Mathematics High School

The diagram shows triangle PQR.
PSR is a straight line.
size of angle PQS : size of angle SQR = 3:1
S
Work out the size of angle PSQ

The Diagram Shows Triangle PQR.PSR Is A Straight Line.size Of Angle PQS : Size Of Angle SQR = 3:1SWork

Answers

Answer 1

Answer:

Angle PSQ is 61°

Step-by-step explanation:

In the triangle ΔPQR, we have;

m∠QPS = 65°

m∠PRQ = 43°

Line PSR is a straight line

m∠PQS : m∠SQR = 3:1

Therefore;

∠PQR = 180° - (∠QPS + ∠PRQ), by the angle sum theorem of a triangle

∴ ∠PQR = 180° - (65° + 43°) = 72°

∠PQR = 72°

∠PQR = m∠PQS + m∠SQR by angle addition postulate

m∠PQS : m∠SQR = 3:1

∴ m∠PQS = 3 × m∠SQR

∴ ∠PQR = m∠PQS + m∠SQR = 3 × m∠SQR + m∠SQR = 4 × m∠SQR

∠PQR = 4 × m∠SQR

∴ 4 × m∠SQR = ∠PQR = 72°

m∠SQR = 72°/4 = 18°

m∠PQS = 3 × m∠SQR = 3 × 18° = 54°

m∠PQS = 54°

∠PSQ = 180° - (∠QPS + ∠PQS) by the angle sum theorem

∴ ∠PSQ = 180° - (65° + 54°) = 61°

Angle ∠PSQ = 61°.

Related Questions

Write an equation where the variable is divided by a number, and a solution is -4/5

Answers

Answer:

x/-5

Step-by-step explanation:

Just divide by 5 and the denominator will be 5 meaning x would have to be 4.

Make sure your 5 is negative so the whole equation also ends up negative. x/-5=-4/5

y= 2? + 16x + 64
1. Identify a, b, and c
b=
C=

Answers

ask a tutor for help with that my dude I don't know sorry

BRAINLIEST

Plot the following co-ordinates and find the fourth point D to make a square A (-1,3) B (1,-1) C(5,1).

Once you have found the missing coordinate use pythagoras to calculate the length of the sides.

Answers

Answer:

Next coordinate is (-1,-3)

Step-by-step explanation:

draw a graph in graph paper and mark all coordinates

I can’t do this plz help

Answers

the correct answer is (x+4, y-3)
(x+4, y-3) i hope this helps you!

Given 6, 8, and 11 as the three sides of a triangle, classify it as one of the following acute, right or obtuse. Please help and thank you

Answers

9514 1404 393

Answer:

  obtuse

Step-by-step explanation:

You may remember that side lengths of 3, 4, 5 make a right triangle. Doubling those lengths to 6, 8, 10 will still give a right triangle.

The given triangle has a longest side (11) longer than would be appropriate for a right triangle (10), so the largest angle is larger than 90°.

The triangle is obtuse.

__

Comparison of a triangle to a right triangle with two sides the same is one of several ways the triangle can be classified. You can use the Law of Cosines to find the largest angle, or you can use a triangle solver (as we have below).

In case you don't recall that 3-4-5 makes a right triangle, you can use the Pythagorean theorem to find the longest side of a right triangle with the given shorter sides:

  hypotenuse = √(6² +8²) = √100 = 10

Your long side is longer, so your largest angle is larger than 90°.

Law of Cosines:

  angle = arccos((6² +8² -11²)/(2·6·8)) = arccos(-21/96) ≈ 102.6°

9) 8.081 +
+ 0.6 = 10.201
10)
- 3.328 = 0.96​

Answers

9) should be 8.681 so Falso 10) False

Please answer for Brainliest.

Answers

cameron would be making more money because he is making $7.60 per hour. you can find this out by dividing $30.40 by the 4 hours from the table given.

PLEASE FAST ANSWER ME PLEASEEE
During the election for class president, 30% of the students voted for Ruby, and 70% of the students voted for Ellie. 500 students voted in total. How many MORE students voted for Ellie than for Ruby?

Answers

Answer:

150,350

Step-by-step explanation:

FOR RUBY:

500x30/100=150

FOR ELLIE:

500x70/100=350

Answer:

200.

Step-by-step explanation:

100%->500

1%->500÷100=5

Ruby->30%->30×5=150

Ellie->70%->70×5=350

diff->350-150=200(ans)

Find the net change in the value of the function between the given inputs. h(t) = t2 + 2; from −5 to 8

Answers

Answer:

39

Step-by-step explanation:

Given the function :

h(t) = t² + 2

From t = 5 to t = 8

when, t = 5

h(5) = 5² + 2

h(5) = 25 + 2

h(t) at t = 5 ; equals 27

when, t = 8

h(5) = 8² + 2

h(5) = 64 + 2

h(t) at t = 8 ; equals 66

Net Change :

h(8). - h(5)

66 - 27 = 39

help me ASAP!!!!!! Please

Answers

I believe the anwser to be 15cm
69.28 :)
you wanna start by plugging in what you know.
a^2+65^2=95^2

now simplify.
a^2+4,225=9,025

[subtract 4,225 from both sides]
a^2=4,800

get a by itself by doing the opposite. [square root both sides]
a=69.28

hope this helped!

