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Rashid [163]
2 years ago
14

Find the value of x for which ABCD must be a parallelogram.

Mathematics
1 answer:
densk [106]2 years ago
4 0
For a parallelogram, the parallel sides must be the same length. This means you can set their lengths equal to each other. Get like terms on the same side to calculate x.

3x-5=2x+3
3x-5+5=2x+3+5
3x=2x+8
3x-2x=2x-2x+8
x=8

x=8
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What is 6x – 8 = 4 written as a system? y = 6x – 8 y = –4 y = 6x – 8 y = 4 y = –6x + 8 y = 4
mestny [16]

6x – 8 = 4 written as a system. Hence second option is correct

<u>Solution:</u>

Given, equation is 6x – 8 = 4.

We have to find the equivalent system from given options.

First let us solve given equation, 6x – 8 = 4 ⇒ 6x = 4 + 8 ⇒ 6x = 12 ⇒ x = 2

Now, let us solve one by one option ,so that when we get above solution, that is correct option.

  • y = 6x – 8 and y = -4 ⇒ put y = -4 in y = 6x – 8 ⇒ 6x – 8 = -4 ⇒ 6x = 8 – 4

⇒ 6x = 4 ⇒ x ≠ 2, wrong option

  • y = 6x – 8 and y = 4 ⇒ put y = 4 in y = 6x – 8 ⇒ 6x – 8 = 4 ⇒ 6x = 8 + 4 ⇒ 6x = 12 ⇒ x = 2, right option.
  • y = -6x + 8 and y = 4 ⇒ put y = 4 in y = -6x + 8 ⇒ -6x + 8 = 4 ⇒ 6x = 8 – 4 ⇒ 6x = 4 ⇒ x ≠ 2, wrong option

hence, second option is correct.

6 0
3 years ago
Read 2 more answers
Please help PLEASEEEEEEEEE ​
siniylev [52]

Answer:

15

Step-by-step explanation:

You know that it takes 3 mins for 45 sit-ups so then you wanna find how much for 1 minute. It shows 3 mins which is 3 times as much as 1 minute. There, 3/3 = 1. then you have to do it with the sit-ups too. so 45/3 = 15

4 0
3 years ago
2=5x+4-3+5-1 what is the answer for this question
klio [65]
The answer will be x= -3/5
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3 years ago
I will mark as the brainliest
aleksandrvk [35]

Peaks are the highest points of a graph, there are four peaks, which are on the line that corresponds with July, which would be summer.

The answers to question 1. are four, four, summer.


January is the lowest point of the graph which are between 0 and 10, so the average temperature for January would be around 5 degrees.

The highest peaks ( July) are around the 70 degree line.

The answer s for question 2 are 5 and 70 degrees.

8 0
3 years ago
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BIOLOGY
kozerog [31]

Answer:

Step-by-step explanation:

Types of Angle Pairs

Adjacent angles: two angles with a common vertex, sharing a common side and no overlap.

Adjacent Angles

Angles ∠1 and ∠2 are adjacent.

Complementary angles: two angles, the sum of whose measures is 90°.

Complementary Angles

Angles ∠1 and ∠2 are complementary.

Complementary are these angles too(their sum is 90°):

Complementary Angles

Supplementary angles: two angles, the sum of whose measures is 180°.

Supplementary Angles

Angles ∠1 and ∠2 are supplementary.

 

Angle pairs formed by parallel lines cut by a transversal

When two parallel lines are given in a figure, there are two main areas: the interior and the exterior.  

When two parallel lines are cut by a third line, the third line is called the transversal. In the example below, eight angles are formed when parallel lines m and n are cut by a transversal line, t.  

There are several special pairs of angles formed from this figure. Some pairs have already been reviewed:  

Vertical pairs:

∠1 and ∠4  

∠2 and ∠3  

∠5 and ∠8  

∠6 and ∠7  

Recall that all pairs of vertical angles are congruent.  

Supplementary pairs:

∠1 and ∠2  

∠2 and ∠4  

∠3 and ∠4  

∠1 and ∠3  

∠5 and ∠6  

∠6 and ∠8  

∠7 and ∠8  

∠5 and ∠7  

Recall that supplementary angles are angles whose angle measure adds up to 180°. All of these supplementary pairs are linear pairs. There are other supplementary pairs described in the shortcut later in this section. There are three other special pairs of angles. These pairs are congruent pairs.

Alternate interior angles two angles in the interior of the parallel lines, and on opposite (alternate) sides of the transversal. Alternate interior angles are non-adjacent and congruent.  

 

Alternate exterior angles two angles in the exterior of the parallel lines, and on opposite (alternate) sides of the transversal. Alternate exterior angles are non-adjacent and congruent.  

 

Corresponding angles two angles, one in the interior and one in the exterior, that are on the same side of the transversal. Corresponding angles are non-adjacent and congruent.  

 

Use the following diagram of parallel lines cut by a transversal to answer the example problems.  

 

Example:  

What is the measure of ∠8?  

The angle marked with measure 53° and ∠8 are alternate exterior angles. They are in the exterior, on opposite sides of the transversal. Because they are congruent, the measure of ∠8 = 53°.  

Example:  

What is the measure of ∠7?  

∠8 and ∠7 are a linear pair; they are supplementary. Their measures add up to 180°. Therefore, ∠7 = 180° – 53° = 127°.

1. When a transversal cuts parallel lines, all of the acute angles formed are congruent, and all of the obtuse angles formed are congruent.  

 

In the figure above ∠1, ∠4, ∠5, and ∠7 are all acute angles. They are all congruent to each other. ∠1 ≅ ∠4 are vertical angles. ∠4 ≅ ∠5 are alternate interior angles, and ∠5 ≅ ∠7 are vertical angles. The same reasoning applies to the obtuse angles in the figure: ∠2, ∠3, ∠6, and ∠8 are all congruent to each other.

2. When parallel lines are cut by a transversal line, any one acute angle formed and any one obtuse angle formed are supplementary.  

 

From the figure, you can see that ∠3 and ∠4 are supplementary because they are a linear pair.

Notice also that ∠3 ≅ ∠7, since they are corresponding angles. Therefore, you can substitute ∠7 for ∠3 and know that ∠7 and ∠4 are supplementary.

Example:  

In the following figure, there are two parallel lines cut by a transversal. Which marked angle is supplementary to ∠1?  

 

The angle supplementary to ∠1 is ∠6. ∠1 is an obtuse angle, and any one acute angle, paired with any obtuse angle are supplementary angles. This is the only angle marked that is acute.

4 0
3 years ago
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