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

What is HB? Triangle Mid-segment Theorem

Answers

Answer:

HB = 13

Step-by-step explanation:

In triangle GHJ, points A, B, C are mid points of the sides GH, HJ, GJ respectively.

Therefore by Mid-segment Theorem.

[tex]AC = \frac{1}{2} HJ \\ \\ 3y - 5 = \frac{1}{2} (4y + 2) \\ \\ 3y - 5 = \frac{1}{2} \times 2 (2y + 1) \\ \\ 3y - 5 = 2y + 1\\ \\ 3y - 2y = 5 + 1 \\ \\ y = 6 \\ \\ HJ = 4y + 2 \\ \\ HJ = 4 \times 6 + 2 \\ \\ HJ = 24 + 2 \\ \\ HJ = 26 \\ \\ HB= \frac{1}{2} HJ \\ \\ HB= \frac{1}{2} \times 26 \\ \\ \huge \red{ \boxed{ HB= 13}}[/tex]

Who wants to be my gamergirl

Answers

Answer:

Well I'm not a girl soo No.

Step-by-step explanation:

Pretty please help me:)

Answers

Answer:

Step-by-step explanation:

a. Yes is proportional with the cost because they depend on one another

b. (0,0) means if we buy 0 cookies we pay $0

c. (1, 0.50) means that if we buy 1 cookie we have to pay $0.50

d. the unit rate is how much we pay for one cookie so is $0.50 per 1 cookie

The length of rectangle A is 7.4 cm and the width is 4.8 cm. The perimeter of rectangle B is 14.9 cm. How much is the perimeter of rectangle A than the perimeter of rectangle B?

Answers

Answer: 9.5 cm

Step-by-step explanation:

First we have to find the perimeter of rectangle A:

Formula for perimeter of a rectangle or square is: [tex]2(a+b)[/tex]

Putting the length and width in: [tex]2(7.4+4.8)[/tex]

Solve it to get: 24.4 cm

Subtract 14.9 from 24.4 to get 9.5 cm

3. Six neighborhood children - Leisha, Benito, Delia, Charlotte, Weldon, and Zina- were measured
yesterday. Weldon is taller than Delia but shorter than Zina. Leisha is taller than Benito but shorter than
Delia and Weldon. Benito isn't the shortest. Can you list the kids in order of height from tallest to shortest?
Please Help
WORTH 100 points!!!

Answers

zina, weldon, delia, leisha, bento, charlotte

Write the slope intercept form of the equation of the line through the given point plz

Answers

Answer:

y = 5/2x + 5

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDASEquality Properties

Algebra I

Slope-Intercept Form: y = mx + b

m - slope b - y-intercept

Step-by-step explanation:

Step 1: Define

Slope m = 5/2

Point (-4, -5)

Step 2: Find y-intercept b

Define:                              y = 5/2x + bSubstitute in point:          -5 = 5/2(-4) + bMultiply:                            -5 = -10 + bIsolate b:                           5 = bRewrite:                             b = 5

Step 3: Write linear equation

y = 5/2x + 5

If Jasper can walk
1/2
mile in 1/4 hour, how long will it take him to walk 1.5 miles?

Answers

45 mins

Step-by-step explanation:

A quarter of an hour is 15 mins. If jasper walks 1/2 a mile in 15 mins then in 1.5 miles is 3 times that. 15x3 is 45.

What is the image of (−3,9) after a reflection over the line y = x?

Answers

Answer:(9,-3)

Step-by-step explanation:

You just have to flip the numbers

HELP PLEASE ANSWER FULL QUESTION

Answers

Answer:

the constant of proportionality is the ratio between two directly proportional quantities.

b. k=y/x or y = k*1/x

Graph the line.
y=x-8

please hurry, 15 points

Answers

Answer:

graph your y intercept at negative 8 and then continue to go up one right one

Answer:

go down 8 then go up one over one the rest of the way. go to desmos to answer all your graphing questions.

Step-by-step explanation:

brainliest pls

i accedentaly wrote this

Answers

Answer:

uh

Step-by-step explanation:

this is for pre-calc can someone pls help

Answers

Answer:

Question 18: 453,600

Step-by-step explanation:

If a/b= 8 and ac -5 = 11, then bc =?

