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Mariulka [41]
3 years ago
10

Fred and Victoria provide the following proofs for vertical angles to be equal.

Mathematics
2 answers:
Delvig [45]3 years ago
5 0
Both Fred and Victoria are correct.
mina [271]3 years ago
4 0

Answer:

Both Fred and Victoria's proofs are correct.


Step-by-step explanation:

Fred's proof:

  • angle 2 + angle 3 = 180° (t is a straight line) IT IS TRUE THAT t IS A STRAIGHT LINE
  • angle 1 + angle 2 = 180° (PQ is a straight line) IT IS TRUE THAT PQ IS A STRAIGHT LINE
  • Therefore, angle 1 + angle 2 = angle 2 + angle 3 (Transitive Property of Equality) THIS IS AN EXAMPLE OF THE TRANSITIVE PROPERTY OF EQUALITY
  • Hence, angle 1 = angle 3 (Subtraction Property of Equality)THIS IS AN EXAMPLE OF THE SUBTRACTION PROPERTY OF EQUALITY

Victoria's proof:

  • angle 1 + angle 4 = 180° (t is a straight line) <u>TRUE</u>
  • angle 1 + angle 2 =180° (PQ is a straight line) <u>TRUE</u>
  • Therefore, angle 1 + angle 2 = angle 1 + angle 4 (Transitive Property of Equality)<u> TRUE</u>
  • Hence, angle 2 = angle 4 (Subtraction Property of Equality) <u>TRU</u>
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Use the distributive property to create an equivalent expression to 7(2j + 3 + 2j).
Scorpion4ik [409]

Answer:

28j + 21

Step-by-step explanation:

combine like terms

7(2j+ 3+ 2j)

7(4j+3)

Distribute

7(4j + 3)

=

28j + 21

6 0
2 years ago
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The perimeter of a rectangular field is 328 yards. If the length of the field is 89 yards, what is its width?
miv72 [106K]

<u>Set up an equation based on the information given</u>

89 + 89 + x + x = 328

<u>Combine like terms</u>

89 + 89 = 178

x + x = 2x

2x + 178 = 328

<u>Solve</u>

2x + 178 = 328

328 - 178 = 150

2x = 150

x = 75

Answer

The width of the rectangular field is 75 yards.

7 0
3 years ago
Pranav ate pizza for dinner on Monday night and had 2/3 of the pizza left over. On Tuesday night, he ate 1/2 of what was left. H
ale4655 [162]

Answer: 1/3

Step-by-step explanation:

From the question, we are informed that Pranav ate pizza for dinner on Monday night and had 2/3 of the pizza left over. We are further told that on Tuesday night, he ate 1/2 of what was left.

The amount of pizza that Pranav ate on Tuesday will be:

= 1/2 × 2/3

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She ate 1/3 on Tuesday

6 0
3 years ago
Write an equation for a like that is parallel to the given point. Explain how you found the equation.
pishuonlain [190]

Answer:

The line would be y = 2x + 5

Step-by-step explanation:

To find a parallel line, we first need to note that the slope of the original line is 2. This means the slope of our new line will also be 2 because parallel lines have the same slope.

So we use the slope we found along with the point given in point-slope form. Then we solve for y.

y - y1 = m(x - x1)

y - 11 = 2(x - 3)

y - 11 = 2x - 6

y = 2x + 5

7 0
3 years ago
Cheryl wants to find the number of hours seventh-graders do homework each week. There are 297 boys and girls in seventh grade. I
Dafna1 [17]
There are a total of 297 students in the 7th grade. Rough estimates would say that about half of that number are boys and half are girls. Asking only 50 random girls would be biased because not only would it not be all of the girls (the number of girls would be around 148 or 149) but it would also be ignoring the roughly 148 to 149 boys there are on estimate. The sample would be biased because it would be ignoring the opinions of more than half the seventh grade.
8 0
3 years ago
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