Mathematics High School

In the circle shown below T is the center of the circle, and segments PN and SQ are diameters, and segment PR is tangent to the circle. The measure of angle SQN is 66 degrees

33 degrees
42 degrees
66 degrees
48 degrees

In The Circle Shown Below T Is The Center Of The Circle, And Segments PN And SQ Are Diameters, And Segment

Answers

Answer 1
Angle SQN = 66 degrees (given)
----------------------------
Use the inscribed angle theorem to get

Minor Arc SN = 2*(angle SQN)
Minor Arc SN = 2*(66)
Minor Arc SN = 132 degrees
----------------------------
Arc PSN is a semicircle so it is 180 degrees, meaning that...

Arc PSN = (minor arc PS) + (minor arc SN)
180 degrees = (minor arc PS) + (132 degrees)
180 = (minor arc PS) + 132
180 - 132 = (minor arc PS) + 132 - 132
48 = minor arc PS
minor arc PS = 48 degrees
central angle RTP = minor arc PS = 48 degrees
----------------------------
Focus on triangle PTR; isolate angle PRT

(angle TPR) + (angle PRT) + (angle RTP) = 180
(90) + (angle PRT) + (48) = 180
(90+48) + (angle PRT) = 180
138 + (angle PRT) = 180
138 + (angle PRT) - 138 = 180 - 138
angle PRT = 42 degrees
----------------------------
----------------------------
Final Answer: 
The measure of angle PRT is 42 degrees

Related Questions

Mark has a container in the shape of a cube. He uses 64 cubes with side lengths of 1 inch to completely fill the container. What is the edge length of the container?

Answers

This means the area is 64 inches^2:

x * x = 64
x = 8

Hope this helps!

Answer:

4 inches is the edge length of the container.

Step-by-step explanation:

Length of the small cubes = a = 1 inch

Volume occupied each small cube = v = [tex]a^3=(1 inch )^3= 1 inches^3[/tex]

Length of the big cube = A

Volume of the big cube = V

[tex]V=A^3[/tex]

He uses 64 cubes with side lengths of 1 inch to completely fill the container.

[tex]V=64\times v=64\times 1 inches^3[/tex]

[tex]A^3=64\times 1 inch^3[/tex]

A = 4 inch

4 inches is the edge length of the container.

how do you work out px+py=a?

Answers

[tex]\bf px+py=a\implies \stackrel{\textit{common factor}}{p}(x+y)=a\implies p=\cfrac{a}{x+y}[/tex]

___ L = 240 kL ?

A. 24,000
B. 240,000
C. 0.240
D. 2.4

Answers

Answer: B.240,000
240 Kiloliter =240,000 Liter

PLEASE HELP!

Solve for x.

x/3≤−6



A) x≤−18

B) x≤−2

C) x≥−2

D) x≥−18

Answers

The answer is A) x≤−18

A fair coin is tossed 10000 times the odds of getting exactly 5000 heads is closest to

Answers

Both heads and tails because there are only 2 choices

Answer:

5000 tails there are only two sides on  coin

Step-by-step explanation:

plz help me with number 9

and show work so i can understand thx

Answers

The answer is A, and there's no work needed, because the unit of millimeters is the most precise.

I think the answer is C, since it is measured to 2 decimal places



please help fast and show all work thanks

Answers

(-1-16^)^2+(14-16)^2
(-7)^2+(-2)^2
49+4
53= 7.3
So 7.3 is your answer

What is the measure of angle x, In degrees?

Helps please!!

Answers

Because segments XY and XZ are of equal length, angle Y and angle Z must be congruent.

All inner angles must add to 180 degrees since it's a triangle.
70+70+x=180
140+x=180
x=40

Final answer: D

Answer:

40° is the right answer for apex learners

I need to find the answer to 2/3 - 1/5. What is it?

