Mathematics High School

In ΔPQR, find the measure of ∡ P. (4 points)

Triangle PQR where angle Q is a right angle. PQ measures 33 point 8. PR measures 57 point 6. Measure of angle P is unknown

Answers

Answer 1
Final answer:

In a right triangle, use the Pythagorean theorem and the cosine function to find the measure of angle P.

Explanation:

In triangle PQR, where angle Q is a right angle, we can use the Pythagorean theorem to find the measure of angle P. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. In this case, PR is the hypotenuse and PQ and QR are the other two sides.

Using the given measurements, PQ = 33.8 and PR = 57.6. To find the measure of angle P, we can use the cosine function. Cosine is the ratio of the adjacent side to the hypotenuse, so we have cos P = PQ / PR.

Plugging in the given values, we have cos P = 33.8 / 57.6. Using a calculator, we find that cos P ≈ 0.586. To find the measure of angle P, we can take the inverse cosine of this value, which is approximately 54.3 degrees.

Related Questions

A closet is in the shape of a right rectangle prism it measures 4 1/4 feet long 3 1/4 feet wide and 6 feet tall. What is the volume of the closet

Answers

82.875 or 82 7/8 ft cubed

The answer is 100% 82 [tex]7/8[/tex]. I have taken the test it was correct!

Which expression is equivalent to sec^2 x cot^2 x?

Answers

sec33-xcot63y(451-xy)=0

can somebody tell me the area of these figures:

Answers

1) A = bh = 16*15 = 240 . . . . square units

2) There are a number of ways to decompose the shaded area, or to construct the shaded area. We'll do the latter.

The shaded area is 1/2 of a 4x4 square plus a small triangle below the center of the "butterfly". The latter has a base of 2 and a height of 1, so an area of
.. (1/2)*2*1 = 1
The total area is 4^2/2 +1 = 9 . . . . square units

A garden snail traveled 1⁄40 of a mile in 1⁄2 an hour. What was the speed of the snail? 80 miles per hour

Answers

where you asking if a snail had traveled for 80 hours? if so, it traveled 4 miles.

or if you're asking the snails speed, if so it's 0.025 miles in 30 mins and 0.05 miles an hour.

What is the area of the trapezoid? Enter your answer in the box. in2 The figure shows a trapezoid. The parallel bases of the trapezoid are horizontal, and top base is shorter than the bottom base. Vertical line segments are drawn inside the trapezoid from the upper vertices perpendicular to the bottom base. These segments are each 18 inches and divide the trapezoid into two right triangles and a rectangle. The rectangle lies between the two triangles. The bases of the triangles and rectangle make up the bottom base of the trapezoid. The base of each triangle is 6 inches, and the base of the rectangle is 15 inches.

Answers

1. The area of the trapezoid (At) is:
 
 At=A1+A2
 
 At is the area of the trapezoid.
 A1 is the area of the right triangles.
 A2 is the area of the rectangle.
 
 2. You can find the area of the right triangles (A1) by applying the formula for calculate the area of a triangle and multiply it by 2, because both triangles have the same dimensions. Then:
 
 A1=2(bxh/2)
 
 b is the base (b=6 inches).
 h is the height (h=18 inches).
 
 A1=2(6 inchesx18 inches/2)
 A1=2(108 inches²/2)
 A1=108 inches²
 
 3. Now, you must find the area of the rectangle by applying the following formula:
 
 A2=bxh
 
 b is the base of the rectangle (b=15 inches).
 h is the height ot the rectangle (h=18 inches).
 
 A2=(15 inches)(18 inches)
 A2=270 inches²
 
 4. Therefore, the area of the trapezoid (At) is:
 
 At=A1+A2
 At=108 inches²+270 inches²
 At=378 inches²

What of following best describes the expression 9(x+7)

Answers

Hello there!

•this expression is a product between two factors because they are being MULTIPLIED to each other.
•this expression is has two factors, a constant and a 2-term factor. The constant is 9 and the two term factor is (x+7).

