Can someone help me on this Proofs problems? It's just number one and two.

Can Someone Help Me On This Proofs Problems? It's Just Number One And Two.

Answers

Answer 1

See Explanation

Step-by-step explanation:

1. By interior angle sum Postulate of a triangle.

[tex] m\angle a+ m\angle y +m\angle z= 180\degree.... (1)\\\\

m\angle a+ m\angle w +m\angle x= 180\degree.... (2)\\\\[/tex]

From equations (1) & (2), we find:

[tex] m\angle a+ m\angle y +m\angle z= m\angle a+ m\angle w +m\angle x\\\\

m\angle y +m\angle z= m\angle w +m\angle x\\[/tex]

Hence proved

2. In [tex] \triangle PQS, \: \angle QSR [/tex] is exterior angle.

Therefore, by remote interior angle theorem, we have:

[tex] m\angle QPS + m\angle PQS= m\angle QSR\\\\

x + m\angle PQS= 2x\\\\

m\angle PQS= 2x-x\\\\

m\angle PQS = x.... (1)\\\\

m\angle QPS = x.... (given).... (2)\\[/tex]

From equations (1) & (2), we find:

[tex] m\angle PQS = m\angle QPS\\\\

\therefore \angle PQS \cong \angle QPS\\\\

\therefore PS \cong QS\\(sides\: opposite \: to\: congruent \:\angle s) \\\\[/tex]

[tex] \therefore \triangle PQS [/tex] is an isosceles triangle.

Thus proved.


Related Questions

A parachutist's speed during a free fall reaches 264 feet per second. What is this speed in meters per second? At this speed, how many meters will the parachutist fall during 10 seconds of free fall? In your computations, assume that 1 meter is equal to 3.3 feet. Do not round your answers.
Speed:

Distance fallen in 10 seconds:

Answers

Answer:  They will fall 800 meters. And they are falling 80 meters per second.

Step-by-step explanation: You must first take 264 divided by 3.3 which equals 80, then multiply is by 10.

Total distance fallen in 10 seconds is given by the equation A = 800 meter

What is Speed?

Speed is defined as the rate of change of position of an object in any direction. Speed is measured as the ratio of distance to the time in which the distance was covered. Speed is a scalar quantity as it has only direction and no magnitude

Speed = Distance / Time

Given data ,

Let the total distance fallen in 10 seconds be represented as A

Now , the value of A is

The parachutist's speed during free fall = 264 feet/second

Now , 1 meter = 3.3 feet

So , 1 feet = ( 1/3.3 ) meter

So , the value of 264 feet = 264 x ( 1/3.3 ) meter

On simplifying the equation , we get

The value of 264 feet/second = 80 meter/second

Now , the distance traveled by the parachutist every second = 80 meter

So , the distance traveled by the parachutist in 10 seconds = 10 x distance traveled by the parachutist every second

Substituting the values in the equation , we get

The distance traveled by the parachutist in 10 seconds A = 10 x 80

On simplifying the equation , we get

The distance traveled by the parachutist in 10 seconds A = 800 meter

Therefore , the value of A is 800 meter

Hence , the total distance is 800 meter

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A caterer charges $275 for 15 people and $425 for 25 people. The cost, y, is a
linear function of the number of people. Write an equation in slope-intercept
form for this situation.

Answers

Answer:

y = 15x + 50

Step-by-step explanation:

We set out by finding the slope

the two points give are (15,275) and (25,425)

Slope m is;

y2-y1/x2-x1 = (425-275)/25-15 = 150/10 = 15

So the equation is like;

y = 15x + b

To get b, let us use the point (15,275)

We have

275 = 15(15) + b

b = 275-225

b = 50

So the equation is;

y = 15x + 50

TRUE OR FALSE: When writing a number in scientific notation, the first number must be between 1 and 9

Answers

A number is written in scientific notation if it's composed of a whole number or decimal between 1 and 10 (including 1, but not 10) times a power of ten.

Answer:

True! Well kind of  

Step-by-step explanation: Its actually between 1 and 10 (nothing below 1 and nothing higher than ten) ✝️❤️

It takes a total of 3 hours to wash every window on a building. There are 30 windows. How many minutes does it take to wash just one window?
0 6 minutes
60 minutes
180 minutes
5.400 minutes

Answers

Answer:

6 minutes

Step-by-step explanation:

3 hours = 180 minutes

180 minutes / 30 windows= 6 minutes per window

The answer is 6 minutes and use quizlet or Socratic next time


What is the value of x in the equation:
1/3(x+3)+ 4 = -4+2
/3x

Answers

Answer:

Step-by-step explanation:

