Mathematics: find the measure of x, y, and z

find the measure of x, y, and z, №12685769, 23.07.2021 07:18

Advanced Placement (AP)

Find the measure of X, Y and Z in simplest form:

Step-by-step answer

P Answered by PhD

Answer/Explanation:

12^2 = 16*x (altitude to hypotenuse theorem)

Solve for x using this equation

144 = 16x

$\frac{144}{16} = x$ (division property of equality)

9 = x

x = 9

y^2 = 12^2 + x^2 (pythagorean theorem)

y^2 = 12^2 + 9^2 (substitution)

y^2 = 144 + 81

y^2 = 225

$\sqrt{y^2} = \sqrt{225}$

y = 15

z^2 = (x + 16)^2 - y^2 (pythagorean theorem)

z^2 = (9 + 16)^2 + 15^2 (substitution)

z^2 = 25^2 + 15^2

z^2 = 625 + 225

z^2 = 850

$\sqrt{z^2} = \sqrt{850}$

$z = \sqrt{25*34}$

$z = 5\sqrt{34}$

Advanced Placement (AP)

Find the measure of X, Y and Z in simplest form:

Step-by-step answer

P Answered by PhD

Answer/Explanation:

12^2 = 16*x (altitude to hypotenuse theorem)

Solve for x using this equation

144 = 16x

$\frac{144}{16} = x$ (division property of equality)

9 = x

x = 9

y^2 = 12^2 + x^2 (pythagorean theorem)

y^2 = 12^2 + 9^2 (substitution)

y^2 = 144 + 81

y^2 = 225

$\sqrt{y^2} = \sqrt{225}$

y = 15

z^2 = (x + 16)^2 - y^2 (pythagorean theorem)

z^2 = (9 + 16)^2 + 15^2 (substitution)

z^2 = 25^2 + 15^2

z^2 = 625 + 225

z^2 = 850

$\sqrt{z^2} = \sqrt{850}$

$z = \sqrt{25*34}$

$z = 5\sqrt{34}$

Mathematics

Step-by-step answer

P Answered by Master

29

The measure of angle x is 122.5 degrees.

The measure of angle y is 57.5 degrees

Step-by-step explanation:

180=y+x

y=x-65

180= (x-65)+x

180=2x-65

245=2x

x=122.5

y=122.5-65= 57.5

Mathematics

The measures of two supplementary angles total 180 degrees. the measure of angle y is 65 degrees less than the measure of angle x. what are the measures of the angles? a)the measure of angle x is 122.5 degrees. the measure of angle y is 57.5 degrees. b)the measure of angle x is 115 degrees. the measure of angle y is 65 degrees. c)the measure of angle x is 57.5 degrees. the measure of angle y is 122.5 degrees. d)the measure of angle x is 65 degrees. the measure of angle y is 115 degrees.

Step-by-step answer

P Answered by Specialist

The right answer is A. The measure of angle x is 122.5 degrees. The measure of angle y is 57.5 degrees.

Step-by-step explanation:

We've been told that the addition of both angles is equal to 180 degrees (because they're supplementary angles). We may write this information in the form of an equation like this:

x+y=180 (equation 1)

Additionally, we've been told that the measure of angle y is 65 degrees less than the measure of angle x. So this can be written like this:

x-y=65 (equation 2)

So, we can use equations 1 & 2 to find the values of x and y.

From eq. 2 we have that:

x-y=65

x=65+y (equation 3)

Now, let's replace this in equation 1

x+y=180

(65+y)+y=180

65+2y=180

$y=\frac{180-65}{2}=57.5$

Finally, we may replace the found value of y in the equation 3 to find the value of x.

x=65+y=65+57.5=122.5

The right answer is A. The measure of angle x is 122.5 degrees and the measure of angle y is 57.5 degrees.

Mathematics

WILL GIVE BRAINLIEST Mariah cuts a rectangle along its diagonal. Two congruent triangles are created. The two angles created by the diagonal have a sum of 90°. The smaller angle is 1/5 the measure of the larger angle. Let x represent the measure of the larger angle and let y represent the measure of the smaller angle. What is a system of equations that can be used to find the measures of the two angles? A. x + y = 90 and y = x - 1/5 B. y = 90 + x and y = 5 + x C. y = 90 + x and y = 5x D. x + y = 90 and y = x/5

Step-by-step answer

P Answered by PhD

4

Stated Below:

Step-by-step explanation:

x + y = 90 because the 2 angles add up to 90 .

Now, m < x = five times m < y, so x = 5y or y = x/5

So the last choice is the correct one.

