Fill in the missing reasons in the Two-column proof below.
Given: m∠2 + m∠3 + m∠4 = 180°
Prove: m∠1= m∠3 + m∠4

Statement Reasons
a. m∠2 + m∠3 + m∠4 = 180° a.
b. m∠1 + m∠2 = 180° b.
c. m∠1 + m∠2 = m∠2 + m∠3 + m∠4 c.
d. m∠1 + m∠2 - m∠2 = m∠2 + m∠3 + m∠4 -m∠2 d.
e. m∠1 = m∠3 + m∠4 e.

Answers

Answer 1

a. Given (This is part of the original problem)
b. Supplementary angles form 180 degrees (The definition of supplementary angles is that two or more angles have a sum of 180 degrees. DC is a straight line and has a measure of 180 degrees)
c. Substitution (Given the two previous statements, they are each equal to 180 degrees. Since 180=180 then you can substitute the angles in the equation.)
d. Subtraction (m<2 is being subtracted)
e. Subtraction postulate (Since the same quantity was being subtracted from each side of the equation, they are still equal)

Related Questions

I've never really understood these, can someone just help?

Answers

I know for sure that that is a whole number. I hop this much helps a little bit.

it would be whole real and natural hope I helped u beautiful

what is 528 1/5 - 89 3/5

Answers

the answer is 438.6...
(528+1/5)-(89+3/5)=438.6

Susan has raised $234 by selling 18 equally priced wreaths for the band fund-raiser. Which of the following equations can be used to find the price, y, of each wreath?

Answers

We know that Susan has raised $234 by selling 18 equally priced wreaths. So the find the price, y, of one wreath, we need to divide 234 by 18. And that can be done using the equation 18y = 234.

How?
18y = 234

Divide both sides by 18
(18y)/18 = 234/18
y = 234/18
y = 13

So using the equation 18y = 234, we were able to find the price of each wreath: y = $13

Hope this helps! :)

18x = $234 equation help Susan to find the price of each wreath, which is equals to $13.

What is linear equation in one variable?

" Linear equation in one variable is mathematical expression of writing an equation in which highest degree of the variable is one."

According to the question,

Amount raised by Susan = $234

Number of wreaths =18

'x' represents the price of each wreath .

As per the condition given , linear equation we get,

18x = $234

⇒x = 234 / 18

= $13

Hence, 18x = $234 equation help Susan to find the price of each wreath, which is equals to $13.

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Mark and Don are planning to sell each of their marble collections at a garage sale. If Don has 2 more than 3 times the number of marbles Mark has, how many does each boy have to sell if the total number of marbles is 78 ?

Answers

3x+2 is how many don has, and mark has x marbles, then 4x + 2 is the total, and x = 19, then your answers are 19, and 59.

Don has 59 and Mark has 19

What is the equation?

An equation is a mathematical expression that contains an equal symbol. Equations often contain algebra. Algebra is used in math when you do not know the exact number in a calculation.

Types of Equations

Linear EquationsQuadratic EquationsCubic Equations

Mark + Don = 78 marbles

Let, M = Mark and D = Don

M = 78-D We'll use this value for M next:

D = 3M+2

D = 3(78-D)+2

D = 234-3D+2

4D = 236

D = 59

Don has 59 and Mark has 78-59 = 19

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Type the correct answer in the box below.

Use numerals instead of words. If necessary, use / for the fraction bar(s). A line passes through point (-2, 5) and has a slope of . Points A(x, 3) and B(-2, y) lie on the line. The value of x is , and the value of y is . (already solved))

2. -1/2 + (1 1/4)
Type the correct answer in the box below.

Answers

Regroup the terms
2nd as a fraction is 3/4, converted to decimal is 0.75 :)

How much pure water must be mixed with 10 liters of a 25% acid solution to reduce it to a 10% acid solution?

Answers

The solution is 25% acid, which means 2.5 liters acid (10 x .25).
you need that 2.5 liters to be 10%, or 1/10th the total.
the total would have to be 25 liters (2.5 x 10) so when you add to 10 to get 25 you get 15 liters. Hope I helped!

How much pure water must be mixed with 10 liters of a 25% acid solution to reduce it to a 10% acid solution?

15L

there were 18 cans ona shelf. a customer bought 7 cans. then jake put 6 cans on the shelf. how many cans are on the shelf now?

Answers

18-7+6=17

17 cans are on the shelf.

