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Vikki [24]
4 years ago
8

During a tunnel construction project, engineers used explosives to excavate partway into a mountain. Because of time constraints

and environmental concerns, they later used a tunnel boring machine (TBM) to excavate the rest of the tunnel. The table shows the length of the completed tunnel, y, after different numbers of days, x, since the TBM started working. Number of Days Length of Tunnel (feet) 0 225 5 350 20 725 30 975 55 1,600 The length of the completed tunnel can be calculated using the equation . If the project will be completed 86 days after the TBM was introduced, the length of the completed tunnel will be feet.
Mathematics
1 answer:
AnnyKZ [126]4 years ago
5 0

The given data can be tabulated as:

number of days,x                            length of tunnel (ft), y

0                                                                              225

5                                                                              350

20                                                                           725

30                                                                           975

55                                                                           1,600

 

To check if the growth is linear, the slope at points (0, 225) and (5, 350), and (0, 225) and (20, 725) should be equal. The formula for slope is:

m = (y2 – y1) / (x2 – x1)

 

Finding for slope (0, 225) and (5, 350):

m = (350 – 225) / (5 – 0) = 25

 

Finding for slope (0, 225) and (20, 725):

m = (725 – 225) / (20 – 0) = 25

 

Therefore the equation is linear in the form of:

y = mx + b

where b is the value of y at x = 0, so b = 225

 

The complete equation is:

y = 25x + 225

 

At x = 86 days

y = 25(86) + 225

y = 2,375 ft

 

Therefore the length of the completed tunnel is 2,375 feet.

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Answer:

16%

Step-by-step explanation:

406 / 350 = 1.16

406 is 116% of 350

so 350 + 16% is 406

because 350 * 0.16 = 56

56 is 16%

350 + 56 = 406

:)

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3 years ago
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gizmo_the_mogwai [7]

Answer: x=10

Step-by-step explanation:

1/5(x-2)=1/10(x+6)

1/5x -2/5=1/10x + 6/10

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1/5x =1/10x + 1

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3 0
3 years ago
Help needed! no links please, they're annoying.
denis23 [38]
The area of a rectangle is length*width.

The length of this 3x and the width is 2x-3. This means that, to find the area, you need to multiply 3x and 2x-3.

Start by writing out this equation:
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Then, plug in your given values:
A= 3x*2x-3 (you can also write it as A= 3*x*2*x-3)

Then, following the order of operations, you start by multiplying. This makes your equation become A = 6x^2 -3. (^2 means squared). It turns into this because 3 * 2 is 6 and x * x is x^2 and you still haven’t used the 3 yet.

After this, there is nothing more that you can do to simplify the equation. Therefore, the area is 6x^2 - 3.

I hope this helped!
4 0
3 years ago
Mr. Larsen's third grade class has 22 students, 12 girls and 10 boys. Two students must be selected at random to be in the fall
kupik [55]

The probability of no boys being chosen will be 0.29.

<h3>What is probability?</h3>

Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.

Mr. Larsen's third-grade class has 22 students, 12 girls, and 10 boys.

Two students must be selected at random to be in the fall play.

Then the probability of no boys being chosen will be

Total event = ²²C₂ = 231

Favorable event = ¹²C₂ = 66

Then the probability will be

P = 66 / 231

P = 0.2857

P ≅ 0.29

More about the probability link is given below.

brainly.com/question/795909

#SPJ1

4 0
2 years ago
Which of the following is x=-5 a solution ?
Katarina [22]

Answer:

C and D

Step-by-step explanation:

Plug X in and see which equations/expressions are true

8 0
3 years ago
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