Answers

Answer:

bc = 2

Step-by-step explanation:

From [tex]a/b = 8[/tex]

[tex]a=8b[/tex] (times b on both sides)

We can then substitute [tex]a[/tex] for [tex]8b[/tex]:

[tex]ac-5=11[/tex] (given equation)

[tex]8bc-5=11[/tex]

[tex]8bc=16[/tex]

[tex]bc=2[/tex]

I hope this helps :)

what does congruent mean in geomatry?

Answers

Answer:

Congruent means same shape and same size. So congruent has to do with comparing two figures, and equivalent means two expressions are equal. So to say two line segments are congruent relates to the measures of the two lines are equal. Comment on David Severin's post “Congruent means same shape and same size.

Step-by-step explanation:

Answer:B

Step-by-step explanation:

Your Welcome;)

1
What is the equation of the line parallel to 8x - 16y= -14 and passing through (3, 0)?

Answers

Answer:

8x -16y = 24

Step-by-step explanation:

8x - 16y= -14

A parallel line (i.e. same slope) will be: 8x - 16y= c

We have to find the value of "c".

If it passes through (x, y) = (3, 0) ⇒ 24 - 0 =  c,

so equation is 8x -16y = 24

Will give brainlyest Will give brainlyest Will give brainlyest Will give brainlyest Will give brainlyest.idk and if you give me the answer can you tell me if I put it on the far right or left

Answers

Answer:

so i tried to draw it.

Step-by-step explanation:

Answer:

left

Step-by-step explanation:

plz i need 4 more brainlyests to pass

What is the y-intercept for -1,3 1,-2

Answers

I’m pretty sure it’s 1

A student factors a^6 - 64 to (a^2-4)(a^4 + 4a^2+ 16).
Which statement about (a^2 - 4)(a^4 + 4a^2 + 16) is correct?

Answers

Answer:

Option (b) is correct.

The expression is equivalent, but the term is not completely factored.

Step-by-step explanation:

edge 2020

Anyone know this question.
I need help quick.
Thanks.​

Answers

what question????????

Decrease £7200 by 5%
and what increases £2700 by 20%

Answers

Answer:

Decrease:£7,560

increase:£3,240

AnOtHeR MATH QUESTION (SMH). HELP PLEASE !!!

Answers

Answer:

For the function: [tex]g(x)=-x^2-3x+5[/tex], the average rate of change of function over the interval [tex]-7\leq x\leq 2[/tex] is 2

Step-by-step explanation:

We are given function: [tex]g(x)=-x^2-3x+5[/tex], we need to find average rate of change of function over the interval [tex]-7\leq x\leq 2[/tex]

The formula used is: [tex]Average \ rate \ of \ change=\frac{g(b)-g(a)}{b-a}[/tex]

We have b=2 and a= -7

Finding f(b) and f(a)

Finding g(b) by putting x=2

[tex]g(x)=-x^2-3x+5\\g(2)=-(2)^2-3(2)+5\\g(2)=-4-6+5\\g(2)=-10+5\\g(2)=-5[/tex]

Finding g(a) by putting x=-7

[tex]g(x)=-x^2-3x+5\\g(-7)=-(-7)^2-3(-7)+5\\g(-7)=-49+21+5\\g(-7)=-23[/tex]

Now, finding average rate of change when g(b)=-5 and g(a)=-23

[tex]Average \ rate \ of \ change=\frac{g(b)-g(a)}{b-a}\\Average \ rate \ of \ change=\frac{-5-(-23)}{2-(-7)}\\Average \ rate \ of \ change=\frac{-5+23}{2+7}\\Average \ rate \ of \ change=\frac{18}{9}\\Average \ rate \ of \ change=2[/tex]

So, Average rate of change = 2

Therefore for the function: [tex]g(x)=-x^2-3x+5[/tex], the average rate of change of function over the interval [tex]-7\leq x\leq 2[/tex] is 2

how do you do multiplication in 7th grade mathimatics

Answers

Answer:

Learn your timetables daily.

Step-by-step explanation:

You can find songs online to help you memorize and understand them in the simplest form.

Answer:

you should practice your timetables and do some math practice so you could understand other math like division.