18-7 =11
11+6 =17

So 17 is your answer :)

Factor the expression. 49b^2+70b+25

Answers

Hope i helped follow me!!(7b+5)^2

Bryan reads for x minuets. Kelly Reads for 1/4 the amount of time Brian reads.
Which statement explains 1/4x and 0.25x can each find the number of minuets jelly reads?

A. The fraction 1/4 is equivalent to the decimal 0.75 .there for 1/4 X can be written as 0.75X.

B. Multiplying by 1/4 is the same as multiplying by 25%.

C. The expressions are not equivalent.

D. Multiplying by four is the same as multiplying by 25%

Answers

Option B is correct.
1/4 = 0.25 = 25%, so 1/4x = 0.25x = 25% of x

simplify the expression (0.4)^{3}.

Answers

0.4 ^3 = 0.4 x 0.4 x 0.4

0.4 x 0.4 = 0.16

0.16 x 0.4 = 0.064

your answer is 0.064

hope this helps

Ok, so you got 0.4 to the power of three so that means you have to solve

0.4 x 0.4 x 0.4

0.4 x 0.4 = 0.16

0.16 x 0.4 = 0.064

So the answer would be 0.064

Each day Ernesto drives 52 miles. If he can drive 26 miles on one gallon of Gasoline, how many days can he drive on 14 gallons of gasoline?

Answers

It will take him 2 days to use up four gallons and 7 days to use it all up

A carton of juice contains 64 ounces. Ms.Wilson bought 6 cartons of juice how many ounces of juice did she buy

Answers

384 ounces of juice

she bought 384 ounces of juice. Hope this helps

At a supermarket pineapple juice sells at $1 per pint (16 ounces). Greg wants to buy 18 40-ounce cans of pineapple juice from the supermarket. How much does he have to pay altogether?

Answers

$45. You take the 40 ounce cans and multiply that by 8, those numbers create the overall amount of ounces he needs. The store sells by 16 punces and right now he needs 720 ounces. You take 720 and divide it by 16 to get 45 pints/$

Greg would need to pay a total of $45 for 18 40-ounce cans of pineapple juice, after converting the total ounces to pints at the given price of $1 per pint.

To determine how much Greg needs to pay for 18 40-ounce cans of pineapple juice, we first need to calculate the total number of ounces Greg is purchasing and then convert that to pints since the price is given per pint. One pint equals 16 ounces, so we can use this to find the cost.

Step-by-Step Calculation:

Calculate the total ounces of pineapple juice.

18 cans imes 40 ounces per can = 720 ounces total.

Convert ounces to pints since the price is per pint.

720 ounces ÷ 16 ounces per pint = 45 pints.

Calculate the total cost.

45 pints imes $1 per pint = $45 total.

Therefore, Greg has to pay a total of $45 for 18 40-ounce cans of pineapple juice.

He first term of a sequence is 2, and each subsequent term is the reciprocal of the square of the preceding term. what is the positive square root of the fifth term?

Answers

In the given sequence, each subsequent term is the reciprocal of the square of the preceding term.

We know that the first term is 2, this means that the second term is:
1/(2)^2 which is 1/2
The third term in the sequence would be:
1/(1/4)^2 = 1/(1/16) = 16
The forth term in the sequence would be:
1/(16)^2 = 1/256
The fifth term in the sequence would be:
1/(1/256)^2 = 1/(1/65536) = 65536

Now, the question asks for the positive root of the 5th term, this means the positive root of 65536 which is 256

Which equation represents a proportional relationship? y= 1 /2x or y=2(x+ 1 3 ) or y = 3x or y=−3x+2

Answers

y = -3x + 2 represents a proportional relationship.

The area of a parallelogram is 45 square miles. Find the base and height.

Answers

51 and 39 are your answers :D

Please help me to answer these questions!!

1- There are 40 ping-pong balls in a box. 16 of them are dented. Find the ratio of the number is dented ping-pong balls to the total number of ping-pong balls in the box if another 12 dented ping-pong balls are added into the box??
=

2- The total height of three friends, Sasha, Tess and Wendy, is 470 cm. The ratio of the height of Sasha to the height of Tess is 3 : 4. Wendy is 30 cm taller than Tess. Find the ratio of Tess’ height to Wendy’s height??
=

3- Josh, Ben and Rick have 70 marbles altogether. The ratio of the number is marbles Josh has to the number of marbles Rick has is 1 : 2. However, Ben has 15 marbles fewer than Rick. How many marbles does Ben have?
=

Answers

Final answer:

The ratio of dented ping-pong balls to the total number of ping-pong balls is 28/52. The ratio of Tess' height to Wendy's height is 8/9. Ben has 19 marbles.

