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solmaris [256]
3 years ago
11

A, B & C form the vertices of a triangle.

Mathematics
1 answer:
Savatey [412]3 years ago
4 0

Answer:

BC = 17.2.

Step-by-step explanation:

Since CAB = 90º, this is a right triangle.

The triangle format is given below:

C

A           B

We have that AB = 8.6, and angle B measures 60º.

Length of BC:

BC is the hypotenyse.

Side AB is adjacent to angle B = 60º.

In a right triangle, angle \alpha, it's adjacent side with length s and the hypotenuse h are related by the cosine of the angle, that is:

\cos{\alpha} = \frac{s}{h}

In this question, we have an angle of 60º, with has cosine 0.5. We also have that side AB = s = 8.6, and the hypotenuse h is side BC. So

\cos{\alpha} = \frac{s}{h}

0.5 = \frac{8.6}{h}

0.5h = 8.6

h = \frac{8.6}{0.5}

h = 17.2

BC = 17.2.

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0x + y = 1 is the standard form of (3, 1) with m = 0

<u>Solution:</u>

We have been given a point and slope of an equation and have been asked to write it in the standard form.

The standard form of a line is in the form Ax + By = C where A is a positive integer, and B, and C are integers. The standard form of a line is just another way of writing the equation of a line.

The given point is (3,1) and the slope is 0

To write in standard form we will first write it in point slope form and then rearrange it into a standard from.

The point slope form of line is given as:

y-y_{1}=m\left(x-x_{1}\right)

Where "m" is the slope of the line

Here in this problem, m = 0 , x_1 = 3 and y_1 = 1

y - 1 = 0(x - 3)

y - 1 = 0

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since the above equation doesn’t have an ‘x’ term we convert into a standard form as follows:

0x + y = 1

This is the standard form for the given point and slope of a line.

6 0
3 years ago
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Christopher surveyed 30 students about their favorite type of pet. The results are shown in the table.
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3 years ago
In the figure, △ A B C ∼△ F G H . Find the value of x.
Lina20 [59]
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A national survey of small-business owners was conducted to determine the challenges for growth for their businesses. The top ch
krek1111 [17]

Answer:

A) 12/37

B) 12/46

C) 25/54

D) 29/100

Step-by-step explanation:

Let event A = small-business owner selected economy,

event B = small-business owner selected finding qualified workers,

Thus, probabilities;

P(A)=46/100

P(B)=37/100

P(A∩B)=12/100

A) P(A ∩ B)/P(B) = (12/100)/(37/100) = 12/37

B) P(A∩B)/P(A) = (12/100)/(46/100)= 12/46

C) P(B∩A')= P(B) − P(A∩B) =

37/100 - 12/100 =25/100

P(B∩A')/P(A') =

(25/100)/(1-46/100) = 25/54

D) Using inclusion-exclusion principle;

P(A∪B) = P(A)+P(B)−P(A∩B)=

46/100 + 37/100 - 12/100 = 71/100

Hence, the probability that the owner believes neither that the economy is a challenge for growth nor that finding qualified workers is a challenge for growth is;

P( A' ∩ B') = 1 − P(A∪B)= 1− (71/100)= 29/100

3 0
3 years ago
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