Jordan and Roman travel the same route to work. Jordan leaves for work one morning and drives at a rate, r, of 56 mph. Roman leaves the house soon after, when Jordan has already traveled 2 mi. Roman drives at a rate of 60 mph. How long after Jordan leaves home will Roman catch up to her? How many miles into their commute will this occur? Which system of equations models this problem?

The midpoint formula is as follows

[tex]M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]

Plug in the information we know.

[tex](1,-2)=(\frac{7+x_2}{2},\frac{2+y_2}{2})[/tex]

Solve for [tex]x[/tex]

[tex]1=\frac{7+x_2}{2}[/tex]

[tex]2=7+x_2[/tex]

[tex]x_2=-5[/tex]

Solve for [tex]y[/tex]

[tex]-2=\frac{2+y_2}{2}[/tex]

[tex]-4=2+y_2[/tex]

[tex]y_2=-6[/tex]

The other endpoint of the segment is [tex](-5,-6)[/tex]

Hope this helps.

頑張って!

Answer:

37c

Step-by-step explanation:

6c+(7c+7c)+8c+9c

6c+14c+(8c+9c)

6c+(14c+17c)

6c+31c

37c

Answer:

108

Step-by-step explanation:

Answer: D

Step-by-step explanation: hope this helped u.

Answer:

Alright bear with me, this is gonna be a long one.

The Y INTERCEPT

So the y-intercept is going to be where the line intersects the Y-AXIS. The y-axis is the vertical part of the graph with the numbers on it.

So, for the first one, the line goes through the origin which means that that the y intercept is going to be (0,0)

The next one, the line intersects the y-axis at (0,1)

Here's a tip: the y-intercept will always have 0 as it's x coordinate.

The Slope

Alright, the slope of a vertical line can be found using an equation. Most typically people will describe the slope as RISE/RUN meaning how many units you move up "rise" and how many units you move horizontally "run" to touch the line. Of course, it's easier when you can identify points.

So to make this a little bit easier to understand, I will show you how to use the equation to find the slope.

[tex]\frac{y2-y1}{x2-x1}[/tex]

So for this equation, what you need is two coordinates. So for the first graph, I'm going to use the points (0,0) and (1,3)

[tex]\frac{3-0}{1-0}[/tex]

So we make the three y2 because it's the second y coordinate and the y1 would be 0. Same applies to the x coordinates but use the x values.

the slope for the first graph would be 3/1

FOR THE SECOND GRAPH

[tex]\frac{y2-y1}{x2-x1}[/tex]

Here's our equation now pick two points. I'll be using (-5,4) and (0,1)

[tex]\frac{1-4}{0-(-5)}[/tex]

Don't forget that a negative-a negative = positive

which will leave you with

[tex]\frac{-3}{5}[/tex]

since it can't be simplified any further, your slope is -3/5.

I hope I was able to help you understand this a bit better :)  

Step-by-step explanation:

An odd function is where g(x) = -g(-x).

Therefore the answer is g(x) = 4x, as it passes through the origin and g(x) is positive when x is positive, and g(x) is negative when x is negative.

The odd function will be g(x) = 4x. Then the correct option is D.

A true function f(x) is said to be an odd function if the output value of f(-x) is the same as the negative of f(x) for all values of x in the domain of f.

The equation should be stored in an odd function:

f(-x) = -f(x)

Let's check all the options.

A. The function is g(x) = x².

Substitute x = -x, then we have

g(x) = (-x)²

g(x) = x²

This is an even function.

B. The function is g(x) = 5x – 1.

Substitute x = -x, then we have

g(x) = 5(–x) – 1

g(x) = – (5x + 1)

This is a neither even nor odd.

C. The function is g(x) = 3.

Substitute x = -x, then we have

g(x) = 3

This is an even function.

D. The function is g(x) = x.

Substitute x = -x, then we have

g(x) = -x

g(x) = x

This is an odd function.

Then the correct option is D.

More about the odd function link is given below.

https://brainly.com/question/14264818

#SPJ2

Answer:

  D, E

Step-by-step explanation:

The applicable formula is ...

  s = rθ

so, for θ = 1.5, the arc length is 1.5 times the radius. The true statements are ...

  D) The length of the arc defined by the angle is 1.5 times longer than the radius.

  E) The ratio of arc length to radius is 1.5.

Answer:

1.00304 * 10^10

Step-by-step explanation:

The first one dark blue I think

Answer:

Let the number be x.