Explanation:

Question 1:

To find the ratio of dented ping-pong balls to the total number of ping-pong balls, you need to add the number of dented balls before and after adding 12 more dented balls.

Given that there are initially 16 dented balls in a total of 40 balls, the ratio is 16/40.

After adding 12 more dented balls, the total number of dented balls becomes 16 + 12 = 28.

The total number of ping-pong balls is 40 + 12 = 52.

Therefore, the ratio of dented balls to the total number of balls is 28/52.

Question 2:

Let's assign variables for the heights of Sasha, Tess, and Wendy.

Let the height of Sasha be 3x.

Since the ratio of Sasha's height to Tess's height is 3:4, the height of Tess can be represented as 4x.

Wendy is 30cm taller than Tess, so Wendy's height is (4x + 30).

The total height of the three friends is 470cm, so we can write the equation 3x + 4x + (4x + 30) = 470.

Simplifying the equation gives us 11x + 30 = 470, and solving for x gives us x = 40.

Therefore, the ratio of Tess's height to Wendy's height is 4x/(4x + 30) = 4*40/(4*40 + 30) = 160/190 = 8/9.

Question 3:

Let's assign variables for the number of marbles Josh, Ben, and Rick have.

Let the number of marbles Josh has be x.

Since the ratio of Josh's marbles to Rick's marbles is 1:2, the number of marbles Rick has is 2x.

Ben has 15 fewer marbles than Rick, so Ben has (2x - 15) marbles.

These three quantities sum up to 70, so we can write the equation x + 2x + (2x - 15) = 70.

Simplifying the equation gives us 5x - 15 = 70, and solving for x gives us x = 17.

Therefore, Ben has 2x - 15 = 2*17 - 15 = 19 marbles.

Write a word phrase to represent the numerical expression 4+(27-10)

Answers

a word phrase that represented the numerical expression would be four plus the difference of 27 and 10

In linear equation ,the numerical expression would be four plus the difference of 27 and 10.

What are instances of linear equations?Ax+By=C represents a two-variable linear equation in its standard form. A standard form linear equation is, for instance, 2x+3y=5.Finding both intercepts of an equation in this form is rather simple (x and y).When resolving systems of two linear equations, this form is also incredibly helpful.A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

given numerical expression = 4 + (27 - 10)

so,

4 + (27 - 10)

It should be the sum of 4 and a difference of 27 and 10

a word phrase that represented the numerical expression would be four plus the difference of 27 and 10.

4 + (27 - 10)

= 4 + 17

= 21

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A car travels 2 1/3 miles in 3 1/2 minuets at a constant speed

Answers

2 1/3 miles / 3 1/2 minutes

7/3 * 2/7 = 14/21 = 2/3 mile per minute

A) d = 2/3m

2/3 mile per minute *60 minutes = 40 miles per hour

d=40h

Or is it c. 10.96 or d 13.0 (sorry the rest couldn’t fit in the picture) please help me I don’t get it.

Answers

We have a right triangle with legs of 6 and 8. The hypotenuse is unknown so let it be x for now

Plug these three values
a = 6
b = 8
c = x
into the Pythagorean Theorem below. Then solve for x

a^2 + b^2 = c^2
6^2 + 8^2 = x^2
36+64 = x^2
100 = x^2
x^2 = 100
sqrt(x^2) = sqrt(100) ... apply the square root to both sides
x = 10

The final answer is 10 ft. This option isn't listed which makes me think your teacher made a typo somewhere.

770 Times 6 equals 77 Times 6 Times 100

Answers

Hello There!

If you are asking for this in numerical form it is:

770 x 6 = 77 x 6 x 100
If you are asking whether it is true or not, well let's check:
770 x 6 = 4620
77 x 6 x 100 = 46200.

Therefore it is false, as there is a times 10 difference between the 2 sides.

Hope This Helps You!
Good Luck :)

- Hannah ❤

Write an example of the distributive property.

Answers

3(3x9)

3x3=9
3x9=27
9+27=36

4 Times 1 5 Times 1 4 plus 5 is 9

Which expression has an estimated product of 60

Answers

Specific mathematical expressions are needed to determine which has an estimated product of 60, for instance, combinations like 10 times 6 or 15 times 4.