Answers

2/3 - 1/5

make a common denominator

10/15 - 3/15

simplify

7/15 is your answer

hope this helps

Solve each system by elimation 2x-3y=6 and 6x-9y=9

Answers

6x - 9y = 9....divide everything by 3
2x - 3y = 3
-3y = -2x + 3
y = 2/3x - 1....slope is 2/3, y int is -1

2x - 3y = 6
-3y = -2x + 6
y = 2/3x - 2...slope is 2/3, y int is -2

same slope, different y int means parallel lines means no solutions

Relationship a has a greater rate than relationship
b. this table represents relationship
b. hours worked 2 4 5 8 amount paid 30.40 60.80 76 121.60 which equation could represent relationship a? select each correct answer. y = 14.9x y = 16.4x y = 15.4x y = 15.2x

Answers

Relationship a y=15.2X,
Used slope formula (Y2-Y1)/(X2-X1),
(60.80-30.40)/(4-2)=30.40/2=15.2

The required equation is y = 15.2x which could represent relationship A.

which is the correct answer would be an option (B).

What is a Linear Function?

A linear function is defined as a function in the form of f(x) = mx + c where 'm' and 'c' are real numbers.

We have been given that relationship A has a greater rate than relationship B.

Hours Worked                   Amount Paid

2                                              30.4

4                                               60.8

5                                               76

8                                             121.60

Let the number of hours worked x and the total amount paid y.

As per the given functions

⇒ y = 15.4x ...(i)

⇒ y = 15.2x ...(ii)

⇒ y = 16.4x ...(iii)

⇒ y = 14.9x ...(iv)

As per the linear function (ii),

⇒ y = 15.2×2

⇒ y = 30.4

The above is satisfy the point, therefore, it represents relationship A

Hence, the required equation is y = 15.2x which could represent relationship A.

Learn more about the linear function here:

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Which of the following products represents 6 1/2% tax, in dollars, on a price of $14.29? a. (0.00675)(14.29) b. (0.0675)(14.29) c. (0.675)(14.29) d. (6.75)(14.29)

Answers

to Convert a percentage to a decimal, you divide the percentage number by 100.
6.5% ÷ 100 = .065.
This is the rate you will multiply $14.29 by to get the amount of sales tax you must pay.

The correct answer is (0.065) (14.29) = $0.93

Based on the information provided, none of the above options are correct. 
The options provided would make more sense if it were a 6 3/4% tax, and the answer would be B. 

Answer:

B

Step-by-step explanation:

6 3/4% tax

Ray divides ∠COA into two angles of what measure?
20
30
40
35

Answers

The answer to ur question is 20 degree angles cause each dot is 5 degrees so that would equal 20 after you split them up

Answer:

20

Step-by-step explanation:


Eight plus the quotient of a number and 3 is -2

Answers

" the quotient" means divide

eight plus the quotient of a number and 3 is -2...

8 + (n/3) = -2 <== ur equation
n/3 = -2 - 8
n/3 = - 10
n = -10 * 3
n = -30 <== ur number
8+(n/3)=-2
N/3=-2-8
N=-30

Prove that the cube root of 2 is irrational.

Answers

The cube root of 2 is irrational. The proof that the square root of 2 is irrational may be used, with only slight modification. Assume the cube root of 2 is rational. Then, it may be written as a/b, where a and b are integers with no common factors. (This is possible for all nonzero rational numbers). Since a/b is the cube root of 2, its cube must equal 2. That is, (a/b)3 = 2 a3/b3 = 2 a3 = 2b3. The right side is even, so the left side must be even also, thatis, a3 is even. Since a3 is even, a is also even (because the cube of an odd number is always odd). Since a is even, there exists an integer c such that a = 2c. Now, (2c)3 = 2b3 8c3 = 2b3 4c3 = b3. The left side is now even, so the right side must be even too. The product of two odd numbers is always odd, so b3 cannot be odd; it must be even. Therefore b is even as well. Since a and b are both even, the fraction a/b is not in lowest terms, thus contradicting our initial assumption. Since the initial assumption cannot have been true, it must be false, and the cube root of 2 is irrational.

Angles A and B are the acute angles of a right triangle. If the tangent of A is 2.1445, then angle B measures

25
64
65

Answers

tan A = 2.1445
A = tan^(-1) 2.1445 = 64.999 ≈ 65°
In a right triangle:
A + B = 90°
65° + B = 90°
B = 90° - 65° = 25°
Answer:
A ) 25° (or your first option)

The requried measure of angle B is 25 degrees. Option A is correct.

