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lutik1710 [3]
3 years ago
8

The length of a rectangle is 15 and its width is w. The perimeter of the rectangle is, at most, 50. Which inequality can be used

to find the longest possible width?
1) 30 + 2w < 50
2) 30 + 2w ≤ 50
3) 30 + 2w > 50
4) 30 + 2w ≥ 50
Mathematics
1 answer:
Vladimir79 [104]3 years ago
5 0

Answer:

2) 30 + 2w ≤ 50

Step-by-step explanation:

First, let's find the perimeter of the rectangle in terms of w. We have 2*(15+w) = 30+2w because the perimeter of a rectangle can be written as 2*(length + width). The problem says that the perimeter is at most 50. This means that it cannot be greater than 50, so it would have to be less than or equal to 50. It can be equal to 50 because that is what at most means. Putting this information into an inequality, we get 30 + 2w ≤ 50.

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The measures of two angles of a triangle are 49° and 75°. Find the measure of the third angle in degrees.
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Answer: 56 degrees


Step by step:
The three angles in a triangle add up to 180 degrees.
49 + 75 + the third angle = 180
Let’s simplify.
180 - 49 - 75 = the third angle
So, by subtracting, we know that the third angle is 56 degrees!


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3 years ago
Based on the information given say whether or not △ABC∼△FED. Explain your reasoning.
GalinKa [24]

Answer:

Yes, △ABC ∼ △FED by AA postulate.

Step-by-step explanation:

Given:

Two triangles ABC and FED.

m∠A = m∠B

m∠C = m∠A + 30°

m∠E = m∠F = x

m∠D = 2x-20°.

Now, let m∠A = m∠B = y

So, m∠C = m∠A + 30° = y+30

Now, sum of all interior angles of a triangle is 180°. Therefore,

m∠A + m∠B +  m∠C = 180

y+y+y+30=180\\3y=180-30\\3y=150\\y=\frac{150}{3}=50

Therefore, m∠A = 50°, m∠B = 50° and m∠C =  m∠A + 30° = 50 + 30 = 80°.

Now, consider triangle FED,

m∠D+ m∠E + m∠F = 180

2x-20+x+x=180\\4x=180+20\\4x=200\\x=\frac{200}{4}=50

Therefore,  m∠F = 50°  

m∠E = 50° and  

m∠D =  2x-20=2(50)-20=100-20=80\°

So, both the triangles have congruent corresponding angle measures.

m∠A = m∠F = 50°

m∠B = m∠E = 50°

m∠C = m∠D = 80°

Therefore, the two triangles are similar by AA postulate.

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Casey's sister is 3 times as old as he is. His sister is 21 years old. Let c represent Casey's age. Which of the following would
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Answer:

casey's age is 7

Step-by-step explanation:

if his sister is 3 times as old as he is then she is older therefore you would devide.

21/3=7

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