This means the answer is...
The product of a constant factor 9 and a 2-term factor x+7

I really hope this helps!
Best wishes :)

How do i find the average speed for his question: "A bicycle racer rides from a starting marker at 10m/s. She then rides back along the same rout from the turnaround marker at 16m/s. What is her average speed for the whole race?",

Answers

To find the average speed for the whole race, you just have to add the speed from a starting marker and the speed from the turnaround marker going back and divide it by 2 since there are only two speeds involved.

10 m/s + 16m/s = 26 m/s / 2 = 13 m/s

Therefore, the average speed for the whole race is 13 m/s.

Average speed = Total Distance/Total time ------(1) Let us assume that the distance from starting marker to turnaround marker is 'x' Total distance travelled = 2x Speed from starting marker to turnaround marker , s1 = 10 m/s Speed from turnaround market to starting market , s2 - 16 m/s Let, Time taken from starting marker to turnaround marker be t1 Time taken from turnaround marker to starting marker be t2. Applying these values in equation (1), Average speed = (2x)/(t1+t2) -------(2) From (1), t1 = x/s1 = x/10 t2 = x/s2 = x/16 Substituting the above in (2), Average speed = (2x)/(x/10+x/16) m/s = (2x)/(13x/80) m/s = 160/13 m/s = 12.3 m/s We can also arrive at the average speed by using the formula 2(s1)(s2)/(s1+s2)

PLZ i need anwse ASAP

The figure is the net for a rectangular prism.

What is the surface area of the rectangular prism represented by the net?

Answers

Surface area is the sum of area of all the faces .

In the net diagram, we have 6 faces. So we have to find the area of each face and add them to find the surface area .

And since each face is rectangle in shape, so we will use the formula of area of rectangle, which is

[tex]Area= length*width[/tex]

So the required surface area is

[tex]A = (11*5)+(11*4)+(11*5) +(11*4)+(5*4)+(5*4)

\\

A = 55+44+55+44+20+20 =238 mm^2[/tex]

And that's the required surface area of the rectangular prism .

What is the value of n? Enter your answer in the box. n =

Answers

For two chords AB and PQ intersecting inside the circle, then AX × XB = PX × XQ.
In this case;
 5 × 7 = 4(n+8)
  35  = 4n + 32
      4n = 3
        n = 0.75 
Therefore; the value of x is 0.75

Answer:

6

Step-by-step explanation:

Is it possible for a system to have more than one solution? Explain your answer

Answers

A linear system can have infinite solutions if both systems represent the same line. if a linear system down not represent the same line then it can only have one or no solutions. No solution is if the system is representing parallel lines and one solution represents an intersection of the two lines.  in a nonlinear system you can have infinite or up to a maximum of intersections as the highest degree of the systems.

You want to make a scaled-down model of the statue of liberty that fits neatly on top of a pedestal with a 20 x 20 in horizontal surface. the actual statue of liberty is approximately 152 ft tall over a 40 x 40 ft base.
a.what is the scaling factor between the statue of liberty and your model? in other words, how many more times bigger is the statue of liberty than your model? show your work.
b.how tall should your model be, in inches? show your work.

Answers

a.what is the scaling factor between the statue of liberty and your model?

we know that
[scale factor[=[model]/[actual]
the pedestal model is 20 in*20 in
the pedestal actual is 40 ft* 40 ft
then
[scale factor]=[20 in]/[40 ft] ---------->[1 in]/[2 ft]-------> scale=1/2

the answer Part A) is 
the scale factor is [1 in]/[2 ft]

b.how tall should your model be, in inches? 
the actual statue of liberty is approximately 152 ft tall

[scale factor]=[model]/[actual]---------> [model]=[scale factor]*[actual]
[model]=[1/2]*[152]----------> 76 in

the answer part B) is 76 in tall

The length of a rectangle is 1 inch less than twice the width. the area is 21 inches^2 what is the length?

Answers

Hi.

Formula for area: A = 2l + 2w, where l is the length and w is the width.

Given information:
• l = 2w - 1
• A = 21 in^2

We can plug in our values accordingly and solve for w.

