What is the supplement of an angle that measures 77°? (1 point)

The correct statement regarding the supplement of an angle that measures 77° is:

• The supplement is 103° because 180° - 77° = 103°.

Supplementary angles add up to 180°, so you subtract 77° from 180° to find the supplement.

If triangle DEF has sides measuring 50, 40, and 32, is the triangle a right triangle? If it is a right triangle, answer with the number 90. If it is not a right triangle, answer with the number 0. (1 point)

To determine if triangle DEF with sides measuring 50, 40, and 32 is a right triangle, we can use the Pythagorean theorem, which states that for a triangle with sides \(a\), \(b\), and hypotenuse \(c\):

\[ a^2 + b^2 = c^2 \]

We first identify the longest side, which is 50. Thus, we will check if:

\[ 40^2 + 32^2 = 50^2 \]

Calculating each side:

• \(40^2 = 1600\)
• \(32^2 = 1024\)
• \(50^2 = 2500\)

Now, we add \(40^2\) and \(32^2\):

\[ 1600 + 1024 = 2624 \]

Next, we compare this to \(50^2\):

\[ 2624 \neq 2500 \]

Since the equation does not hold true, triangle DEF is not a right triangle. Therefore, the answer is:

0

Which answer is it

The answer is 0, indicating that triangle DEF is not a right triangle.

If a right triangle has a leg with length 12 and the hypotenuse is 16, how long is the other leg? Round to the nearest tenth, if necessary. (1 point)

To find the length of the other leg in a right triangle where one leg (\(a\)) is 12 and the hypotenuse (\(c\)) is 16, you can use the Pythagorean theorem:

\[ a^2 + b^2 = c^2 \]

Here, let \(b\) be the length of the other leg. Plugging in the values we have:

\[ 12^2 + b^2 = 16^2 \]

Calculating the squares:

\[ 144 + b^2 = 256 \]

Now, subtract 144 from both sides:

\[ b^2 = 256 - 144 \] \[ b^2 = 112 \]

Taking the square root of both sides:

\[ b = \sqrt{112} \approx 10.583 \]

Rounding to the nearest tenth, the length of the other leg is approximately:

10.6.

A triangle has sides a, b, and c. Use the Converse of the Pythagorean
Theorem to determine whether a right triangle can be formed if a = 3, 6 = 4
, and c = 5.
Option A: Yes, a right triangle can be formed.
Option B: No, a right triangle cannot be formed.
Choose 1 for Option A or 2 for Option B.
(1 point)

To determine whether a right triangle can be formed with sides \(a = 3\), \(b = 4\), and \(c = 5\) using the Converse of the Pythagorean Theorem, we check if:

\[ a^2 + b^2 = c^2 \]

Calculating the squares:

• \(a^2 = 3^2 = 9\)
• \(b^2 = 4^2 = 16\)
• \(c^2 = 5^2 = 25\)

Now we check if:

\[ 9 + 16 = 25 \] \[ 25 = 25 \]

Since the equation holds true, a right triangle can be formed.

Therefore, the answer is 1 for Option A: Yes, a right triangle can be formed.

Keysha is building a coffee table. It's going to be in the shape of a rectangular prism, without the faces. She wants to make the table decorative by adding metal diagonals. The length of the coffee table will be 44 in., the width 24 in., and the height 14 in. Find the length Keysha should make each diagonal. Round the answer to the nearest tenth. (1 point)

To find the length of the diagonal of a rectangular prism, you can use the formula for the space diagonal, which is given by:

\[ d = \sqrt{l^2 + w^2 + h^2} \]

where:

• \(d\) is the diagonal length,
• \(l\) is the length,
• \(w\) is the width, and
• \(h\) is the height.

Given:

• Length (\(l\)) = 44 in,
• Width (\(w\)) = 24 in,
• Height (\(h\)) = 14 in.

Now, substitute the values into the formula:

\[ d = \sqrt{(44)^2 + (24)^2 + (14)^2} \]

Calculating each square:

\[ (44)^2 = 1936 \] \[ (24)^2 = 576 \] \[ (14)^2 = 196 \]

Now, sum them:

\[ d = \sqrt{1936 + 576 + 196} = \sqrt{2708} \]

Now, calculate the square root:

\[ d \approx 52.0 \]

Rounding to the nearest tenth, the length Keysha should make each diagonal is approximately:

52.0 in.