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klasskru [66]
1 year ago
12

Solve the following system of equations. Show all work and solutions.

Mathematics
1 answer:
Hitman42 [59]1 year ago
4 0
  • y=2x²+6x+1
  • y=-4x²+1

Make the equations equal and solve for x

  • 2x²+6x+1=-4x²+1
  • 6x²+6x=0
  • 6x(x+1)=0
  • 6x=0 or x+1=0
  • x=0 or x=-1

For x=0

  • y=-4(0)+1=1

For x=-1

  • y=-4(1)+1=-3

The solutions are

  • (0,1) and (-1,-3)

Graph attached

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A person drove from 8 am Tuesday to 5 pm Wednesday. Total drive 396 miles. He have lunch for 30 minutes on Tuesday and sleep ove
777dan777 [17]

Answer: 18mph

Step-by-step explanation:

Given data

total distance driven = 396 miles

time driven = 8 am Tuesday to 5 pm Wednesday

total time driven in hours = 33 hours

lunch break time = 30 min Tuesday  + 30 min Wednesday

= 60 min

= 1 hour

sleep time = 7 pm Tuesday to  5 am Wednesday

= 10 hours

solution:

To find the average speed,

we are given total time driven = 33hrs.

lunch + rest time = 10hrs + 1hr

= 11hrs

total time travelled =drive time - rest + lunch time

= 33 - 11

= 22hrs

therefore;

average speed = distance / time traveled.

average speed = 396 / 22

average speed = 18 mph

6 0
2 years ago
On Friday,a museum had 185 visitors. On Saturday,there were twice as many visitors as Friday. On Sunday,50 fewer people visited
RoseWind [281]
Friday - 185

Saturday - 185 x 2
= 370

Sunday - 370 - 50
= 320
3 0
3 years ago
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How many cubic feet of water are in the pool?
galben [10]

Answer:

It depends on the size of the

Step-by-step explanation:

Like the width ,length and all that

give me the size of the pool and will assist

8 0
3 years ago
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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
ANEK [815]

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]

6 0
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What is the slope of the line that passes through (2, 3) and has a y-intercept of -1?
sashaice [31]
I believe that the slope would be 4/2 or 2, but i wouldn’t take my word for it
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