What do studies tell about people's way of life in traditional societies??

(Note: Please don't give me silly answer)​

Answers

Step-by-step explanation:

buffet or tells about the beliefs values behaviour and material object that constitute a people's way of life

Answer:

In sociology, traditional society refers to a society characterized by an orientation to the past, not the future, with a predominant role for custom and habit. Such societies are marked by a lack of distinction between family and business, with the division of labor influenced primarily by age, gender, and status.

Step-by-step explanation:

Hope it is helpful.....

^^^^^^^^^^^^^^^^^^^^^^^^

Answers

Answer:

117

Step-by-step explanation:

brainliest please

what is the distance between (-1, 2) and (5, -2)on a graph put into a decimal form. ​

Answers

Given:

The two points are (-1,2) and (5,-2).

To find:

The distance between the given points.

Solution:

Distance formula:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Using the distance formula, the distance between the given points is

[tex]d=\sqrt{(5-(-1))^2+(-2-2)^2}[/tex]

[tex]d=\sqrt{(5+1)^2+(-4)^2}[/tex]

[tex]d=\sqrt{(6)^2+16}[/tex]

[tex]d=\sqrt{36+16}[/tex]

On further simplification, we get

[tex]d=\sqrt{52}[/tex]

[tex]d=7.2111[/tex]

[tex]d\approx 7.21[/tex]

Therefore, the the distance between the given points is about 7.21 units.

What is the value of each expression?
7/8 + 4/8

Answers

7/8 + 4/8 = 11/8 = 1 3/8 = 1.375

Answer:

7/8 + 4/8 = 1 3/8.

Step-by-step explanation:

In words the answer is 1 and 3/8.

Rotate the triangle 180 degrees around the origin

Answers

If you rotate the triangle 180 degrees around the origin I’ll only go half way of that triangle

someone please answerrrrrr

Answers

The third answer because it is a linear increasing line

4x + 5y = 22
7x - 3y = -32

Answers

Answer:

x = -2

y = 6

Step-by-step explanation:

i multiplied the 1st equation by 3 and the 2nd by 5 to get the y-terms to zero out

   12x + 15y = 66

+  35x - 15y = -160

   47x = -94

x = -94/47

x = -2

substitute -2 for 'x' to solve for 'y':

4(-2) + 5y = 22

-8 + 5y = 22

5y = 30

y = 6

   

Rick's cat weighs 7 pounds. His neighbor says her puppy weighs 103 ounces.
Does Rick's cat weigh more than the puppy?
1 pound = 16 ounces )
How much does Rick's cat weigh in ounces?

Answers

Answer:

1. Yes

2. 112 ounces

Step-by-step explanation:

To answer this question, we should first convert the amount of pounds Rick's cat weighs into ounces, so that both measurements are in the same unit. Since 1 pound is the same as 16 ounces, we can multiply 7 pounds by 16 ounces:

7 * 16 = 112

So, Rick's cat weighs 112 ounces, which is more than his neighbor's puppy, which only weighs 103 ounces. so for the first question, the answer is:

Yes, Rick's cat weighs more than the puppy.

And the second answer is:

Rick's cat weighs 112 ounces.

Hope this helps :)

8. Solve for x. Round to the nearest tenth. (4pts)
55°
7
x=

Answers

Answer: I think 2

Step-by-step explanation:

Because

Im such an idiot for not paying attention in class but someone help PLEASE the assignment is due at 3:05 and its 2:50

Answers

Answer:

Help with what?

A box of cereal contains 510 grams of cereal. To make a bowl of cereal, n grams of cereal is removed from the box. What equation models the relationship between the quantity of cereal removed, n, and the quantity of the cereal remaining in the box, b?

Answers

Answer:

its 34

Step-by-step explanation: i

do y’all know this one?

Answers

Step-by-step explanation:

For first triangle,

sin 45 = 3 / d

1 / root 2 = 3 / d

d = 3 root 2

For second triangle,

tan 60 = 7 / a

root 3 = 7 / a

a = 7 / root 3

help me pls!!!! :c rip

Answers

Answer:

p^⁴/5

Step-by-step explanation:

Step-by-step explanation:

p^4/5. I just know the answer

brainliest for ripromano please anybody else dont answer

Answers

Answer:

ahhh you didnt have to !!

