Alex is a high school sophomore who recently learned about the importance of

What are the x- and y- coordinates of point E, which partitions the directed line segment from J to K into a ratio of 1:4? (–13,

Lana71 [14]

I added a screenshot of the complete question.

Answer:

(-7, -1)

Explanation:

The formulas given to calculated the x and y coordinates are as follows:

$x = (\frac{m}{m+n})(x_{2}-x_{1}) + x_{1}\\\\y = (\frac{m}{m+n})(y_{2}-y_{1}) + y_{1}$

Let's define the variables used:

(x₁ , y₁) are the coordinates of the first point while (x₂ , y₂) are the coordinates of the second point.

We are given that the segment is directed from J to K, therefore:

First point is J ..........> (x₁ , y₁) is (-15, -5)

Second point is K ....> (x₂ , y₂) is (25, 15)

m and n defined the portion of the partitioned segment (JE : EK). It is given that this ratio is 1:4. Therefore:

m = 1 and n = 4

Finally, let's substitute with these variables in the equations as follows:

$x = (\frac{1}{1+4})(25-(-15)) + (-15) = -7\\\\y = (\frac{1}{1+4})(15-(-5)) + (-5) = -1$

Based on the above, the coordinates of point E are (-7, -1)

Hope this helps :)

8 0

2 years ago

Read 2 more answers

Problem 5 (4+4+4=12) We roll two fair 6-sided dice. Each one of the 36 possible outcomes is assumed to be equally likely. 1) Fin

tekilochka [14]

Answer:

1

$p(b) = \frac{1}{6}$

2

$p(k) = \frac{1}{3}$

3

$P(a) = \frac{1}{3}$

Step-by-step explanation:

Generally when two fair 6-sided dice is rolled the doubles are

(1 1) , ( 2 2) , (3 3) , (4 4) , ( 5 5 ), (6 6)

The total outcome of doubles is N = 6

The total outcome of the rolling the two fair 6-sided dice is

n = 36

Generally the probability that doubles (i.e., having an equal number on the two dice) were rolled is mathematically evaluated as

$p(b) = \frac{N}{n}$

$p(b) = \frac{6}{36}$

$p(b) = \frac{1}{6}$

Generally when two fair 6-sided dice is rolled the outcome whose sum is 4 or less is

(1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (3, 1)

Looking at this outcome we see that there are two doubles present

So

The conditional probability that doubles were rolled is mathematically represented as

$p(k) = \frac{2}{6}$

$p(k) = \frac{1}{3}$

Generally when two fair 6-sided dice is rolled the number of outcomes that would land on different numbers is L = 30

And the number of outcomes that at least one die is a 1 is W = 10

So

The conditional probability that at least one die is a 1 is mathematically represented as

$P(a) = \frac{W}{L}$

=> $P(a) = \frac{10}{30}$

=> $P(a) = \frac{1}{3}$

3 0

2 years ago

After years of maintaining a steady population of 32,000, the population of a town begins to grow exponentially. After 1 year an

galben [10]

Answer:

$y=32000(1+0.08)^x$

Step-by-step explanation:

Exponential growth function is $y=a(1+r)^x$

Where 'a' is the initial population

r is the rate of growth and x is the time period in years

a steady population of 32,000. So initial population is 32,000

an increase of 8% per year. the rate of increase is 8% that is 0.08

a= 32000 and r= 0.08

Plug in all the values in the general equation

$y=a(1+r)^x$

$y=32000(1+0.08)^x$

$y=32000(1+0.08)^x$

4 0

2 years ago

Read 2 more answers

Coach De Leon purchases sports equipment. Basketballs cost $20.00 each, and soccer balls cost $18.00 each. He had a budget of $1

zepelin [54]

Answer:

18s+20b<_150

Step-by-step explanation:

He can buy 5 basketballs and 2 soccer balls. This equation is correct because 18x2 is 36 and 20x5 is 100. So that will be a total of $100. This makes the equation 100<_150. You can infer that this equation is true.

8 0

1 year ago

A downhill skier was able to move 560 meters in 25 seconds. What is the skier’s average speed? (Round your answer to the nearest

salantis [7]

Average speed is the total distance traveled by an object at a certain period of time. To calculate for the average speed we divide the total distance covered by the total time. We do as follows:

Average speed = 560 meters / 25 seconds = 22.4 m/s

6 0

2 years ago