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3 years ago

Using Geometric Mean, solve for x.

Mathematics

1 answer:

ehidna [41]3 years ago

3 0

Answer:

x = 6 units

Step-by-step explanation:

By geometric mean property:

$x = \sqrt{9 \times 4} \\ \\ x = \sqrt{36} \\ \\ x = 6 \: units$

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The endpoints of segment RS are R(-4, 3) and S(8, -5). Complete each statement using a fraction.

Ray Of Light [21]

Answer:

a. (-1 , 1) is the point at 1 : 3 of the way from R to S

b. (5 , -3) is the point at 3 : 1 of the way from R to S

Step-by-step explanation:

* Lets explain how to solve the problem

- If point (x , y) divide a line segment whose end points are

$(x_{1},y_{1})$ and $(x_{2},y_{2})$ , at ratio

$m_{1}:m_{2}$ from the first point, then

$x=\frac{x_{1}m_{2}+x_{2}m_{1}}{m_{1}+m_{2}}$ and

$y=\frac{y_{1}m_{2}+y_{2}m_{1}}{m_{1}+m_{2}}$

* Lets solve the problem

∵ RS is a line segment whose end points are R (-4 , 3) and S (8 , -5)

∵ Point (-1 , 1) divides it at ratio $m_{1}:m_{2}$ from R

- By using the rule above

∴ $-1=\frac{-4m_{2}+8m_{1}}{m_{1}+m_{2}}$

- By using cross multiplication

∴ $(-1)m_{1}+(-1)m_{2}$ = $-4m_{2}+8m_{1}$

- By collecting $m_{1}$ in one side and $m_{2}$ in the

other side

∴ $3m_{2}=9m_{1}$

- Divide both sides by 3

∴ $m_{2}=3m_{1}$

∴ $m_{1}=\frac{1}{3}m_{2}$

∴ (-1 , 1) is the point at 1 : 3 of the way from R to S

∵ RS is a line segment whose end points are R (-4 , 3) and S (8 , -5)

∵ Point (5 , -3) divides it at ratio $m_{1}:m_{2}$ from R

- By using the rule above

∴ $5=\frac{-4m_{2}+8m_{1}}{m_{1}+m_{2}}$

- By using cross multiplication

∴ $5m_{1}+5m_{2}$ = $-4m_{2}+8m_{1}$

- By collecting $m_{1}$ in one side and $m_{2}$ in the

other side

∴ $9m_{2}=3m_{1}$

- Divide both sides by 3

∴ $3m_{2}=m_{1}$

∴ $\frac{m_{1}}{m_{2}}=3$

∴ (5 , -3) is the point at 3 : 1 of the way from R to S

8 0

4 years ago

Solve for b:<br> a/b = c

irina [24]

Multiply each term by
b

and simplify.
a = cb

Rewrite the equation as
cb = a
Divide each term by
c

and simplify.
b = a/ c

4 0

3 years ago

Read 2 more answers

If I drowned 21 kids then I threw 2 kids down the hill how many kids do I have <br> pls help

maria [59]

Answer:

Step-by-step explanation:

thats kinda scary

8 0

4 years ago

Need all 3 cuz this is dumb

marusya05 [52]

A a b...............................

3 0

3 years ago

A university has 40,140 students. In a random sample of 210 students, 14 speak three or more languages. Predict the number of st

Alekssandra [29.7K]

Answer:

2676 students

Step-by-step explanation:

Total number of students =. 40,140

During study:

Sample size = 210

Number of samples who speak 3 or more languages = 14

Proportion who speak 3 or more languages :

14 / 210 = 0.0666666

Applying the proportion to the total. Population :

0.0666666 * total number of students

0.0666666 * 40140

= 2675.997324

= approximately 2676 students

4 0

3 years ago