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Vera_Pavlovna [14]

2 years ago

6

The isosceles trapezoid is part of an isosceles triangle with a 26° vertex angle. What is the measure of an acute base angle of

the trapezoid?

2 answers:

JulijaS [17]2 years ago

7 0

The angle of the trapezoid is 77 degrees

ICE Princess25 [194]2 years ago

6 0

Answer: The measure of an acute base angle of the trapezoid BPQC is 77°.

Step-by-step explanation: As given in the question, the isosceles trapezoid BPQC is a part of the isosceles triangle ABC with same base BC. And, the vertex angle, m∠A = 26°.

We are to find the measure of an acute base angle of the trapezoid. That is, measure of angle B or angle C.

Since ΔABC is an isosceles triangle, so

$AB=BC\\\\\Rightarrow m\angle C=m\angle B.$

Now, using the angles sum property of a triangle, we have

$m\angle A+m\angle B+m\angle C=180^\circ\\\\\Rightarrow 26^\circ+m\angle B+m\angle B=180^\circ\\\\\Rightarrow 2m\angle B=154^\circ\\\\\Rightarrow m\angle B=77^\circ.$

So, m∠B = m∠C = 77°.

Thus, the measure of an acute base angle of the trapezoid BPQC is 77°.

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Carmen is a professor at a local university. In collecting data on her Introduction to Business course for a year, she wants to

AVprozaik [17]

Answer:

$\boxed {\boxed {\sf z=2.2}}$

Step-by-step explanation:

The z-score tells us how many standard deviations a value is away from the mean.

The formula is:

$z=\frac{x- \overline{x}}{s}$

where x is the value, $\overline {x}$ is the mean, and s is the standard deviation.

We want to find the z-score for the score of an 83, the mean is 72, and the standard deviation is 5.

$x=83 \\\overline {x}= 72 \\s=5$

Substitute the values into the formula.

$z=\frac{83-72}{5}$

Solve the numerator.

$z=\frac{11}{5}$

Divide.

$z=2.2$

The z-score is 2.2, which means the score of 83 is 2.2 standard deviations above the mean.

3 0

3 years ago

A number cube labeled 1 to 6 is rolled 450 times. Which is the best prediction for the number of times that the number cube will

Vedmedyk [2.9K]

Haha, I don't think those answers belong to the question asked :P

The probability of rolling less than 3 is 2/6=1/3

So if you rolled 450 times you should expect to roll less than 3:

450(1/3)=150 times.

3 0

3 years ago

In Triangle XYZ, measure of angle X = 49° , XY = 18°, and

marissa [1.9K]

Answer:

There are two choices for angle Y: $Y \approx 54.987^{\circ}$ for $XZ \approx 15.193$ , $Y \approx 27.008^{\circ}$ for $XZ \approx 8.424$ .

Step-by-step explanation:

There are mistakes in the statement, correct form is now described:

<em>In triangle XYZ, measure of angle X = 49°, XY = 18 and YZ = 14. Find the measure of angle Y:</em>

The line segment XY is opposite to angle Z and the line segment YZ is opposite to angle X. We can determine the length of the line segment XZ by the Law of Cosine:

$YZ^{2} = XZ^{2} + XY^{2} -2\cdot XY\cdot XZ \cdot \cos X$ (1)

If we know that $X = 49^{\circ}$ , $XY = 18$ and $YZ = 14$ , then we have the following second order polynomial:

$14^{2} = XZ^{2} + 18^{2} - 2\cdot (18)\cdot XZ\cdot \cos 49^{\circ}$

$XZ^{2}-23.618\cdot XZ +128 = 0$ (2)

By the Quadratic Formula we have the following result:

$XZ \approx 15.193\,\lor\,XZ \approx 8.424$

There are two possible triangles, we can determine the value of angle Y for each by the Law of Cosine again:

$XZ^{2} = XY^{2} + YZ^{2} - 2\cdot XY \cdot YZ \cdot \cos Y$

$\cos Y = \frac{XY^{2}+YZ^{2}-XZ^{2}}{2\cdot XY\cdot YZ}$

$Y = \cos ^{-1}\left(\frac{XY^{2}+YZ^{2}-XZ^{2}}{2\cdot XY\cdot YZ} \right)$

1) $XZ \approx 15.193$

$Y = \cos^{-1}\left[\frac{18^{2}+14^{2}-15.193^{2}}{2\cdot (18)\cdot (14)} \right]$

$Y \approx 54.987^{\circ}$

2) $XZ \approx 8.424$

$Y = \cos^{-1}\left[\frac{18^{2}+14^{2}-8.424^{2}}{2\cdot (18)\cdot (14)} \right]$

$Y \approx 27.008^{\circ}$

There are two choices for angle Y: $Y \approx 54.987^{\circ}$ for $XZ \approx 15.193$ , $Y \approx 27.008^{\circ}$ for $XZ \approx 8.424$ .

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2 years ago

(x+40)(x+40) show steps

pishuonlain [190]

(x + 40) * (x + 40) =

(x + 40)² =

x² + 80x + 1600

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3 years ago

Which of the following points lies on the circle whose center is at the origin and whose radius is 10?

aliina [53]

The answer is (6,-8)

7 0

2 years ago