What is the triangle?

The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°

Here,
In a right triangle, the tangent of an acute angle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.

Let A be one of the acute angles of the right triangle. Then, we have:

tan(A) = opposite/adjacent

Given that the tangent of angle A is 2.1445, we can write:

2.1445 = opposite/adjacent

Since angle B is also an acute angle of the same right triangle, we have:

tan(B) = opposite/adjacent

But since the sum of the angles of any triangle is 180 degrees, and one of the angles in this triangle is a right angle (90 degrees), we have:

A + B + 90 = 180

B = 90 - A

Substituting the expression for B into the equation for the tangent of angle B, we get:

tan(90 - A) = opposite/adjacent

tan(90 - A) = (1/tan(A)) x adjacent/opposite

tan(90 - A) = (1/2.1445) x adjacent/opposite

tan(90 - A) = 0.466

Taking the inverse tangent of both sides, we get:

90 - A = tan⁻¹0.466)

90 - A = 25.38

A = 90 - 25.38

A = 64.62

Therefore, the measure of angle B is,
B = 90 - A
  = 90 - 64.62 = 25.38 degrees

Thus, the requried measure of angle B is 25 degrees.

Learn more about triangles here:
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A gold mine has two​ elevators, one for equipment and another for the miners. The equipment elevator descends 66 feet per second. The elevator for the miners descends 1616 feet per second. One​ day, the equipment elevator begins to descend. After 2323 ​seconds, the elevator for the miners begins to descend. What is the position of each elevator relative to the surface after another 1616 ​seconds? At that​ time, which elevator is​ deeper? The position of the equipment elevator relative to the surface is negative 234−234 feet. The position of the elevator for the miners relative to the surface is nothing feet.

Answers

Given that the equipment elevator descends at 6 feet per second.

The total number of seconds travelled by the equipment elevator is 23 + 16 = 39 seconds.

Thus the position of the equipment elevator relative to the surface is given by -(6 x 39) = -234 feet.

Given that the miners elevator descends at 16 feet per second.

The total number of seconds travelled by the miners elevator is 16 seconds.

Thus, the position of the miners elevator relative to the surface is given by -(16 x 16) = -256 feet.

At that time the miners' elevator is deeper.

What happens to light energy from the Sun when it reaches the surface of Earth?

A.
The light energy is multiplied when it reaches the plants on Earth.

B.
The light energy is destroyed when plants are eaten by herbivores.

C.
The light energy is transformed to chemical energy by photosynthesis.

D.
The light energy is converted to potential energy by cellular respiration.

Answers

you're answer is C hope that helps

In the diagram, AB = 10 and AC = 2√10. What is the perimeter of △ABC?

A. 10 units
B. 10 + 2√10 units
C. 20 units
D. 20 + 2√10 units

Answers

Answer:

D. 20 + 2√10 units

Step-by-step explanation:

Perimeter is the distance all round a figure.


AB = 10. This is given in the question


AC = √((3-5)²+(4--2)²


= √(4+36)


=√40 = 6.32 units


BC = 5 - -5 = 10 units



Perimeter = AB+AC+BC


= 10+6.32+10


= 26.32 units

what is the measure of

Answers

Since opposite angles are equal, 8x+12=5x+57. Subtracting 5x as well as 12 from both sides, we get 3x=45. . Dividing both sides by 3, we get x=15. Plugging x=15 into 5x+57, we get 5*15+57=75+57=132

The running aces card team won $548 playing in poker tournaments last year. the winnings were split evenly among the p players. how much of money did each player receive?

Answers

Each player received 548/p dollars. To find this, simply consider the total amount of money the card team won, which is given as $548. Then consider that that the winnings are being distributed evenly, so each person gets an equal share. Since we are told that there are p players on the team, but not given a specific value for p, all we can do is give the general form of the expression for dividing $548 dollars among p players.

Answer:

Each player received 548/p dollars.

