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nikdorinn [45]
3 years ago
13

Find three consecutive integers for which 3 times the sum of the first and the third is -342

Mathematics
1 answer:
Eddi Din [679]3 years ago
7 0

Answer:

The integers are -58, -57, -56.

Step-by-step explanation:

The difference between two consecutive integers is 1.

If you let the smallest of the three consecutive integers equal x, then the next greater one is x + 1, and the greatest of the three is x + 2.

Integers: x, x + 1, x + 2

The sum of the first and third is: x + x + 2

3 times the sum of the first and third is: 3(x + x + 2)

That product equals -342.

3(x + x + 2) = -342

3(2x + 2) = -342

Divide both sides by 3.

2x + 2 = -114

Subtract 2 from both sides.

2x = -116

Divide both sides by 2.

x = -58

x + 1 = -57

x + 2 = -56

The integers are -58, -57, -56.

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23) m 2 = 7x + 6<br>70°​
lakkis [162]

Answer:

∠2 = 55°

Step-by-step explanation:

Given that the triangle has 2 congruent sides then the triangle is isosceles.

Thus the 2 base angle are congruent, both equal to ∠2

The sum of the 3 angles in a triangle = 180

7x + 6 + 7x + 6 + 70 = 180, that is

14x + 82 = 180 ( subtract 82 from both sides )

14x = 98 ( divide both sides by 14 )

x = 7

Hence

∠2 = 7x + 6 = (7 × 7) + 6 = 49 + 6 = 55°

3 0
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.

5 0
3 years ago
Compare the integers -13 and 15
agasfer [191]
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6 0
2 years ago
Which answers are examples of the Law of Syllogism? Select each correct answer. If two numbers are even then their sum is even.
maxonik [38]
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8 0
3 years ago
Read 2 more answers
{f(x)=2x+1 g(x)=x2+2x−8
n200080 [17]

The value of g(x) = 2[f(x)]² - 1 is g(x) = 8x² + 8x + 1

<h3>How to find a function?</h3>

f(x) = 2x+1

Find

g(x) = 2[f(x)]² - 1

Hence,

g(x) = 2[2x + 1]² - 1

g(x) = 2[4x² + 4x + 1] - 1

g(x) = 8x² + 8x + 2 - 1

g(x) = 8x² + 8x + 1

learn more on function here: brainly.com/question/1442153

#SPJ1

8 0
2 years ago
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