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Oduvanchick [21]
3 years ago
6

For lines c, d, and e.

Mathematics
1 answer:
USPshnik [31]3 years ago
5 0

Answer:

A) x = 6

B) ∠3 = 29°

C) ∠1 = 29°

D) ∠2 = 151°

Step-by-step explanation:

Given line e // line d and line c is transversal

Part A: If ∠3 = 5x-1 and ∠5 = 3x + 11 , find x

∠3 = ∠5 because alternate angles are congruent.

So, 5x - 1 = 3x + 11     Combine like terms

5x - 3x = 11 + 1

2x = 12

x = 6

Part B: If ∠3 = 5x-1 and ∠5 = 3x + 11  , find ∠3

∠3 = ∠5 because alternate angles are congruent.

So, 5x - 1 = 3x + 11     Combine like terms

5x - 3x = 11 + 1

2x = 12

x = 6

∴ ∠3 = 5x - 1 = 5 * 6 - 1 =30 - 1 = 29°

Part C: If ∠3 = 5x-1 and ∠5 = 3x + 11  , find ∠1

∠3 = ∠1 because vertically opposite angles are congruent

∠3 = 29°

∴∠1 = 29°

Part D: If ∠3 = 5x-1 and ∠5 = 3x + 11  , find ∠2

The angles 2 and 3 are supplementary angles.

∠3 = 29°

∠2 + ∠3 = 180°

∠2 = 180° - ∠3 = 180° - 29° = 151°

∴ ∠2 = 151°

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By the definition of a rectangle, JML and KLM are right angles.

<h3>How to explain the information?</h3>

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The city has a section of land that is 3,694.7 feet long. The city wants to partition this lengths to form 10 equal-sized garden
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3 years ago
At a particular restaurant, each onion ring has 65 calories and each slider has 250 calories. A combination meal with onion ring
andre [41]

Answer:

The number of onion rings is <u>3</u> in the combination meal and the number of sliders is <u>2</u> in the combination meal.

Step-by-step explanation:

Given:

At a particular restaurant, each onion ring has 65 calories and each slider has 250 calories. A combination meal with onion rings and sliders has a total of 5 onion rings and sliders altogether and contains 695 calories.

Now, to find the number of onion rings in the combination meal and the number of sliders in the combination meal.

Let the number of onion rings in the combination meal be x.

And let the number of sliders in the combination meal be y.

<u><em>So, the total number of onion rings and sliders are:</em></u>

x+y=5\\\\y=5-x\ \ \ .....(1)

Now, the total number of calories each onion rings and sliders has:

x(65)+y(250)=695

Substituting the value of y from equation (1) we get:

<em />x(65)+(5-x)(250)=695\\\\65x+1250-250x=695\\\\1250-185x=695<em />

<em>Subtracting both sides by 1250 we get:</em>

<em />-185x=-555<em />

<em>Dividing both sides by -185 we get:</em>

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<u><em>The number of onion rings in the combination meal = 3.</em></u>

Now, substituting the value of x in equation (1) we get:

y=5-x\\\\y=5-3\\\\y=2.

<u><em>The number of sliders in the combination meal = 2.</em></u>

Hence, the number of onion rings is 3 in the combination meal and the number of sliders is 2 in the combination meal.

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