[tex]\frac{1}{3} (x+3)+4=-4+\frac{2}{3} x\\multiply~by~3\\x+3+12=-12+2x\\x-2x=-12-3-12\\-x=-27\\or~x=27\\[/tex]

or if it is

[tex]\frac{1}{3} (x+3)+4=-4+\frac{2}{3x}\\ multiply~by~3x\\x(x+3)+12x=-12x+2\\x^2+3x+12x+12x=2\\x^2+27x-2=0\\x=\frac{-27 \pm \sqrt{(27)^2-4*1*-2} }{2*1} \\or~x=\frac{-27 \pm \sqrt{729+8} }{2} \\or~x=\frac{-27 \pm\sqrt{737} }{2}[/tex]

i neeed help asap please

Answers

Answer:

X=8

Step-by-step explanation:

EASY MATH

5x+35=75
5x=40
x=8
set each part equal to each other because vertical angles are congruent

Quadrilateral ABCD is a square and the length of BD¯¯¯¯¯ is 10 cm. What is the length of AE¯¯¯¯¯ ? Enter your answer in the box. the length of AE¯¯¯¯¯ = cm

Answers

Answer:

3

Step-by-step explanation:

I took the test

simplify this expression 9xy4x 3x3y​

Answers

Answer:

81 x y^5

Step-by-step explanation:

Simplify the following:

9×3×3 x y^4 y

3×3 = 9:

9×9 x y^4 y

9 x y^4×9 y = 9×9 x y^(4 + 1):

9×9 x y^(4 + 1)

4 + 1 = 5:

9×9 x y^5

9×9 = 81:

Answer: 81 x y^5

Seismosaurus is the longest known dinosaur. It measured 1800 inches. How far would 3000 Seismosaurus dinosaurs span if they were placed head to tail. Use scientific notation to calculate the length. (PLEASE HELP ME! MY WORK IS DUE TOMORROW)

Answers

Answer:

I am not sure sorry

Step-by-step explanation:

Qual é o oposto de de -3

Answers

Answer:

lo contrario de -3 es positivo tres o 3

How can ΔABC be mapped to ΔXYZ?

First, translate vertex A to vertex
.

Next,
ΔABC to align the sides and angles.

Answers

Answer:

X

Rotate

Step-by-step explanation:

correct on edge 2020

Answer:

a. x

c. rotate

Step-by-step explanation:

edge2021 :)

Student council is selling Roses and Candy Grams for Valentine's Day. Each Candy Gram costs $1.50
and each Rose costs $2.00. The student council made $368 from their sales. They sold a total of 217
Roses and Candy Grams. How many roses were sold? Show all your work for full marks! (Solve the linear
system using substitution or elimination).
Letr represent
Let c represent
I

Answers

Answer:

Number of Roses sold = 132

Number of Candy Grams sold = 85

Step-by-step explanation:

Let the number of Roses sold = [tex]r[/tex]

Let the number of Candy Grams sold = [tex]c[/tex]

Cost of one Rose = $1.50

Cost of [tex]x[/tex] Roses = $1.50 [tex]r[/tex]

Cost of one Candy Gram = $2.00

Cost of [tex]y[/tex] Candy Grams =  [tex]\$2.00 \times c[/tex]

Total number of Roses and Candy Grams sold = 217

i.e.

[tex]r+c=217 ..... (1)[/tex]

Total cost = $368

Writing equation as per question statement:

[tex]\$1.50r+\$2.00c=\$368 ..... (2)[/tex]

Using elimination method, let us eliminate [tex]y[/tex] of the two equations.

Multiplying equation (1) with 2 and subtracting equation (2) from it:

[tex]0.50r=2\times 217 - 368\\\Rightarrow 0.50r=434 - 368\\\Rightarrow 0.50r=66\\\Rightarrow r=132[/tex]

By equation (1):

[tex]c=217-132\\c=85[/tex]

So, the answer is:

Number of Roses sold = 132

Number of Candy Grams sold = 85

If the geometric mean between 1/9 and m is 2, then find the value of m.​

Answers

Answer:

Letmeansareaandb

then1,a,b,64areinGP

∴64=1×r

2

∴r=4

thena=1×r=4

b=1×r

2

=16.

So, the correct option is '4 and 16'

plz help asap
thanks xoxoxoxoxox

Answers

i cannot see a pictureesss
There is no picture

Please help
Tracy is saving to buy a new guitar that costs $253.77 (including tax). Tracy has saved $136.27, and she can save $23.50 each week.
Which equation could you use to find how long it will take to save for the guitar?
$253.77 + $136.27 = $23.50 w
$253.77 - w = $136.27 + $23.50
$136.27 + $23.50 w = $253.77
$23.50 w = $253.77

Answers

Answer:

is  the last one brof

Step-by-step explanation:

I’d say the third one




If I was asked to think of a number and multiply it by 2, I could
write this algebraically as 2x.
Write the following algebraically, using x as your unknown.
"I think of a number, add 3 to it and multiply the result by

Answers

Answer:

6

Step-by-step explanation:

u use the equation 2x

so It looks like this...2(3)

so the result is 6

pls mark me as brainliest

Free cookies Just answer this question! Elena solves the equation x^2=7x by dividing both sides by x to get 7. She says
the solution is 7. Lin solves the equation x^2=7 by rewriting the equation to get
x^2-7=0. When she graphs the equation x^2-7=0, the x-intercepts are (0,0) and
(7,0). She says the solutions are 0 and 7. Why should Elena not divide by x?

