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.
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.
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
The pieces of fabric that Nadine can use in the quilt are:
- 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.
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.
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
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.
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.
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.