Using the image above, set up the equation that would help to determine the value<br> of angle x.

Caleb's mother said they will drive 1 /4 hour to get there, and they will drive another 1 /4 hour back. Once they arrive, Caleb'

Nezavi [6.7K]

Answer: They are away for $2\dfrac{3}{4}\ hours$ from home.

Step-by-step explanation:

Since we have given that

Time to get there = $\dfrac{1}{4}$

Time to get back = $\dfrac{1}{4}$

Number of soccer games = 3

Time for each soccer games = $\dfrac{3}{4}$

So, total time for 3 games would be

$3\times \dfrac{3}{4}=\dfrac{9}{4}$

So, the time for which they will be away from home is given by

$\dfrac{1}{4}+\dfrac{9}{4}+\dfrac{1}4}=\dfrac{1+9+1}{4}=\dfrac{11}{4}=2\dfrac{3}{4}\ hours$

Hence, they are away for $2\dfrac{3}{4}\ hours$ from home.

3 0

4 years ago

A bucket that weighs 4lband a rope of negligible weight are used todraw water from a well that is 80ftdeep. The bucket is filled

liq [111]

Answer:

Workdone = 3200 lb.ft

Step-by-step explanation:

We are told that the bucket is filled with 40 lb of water but water leaks out of a hole in the bucket at a rate of 0.2lb/s

Thus,

Weight of water at any given time (t) would be;

w(t) = 40 - 0.2t - - - - (1)

We are told the bucket is pulled up at a rate of 2ft/s.

Thus, height at time (t); y = 0 + 2t = 2t

Since y = 2t,

Then,t = y/2

Put y/2 for t in eq 1

Thus; w(y) = 40 - 0.2(y/2)

w(y) = 40 - 0.1y

Now, at y = 80 ft, we have;

w(80) = 40 - 0.1(80)

w(80) = 40 - 8 = 32 lb

Since 32 lbs are left, it means there is always water in the bucket.

Thus, work done is;

W = 80,0[∫(Total weight).dy]

W = 80,0[∫[(weight of rope) + (weight of bucket) + (weight of water)]dy]

W = 80,0[∫[0 + 4 + 40 - 0.1y]dy]

Integrating, we have;

W = [44y - y²/20] at boundary of 80 and 0

So,

W = [44(80) - 80²/20] - [0 - 0²/20]

W = 3200 lb.ft

8 0

3 years ago

Marcus bought a booklet of tickets to use at the amusement park. He used 50% of the tickets on rides, 1/4 of the tickets on vide

shtirl [24]

Answer:

No, 25%, 50%, 25%

Step-by-step explanation:

Find the percentage of tickets left:

50 + 25 = 75

(percents are out of 100)

100 - 75 = 25

He saids he used the rest of the tickets at the batting cage so it would be 25% not 24%

7 0

3 years ago

Factor the expression completely 10x-80

kupik [55]

Answer:

10(x−8)

Step-by-step explanation:

10x-80

-> Both have a factor of 10

10x / 10 = x

80 / 10 = 8

10(x - 8)

8 0

3 years ago

A rhombus has perimeter 120 M and one of its diagonal is 50 M find the area of the Rhombus

Mademuasel [1]

The area of the rhombus is 829.1562m².

<h3>What is the area of the rhombus?</h3>

A rhombus is a four sides quadrilateral with the four sides equal in length

The area of a rhombus = $\frac{1}{4}d$ ×√(p² - 4d²)

where p is the perimeter and d is the diagonal

1/4(50) x √(120² - 4 x 50²) =829.1562m²

To learn more about a rhombus, please check: brainly.com/question/22825947

#SPJ1

6 0

2 years ago

Using the image above, set up the equation that would help to determine the value of angle x.