(x-9)/3= (x/7)+1

(x-9)/3= (x+7)/7

Cross multiplying

7x-63= 3x+21

4x= 84

x= 42

Hope this will help :-)

Answer:

what do u look like

Step-by-step explanation:

Answer:

It is fair.

See the chart?

On all coins, there is a 50/50 chance it will be wrong or right.

There are 6 sides.

Half of them are H, and the other half T.

So, there are 3 heads and 3 tails.

3 to 3 is equal, so it is fair.

Hope this helped :)!

Answer:

No, the game is not fair because Julie does not have equal probabilities of winning or losing.

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

Well if y=5x then, the constant variation would have to be 5. Hope that helps.

Answer:

30+0.05x where x is the amount of data over the limit in megabytes.

Answer:

Probability of getting a green marble=5/15=3/5

Probability of getting a black marble=5/15=3/5

Answer:

2 ft

Step-by-step explanation:

Given that Dimensions of rectangular plot are: 26 feet by 30 feet

Length is 26 ft

Width is 30 ft

Area of rectangle = Length [tex]\times[/tex] Width

So, area of given rectangular field is = 26 [tex]\times[/tex] 30 = 780 sq ft

Let the width of the walk = [tex]x[/tex] ft

Kindly refer to the attached image for the given scenario.

Dimensions of the plot with walk = (26+2[tex]x[/tex]) ft by (30+2[tex]x[/tex]) ft

So, area of plot without walk = 780 sq ft

Area of walk = Area with walk - Area of plot

Now, we are given that area of walk = 240 sq ft

So, we get:

240 = (26+2[tex]x[/tex]) [tex]\times[/tex] (30+2[tex]x[/tex]) - 840

[tex]\Rightarrow (26+2x)(30+2x)=780+240\\\Rightarrow 780+4x^2+112x=780+240\\\Rightarrow 4x^2+112x-240=0\\\Rightarrow x^2+28x-60=0\\\Rightarrow x^2+30x-2x-60=0\\\Rightarrow x(x+30)-2(x+30)=0\\\Rightarrow x = 2, -30\ ft[/tex]

[tex]x[/tex] can not be negative, so [tex]x = 2\ ft[/tex]

So, the width of the walk = 2 ft

Answer:14

Step-by-step explanation:

3x + 3 + 3x - 1 = 3x + 8

6x + 2 = 3x + 8

3x + 2 = 8

3x = 6

x = 2

HJ= 3(2) + 8 =6 + 8 = 14

HI= 3(2) - 1 = 6 - 1 = 5

IJ = 3(2) + 3 = 6 + 3 = 9

The numerical value of the length HJ such that will be  I J equals 3X +3, HI equals 3X-1, and HJ equals 3X +8 will be 14.

A line section that can connect two places is referred to as a segment.

In other words, a line segment is just part of a big line that is straight and going unlimited in both directions.

The line is here! It extends endlessly in both directions and has no beginning or conclusion.

Given that the line HJ has a length of 3x+8

HJ = 3x+8

The line segment HI has a length of 3x -1

HI = 3x -1

The line segment IJ is 3x + 3

IJ = 3x + 3

Since line HJ = HI + IJ

3x -1 +  3x + 3 =  3x+8

x= 2

The length of HJ will be

HJ = 3(2) + 8

HJ = 14 hence, 14 will be the correct answer.

For more about line segment

https://brainly.com/question/25727583

#SPJ6

The question is incomplete. Here is the complete question.

Nite Time Inn has a toll-free telephone number so that customers can call at any time to make a reservation. A typical call takes about 4 minutes to complete, and the time required follows an exponential distribution. find the probability that a call takes

a) 3 minutes or less

b) 4 minutes of less

c) 5 minutes of less

d) Longer than 5 minutes

e) Longer than 7 minutes

Answer: a) P(X<3) = 0.882

              b) P(X<4) = 0.908

              c) P(X<5) = 0.928

              d) P(X>5) = 0.286

              e) P(X>7) = 0.174

Step-by-step explanation: Exponential distribution is related with teh amount of time until some specific event happens.

