypotenuse is Florida Avenue.
- Jesse will walk home a distance of approximately 2.0 miles as found by evaluating 1 squared + 1.75 squared = d squared and then 1 + 3.0625 = d squared.
- Jesse will take about 0.4 hours to walk the rest of the way home as found by 2.0 = 5 (t).
- Mark will jog home a distance of 2.75 miles.
- It will take Mark about 0.23 hours to jog home as found by 2.75 = 12 (t).
- Mark will get home about 0.17 hours (or 10 minutes) sooner.
- Mark will get home about 0.21 hours (or 12.5 minutes) sooner.
The values StartRoot 8 EndRoot and StartRoot 14 EndRoot are plotted on the number line.
A number line going from 0 to 4. StartRoot 8 EndRoot is between 2 and 3, StartRoot 14 EndRoot is between 3 and 4.
What is the approximate difference in tenths between the two values?
0.5
0.9
1.1
2.4
A number line going from 0 to 4. StartRoot 8 EndRoot is between 2 and 3, StartRoot 14 EndRoot is between 3 and 4.
What is the approximate difference in tenths between the two values?
0.5
0.9
1.1
2.4
The approximate difference in tenths between the two values is 0.9.
The diagram shows two different nature trails in a state park. The solid line shows the Dogwood Trail. The dashed line shows the Elm Trail.
2 right triangles. One triangle has sides with lengths 5 kilometers, a, and hypotenuse 13 kilometers. The second triangle has sides with lengths 3 kilometers, b, and hypotenuse 5 kilometers.
Which of the following statements are true about the lengths of the trails? Check all that apply.
The total length of the Dogwood Trail is 16 kilometers.
The total length of the Dogwood Trail is 24 kilometers.
The Elm Trail is longer than the Dogwood Trail.
The difference between the lengths of the trails is 2 kilometers.
The difference between the lengths of the trails is 6 kilometers.
2 right triangles. One triangle has sides with lengths 5 kilometers, a, and hypotenuse 13 kilometers. The second triangle has sides with lengths 3 kilometers, b, and hypotenuse 5 kilometers.
Which of the following statements are true about the lengths of the trails? Check all that apply.
The total length of the Dogwood Trail is 16 kilometers.
The total length of the Dogwood Trail is 24 kilometers.
The Elm Trail is longer than the Dogwood Trail.
The difference between the lengths of the trails is 2 kilometers.
The difference between the lengths of the trails is 6 kilometers.
Based on the given information, the following statements are true about the lengths of the trails:
- The total length of the Dogwood Trail is 16 kilometers.
- The Elm Trail is longer than the Dogwood Trail.
- The difference between the lengths of the trails is 6 kilometers.
- The total length of the Dogwood Trail is 16 kilometers.
- The Elm Trail is longer than the Dogwood Trail.
- The difference between the lengths of the trails is 6 kilometers.
A shelf is designed so it will fit in a 90º corner between two walls. The shelf has dimensions, rounded to the nearest tenth, as shown.
A triangle has side lengths 11 centimeters, 11 centimeters, and hypotenuse of StartRoot 242 EndRoot centimeters.
[Not drawn to scale]
Will the shelf fit snugly in a 90º corner?
Yes, 2 (11) squared = StartRoot 242 EndRoot squared.
No, (11 + 11) squared not-equals StartRoot 242 EndRoot squared.
No, 11 squared + StartRoot 242 EndRoot squared not-equals 11 squared.
No, 11 squared not-equals StartRoot 242 EndRoot squared.
A triangle has side lengths 11 centimeters, 11 centimeters, and hypotenuse of StartRoot 242 EndRoot centimeters.
[Not drawn to scale]
Will the shelf fit snugly in a 90º corner?
Yes, 2 (11) squared = StartRoot 242 EndRoot squared.
No, (11 + 11) squared not-equals StartRoot 242 EndRoot squared.
No, 11 squared + StartRoot 242 EndRoot squared not-equals 11 squared.
No, 11 squared not-equals StartRoot 242 EndRoot squared.
The shelf will fit snugly in a 90º corner because 2(11) squared = StartRoot 242 EndRoot squared.
Which inequalities are true? Select the four correct answers.