A = 2l + 2w
21 = 2(2w - 1) + 2w
21 = 4w - 2 + 2w
23 = 6w - 2
23 = 6w
3.83 = w

Plug 3.83 for w into 2w - 1 to find length.

2(3.83) - 1
7.66 - 1
6.66

Finally, check your work by plugging your values into the original equation.

21 = 2(6.66) + 2(3.83)
21 = 13.32 + 7.66
21 = 20.98

Answer:
The length is approximately 6.66 inches.

Emma is 5 years older than 6 times Beth’s age. If Emma is 29 years old what equation represents how to find Beth’s age?

Answers

To calculate Beth's age, we use the equation 29 = 6B + 5, where 29 is Emma's age, B represents Beth's age, and then solve for B, resulting in Beth being 4 years old.

To find Beth's age, we need to set up an equation based on the information provided. We know that Emma is 29 years old and that she is 5 years older than 6 times Beth's age. This relationship can be described with the equation E = 6B + 5, where E is Emma's age and B is Beth's age.

Plugging Emma's age into the equation, we get 29 = 6B + 5.

Next, we solve for B by first subtracting 5 from both sides of the equation, which gives us 24 = 6B. Then, we divide both sides by 6 to find Beth's age: B = 24 / 6.

Finding the value of B tells us that Beth is 4 years old.

Therefore, the equation is 29 = 6B + 5.

Ella's college professors assign homework independently from each other. ella knows that there is a 60% chance that she will have math homework tonight and a 70% chance that she will have english homework. what is the probability that she will not have math or english homework tonight? 10% 12% 42% 70%

Answers

To answer this question, you will multiply the chance of NOT having english homework (100-70=30% chance) by the chance of her NOT having math homework (100-60=40%).

This would be 0.3 x 0.4=0.12 or 12% chance of both occurring.

Answer:

B. 12%  

Step-by-step explanation:

We have been given that Ella knows that there is a 60% chance that she will have math homework tonight and a 70% chance that she will have English homework.

Since we know that probability of not happening an event can be found by subtracting probability of happening the event from 1.

[tex]\text{P(No math homework tonight)}=1-0.6=0.4[/tex]

[tex]\text{P(No English homework tonight)}=1-0.7=0.3[/tex]

Since both events are independent so we will multiply probability of no math homework tonight by probability of no English homework to find no math or English homework tonight.

[tex]\text{P(No math or English homework tonight)}=0.4\times 0.3[/tex]

[tex]\text{P(No math or English homework tonight)}=0.12[/tex]

Converting 0.12 to percent we will get,

[tex]0.12\times 100=12\%[/tex]

Therefore, the probability that Ella will not have math or English homework tonight is 12%.

pls help!!! will make brainliest!

Answers

3.8, 4.6, 5.4, 6.2, 7.0

Which best explains whether or not all isosceles triangles are similar?

All isosceles triangles are similar. Two angles within each triangle are always congruent.
All isosceles triangles are similar. The triangle sum theorem states that the sum of the angles in a triangle is 180°. Therefore, the third angle can always be determined.
All isosceles triangles are not similar. The pair of congruent angles within one triangle is not necessarily congruent to the pair of congruent angles within the other triangle.
All isosceles triangles are not similar. Given only the vertex angle of an isosceles triangle, there is not enough information to determine the measures of the base angles. Therefore, it is not possible to determine if the base angles of one isosceles triangle are congruent to the base angles of another.

Answers

All isosceles triangles are similar. The triangle sim theorem states that the sum o the angles in a triangle is 180 degrees. Therefore, the third angle can always be determined

Answer:

C - All isosceles triangles are not similar. The pair of congruent angles within one triangle is not necessarily congruent to the pair of congruent angles within the other triangle.

Step-by-step explanation:

got it correct on edge

Can someone help me and show me how to solve this?

In the figure, YX is a tangent to circle O at point X.

mXB = 52°
mXA = 104°

What is the measure of ∠XYA?


I can't remember how to solve questions like this since it's been a while. Thanks in advance.