If X is a continuous random variable, probability is calculated as:

[tex]P(X<x) = 1-me^{-mx}[/tex]

in which:

m is decay parameter, given by: [tex]m=\frac{1}{mean}[/tex]

For the Nite Time Inn calls:

[tex]m=\frac{1}{4}[/tex]

m = 0.25

(a) P(X<3)

[tex]P(X<3) = 1-0.25e^{-0.25.3}[/tex]

[tex]P(X<3) = 1-0.25e^{-0.75}[/tex]

[tex]P(X<3) = 1-0.25*0.472[/tex]

P(X < 3) = 0.882

The probability the call takes less than 3 minutes is 0.882.

(b) P(X<4)

[tex]P(X<4) = 1-0.25e^{-0.25.4}[/tex]

[tex]P(X<4) = 1-0.25e^{-1}[/tex]

P(X < 4) = 0.908

The probability the call takes less tahn 4 minutes is 0.908.

(c) P(X<5)

[tex]P(X<5) = 1-0.25e^{-0.25.5}[/tex]

[tex]P(X<5) = 1-0.25e^{-1.25}[/tex]

P(X < 5) = 0.928

The probability of calls taking less than 5 minutes is 0.928.

(d) P(X>5)

Knowing that the sum of probabilities of less than and more than has to equal 1:

P(X<x) + P(X>x) = 1

P(X>x) = 1 - P(PX<x)

[tex]P(X>x) = 1-(1-me^{-m*x})[/tex]

[tex]P(X>x)=me^{-mx}[/tex]

For P(X>5):

[tex]P(X>5) = 0.25e^{-1.25}[/tex]

P(X > 5) = 0.286

The probability of calls taking more than 5 minutes is 0.286.

(e) P(X>7)

[tex]P(X>7)=0.25e^{-0.25.7}[/tex]

[tex]P(X>7)=0.25e^{-1.75}[/tex]

P(X > 7) = 0.174

The probability of calls taking more than 7 minutes is 0.174.

Answer:

the square root is 15=5

Answer:

D: 5.1

Step-by-step explanation:

Answer:

R=a/pt-1/t

Step-by-step explanation:

r= a/pt-1/t

Step-by-step explanation:

The question is incomplete:

Irene's grandfather arrived in Sydney from Athens at 10 pm on Friday after a 25-hour trip. The flight began at 12 noon on Thursday, Athens time. What is the time difference between Athens and Sydney?

A. Athens time is 9 hours behind  Sydney time.

B. Athens time is 9 hours ahead of  Sydney time.

C. Athens time is 15 hours behind  Sydney time.

D. Athens time is 15 hours ahead of  Sydney time.

Answer:

A. Athens time is 9 hours behind  Sydney time.

Step-by-step explanation:

The statement indicates that the flight began at 12 noon on Thursday, Athens time and that it lasted 25 hours. So, you can calculate the Athens time when he arrived after 25 hours which would be 1 pm on Friday. Also, the statement says that Irene's grandfather arrived in Sydney at 10 pm on Friday and now we know that at that moment it was 1 pm on Friday, Athens time. From these, you can calculate the difference between 1 pm and 10 pm that would be 9 hours. Because of this, the answer is that the time difference between Athens and Sydney is that Athens time is 9 hours behind  Sydney time.

Answer:

The vertical line test

Step-by-step explanation:

Basically, draw vertical lines over the function.

If each value of x has a different y-value, then it is a function.  

Answer:

cdf

Step-by-step explanation:

Answer:

A) 46

Step-by-step explanation:

230+9x=14x

230=5x

230/5=x

x=46

CHECK:

230+9(46)=644

14*46=644

Answer:

26 posts

Step-by-step explanation:

find perimeter:

42+42+36+36= 156

divide by 6

156/6=26

Answer:

K (-5, 2); J (-2, 3); I (-1, 1); L (-5, -3)

Step-by-step explanation:

Translating the shape 6 units to the left means that every point/vertex will be moved 6 units to the left of where it is originally drawn.

Point K is at (1, 2). Since we are only moving it left (on the x-axis), the y value will not change. To move K left 6, we have to subtract 6 from its current x-value, 1. We get -5 for the new x-value. Because the y value didn't change, the new location of K is (-5, 2).

Point J is at (4, 3). Subtracting 6 from 4 (the x value) gives us the new x value of -2. Again, the y value does not change and so our new location for J is (-2, 3).

Point I is at (5, 1). If we subtract 6 from 5, we get -1. This is our new x value for I. The new point is (-1, 1). (Once again, the y value does not change).

Point L is at (1, -3). By subtracting 6 from the original x value, 1, we get our new x value: -5. The new point for L is (-5, -3).