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Marina86 [1]
3 years ago
6

If 3 workers can paint a room in 2 hours, then approximately how long does it take 4 workers to paint the same room? Assume the

time needed to paint the room is inversely proportional to the number of workers.
Mathematics
2 answers:
Olin [163]3 years ago
6 0

It takes 1.5 hours for 4 workers to paint the same room

<em><u>Solution:</u></em>

Given that 3 workers can paint a room in 2 hours

To find: Time taken for 4 workers to paint the same room

Assume the time needed to paint the room is inversely proportional to the number of worker

time $ \propto \frac{1}{\text { number of workers }}\\\\time =k \times \frac{1}{\text { number of workers }}

Where, "k" is the constant of proportionality

<em><u>3 workers can paint a room in 2 hours</u></em>

Substitute number of workers = 3 and time = 2 hours

time =k \times \frac{1}{\text { number of workers }}\\\\2 = k \times \frac{1}{3}\\\\k = 6

Therefore,

\text {time}=6 \times \frac{1}{\text { number of workers }}

To find time taken for 4 workers to paint the same room, substitute number of workers = 4 in above expression

time = 6 \times \frac{1}{4} = 1.5

Thus it takes 1.5 hours for 4 workers to paint the same room

Elina [12.6K]3 years ago
6 0

Answer:

1.5 hours.............

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Tomtit [17]

Answer:

There are 40 musicians that are only marching band.

Step-by-step explanation:

Since we knot that there are 25 musicians that do both that means there is 60 - 25 = 35 musicians who do only jazz band. From his we can answer the question because....

100 = a + b + c

Where "a" is the number of musicians who go only to jazz, "b" is the number of people who do both, and "c"  is the number of people that go only to the marching band. From here we can do this....

100 = a + b + c

c = 100 - a - b

Substitute the value we found outa and get.....

c = 100 - 35 - 25

c = 40

3 0
3 years ago
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The vertices of a parallelogram are A(x1, y1), B(x2, y2), C(x3, y3), and D(x4, y4). Which of the following must be true if paral
Iteru [2.4K]

The answer is really none of the above, because all of these have divisions by difference in x, and there are perfectly fine rectangles where those will mean dividing by zero.

To do the problem the way they want us to, we note segments with the same slope are parallel (or collinear); segments with slopes which multiply to -1 are perpendicular.

Let's figure out what each choice is trying to tell us by translating it into parallel and perpendicular. Remember A is point 1, ...

A. ((y_4-y_3)/(x_4-x_3)= (y_3-y_2)/(x_3-x_2)) and ((y_4-y_3)/(x_4-x_3)×(y_3-y_2)/(x_3-x_2))=-1

translated, that's CD║BC and CD⊥BC - contradictory; second half right

B. (y_4-y_3)/(x_4-x_3)= (y_2-y_1)/(x_2-x_1) and ((y_4-y_3)/(x_4-x_3)×(y_2-y_1)/(x_2-x_1))=-1

CD ║ AB and CD ⊥ AB - only the parallelogram half is right

C. (y_4-y_3)/(x_4-x_3)= (y_2-y_1)/(x_2-x_1) and (y_4-y_3)/(x_4-x_3)×(y_3-y_2)/(x_3-x_2)=-1

CD║AB and CD⊥BC - that's TRUE

D. (y_4-y_3)/(x_4-x_3)= (y_3-y_1)/(x_3-x_1) and (y_4-y_3)/(x_4-x_3)×(y_2-y_1)/(x_2-x_1)=-1

CD║AC and CD⊥AB - nope

Answer: C

The way I'd get the proper expression is with the dot product.

A parallelogram is a rectangle when adjacent sides are perpendicular. It only takes one right angle to make them all right.

Two sides are perpendicular when the dot product of their direction vectors is zero. All the answers have y_4 - y_3 so one side is CD. The other side must be BC or AD; AD would give y_4 - y_1 terms which don't appear among the answer, so let's go with BC.

The direction vectors are

D-C = (x_4 - x_3, y_4 - y_3)

C-B = (x_3 - x_2, y_3 - y_2)

For perpendicularity we need a zero dot product:

0 = (D-C)\cdot(C-B) = (x_4 - x_3)(x_3 - x_2) + (y_4 - y_3)(y_3 - y_2)

- (x_4 - x_3)(x_3 - x_2) = (y_4 - y_3)(y_3 - y_2)

That's the correct expression, given it's a parallelogram, to demonstrate it's a rectangle. The divisions make it iffy.

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What is the value of x?? please help
DaniilM [7]

Answer:

x=64

Step-by-step explanation:

Both the semicircle that says 180, and the right angle sign in the image serve to support the idea that all parts of the figure equal 90

Therefore, it is safe to say that you need to subtract 26 from 90 in order to solve for x.

90-26 = 64

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Answer:

5

Step-by-step explanation:

If X equals 2, then 3 times X would be 6. This is because if a number and a variable are put together, you have to multiply them. 6-1 is 5.

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