Answers

XYA = (104 -52)/2

52 /2 = 26

the answer is 26 degrees
I think it is 26
but I'm not completely sure

Divide 5 in a ratio of 1:2:3

Answers

in plain and short, we simply divide 5 by (1+2+3) and then distribute the pieces likewise

[tex]\bf 5\qquad 1:2:3\qquad \cfrac{5}{1+2+3}\implies \cfrac{5}{6} \\\\\\ \stackrel{\textit{ratio of 1}}{1\left( \frac{5}{6} \right)}\qquad \stackrel{\textit{ratio of 2}}{2\left( \frac{5}{6} \right)}\qquad \stackrel{\textit{ratio of 3}}{3\left( \frac{5}{6} \right)}\qquad \implies \qquad \frac{5}{6}~:~\frac{5}{3}~:~\frac{5}{2}[/tex]

add the ratios up, and you'll get 5.

ABCD is a trapezoid with sides AB parallel to CD, where AB = 50, CD = 20. E is a point on the side AB with the property, that the segment DE divides the given trapezoid into two parts of equal area (see figure). Calculate the length AE.

Answers

AE is 35 units in length.

One of the two shapes that DE splits the trapezoid into is a triangle.  Since the two sections of the trapezoid have an equal area, this means that the area of the triangle is 1/2 of the area of the trapezoid.  Using the formulas for the area of a triangle and the area of a trapezoid we get:

1/2bh = 1/2(1/2(B+b)(h))

The base of the triangle, AE, is unknown.  We do know that AE + EB = 50; let x be EB.  That means that AE = 50-x.

B, the "big base" of the trapezoid, is 50.  b in the trapezoid, the little base, is 20.  Using all of this we now have:

1/2(50-x)h = 1/2(1/2(50+20)(h))
1/2(50-x)h = 1/2(1/2(70)h)
1/2(50-x)h=1/2(35)h

Since we have multiplied by 1/2 and h on both sides, we can divide by both of them at the same time to cancel.  This will give us:
(50-x)=35

Subtract 50 from both sides:
50-x=50 = 35-50
-x = -15
x = 15

This means that EB is 15; thus AE = 50-15 =35.

Suppose that c is the center of a circle with radius 13 in and a point p is at a distance of 32 in from
c. find an approximate value of the measure of the angle (in degrees) that is formed by the two tangent lines drawn to the circle from p. if needed, round your answer to three decimals

Answers

The sine of 1/2 the angle = 13 / 32

so this angle =  23.9695 degrees

Therefore the required angle = 2 * 23.9695  =  47.939  to 3 DP's. 

A cylindrical oil storage tank has a height of 10 meters and a diameter of 24 meters. If the tank is full, how much oil does it contain? Round to the nearest tenth of a kiloliter (1 m3 = 1 kL). Use 3.14 for π.

Answers

For this case what you should do is find the volume of the tank in the form of a cylinder.
 By definition, the volume of a cylinder is:
 V = pi * (r ^ 2) * (h)
 Where,
 h: height
 r: radio
 Substituting the values we have:
 V = 3.14 * ((24/2) ^ 2) * (10)
 V = 4521.6 kL
 Answer:
 If the tank is full, it does contain 4521.6 kL of oil

PLEASE HELP!!
Circle 1: center (8, 5) and radius 6
Circle 2: center (−2, 1) and radius 2
What transformations can be applied to Circle 1 to prove that the circles are similar?
What scale factor does the dilation from Circle 1 to Circle 2 have?
Show your work.

Answers

We need two definitions. 
Two shapes are congruent if you can turn one into another using translation, rotation, and reflection.
Two shapes are similar if you rescale one them into a shape that is congruent to the other.
We can conclude from this that in euclidian geometry all circles are similar.
We can shrink the first circle to get the second one.
Scale factor would be 1/3 as circle 1 has the radius that is 3 times the radius of circle 2.

The graph represents the height y, in meters, above a lake of a rock x seconds after it is thrown from a ledge. Which statement is true? Select each correct answer.

Answers

Answer:

The graph represents the height y, in meters, above a lake of a rock x seconds after it is thrown from a ledge. Which statement is true? Select each correct answer.

