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3 years ago

Find the value of x if b is the midpoint of AC, AB=3-2x, BC=x-12

Mathematics

2 answers:

Schach [20]3 years ago

8 0

ANSWER:

The value of x if b is the midpoint of AC, AB=3 - 2x, BC = x - 12 is 5

SOLUTION:

Given, B is the midpoint of points A and C

And given the distance values of AB and BC

i.e. AB = 3 – 2x and BC = x -12

we need to find the value of x

now, as B is the midpoint of A and C

Distance between A and B equals to Distance between B and C . So we get,

AB = BC

3 – 2x = x – 12

3 – 2x – (x – 12) = 0

3 – 2x –x +12 = 0

3 -3x + 12 = 0

-3x +15 = 0

-3x = -15

3x = 15

x = $\frac{15}{3}$

x = 5

Hence the value of x is 5.

Galina-37 [17]3 years ago

3 0

-------------------------------------

Answer:

5 = x

--------------------------------------

Step-by-step explanation:

AB ≅ BC (because median cuts a line segment into two equal (congruent ≅) parts

Set up your equation now:

3 - 2x = x - 12

3 + 12 = 2x + x

15 = 3x

15/3 = x

5 = x

Step-by-step explanation:

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A suburban high school has a population of 1376 students. The number of students who participate in sports is 649. The number of

Afina-wow [57]

108 / 1376 is the probability that a student participates in both sports and music.

Step-by-step explanation:

It is given that,

A suburban high school has a population of 1376 students.

Let the event A be the no.of students participated in sports.
Let the event B be the no.of students participated in music.

The number of students who participate in sports is 649.

The number of students who participate in music is 433.

To find the probability of event A (sports) :

P(sports) = No.of students participated in sports / Total students.

⇒ 649 / 1376

∴ P(A) = 649 / 1376

To find the probability of event B (music) :

P(music) = No.of students participated in music / Total students.

⇒ 433 / 1376

∴ P(B) = 443 / 1376

From the question, we know that the probability that a student participates in either sports or music is 974 /1376.

∴ P(A∪B) = 974 / 1376

To find the probability that a student participates in both sports and music :

The formula used here is,

P(A∩B) = P(A) + P(B) - P(A∪B)

⇒ 649 / 1376 + 433 / 1376 - 974 /1376

⇒ 108 / 1376

∴ P(A∩B) = 108 / 1376

5 0

3 years ago

Triangle ABC is a right triangle and cos(22.6o)=StartFraction b Over 13 EndFraction. Solve for b and round to the nearest whole

Art [367]

Answer:

a = 5 and b = 12

Step-by-step explanation:

Step 1: Find angle B

Angle C = 90°

Angle A = 22.6°

Angle B = B

All angles in a triangle are equal to 180°.

Angle A + Angle B + Angle C = 180°

22.6 + 90 + B = 180°

B = 180 - 112.6

B = 67.4°

Step 2: Find the value of side AC 'b'

Hypotenuse = 13

Adjacent = b

Angle A = 22.6°

Cos (Angle) = Adjacent/Hypotenuse

Cos (22.6) = b/13

b = 12

Step 3: Find the value of side CB 'a'

Hypotenuse = 13

Opposite = a

Angle A = 22.6°

Sin (angle) = Opposite/Hypotenuse

Sin (22.6°) = a/13

a = 4.99 rounded off to 5

Therefore, the value of a=5 and b=12.

8 0

4 years ago

Read 2 more answers

Find the x - and y -intercepts of the graph of the linear equation 3x+6y=24 .

True [87]

Answer:

x-intercept(s):

(8,0)

y-intercept(s):

(0,4)

5 0

2 years ago

Read 2 more answers

what is the slope- intercept form of the equation of the line that passes through the points (-3,2) and(1,5)

erma4kov [3.2K]

Answer:

y = $\frac{3}{4}$ x + $\frac{17}{4}$

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (- 3, 2) and (x₂, y₂ ) = (1, 5)

m = $\frac{5-2}{1+3}$ = $\frac{3}{4}$ , hence

y = $\frac{3}{4}$ x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (1, 5 ), then

5 = $\frac{3}{4}$ + c ⇒ c = 5 - $\frac{3}{4}$ = $\frac{17}{4}$

y = $\frac{3}{4}$ x + $\frac{17}{4}$ ← in slope-intercept form

6 0

3 years ago

Suppose the time a child spends waiting at for the bus as a school bus stop is exponentially distributed with mean 7 minutes. De

Gala2k [10]

Answer:

The probability that the child must wait between 6 and 9 minutes on the bus stop on a given morning is 0.148.

Step-by-step explanation:

Let the random variable X represent the time a child spends waiting at for the bus as a school bus stop.

The random variable X is exponentially distributed with mean 7 minutes.

Then the parameter of the distribution is, $\lambda=\frac{1}{\mu}=\frac{1}{7}$ .

The probability density function of X is:

$f_{X}(x)=\lambda\cdot e^{-\lambda x};\ x>0,\ \lambda>0$

Compute the probability that the child must wait between 6 and 9 minutes on the bus stop on a given morning as follows:

$P(6\leq X\leq 9)=\int\limits^{9}_{6} {\lambda\cdot e^{-\lambda x}} \, dx$

$=\int\limits^{9}_{6} {\frac{1}{7}\cdot e^{-\frac{1}{7} \cdot x}} \, dx \\\\=\frac{1}{7}\cdot \int\limits^{9}_{6} {e^{-\frac{1}{7} \cdot x}} \, dx \\\\=[-e^{-\frac{1}{7} \cdot x}]^{9}_{6}\\\\=e^{-\frac{1}{7} \cdot 6}-e^{-\frac{1}{7} \cdot 9}\\\\=0.424373-0.276453\\\\=0.14792\\\\\approx 0.148$

Thus, the probability that the child must wait between 6 and 9 minutes on the bus stop on a given morning is 0.148.

6 0

3 years ago