On the weekend, I spent 6 3/5 hours reading and 1 1/4 hours at the gym. How much less time did I spend at the gym then reading?

locate the point on the line segment A (3,-5) and B (13,-15) given that the point is 4/5 of the way from A to B. Show your work

rjkz [21]

Answer:

The coordinates of the point on the line segment between A (3 , -5) and B (13 , -15) given that the point is 4/5 of the way from A to B would be: (11 , -13)

Step-by-step explanation:

As the line segment has the points:

A(3, -5)

B(13, -15)

Let (x, y) be the point located on the line segment which is 4/5 of the way from A to B.

Using the formula

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

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

Here, the point (x , y) divides the line segment having end points (x₁, y₁) and (x₂, y₂) in the ratio m₁ : m₂ from the point (x₁, y₁).

As (x, y) be the point located on the line segment which is 4/5 of the way from A to B, meaning the distance from $A$ to $(x , y)$ is $4$ units, and the

distance from $(x , y)$ to B is 1 unit, as $5 - 4 = 1$ .

Thus

m : n = 4 : 1

so

Finding x-coordinate:

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

$x=\frac{\left(3\right)\left(1\right)+\left(13\right)\left(4\right)}{4+1}$

$\mathrm{Remove\:parentheses}:\quad \left(a\right)=a$

$x=\frac{3\cdot \:1+13\cdot \:4}{4+1}$

$x=\frac{55}{4+1}$ ∵ $3\cdot \:1+13\cdot \:4=55$

$x=\frac{55}{5}$

$\mathrm{Divide\:the\:numbers:}\:\frac{55}{5}=11$

$x=11$

Finding y-coordinate:

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

$y=\frac{\left(-5\right)\left(1\right)+\left(-15\right)\left(4\right)}{4+1}$

$\mathrm{Remove\:parentheses}:\quad \left(a\right)=a$

$y=\frac{-5\cdot \:\:1-15\cdot \:\:4}{4+1}$

$=\frac{-65}{4+1}$ ∵ $-5\cdot \:1-15\cdot \:4=-65$

$=\frac{-65}{5}$

$\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{-a}{b}=-\frac{a}{b}$

$y=-\frac{65}{5}$

$y=-13$

so

The x-coordinate = 11

The y-coordinate = -13

Therefore, the coordinates of the point on the line segment between A (3 , -5) and B (13 , -15) given that the point is 4/5 of the way from A to B would be: (11 , -13)

7 0

2 years ago

Last year, 9 companies decided to include their coupon in a local coupon pack. Each company had to print 589 copies of their cou

Bad White [126]

Answer:

5301

Step-by-step explanation:

There are 9 companies that needed to print 589 coupons each. Multiply the two numbers:

9 * 589 = 5301

7 0

2 years ago

the probability that we encounter a green light at the corner of college and main is 0.35, a yellow light 0.04, and a red light

Ostrovityanka [42]

Answer:

21% probability you will hit a green light on monday and a red light on tuesday

Step-by-step explanation:

When two events, A and B, are independent, we have that:

$P(A \cap B) = P(A) \times P(B)$

In this problem, we have that:

Event A: Green light on monday.

Event B: Red light on tuesday.

The probability that we encounter a green light at the corner of college and main is 0.35

This means that $P(A) = 0.35$

The probability that we encounter a red light is 0.61:

This means that $P(B) = 0.61$

These events are independent, that is, the light color on Tuesday is independent of the color on Monday. So

$P(A \cap B) = P(A) \times P(B) = 0.35 \times 0.6 = 0.21$

21% probability you will hit a green light on monday and a red light on tuesday

8 0

3 years ago

I don't get this question can someone help?

dedylja [7]

Answer:

I dont know

Step-by-step explanation:

yo yo

6 0

2 years ago

In a group of Year 9 students, the ratio of boys to girls is 9 : 7. There are 4 more boys than girls in this group. How many stu

KATRIN_1 [288]

Answer: 32

Step-by-step explanation:

There are 18 boys and 14 girls (4 more boys than girls. 32 students total.

7 0

2 years ago