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
wlad13 [49]
3 years ago
15

Drag each set of column entries to the correct location in the matrix equation. Not all sets of entries will be used. A biker ne

eds to pass two checkpoints before completing a race. The total distance for the race is 120 miles. The distance from the starting point to checkpoint 1 is 35 miles more than half the distance from checkpoint 1 to checkpoint 2. The distance from checkpoint 2 to the finish line is 20 miles less than twice the distance from checkpoint 1 to checkpoint 2. Let x represent the distance from the starting point to checkpoint 1, y represent the distance from checkpoint 1 to checkpoint 2, and z represent the distance from checkpoint 2 to the finish line. Complete the matrix equation that models this situation, A-1B = X.

Mathematics
2 answers:
ANEK [815]3 years ago
6 0

Answer:

The matrix equation is \left[\begin{array}{ccc}1&1&1\\1&-1/2&0\\0&2&-1\end{array}\right]=\left[\begin{array}{c}120&35&20\end{array}\right]

Step-by-step explanation:

* Lets change the story problem to equations

- The distance between the starting point and checkpoint 1 is x

- The distance between checkpoint 1 to checkpoint 2 is y

- The distance between checkpoint and the finish line is z

- The total distance for the race is 120 miles

∴ x + y + z = 120 ⇒ (1)

-The distance from the starting point to checkpoint 1 is 35 miles

 more than half the distance from checkpoint 1 to checkpoint 2

∵ The distance from the starting point to checkpoint 1 is x

∵ The distance from checkpoint 1 to checkpoint 2 is y

- x is more than half y by 35

∴ x = 35 + (1/2) y ⇒ subtract (1/2) y from both sides

∴ x - (1/2) y = 35 ⇒ (2)

- The distance from checkpoint 2 to the finish line is 20 miles less

 than twice the distance from checkpoint 1 to checkpoint 2

∵ The distance from checkpoint 2 to the finish line is z

∵ the distance from checkpoint 1 to checkpoint 2 is y

- z is less than twice y by 20

∴ z = 2y - 20 ⇒ add 20 to both sides

∴ z + 20 = 2y ⇒ subtract z from both sides

∴ 2y - z = 20 ⇒ (3)

* Now lets write the three equations

# x + y + z = 120 ⇒ (1)

# x - (1/2) y = 35 ⇒ (2)

# 2y - z = 20 ⇒ (3)

- Now lets write the matrix equation that models this situation

∴ \left[\begin{array}{ccc}1&1&1\\1&-1/2&0\\0&2&-1\end{array}\right]=\left[\begin{array}{c}120&35&20\end{array}\right]

Dimas [21]3 years ago
4 0

These are the options:

You might be interested in
Simplify.<br> In e =<br> In e 2x=<br> In 1 =
Shalnov [3]

Answer:

ln e = 1

ln e 2x = 2x

ln 1 = 0

Step-by-step explanation:

ln e

ln(2.718282) = 1

In e 2x

ln(2.718282)(2)x = 2x

ln 1 = 0

5 0
3 years ago
Find the average of the data set: {12, 8, 4, 6, 10}<br><br> NEED HELP ASAP!!!!!!!
kari74 [83]

8

This is the answer....

4 0
3 years ago
Read 2 more answers
T - 6.2 &lt; 4 help me please
enyata [817]

Answer:

t < 10.2

Step-by-step explanation:

Step 1: Add 6.2 to both sides.

  • t - 6.2 + 6.2 < 4 + 6.2
  • t < 10.2

Therefore, the answer is t < 10.2.

Have a lovely rest of your day/night, and good luck with your assignments! ♡

6 0
3 years ago
What is the angular velocity of a 6–foot pendulum that takes 3 seconds to complete an arc of 14.13 feet? Use 3.14 for π
iren2701 [21]
1) Calculate the whole arc (complete circumference):


Circumference = 2π*radius


radius = 6 foot


=> Circumference = 2 * 3.14 * 6 foot = 37.68


2) Calculate the time to make a whole round, by making a proportion with the two ratios:


 ratio 1 = x / 37.68 =


ratio 2 = 3 / 14.13


ratio 1 = ratio 2 =>

   x                  3s
----------  =   -----------
37.68 ft        14.13 ft


=> x = 3 * 37.68 / 14.13 = 8 s


3) Calcuate the angular velocity as the 2π rad (which is the total angle of a circle) divided by the time.


So the angular velocity is 2π rad / 8 s = 2*3.14 foot / 8 s = 0.785 rad / s



Answer: 0.785 rad / s


3 0
3 years ago
There are 364 students who are enrolled in an introductory biology course. If there are five boys to every eight girls, how many
Butoxors [25]

Answer:

The number of boys in the course will be = 140

Step-by-step explanation:

Given:

Total number of students enrolled in an introductory biology course = 364

There are 5 boys to every 8 girls in the course.

To find how many boys are in the course.

Solution:

Since, there are 5 boys to every 8 girls in the course.

So, ratio of boys to girls enrolled in the course = 5 : 8

Let the number of boys in the course be = 5x

Then number of girls in the course will be =  8x

Total number of students would be given as:

⇒ <em>Number of boys + Number of girls</em>

⇒ 5x+8x

⇒ 13x

Total number of students given = 364.

Thus, we have:

13x=364

solving for x

Dividing both sides by 13.

\frac{13x}{13}=\frac{364}{13}

∴ x=28

So, number of boys in the course will be = 5\times 28 = 140

5 0
3 years ago
Other questions:
  • during a long race a professional cyclist was able to sustain a speed of 20 miles per hour. How far could this cyclist travel at
    15·1 answer
  • What is 9/10 subtracted by 1/6
    7·2 answers
  • Simplify<br> y = (x + 1)2 -
    11·2 answers
  • Please help! I'm am not that great at graphing like this...<br><br> Thanks a bunch! :)
    5·1 answer
  • Kyle makes his own breakfast every Saturday. It usually takes ten minutes to make the breakfast and five minutes to eat the brea
    14·1 answer
  • a soccer ball has a circumference of about 28inches while the goal is 24 feet wide how many soccer balls would be needed to cove
    9·2 answers
  • You put $491 in your savings account with a 3% interest rate, how much will you earn over a year
    10·1 answer
  • Bill makes four payments a year of $128.25 for life insurance; four payments of $161.82 for real estate taxes; twenty-four payme
    13·1 answer
  • [Geometry]<br> Is ABC DEF? If so, name the postulate that applies.
    8·2 answers
  • What is 11/2 reduced? 11/2 is a fraction:)
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!