Solve the proportion. 2/8 = -30/x

Answers

To solve a proportion set it up like
[tex]\frac{2}{8} = -\frac{30}{x} [/tex]

Now cross multiply the -30 and the 8 so -30 x 8 = -240
Now take the -240 and divide it by 2
[tex] \frac{-240}{2} = -120[/tex]
So x = -120 

Answer = 120

The solution to the proportion 2/8 = -30/x is x = -120, found by cross multiplying and simplifying the resulting equation.

To solve the proportion 2/8 = -30/x, we will cross multiply to find the value of x. After cross multiplying, we obtain 2x = -30  imes 8. Simplifying this gives us 2x = -240, and dividing both sides by 2 yields x = -120. So the solution to the proportion is x = -120.

A forest owned by the Jumbo Lumber Corporation contains 7,054 trees. If Jumbo Lumber cuts down 37 trees every day, which function can be used to find the number of trees, n, left in the forest after t days?

Answers

Answer:

n(t)= 7,054 - 37t

Step-by-step explanation:

474: the 4 in the ones place is _____ the value of the 4 in the hundreds place.

Answers

Final answer:

In the number 474, the 4 in the ones place is less than the value of the 4 in the hundreds place by a factor of 100 because each position to the left in the place value system is worth ten times more than the one to its right.

Explanation:

The question deals with the concept of place value in mathematics. Specifically, it requires understanding how the value of a digit changes based on its position within a number. In the number 474, the 4 in the ones place has a value of 4, whereas the 4 in the hundreds place has a value that is 100 times greater, since each move to the left in place value represents a multiplication by 10. Therefore, the 4 in the ones place is less than the value of the 4 in the hundreds place. Here's a simple breakdown of the place values in the given number 474:

The first 4 (from left to right) is in the hundreds place, so its value is 4 x 100 = 400.The second 4 is in the ones place, so its value is 4 x 1 = 4.

Since 1 is less than 100, the 4 in the ones place is worth less than the 4 in the hundreds place by a factor of 100.

Final answer:

The value of the 4 in the ones place is 10 times the value of the 4 in the hundreds place.

Explanation:

The 4 in the ones place is 10 times the value of the 4 in the hundreds place.

Cube root of 0.000064

Answers

Cube root of 0.000064 = 0.04

hope it helps
------------------

Chan Hee bought 3.4 pounds of coffee that cost $6.95 per pound. How much money did he spend on coffee?

Answers

That would be 3.4 * 6.95  =  $23.63   answer

What is the next term in the sequence? 44, 22, 11, 5.5...

Answers

This is a geometric sequence and the common ratio is 0.5.

So, the next term will be 2.75.

Scott and Teri read mystery novels. Teri has read 3 less than 5 times as many as Scott. She has read 17. How many has Scott read?

Answers

Scott read 4. Put it this way: x=4. If = 4, then put it into an equation. 5x-3= 17. So, you add three to both sides, then it comes out as this: 5x= 20. Divide by five, and you get x= 4.
Setup an equations:
S = # Scott has read
T = # Teri has read

T = 5S - 3   (3 less than means subtraction but switch term order)
17 = 5S - 3 ( substitute 17 for T because Teri read 17)
4 = S (when you solve the equation)
Therefore, Scott read 4 books.

The township of Brock is growing at a rate of 6.5% per annum. How many people are there in Brock township now, if there will be 15000 in 4.5 years?

Answers

The formula is
A=p (1+r)^t
A people after 4.5 years 15000
P current people ?
R rate of growth 0.065
T time 4.5 years
Solve the formula for p to get
P=A÷(1+r)^t
P=15,000÷(1+0.065)^(4.5)
P=11,298.42 round your answer to get 11298

Hope it helps!

Find three solutions of the equation (x^2-9)(x^3-8)=0

Answers

(x^2-9)(x^3-8)=0

as you can see that (x^2-9) is in the form of a^2 - b^2 which equals (a+b)(a-b)

x^2 - 9
= (x)^2 -(3)^2
= (x+3)(x-3)


now, the equation becomes
(x+3)(x-3)(x^3-8)=0

(x+3) =0
x = -3


(x-3) = 0
x = 3

x^3 -8 = 0
x^3 = 8
x = cube rt. 8
= 2

so, the three solutions are -3, 3 and 2.
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