Mathematics

Mariah cuts a rectangle along its diagonal. two congruent triangles are created. the two angles created by the diagonal have a sum of 90°. the smaller angle is 1/5 the measure of the larger angle. let x represent the measure of the larger angle and let y represent the measure of the smaller angle. what is a system of equations that can be used to find the measures of the two angles? x + y = 90 and y = x – 1/5 y = 90 + x and y = 5 + x y = 90 + x and y = 5x x + y = 90 and y = x/5

Step-by-step answer

P Answered by Specialist

58

D) x + y = 90 and y = x/5

Physics

Question 1 This question is a long free-response question. Show your work for each part of the question. In a physics lab, a group of students are provided with a sphere of unknown mass, a roll of string, a ring stand, and measuring devices that are commonly found in a physics lab. The students must graphically determine the acceleration due to gravity near Earth’s surface by putting the sphere into simple harmonic motion. (a) State a basic physics principle, law, or equation that the students could use to graphically determine the acceleration

Step-by-step answer

P Answered by Master

58

1) g = 4π² / m, 3) xaxis the length of the pendulums and the y axis the period squared

Explanation:

a) students can approximate this system to a simple pendulum, in this case the angular velocity is

w = √ g / l

angular velocity, frequency and period are related

w = 2π f = 2π / T

we substitute

T = 2π√ l / g

with this equation they can determine the value of the acceleration of gravity, for this they measure the period for various lengths of the pendulum and graph

T² = 4π² l / g

We graph T² vs l

where this is the equation of a line if the independent variable is y = T² and x = l

y = (4π² / g) l

so the slope is

m = 4π² / g

clearing

g = 4π² / m

where the slope can be found with the values of the line not the experimental values.

2) to carry out the experiment, or the thread is attached to the sphere, the length of the pendulum that goes from the pivot point to the center of the sphere is measured with a tape measure and a small finished angle is turned or less than 10th is released, it is good to wait for the first oscillation to walk, the time of a determined number of oscillations is generally measured 10 or 20, the period is calculated

T = t / n

a table of T² against the length is made and it is plotted with the length in the ax ax, we look for the slope and hence the acceleration of gravity

3) on the independent x-axis, the controlled variable must be plotted, which is the length of the pendulums, and on the y-axis, the dependent variable is the period squared

4) of the equation of the line

m = 4pi2 / g

where it ends up reaching the floor

g = 4pi2 / m

5) when the spring is cut, the sphere remains under the effect of gravity acceleration, the harmonic movement disappears and the sphere is in a vertical movement

Mathematics

Mariah cuts a rectangle along its diagonal. two congruent triangles are created. the two angles created by the diagonal have a sum of 90°. the smaller angle is 1/5 the measure of the larger angle. let x represent the measure of the larger angle and let y represent the measure of the smaller angle. what is a system of equations that can be used to find the measures of the two angles? x + y = 90 and y = x – 1/5 y = 90 + x and y = 5 + x y = 90 + x and y = 5x x + y = 90 and y = x/5

Step-by-step answer

P Answered by Master

58

D) x + y = 90 and y = x/5

Mathematics

Please hurry on a time limit The diagram below shows the scalene triangle WXY. The measure of Angle W X Y is Triangle X W Y. Sides W Y and X Y extend to form an exterior angle at point Y with a measure of 46 degrees. Which is true about the diagram? Select two options. A. The measure of angle W Y X = 46 degrees B. The measure of angle Y W X = 63 degrees C. The measure of angle Y W X = 134 degrees D. The measure of angle Y W X = 46 degrees E.The measure of angle W Y X = 134 degrees

Step-by-step answer

P Answered by Master

47

P. S I’m not very sure but I tried my best

The two options are:
A and B

I hope this helps

Mathematics

The figure below shows a right triangle: A right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units. The angle b What is r ÷ q equal to? (3 points) Group of answer choices tan y° sin x° sin y° tan x° Flag this Question Question 23 pts (07.01 MC) Look at the figure below: An image of a right triangle is shown with an angle labeled y degrees. If sin y° = s divided by 8 and tan y° = s divided by t, what is the value of cos y°? (3 points) Group of answer choices cos y° = 8s cos y° = 8t cos y°=

Step-by-step answer

P Answered by PhD

1) tan x°;
2) cos y°= 8 divided by t;
3) 145 divided by tan 65 degrees;
4) cosec x° = hypotenuse ÷ opposite;
5) 2 divided by cot 40 degrees;
6) 22.62°;
7) 52.02;
8) cos 0° = 1, because the cosine and sine are complements;
9) 3 tan 50°;
10) 3.0 meters.

find the measure of x, y, and z

Faq

Try asking the Studen AI a question.