Use the standard normal table to find the​ z-score that corresponds to the cumulative area 0.4661. if the area is not in the​ table, use the entry closest to the area. if the area is halfway between two​ entries, use the​ z-score halfway between the corresponding​ z-scores.

Answers

Answer: The corresponding z-score would be -0.085 for a cumulative area of 0.4661.

When you look on a normal distribution table, you will see that the value of 0.4661 falls between z-scores of -0.08 and -0.09. Therefore, we should find the middle of those 2 numbers to get the best possible approximation. That would be -0.085 for the z-score.

The z-score at the cumulative area of 0.4661 is -0.085

How to determine the z-score?

The cumulative area is given as:

0.4661

This means that:

P = 0.4661

Next, we use a standard normal table to find the​ z-score.

From the standard normal table of z-scores, we have:

z = -0.085 when P = 0.4661

Hence, the z-score at the cumulative area of 0.4661 is -0.085

Read more about z-scores at:

brainly.com/question/25638875

#SPJ6

PLZ HELP ASAP
IM PRETTY SURE ITS C OR MAYBE A

PLEASE EXPLAIN

Answers

You're correct it is C the dot graph displays different values of six signifying the amount of something in those pairs. such as two people having 0 pets.
C is the correct answer.
As you can tell, it deals with six options. So B and D are out of the story since the first one deals with 0 to 15 dollars and option D deals with 0 to 15 as well. With Henry, the option makes sense because there are 15 dots and with 0-6 dealing with pets makes sense since someone can have no pets or even 6 pets.

The sears tower in Chicago is 1,450 feet tall. A model of the tower is 24 inches tall. What is the ratio of the height of the model to the the height of the actual Sears tower?
a. 1:725
b. 725:1
c. 12:725
d. 725:12,

Answers

Answer: c Explanation:- Given:- Actual height of tower is 1450. Model height of tower is 24. To find the ratio of height we divide it (24/1450) hence the answer is c 12:725

Answer:

ANSWERS LOL

Step-by-step explanation:

SS Geometry B: Unit 3: Similarity

1. A

2. B

3. A

4. B

5. C

6. A

7. A

8. C

9. C

10. B

11. C

12. ESSAY

13. ESSAY

Math help please????

Answers

The y-intercept is 4. Divide by three to get y alone (12/3=4)
All you do is divide 3 on both sides, and it results to:

[tex]y = \frac{-4}{3} x + \frac{12}{3} [/tex]

The y intercept simplifies to 4

y-int = 4


An inequality is shown below. x + 2.5 < 20 What is the greatest value of x from the set {10.5, 12.5, 17.5, 19.5} that makes the inequality true?

A 10.5

B 12.5

C 17.5

D 19.5

Answers

C is the final answer :)

Find the value of x.

Answers

A triangle's angles (in all) = 180 degrees

78 + 27 + x = 180

simplify:

78 + 27 + x = 180

105 + x = 180

subtract 105 from both sides

x + 105 (-105) = 180 (-105)

x = 180 - 105

x = 75° is your answer

hope this helps
Hi there!

Since the sum of all angles in any triangle always equals 180°, we can just subtract to find x.

180 - 27 - 78
= 153 - 78
= 75

So, the value of x is 75°.

Hope this helps!

What is the simple interest on $360 borrowed for 30 months at 12.3%? 
(PLEASE EXPLAIN)

Answers

Interest  = principal * rate * time / 100   = 360 * 12.3 * 2.5   / 100  (Note 30 months = 2.5 years)

Answer is  $110.70
Hello there! I can help you! The formula for simple interest is prt. We multiply the principal (inital amount) by the interest rate (in decimal form) by the time (could be in months or years). For this expression, our principal is $360. The interest rate is 12.3% (0.123 in decimal form). We will multiply those two numbers first. 360 *12.3% is 44.28. That's $44.28 in interest per year, but we're not done. Now, we multiply that by the amount of time, which is 30 months. In this case, we will convert that to years. 30/12 is 2.5. That is 2.5. We will multiply the interest by 2.5. 44.28 * 2.5 is 110.7. There. The simple interest is $110.70.
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