1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
il63 [147K]
3 years ago
6

Runner A is initially 5.1 km west of a flagpole and is running with a constant velocity of 8.5 km/h due east. Runner B is initia

lly 4.1 km east of the flagpole and is running with a constant velocity of 7.4 km/h due west. How far are the runners from the flagpole when their paths cross? Answer in units of km.
Mathematics
1 answer:
Sati [7]3 years ago
8 0

Find the total distance between the two runners:

5.1 + 4.1 = 9.2 km apart.

We want to calculate the distance each runner does:

Runner A distance = X km, rate = 8.5 km/ hr.

Time = X / 8.5

Runner B distance = (9.2 - x) Total distance between the runners minus what runner A runs equals where they meet).

Rate = 7.4 km/hr.

Time = (9.2-x) / 7.4

Now to find where they meet set the two equations equal:

x / 8.5 = (9.2-x) / 7.4

Cross Multiply:

7.4x = 78.2 - 8.5x

Add 8.5x to both sides:

15.9x = 78.2

Divide both sides by 15.9:

x = 78.2 / 15.9

x = 4.918 = 4.9 km.

Since X is the distance runner A runs, subtract that from his distance from the flag pole:

5.1 - 4.9 = 0.2

The runners meet 0.2 km west of the flag pole.

You might be interested in
Three pies were made for a party. Each pie was cut into eight pieces. 3⁄8 of the apple pie was left. 1⁄2 of the cherry pie was l
miskamm [114]

Answer:

There are 13 pieces of pie left.

Step-by-step explanation:

So there are 3 pieces of apple pie left, there are 4 pieces of cherry pie left, and there are 6 pieces of pumpkin pie left. 3 + 4 + 6 = 13.

3/8 = 3 pieces because each fraction in this one equals one piece. So the numerator is how many left.

1/2= 4 because you just divide 8 by 2.

3/4 = 2 because you can multiply the fraction by 2 and get 6/8. Then the numerator is how many that's left.

I hope I helped.

3 0
3 years ago
What is the complete factorization of the polynomial below x^3+2x^2+4x+8
vagabundo [1.1K]

Answer:

c) (x + 2)(x + 2i)(x - 2i)

Step-by-step explanation:

x^3 + 2x^2 + 4x + 8

= (x^3 + 2x^2) + (4x + 8)

= x^2( x + 2) + 4(x + 2)

= (x + 2)(x^2 + 4)

= (x + 2)(x^2 - 4i^2)  ---------------------------->(i^2 = -1)

= (x + 2)(x + 2i)(x - 2i)

3 0
3 years ago
Read 2 more answers
8% of what number is 2?
azamat

Answer:

The number is 25

Step-by-step explanation:

Is means equals and of means multiply

8% *N = 2

Change to decimal form

.08 N =2

Divide by .08

.08N/.08 = 2/.08

N =25

5 0
3 years ago
Read 2 more answers
Hello can you answer these?
Elenna [48]

Answer:

The first one is C

Step-by-step explanation:

The ramp is equal to 180

180-6 = 174

3 0
3 years ago
Will award Brainlyest!!! Choose the equation that represents a line that passes through points (−3, 2) and (2, 1).
Pachacha [2.7K]

Answer:2. Rate of change, or slope, is the change in y over change in x. Remember that a point is given in (x, y). Also that you need two points to find the change.

If you have two points, (x1, y1) and (x2, y2), the rate of change or slope

In your problem, the given points are (0, -1) and (2, -11)

The "initial value" is the y-intercept - where the graph intersects the y-axis and also where x = 0. The given point (0, -1) has x = 0, so the initial value is -1.

4. Remember the model equation for a graph of a line is

y = mx + b,

where m is slope and b is y-intercept - where the graph intersects the y-axis and also where x = 0.

The x-axis of the graph would be number of weeks, since it is independent.

The y-axis of the graph would be how much money she has.

Since she starts (at 0 weeks) at $25, the first point would be (0, 25). Notice here that it is the y-intercept since x = 0. The value of b in the model equation of a line y = mx + b would be 25.

The rate of change, or slope, is $5/week. This is m in the model equation of a line y = mx + b.

Putting b = 25 and m = 5 into the model equation y = mx + b (remember we use this equation because it works for all lines), the equation would be

y = 5x + 25.

4.

The slope of this will be -0.5degrees/hr, or just -0.5 if it is used as m in the 

y = mx+b equation. The slope is negative because it "decreases".

5. 

Plot each point and connect the dots. Remember the first number corresponds to the x-axis and the second to the y-axis.

For example in the table for x = -2 and y = -6, the point is (-2, -6), and from the origin (0,0) you go left 2 on the x-axis and down 6 to plot the point.

9.

I think you can do this if you can do #3, but now you have to find b by plugging in given values.

y = mx + b

y = 1212x + b

We can plug in the given point (3,1) to find b.

1 = 1212(3) + b

b = -3625

y = 1212 - 3625

10. Don't know which function you are referring to.

The slope is $10/week, or m = 10.

A point is (4, 90) because "After 4 weeks, Roberta has $90."

The y-intercept is 50 because x (weeks) = 0 at that time.

y = mx + b

y = 10x + 50

8 0
3 years ago
Read 2 more answers
Other questions:
  • Which of the following is a parent function? A.f(x)=1/2 3^x B.f(x)=-3x^3 +1 C.2^x D.3^x -x/3
    10·1 answer
  • In the elipse shown below each point marked with a dot is called an
    13·1 answer
  • Please answer A B C or D:
    9·1 answer
  • 0.25 to 0.5 Find the percent of change. Round to the nearest tenth of a percent if necessary.
    11·2 answers
  • Problem 2. 1/8×5/6, And answer in simplest form
    11·1 answer
  • selena has developed A function that models the amount of time it will take to feel like concert hall as a function of the numbe
    8·1 answer
  • 11.
    13·1 answer
  • if a real estate agent sold a house for $120,800 and earns a 3% commission determine how much money the agent earned?​
    7·1 answer
  • You have 6 boys to every 5 girls in math class, how many boys are in the class?
    8·1 answer
  • The sum of a rational number and a rational number is sometimes rational​
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!