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scZoUnD
2 months ago
3

Complete the two-column proof. Given: ∠2 and ∠5 are supplementary Prove: l is parallel to m Need help quick

Mathematics
1 answer:
Leona [12.6K]2 months ago
5 0
1) Statement: ∠2 and ∠5 are supplementary.

Reason: This is given.

2) Statement: ∠2 and ∠3 have the same measure.

Reason: Vertically opposite angles are always equal.

3) Statement: If ∠2 equals ∠3 and ∠2 is supplementary to ∠5, then ∠3 must be supplementary to ∠5.

Reason: By applying the substitution property.

4) Statement: Lines l and m are parallel.

Reason: According to the converse of the Same-Side Interior Angles Theorem, if two lines are intersected by a transversal and the consecutive interior angles are supplementary, then those lines are parallel.

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Eric plays basketball and volleyball for a total of 95 minutes every day. He plays basketball for 25 minutes longer than he play
lawyer [12517]

Answer:

Part A:

x+y= 95

x = y+25

Part B: 35 minutes

Part C: No

Step-by-step explanation:

  • Part A:

Eric spends a total of 95 minutes daily playing basketball and volleyball combined.

x+y= 95

Where:

x =minutes Eric plays basketball

y = minutes he allocates to volleyball

He dedicates 25 minutes more to basketball compared to volleyball.

x = y+25

Equations are:

x+y= 95

x = y+25

  • Part B:

Substituting x=y+25 into the first equation yields:

(y+25) + y =95

Solving for y

y+25+y =95

25+2y=95

2y=95-25

2y=70

y = 70/2

y = 35 minutes

Part C: No

If x = 35

x+y= 95

35+y =95

y= 95-35

y = 60 minutes

Inserting y=60 into the other equation:

x = y+25

35 = 60+25

35 ≠85

5 0
1 month ago
Micaela has a bat that is 30 inches long. She wants to fit it in a cube shaped box that has sides that are 17 inches. Will the b
PIT_PIT [12445]
No, the bat won't fit because 30 divided by 17 equals 1.765

6 0
23 days ago
Read 2 more answers
Explain the error in the solution below. What additional step needs to be completed? log x – log53 = 2log53 log x = 3log53 log x
PIT_PIT [12445]
The mistake lies in the fact that the logarithms have different bases. The one-to-one property of logarithms cannot be applied unless the bases are identical. <span>To correct this, the change of base formula should be used to express the logarithms with a uniform base.
I have confirmed this using Edge.</span>
5 0
1 month ago
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The following bar chart shows the number of different types of animals at two county fairs. Fair X had a total of 645 animals, a
Zina [12379]

Answer:

The proportion of goats at fair Y exceeds that of goats at fair X.

Step-by-step explanation:

From the bar chart,  we see there were 100 goats at both fairs X and Y.

Calculating the percentage of goats at each fair we find:

Fair X = 100/645 * 100 = 15.5%

Fair Y = 100/590 * 100 = 16.9%

This indicates that fair Y had a higher percentage of goats compared to fair X.

6 0
27 days ago
Find the value of y if EF = EG.​
AnnZ [12381]

Answer:

55°

Step-by-step explanation:

The problem does not have a suitable diagram. Please check the attachment for the diagram.

Observing the diagram, it is evident that the triangle is isosceles, as it has two sides that are congruent (i.e., the same length). Since these sides are identical, the base angles are consequently also equal.

From the diagram, <EFG = <EGF

Since  <EFG  = 55°, it follows that  <EGF = y = 55°

Thus, the value of y is established as 55°

5 0
24 days ago
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