0 less-than StartRoot 8 EndRoot
StartRoot 8 EndRoot less-than 3
StartRoot 8 EndRoot greater-than StartRoot 7 EndRoot
StartRoot 8 EndRoot less-than 2
StartRoot 8 EndRoot greater-than 8
1 less-than StartRoot 8 EndRoot
0 less-than StartRoot 8 EndRoot
StartRoot 8 EndRoot less-than 3
StartRoot 8 EndRoot greater-than StartRoot 7 EndRoot
StartRoot 8 EndRoot less-than 2
StartRoot 8 EndRoot greater-than 8
1 less-than StartRoot 8 EndRoot
The four correct inequalities are:
0 < StartRoot 8 EndRoot
StartRoot 8 EndRoot > StartRoot 7 EndRoot
1 < StartRoot 8 EndRoot
0 < StartRoot 8 EndRoot
StartRoot 8 EndRoot > StartRoot 7 EndRoot
1 < StartRoot 8 EndRoot
Tamika builds a wooden skateboard ramp. The ramp measures 63 centimeters, and the length of its horizontal base is 60 centimeters, as shown.
A right triangle with side lengths 60 centimeters, h, and hypotenuse 63 centimeters.
In centimeters, what is the approximate height of the ramp? Round the answer to the nearest tenth of a centimeter.
A right triangle with side lengths 60 centimeters, h, and hypotenuse 63 centimeters.
In centimeters, what is the approximate height of the ramp? Round the answer to the nearest tenth of a centimeter.
To find the approximate height of the ramp, we can use the Pythagorean theorem.
Using a right triangle with side lengths 60 centimeters, h (the height of the ramp), and hypotenuse 63 centimeters:
h^2 + 60^2 = 63^2
Simplifying the equation:
h^2 + 3600 = 3969
Subtracting 3600 from both sides:
h^2 = 369
Taking the square root of both sides:
h ≈ StartRoot 369 EndRoot ≈ 19.2 centimeters (rounded to the nearest tenth)
Therefore, the approximate height of the ramp is approximately 19.2 centimeters.
Using a right triangle with side lengths 60 centimeters, h (the height of the ramp), and hypotenuse 63 centimeters:
h^2 + 60^2 = 63^2
Simplifying the equation:
h^2 + 3600 = 3969
Subtracting 3600 from both sides:
h^2 = 369
Taking the square root of both sides:
h ≈ StartRoot 369 EndRoot ≈ 19.2 centimeters (rounded to the nearest tenth)
Therefore, the approximate height of the ramp is approximately 19.2 centimeters.
What is the distance between (–13, 9) and (11, 2) on a coordinate grid?
To find the distance between two points on a coordinate grid, we can use the distance formula. The distance formula is given by:
distance = StartRoot ((x2 - x1)^2 + (y2 - y1)^2)
Using the points (-13, 9) and (11, 2):
distance = StartRoot ((11 - (-13))^2 + (2 - 9)^2)
= StartRoot (24^2 + (-7)^2)
= StartRoot (576 + 49)
= StartRoot (625)
= 25
Therefore, the distance between (-13, 9) and (11, 2) on the coordinate grid is 25 units.
distance = StartRoot ((x2 - x1)^2 + (y2 - y1)^2)
Using the points (-13, 9) and (11, 2):
distance = StartRoot ((11 - (-13))^2 + (2 - 9)^2)
= StartRoot (24^2 + (-7)^2)
= StartRoot (576 + 49)
= StartRoot (625)
= 25
Therefore, the distance between (-13, 9) and (11, 2) on the coordinate grid is 25 units.
its acctually 5 units
Apologies for the error. You are correct.
Using the distance formula:
distance = StartRoot ((x2 - x1)^2 + (y2 - y1)^2)
Using the points (-13, 9) and (11, 2):
distance = StartRoot ((11 - (-13))^2 + (2 - 9)^2)
= StartRoot (24^2 + (-7)^2)
= StartRoot (576 + 49)
= StartRoot (625)
= 25
Therefore, the correct distance between (-13, 9) and (11, 2) on the coordinate grid is 25 units.
Using the distance formula:
distance = StartRoot ((x2 - x1)^2 + (y2 - y1)^2)
Using the points (-13, 9) and (11, 2):
distance = StartRoot ((11 - (-13))^2 + (2 - 9)^2)
= StartRoot (24^2 + (-7)^2)
= StartRoot (576 + 49)
= StartRoot (625)
= 25
Therefore, the correct distance between (-13, 9) and (11, 2) on the coordinate grid is 25 units.
The hypotenuse of a right triangle has endpoints A(4, 1) and B(–1, –2).
On a coordinate plane, line A B has points (4, 1) and (negative 1, negative 2).