Step-by-step explanation:

Amanda is hiking with her daughter, Mia who is only 1 yaar old and has very short leg. For every 3 steps Amanda makes, Mia takes 5 steps just to keep up.

Need help fast trying to take a test plsss help

Answers

Amanda table values: 3, 6, 15, 30
Mia Table values: 5, 10, 25, 50

find the slope from the graph (help please)

Answers

For the slope I got 0

Please help! Thanks!!

Answers

Answer:

x=12

Step-by-step explanation:

(2x-4)/5=4

We move all terms to the left:

(2x-4)/5-(4)=0

We multiply all the terms by the denominator

(2x-4)-4*5=0

We add all the numbers together, and all the variables

(2x-4)-20=0

We get rid of parentheses

2x-4-20=0

We add all the numbers together, and all the variables

2x-24=0

We move all terms containing x to the left, all other terms to the right

2x=24

x=24/2

x=12

Answer:

x = 12

Step-by-step explanation:

Given

[tex]\frac{2x-4}{5}[/tex] = 4 ( multiply both sides by 5 to clear the fraction )

2x - 4 = 20 ( add 4 to both sides )

2x = 24 ( divide both sides by 2 )

x = 12

Refer to the system of linear equations shown below. Which of the following statements gives the best choice for multiplying to solve this system using the elimination method? 3x−6y=4 6x+11y=−2

I NEED IT URGENtLY

Answers

Answer: I just took the test and the answer is Student should show that the solution to the system of equations 7x - y = 4 and 2x - 3y = 1 is the same as the solution to the given system of equations.

Step-by-step explanation:

The solution for the given system of linear equations is (32/69, -10/23).

The given system of equations are 3x-6y=4 and 6x+11y=-2.

What is a linear system of equations?

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

Here,

3x-6y=4 ---------(I) and 6x+11y=-2 ---------(II)

Multiply equation (I) by 2, we get

6x-12y=8 ---------(III)

Subtract equation (III) from (II), we get

6x+11y-(6x-12y)=-2-8

⇒ 23y=-10

⇒ y=-10/23

Substitute y=-10/23 in (I), we get

3x-6(-10/23)=4

⇒ 3x+60/23=4

⇒ 3x=4-60/23

⇒ x=32/69

So, solution is (32/69, -10/23)

Therefore, the solution for the given system of linear equations is (32/69, -10/23).

To learn more about the linear system of an equations visit:

https://brainly.com/question/27664510.

#SPJ2

Oy I hate this subject I swear just a few more but still giving out brainliest and points!

Answers

Answer:

C

Step-by-step explanation:

your y values which produce the range differ between 2 and 10 which means that will be your range. All of the values are real.

Item 29
Divide.
6.8÷4
6.8÷4

Answers

Answer:

1.7

Step-by-step explanation:

You can just use a calculator to make the work easier.

Check your answers by clicking all of the items
you included in your explanation.
A.A large portion of an organism's mass is in
the form of water.
B.Water contains two hydrogen atoms and one
oxygen atom.
C.The mass of oxygen is sixteen times that of
hydrogen.

Answers

Answer:

A and C

Step-by-step explanation:

What is the 38th term of 459,450,441,..

Answers

Answer:

The 38th term of 459,450,441,.. will be:

[tex]a_{13}=351[/tex]

Step-by-step explanation:

Given the sequence

[tex]459,450,441,..[/tex]

An arithmetic sequence has a constant difference 'd' and is defined by

[tex]a_n=a_1+\left(n-1\right)d[/tex]

computing the differences of all the adjacent terms

[tex]450-459=-9,\:\quad \:441-450=-9[/tex]

so

[tex]d=-9[/tex]

The first element of the sequence is

[tex]a_1=459[/tex]

so the nth term will be

[tex]a_n=-9\left(n-1\right)+459[/tex]

[tex]a_n=-9n+468[/tex]

Putting n=38 to find the 38th term

[tex]a_n=-9n+468[/tex]

[tex]a_{13}=-9\left(13\right)+468[/tex]

[tex]a_{13}=-117+468[/tex]

[tex]a_{13}=351[/tex]

Therefore, the 38th term of 459,450,441,.. will be:

[tex]a_{13}=351[/tex]

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