Step-by-step explanation:

thank you so much, ill do the same!! check my page for a question w free brainliest

someone pls help:>>

Answers

Answer:  n^2 + 1

Explanation:

Imagine that you cross out the top-most square for each step of each diagram. The squares not crossed out have the following counts: 1, 4, 9

This is the sequence of perfect squares. So the rule will have us take the number n, and square it to get n^2. Then we add on the squares we crossed out earlier. This explains the "plus 1" at the end to get the answer of n^2+1

Answer:

[tex] {n}^{2} + 1 \\ \: respresents \: the \: following \: \\ function[/tex]

i hope it helped.

PLEASE HELP!!
How could writing a problem using an exponent be easier to understand than repeated multiplication?

Answers

Answer:

One reason, is because it clearer and easier to read.

Seeing two numbers (3^5) can let you know, in this example, 3x3x3x3x3 is harder to understand than 3^5.

3 is the number being multiplied, and 5 tells you how many times.

~Hope this helps~

y = 6x - 13
5x - 2y = 5
Using the substitution method

Answers

Answer:

x=3, y=5

Step-by-step explanation:

What is the graph of the solution set of b - 42 -1?

Answers

Answer:Your answer would be F

Step-by-step explanation:

Please help me I would really appreciate it!!!!?!!

Jeffrey's birthday cost $21, plus an additional $2 for each guess he invites. How many guests can there be, at most, if jeffrey can afford to spent a total of $131 on his birthday party?​

Answers

Answer:

55 guests

Step-by-step explanation:

131 = 21 + (2x)

subtract 21 from both sides

110 = 2x

x = 55 guests

Answer:

55 guests

Step-by-step explanation:

if he can afford to spend a total of $131, then you subtract the birthday cost ( $21 ) and divide the answer of those two ( $110 ) by $2 ( the amount for each guest ) which is 55, therefore, 55 is the largest number of guests Jeffrey can afford.

GIVING BRAINLIEST! The triangles below are similar. How tall is the tree? Please show process.

Answers

Answer:

18m tall?

Step-by-step explanation:

Answer:

20 m

Step-by-step explanation:

The scale factor between the two triangles is 1/10 because of how 3/30 is 1/10.

Therefore we can calculate the height of the tree by multiplying the height of the smaller triangle by 10 to find the height of the tree.

2*10 = 20m

Other Questions
In the early part of the 18th century, production of goods moved from small workshops to large factories.TrueFalse In many countries, the religion of the monarch determined the religion of the people. How did the Framers of the Constitution ensure the power of the American government over religion would be limited? I need help plzA They provided a list of approved religions in the Constitution.B They included freedom of religion in the Bill of Rights.C They made it so that the religion of the country changed every 4 years.D They said that state governments could choose which religions were practiced. Fast-food restaurants work to make their products uniform Why did many Americans view the Federalists as traitors during the War of 1812?A. Members from the Federalist party refused to fight in the war and held public rallies against it.B. Several prominent Federalists were discovered to be spies for the British but were saved by the British before they could be properly put on trial.C. The Federalists had long supported peace with Great Britain, so when anger grew over British behavior, people were also angry with the Federalist PartyD. The Federalists refused to approve funding to manufacture more ships and weapons that Americans felt the United States needed to defeat Great Britain. Which group is most likely to continue to drop over time? what is beauty in art Solve for in the diagram below.110K(8x + 30)= The FDA Food Code safeguards the public's health and confirms to the consumer that food is safe to eat.O FalseO True HELP ASAP!!! PLEASE :) Yo soy ___ de baloncesto.A. equipoB. partidoC. jugador Could anyone mind helping I have until 9 Select all factors that could result in a lower temperature measurement.fast body processesslow body processestemperature being taken first thing in the morningtemperature being taken at the very end of the day 20 POINTS!!!!!!!!! Why is a wetland important to the environment?A.) They act as a sponge that holds rainwater, snow melt, and flood waters, which helps prevent floodsB.)Wetlands also filter water, cleaning the groundwaterC.) Fish and shellfish, various birds and mammals require coastal wetlands to survive. For instance, many animals raise their young in coastal marshes.D.) All of the above Which one is it?Aesthetic needs are: A.The need to be secure, safe, and out of danger.B. The need to know, to explore, and to understand. C. The need to achieve one's full potential as a person. D. The need to feel like you belong, are loved, and are valued. 2+2 its really really hard its the hardest problem i have ever done PLEASE HURRY~ DUE SOONYou ride your bicycle along the outer edge of the park. Then you take a shortcut back to where you started. Find the length of the shortcut. Round your answer to the nearest tenth.Answers:100m60m116.6m160m Answer please I have a timer! write a 3-5 paragraph essay explaining your understanding of Ghettos. what is the meaning of "tribulation" in paragraph 14? HELP! Need to finish this or my dad will go nuts.