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Colt1911 [192]
3 years ago
14

In ABC, A = 4x, B = 3x + 1, C = 7x + 11. List the sides of ABC in order from shortest to longest.

Mathematics
1 answer:
BlackZzzverrR [31]3 years ago
7 0

Sum of all angles of a triangle is equal to 180°. Therefore,

A + B + C = 180

Given that, A = 4x, B = 3x + 1, C = 7x + 11.

Hence, we can set up an equation as following:

4x + 3x + 1 + 7x + 11 = 180

14x + 12 = 180 Combine the like terms.

14x + 12 -12 = 180 - 12 Subtract 12 from each sides.

14x = 168

\frac{14x}{14} =\frac{168}{14} Divide each sides by 14.

So, x= 12.

Now by plug in x=12 in the given expressions of A, B and C we can get the measure of eah angles of the triangle. Therefore,

A = 4x = 4(12) = 48

B= 3x + 1= 3(12) + 1 = 36 + 1 = 37

C= 7x + 11 = 7(12) + 11 = 84 + 11 =95

From the above result we can see that C is the largest angle and B is the smallest angle.

There is a relationship of a triangle which state that the largest side is opposite side of the largest angle and similarly smallest side is opposite side of the smallest angle.

Here AB is the opposite side of the largest angle C. So, AB is the largest side.

Similarly AC is the smallest side.

So, the order from shortest to longest is B: AC, BC, AB

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B.False

Step-by-step explanation:

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GEOMETRY. Identify the angles that each have a measure of 117º
sergiy2304 [10]

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It should be 4, 6, and 8

Step-by-step explanation:

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6 0
3 years ago
What is 112.491 written in word form?​
bearhunter [10]

Answer:

112.491 = one hundred twelve and four hundred ninety-one

thousandths.

Step-by-step explanation:

6 0
2 years ago
After 200 feet of drilling on the first well, a soil test is taken. The probabilities of finding the particular type of soil ide
dimaraw [331]

Answer:

The revised probabilities are;

The probability of finding soil with oil  = 0.8  

The probability of finding soil with good oil = 0.16

The probability of finding medium quality oil =  0.64

Step-by-step explanation:

The given probability of finding soil with high quality oil, P(QO) = 0.20

The probability of finding soil with medium-quality oil, P(OM) = 0.80

The probability of finding soil with no oil, P(ON) = 0.2

Therefore, given that the probability of finding soil with no oil = 0.2, we have;

The probability of finding soil with oil, P(OP) = 1 - the probability of finding soil with no oil

P(OP) = 1 - 0.2 = 0.8

Which gives;

The probability, P(FG) of finding soil with oil and that the oil is good is given as follows;

P(FG) = P(QO) × P(OP) = 0.2 × 0.8 = 0.16

The probability of finding good oil = 0.16

Similarly;

The probability of finding medium quality oil P(FM) =  P(OM) × P(OP) = 0.8 × 0.8 = 0.64

Which gives the revised probability as follows;

The probability of finding soil with oil, P(OP) = 0.8  

The probability of finding soil with good oil, P(FG) = 0.16

The probability of finding medium quality oil, P(FM) =  0.64.                

3 0
3 years ago
If C(5,-5) and D(7,3), then what is the length of CD?​
Aleks04 [339]

Answer:

≈ 6.16

Step-by-step explanation:

Calculate the distance (d) using the distance formula

d = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = C(5, - 5) and (x₂, y₂ ) = D(7, 3)

d = √ (7 - 5)² + (3 + 5)²

  = √ 2² + 8² = √ 4 + 64 = √68 ≈ 6.16 ( to 2 dec. places )

8 0
3 years ago
Read 2 more answers
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