A = 1/2(a + b)h for h

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

AnnyKZ [126]

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.

5 0

3 years ago

You are hanging 3 display shelves with the same width on a wall so that there is 18 inches of space above each shelf for placing

Kazeer [188]

Answer:

You need to have a minimum of 16 inches of clearance.

Step-by-step explanation:

4 0

3 years ago

Carl used 10 2/9 an inch of string to tie a parcel and another 5 1/4 of an inch of string to tie a box, how much string is left

NARA [144]

Answer:

20-(10 2/9)-(5 1/4)= 4.52777777778 inches decimal or 163/36

Step-by-step explanation:

Simplify the following:

20 - (10 + 2/9) - (5 + 1/4)

Put 10 + 2/9 over the common denominator 9. 10 + 2/9 = (9×10)/9 + 2/9:

20 - (9×10)/9 + 2/9 - (5 + 1/4)

9×10 = 90:

20 - (90/9 + 2/9) - (5 + 1/4)

90/9 + 2/9 = (90 + 2)/9:

20 - (90 + 2)/9 - (5 + 1/4)

90 + 2 = 92:

20 - 92/9 - (5 + 1/4)

Put 5 + 1/4 over the common denominator 4. 5 + 1/4 = (4×5)/4 + 1/4:

20 - 92/9 - (4×5)/4 + 1/4

4×5 = 20:

20 - 92/9 - (20/4 + 1/4)

20/4 + 1/4 = (20 + 1)/4:

20 - 92/9 - (20 + 1)/4

20 + 1 = 21:

20 - 92/9 - 21/4

Put 20 - 92/9 - 21/4 over the common denominator 36. 20 - 92/9 - 21/4 = (36×20)/36 + (4 (-92))/36 + (9 (-21))/36:

(36×20)/36 + (4 (-92))/36 + (9 (-21))/36

| 3 | 6

× | 2 | 0

| 0 | 0

7 | 2 | 0

7 | 2 | 0:

720/36 + (4 (-92))/36 + (9 (-21))/36

4 (-92) = -368:

720/36 + (-368)/36 + (9 (-21))/36

9 (-21) = -189:

720/36 - 368/36 + (-189)/36

720/36 - 368/36 - 189/36 = (720 - 368 - 189)/36:

(720 - 368 - 189)/36

720 - 368 - 189 = 720 - (368 + 189):

(720 - (368 + 189))/36

| 1 | 1 |

| 3 | 6 | 8

+ | 1 | 8 | 9

| 5 | 5 | 7:

(720 - 557)/36

| | 11 |

| 6 | 1 | 10

| 7 | 2 | 0

- | 5 | 5 | 7

| 1 | 6 | 3:

Answer: 163/36

4 0

3 years ago

Plz help.........................

Alex17521 [72]

The answer would be d

7 0

3 years ago

Find the perimeter of quadrilateral PQRS with the vertices P(2,4), Q(2,3), R(-2,-2), and S(-2,3).

storchak [24]

Answer:

$P=16.53\ units$

Step-by-step explanation:

we know that

The perimeter of quadrilateral PQRS is equal to the sum of its four length sides

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

we have

the vertices P(2,4), Q(2,3), R(-2,-2), and S(-2,3)

step 1

Find the distance PQ

P(2,4), Q(2,3)

substitute in the formula

$d=\sqrt{(3-4)^{2}+(2-2)^{2}}$

$d=\sqrt{(-1)^{2}+(0)^{2}}$

$d=\sqrt{1}$

$dPQ=1\ unit$

step 2

Find the distance QR

Q(2,3), R(-2,-2)

substitute in the formula

$d=\sqrt{(-2-3)^{2}+(-2-2)^{2}}$

$d=\sqrt{(-5)^{2}+(-4)^{2}}$

$dQR=\sqrt{41}\ units$

step 3

Find the distance RS

R(-2,-2), and S(-2,3)

substitute in the formula

$d=\sqrt{(3+2)^{2}+(-2+2)^{2}}$

$d=\sqrt{(5)^{2}+(0)^{2}}$

$dRS=5\ units$

step 4

Find the distance PS

P(2,4), S(-2,3)

substitute in the formula

$d=\sqrt{(3-4)^{2}+(-2-2)^{2}}$

$d=\sqrt{(-1)^{2}+(-4)^{2}}$

$dPS=\sqrt{17}\ units$

step 5

Find the perimeter

$P=PQ+QR+RS+PS$

substitute the values

$P=1+\sqrt{41}+5+\sqrt{17}$

$P=6+\sqrt{41}+\sqrt{17}$

$P=16.53\ units$

5 0

3 years ago