Answers

x could be equal to zero, and we can't divide by zero, so we shouldn't divide by x.

Why should Elena not divide by x?

Here we have the quadratic equation:

[tex]x^2 = 7x[/tex]

Notice that we don't know the value of x, so technically, x could be equal to zero, and we can't divide by zero, so we shouldn't divide by x.

The quadratic equation can be rewritten as:

x^2 - 7x = 0

x*(x - 7) = 0

(x - 0)*(x - 7) = 0

So the two solutions are x = 0 and x = 7, because x = 0 is a solution, we see that x can be equal to zero, so we can't divide by x.

If you want to learn more about quadratic equations:

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Amrit initiated new venture with cash rupees 20000 and bank balance rupees 80000 journal entry​

Answers

Answer:

100000 rupees great success!

Step-by-step explanation:

Use a sentence to describe c(10)=-3

Answers

Answer:

a number times ten equals negative three

Step-by-step explanation:

A school boy agrees with his schoolmaster that he will pay a penny for every sum he gets wrong, if he wins 3 pence for every one he gets right. After doing 20 sums he is 4 dimes down. How many did he get right?

Answers

Answer:

you see he is 4 pens down you see is 3 pence for every one he gets right. after doing 20 sums he is 4 down so 20 dived by is 5 if there is an answer choice for 16 pick 16 if both pick 5 first trust me.

I NEED HELP ASAP!!!!!!ANY RIGHT ANSWER GETS BRAINLIEST!!!
A bookstore is advertising 25% off all books today. What is the sale price of a book that has a retail price of $18?

a.$13.50
b.$4.50
c.$22.50
d.$16.50

Answers

it’s a
100-25= 75
75 divided by 0.01
0.75 x 18

If anyone plays pokemon go put your code in your answer and I will add you

Answers

that's not why this app is for

Answer:

i don't sorry! my friend does... let me see if i can get their code

Step-by-step explanation:

a car can drive 600 miles on 18 gallons of gasoline. How many miles can a car drive on 15 gallons of gasoline​

Answers

Answer:

Use the cross technique if it’s name like that in English but , I wish you can understand it from what I‘ve written .

it would be about 500 miles. if you divide 600 by 18 to get the miles for 1 gal (about 33.3). then you multiply it by 15 to get the 500 (499.5 rounded up)

Rhonda bought her son an inflatable pool for the summer. It took her twenty minutes
to fill the pool to a depth of 6 inches. What is the unit rate per minute? (inches per minute)

Answers

Answer:

the unit rate would be 0.3 inches per minute (i'm pretty sure)

Step-by-step explanation:

because 6 divided by 20 = 0.3

hope this was correct and i hope this helped have a good rest of your day :)

Find the slope of the line

Answers

Answer:

Slope is y= -1/2x + 6.5

Step-by-step explanation:

my brain is too tired to function someone save me

Answers

Answer:

(3,2)

Step-by-step explanation:

Hope I helped

What is 1/3-5/6/5/6 enter ur answer of simplest form

Answers

Answer: 0.30555555555

Step-by-step explanation:

18(x + 1) = -54 pls help solve this...​

Answers

Answer:

x = 71

Step-by-step explanation:

18(x + 1) = -54

to start off, subtract 18 from both sides

18 - 18(x + 1) = -54 - 18

that should give you

x + 1 = 72

(its safe to take out paranthesis from problem by now) now take away 1 from each side

x + (1 - 1) = 72 - 1

that should give you

x = 71

A company that makes​ hair-care products had 2,000 people try a new shampoo. Of the 2,000 ​people, 6 had a mild allergic reaction. What percent of the people had a mild allergic​ reaction?
*blank* % of the people had a mild allergic reaction.

Answers

Answer:

0.3%

Step-by-step explanation:

Answer:

0.3%

Step-by-step explanation:

Divide 6 by 2000

6/2000 = 0.003

One Way to Solve:

To convert any percentage to a decimal, move the decimal point two spaces back from the percentage

0.003 = 000.3%

the fastest train in the western hemisphere is acela express on a route between boston,massachusetts and new haven,conneticut the train regulary travels 135 miles in 60 minutes what is the speed in mies per minutes on the portion of the route

Answers

Answer:

acela express

Step-by-step explanation:

it travles 135 miles in and hout

Answer:

2.25

Step-by-step explanation:

its right on edg

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