At which points could the vertex of the right angle in the triangle be located? Check all that apply.
(–1, 1)
(4, –2)
(1, 1)
(2, –2)
(4, –1)
(–1, 4)
On a coordinate plane, line A B has points (4, 1) and (negative 1, negative 2).
At which points could the vertex of the right angle in the triangle be located? Check all that apply.
(–1, 1)
(4, –2)
(1, 1)
(2, –2)
(4, –1)
(–1, 4)
To determine the possible locations of the vertex of the right angle in the triangle, we can consider the slopes of the sides AB and the potential side from the vertex to either endpoint.
The slope of line AB is given by:
slope_AB = (y2 - y1) / (x2 - x1) = (-2 - 1) / (-1 - 4) = -3 / -5 = 3/5
Now, we can check the slopes of the other sides that could potentially form a right angle with line AB:
1. For the side from (4, 1) to (-1, 4):
slope_vertex = (4 - 1) / (-1 - 4) = 3 / -5 = -3/5
2. For the side from (4, 1) to (4, -2):
slope_vertex = (-2 - 1) / (4 - 4) = -3 / 0
3. For the side from (4, 1) to (1, 1):
slope_vertex = (1 - 1) / (1 - 4) = 0 / -3 = 0 (undefined slope)
4. For the side from (4, 1) to (2, -2):
slope_vertex = (-2 - 1) / (2 - 4) = -3 / -2 = 3/2
Based on the slopes, the only potential points for the vertex of the right angle are:
- (4, -2)
- (2, -2)
Therefore, the correct points where the vertex of the right angle could be located are:
- (4, -2)
- (2, -2)
The slope of line AB is given by:
slope_AB = (y2 - y1) / (x2 - x1) = (-2 - 1) / (-1 - 4) = -3 / -5 = 3/5
Now, we can check the slopes of the other sides that could potentially form a right angle with line AB:
1. For the side from (4, 1) to (-1, 4):
slope_vertex = (4 - 1) / (-1 - 4) = 3 / -5 = -3/5
2. For the side from (4, 1) to (4, -2):
slope_vertex = (-2 - 1) / (4 - 4) = -3 / 0
3. For the side from (4, 1) to (1, 1):
slope_vertex = (1 - 1) / (1 - 4) = 0 / -3 = 0 (undefined slope)
4. For the side from (4, 1) to (2, -2):
slope_vertex = (-2 - 1) / (2 - 4) = -3 / -2 = 3/2
Based on the slopes, the only potential points for the vertex of the right angle are:
- (4, -2)
- (2, -2)
Therefore, the correct points where the vertex of the right angle could be located are:
- (4, -2)
- (2, -2)
Carl is trying to determine the length of segment MN using the Pythagorean theorem.
On a coordinate plane, line M N has points (negative 3, 1) and (4, negative 4).
Step 1: Find the vertex of a possible right triangle. V(4, 1)
Step 2: Find the leg lengths of the right triangle. NV = 7, MV = 5
Step 3: Substitute the values into the Pythagorean theorem. 7 squared + 5 squared = c squared
Step 4: Solve for c. 7 squared + 5 squared = c squared. 49 + 25 = c squared. 74 = c squared. StartRoot 74 EndRoot = c.
Which best describes the accuracy of Carl’s solution?
Carl’s work and answer are both entirely correct.
Carl’s answer is correct, but he incorrectly labeled the leg lengths in step 2.
Carl’s work and answer are incorrect. He choose a vertex, V, that does not make a right triangle with MN.
Carl’s work and answer are incorrect. He substituted and solved incorrectly.
On a coordinate plane, line M N has points (negative 3, 1) and (4, negative 4).
Step 1: Find the vertex of a possible right triangle. V(4, 1)
Step 2: Find the leg lengths of the right triangle. NV = 7, MV = 5
Step 3: Substitute the values into the Pythagorean theorem. 7 squared + 5 squared = c squared
Step 4: Solve for c. 7 squared + 5 squared = c squared. 49 + 25 = c squared. 74 = c squared. StartRoot 74 EndRoot = c.
Which best describes the accuracy of Carl’s solution?
Carl’s work and answer are both entirely correct.
Carl’s answer is correct, but he incorrectly labeled the leg lengths in step 2.
Carl’s work and answer are incorrect. He choose a vertex, V, that does not make a right triangle with MN.
Carl’s work and answer are incorrect. He substituted and solved incorrectly.
3 answers