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Shtirlitz [24]
2 years ago
8

Can someone help me with this proof

Mathematics
1 answer:
maksim [4K]2 years ago
8 0

Step-by-step explanation:

Given :

Given that lines a and b are parallel, angles 1 and 5 are congruent because they are corresponding angles, and angles 1 and 4 are congruent because they are vertical angles

To find : by which property are angles 4 and 5 congruent

Solution :

We know that if two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent.

Also, we know that if two things are equal to the same thing then they are equal to each other . In this case, we can say that if two angles are congruent to a third angle, then they are congruent to each other. As angles 4 and 5 are both congruent to angle 1, they are congruent to each other but angles 4 and 5 are alternate interior angles. So, if parallel lines have a transversal, alternate interior angles are congruent.

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Which algebraic expression is a polynomial with a degree of 5
anygoal [31]

Answer: For example, the polynomial which can also be expressed as has three terms. The first term has a degree of 5 (the sum of the powers 2 and 3), the second term has a degree of 1, and the last term has a degree of 0. Therefore, the polynomial has a degree of 5, which is the highest degree of any term.

Step-by-step explanation: (If this helps)

8 0
3 years ago
Read 2 more answers
There are 14 juniors and 16 seniors in a chess club. a) From the 30 members, how many ways are there to arrange 5 members of the
Dmitrij [34]

Answer:

a) 17,100,720

b) 4,717,440

c) 10,920

d) 2821

Step-by-step explanation:

14 juniors and 16 seniors = 30 people

a) From the 30 members, how many ways are there to arrange 5 members of the club in a line?

As it is a ordered arrangement

30.29.28.27.26 = 17,100,720

b) How many ways are there to arrange 5 members of the club in a line if there must be a senior at the beginning of the line and at the end of the line?

16.28.27.26.15 = 4,717,440

c) If the club sends 2 juniors and 2 seniors to the tournament, how many possible groupings are there?

Not ordered arrangement. And means that we need to multiply the results.

C₁₄,₂ * C₁₆,₂

C₁₄,₂ = <u>14.13.12!</u> = <u>14.13 </u>= 91

           12! 2!            2    

C₁₆,₂ = <u>16.15.14!</u> = <u>16.15 </u>= 120

           14! 2!            2    

C₁₄,₂ * C₁₆,₂ = 91.120 = 10,920

d) If the club sends either 4 juniors or 4 seniors, how many possible groupings are there?

Or means that we need to sum the results.

C₁₄,₄ + C₁₆,₄

C₁₄,₄ = <u>14.13.12.11.10!</u> = <u>14.13.12.11 </u>= 1001

                  10! 4!               4.3.2.1    

C₁₆,₄ = <u>16.15.14.13.12!</u> = <u>16.15.14.13 </u>= 1820

                  12! 4!               4.3.2.1    

C₁₄,₄ + C₁₆,₄ = 1001 + 1820 = 2821

7 0
3 years ago
A manufacturer Phils various size boxes of flour. Today, the box and are 12 inches tall, 8 inches wide and 3 inches deep. They a
Digiron [165]

Here is what I got:(maybe wrong) 12*8*3 = 288, which is how big the box is. Then, you remove 1.5 inches from the height and get 10.5*8*3, which is 252. Subtract 252 from 288 to get the answer, 36.

8 0
3 years ago
Bob can paint a fence in 5 hours, and working with Jen, the two of them painted a fence in 2 hours. How long would it have taken
irakobra [83]

Answer:\frac{10}{3}

 

Step-by-step explanation:

Given

Bob can Paint a fence in 5 hr

so full job can be done in 5 hr

in 1 hr \frac{1}{5} job is done

suppose Jen done the work in x hr

so in 1 hr \frac{1}{x} part of job is done

Also if they combine they can do the job in 2 hr

so in 1 hr \frac{1}{2}

so \frac{1}{5}+\frac{1}{x}=\frac{1}{2}

\frac{1}{x}=\frac{1}{2}-\frac{1}{5}

\frac{1}{x}=\frac{5-2}{10}

x=\frac{10}{3} hr

3 0
3 years ago
I need help on the answer
kodGreya [7K]

Answer:

Step-by-step explanation:

First, we have to find 1 percent of 950, then we will multiply it by 8, and then we will add the solution to 950 to see if it exceeds her budge. So:

950/100 = 9.5

9.5 (8) = 76

950 + 76 = 1026

1026 > 1000, so she does not have enough money to but the T.V.

5 0
3 years ago
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