All categories

3 years ago

Points A, B, and C are collinear, and B lies between A and C. If AC = 48, AB = 2x+2, and BC = 3x+6, what is BC?

Mathematics

2 answers:

Vesna [10]3 years ago

8 0

Answer:

The value of BC is 30.

Step-by-step explanation:

Given information: A, B, and C are collinear, B lies between A and C, AC = 48, AB = 2x+2, and BC = 3x+6.

If A, B, and C are collinear, B lies between A and C, then by using segment addition property, we get

$AB+BC=AC$

Substitute AC = 48, AB = 2x+2, and BC = 3x+6 in the above equation.

$(2x+2)+(3x+6)=48$

On combining like terms we get

$(2x+3x)+(2+6)=48$

$5x+8=48$

Subtract 8 from both sides.

$5x=48-8$

$5x=40$

Divide 5 from both sides.

$x=8$

The value of x is 8.

We need to find the value of BC.

$BC=3x+6\Rightarrow 3(8)+6=30$

Therefore the value of BC is 30.

aleksandr82 [10.1K]3 years ago

4 0

Answer:

BC=30

Step-by-step explanation:

AC = 48

AB = 2x+2

BC=3x+6

AC= AB + BC

48 = 2x+2+3x+6

48=5x+8

5x=40

x=8

Hence

BC = 3(8)+6

BC=24+6

BC=30

You might be interested in

A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 47.047.0 and

alisha [4.7K]

Answer:

0.025 = 2.5% probability that a given class period runs between 51.5 and 51.75 minutes.

Step-by-step explanation:

An uniform probability is a case of probability in which each outcome is equally as likely.

For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.

The probability that we find a value X lower than x is between c and d is given by the following formula

$P(c \leq X \leq d) = \frac{d - c}{b-a}$

For this problem, we have that:

$a = 47, b = 57, c = 51.5, d = 51.75$ . So

$P(c \leq X \leq d) = \frac{d - c}{b-a}$

$P(51.5 \leq X \leq 51.75) = \frac{51.75 - 51.5}{57 - 47} = 0.025$

0.025 = 2.5% probability that a given class period runs between 51.5 and 51.75 minutes.

4 0

3 years ago

1. Identify the base, b, of the function f (x) = ab" if its graph passes through the points (1, 6) and (2, 18). (1 point)

Oduvanchick [21]

Answer:

B. 5

Step-by-step explanation:

8 0

3 years ago

Use the Distributive Property to find the price of 5 CDs that cost $15.99 each.

Paraphin [41]

The answer is $79.95

6 0

3 years ago

Read 2 more answers

Write a mixed number that is equivalent to 16/3.

mars1129 [50]

A mixed number is an integer--whole number--in front of a fraction. To calculate this, you have to divide the numerator by the denominator and put the remainder over the denominator.

Since 3 goes into 16 wholly 5 <em />times with 1 left over, 16/3 = 5 1/3.

Hope this helps!

3 0

4 years ago

Read 2 more answers

4log(2) x + log(2)5 = log(2)405

Anna71 [15]

Answer:

3/2

Step-by-step explanation:

6 0

3 years ago