The question relates to estimating the product of numerical expressions to determine which one is closest to 60. However, the provided information contains unrelated data and does not present clear mathematical expressions that we can evaluate to find an estimated product of 60. Thus, to accurately answer this question, we would need specific expressions to consider. In general, an expression likely to have an estimated product of 60 would be the multiplication of two numbers whose product is close to 60. For instance, numbers like 10 and 6 or 15 and 4 could be suitable factors in such expressions.

What weight of dry substance is in 150g of a 3% substance solution? What weight of an 8% solution can we have with the same weight of dry substance?

Answers

4.5 g 56.25 g Since the only type of measurement mentioned in this question is weight or mass, I'll assume that the percentage concentration is % m/m (mass/mass). For that type of concentration measurement, simply multiple the percentage by the total mass to get the mass of the desired substance. So 150 g * 3% = 150 g * 0.03 = 4.5g For the amount of 8% solution with the same amount of dry substance, there's 2 ways of calculating the mass of solution. First, use the ratio of percentages, multiplied by the mass of the original solution to get the desired amount of new solution: 3/8 * 150 g = 56.35 g Or calculate it from scratch, like 4.5/X = 8/100 450/X = 8 450 = 8X 56.25 = X In both cases, the result is that you desire 56.25 grams of 8% solution.

Answer:

4.5 and 56.25

Step-by-step explanation:

Write the equation in proper standard form, 9x-2/3y=-4

Answers

i think it is 2/3y=9x+4, forgive me if im wrong

The cost of 8 adults tickets to a movie is $66. What is the cost of one adult ticket?
THE FIRST ONE THAT ANSWERS AND EXPLAINS WHY HE GOT THAT WILL NE MARKED AS BRAINIEST

Answers

If you want to find the cost per adult if 8 of them buy tickets for a total of $66, you would divide the total cost by the number of tickets bought. So, $66 divided by 8 would equal to $8.25 per ticket.

when chef alice makes rice pailaf for 30 people she uses 15 cups of chicken broth and 10 cups of rice dan wants to make the same recipe for 9 people write and use equations to find how much broth and how much rice dan should use

Answers

30 / 2 = 15 cups of chicken broth
30 / 3 = 10 cups of rice

Using the same equation:
9 / 2 = 4.5 cups of chicken broth
9 / 3 = 3 cups of rice

15 cups of chicken broth + 10 cups of rice = 30 people

4.5 cups of chicken broth + 3 cups of rice = 9 people

The number of cups of chicken broth required for 9 people is 4.5.

The number of cups of rice required for 9 people is 3

What is an equation?

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

We have,

Alice makes rice pailaf for 30 people she uses 15 cups of chicken broth and 10 cups of rice.

This can be written as,

15 cups of chicken broth + 10 cups of rice = 30 people _____(1)

Now,

Multiply 9/30 on both sides.

9/30 x 15 cups of chicken broth + 10 cups of rice) = 9/30 x 30 people

9/30 x 15 cups of chicken broth + 9/30 x 10 cups of rice = 9 people

4.5 cups of chicken broth + 3 cups of rice = 9 people

Thus,

The number of cups of chicken broth required for 9 people is 4.5.

The number of cups of rice required for 9 people is 3

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A square has an area of 4x^{2} + 12xy + 9y^{2} square meters. What is the perimeter of the square?

Answers

Answer:

Perimeter = 4L = 4(2x+3y) = 8x+12y

Step-by-step explanation:

Given:

square with area A(x,y) = 4x^2+12xy+9y^2

Find perimeter.

A(x,y) = (2x+3y)^2

Length of each side

L = sqrt( A(x,y) ) = sqrt((2x+3y)^2) = 2x+3y

Perimeter = 4L = 4(2x+3y) = 8x+12y

20 Points Please help.
Write the system of inequalities shown in the graph

Answers

(1,2)....(2,-2)... now its making me write about 20 characters for some reason but anyways there is your answers i think buttt.... have a very nice day good luck on the rest of your school :)

The solution of a linear inequality is the ordered pair that is a solution to all inequalities in the system and the graph of the linear inequality is the graph of all solutions of the system.Graph one line at the time in the same coordinate plane and shade the half-plane that satisfies the inequality.

The expression 3(x^2-1)-(x^2-7x+10) is equivalent to

Answers

It is equivalent to 2x^2 + 7x -13

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