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4 years ago

7

a contruction company can remove 1/4 metric tons of dirt from a construction site in 1/8 hours what is the unit rate in metric t

ons per hour

1 answer:

shtirl [24]4 years ago

4 0

Answer:

2 metric tons in an hour.

Step-by-step explanation:

The best way to do this is to convert all the fractions to decimals. The problem starts out looking like this.

Formula

Rate = Tons removed / hours

Tons Removed = 1/4 metric ton

Time taken = 1/8 hour

$\text{rate = }\frac{\frac{1}{4}} {\frac{1}{8}}$

Rather than doing it with fractions, it is much easier to do it with decimals

1/4 = 0.25

1/8 = 0.125

Now what you get is rate = 0.25 / 0.125 = 2

So 2 metric tons can be removed in an hour

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Mr wells drew a plan for a rectangle dog run three of the vertices are (2 1/3, 7 1/2), (12, 7 1/2), and (12, 1) what are the coo

melisa1 [442]

Answer:

Step-by-step explanation:

let 4th fourth vertex be D (x,y)

A(2 1/3,7 1/2),B(12, 7 1/2),C(12,1)

or A(7/3,15/2),B(12,15/2),C(12,1)

Mid-point of diagonal AC is P((7/3+12)/2,(15/2+1))

Mid -point of diagonal BD is P((12+x)/2,(15/2+y)/2)

(Because mid -point of diagonal is same.)

(12+x)/2=(7/3+12)/2

12+x=7/3+12

x=7/3

(15/2+1)/2=(15/2+y)/2

15/2+1=15/2+y

y=1

so fourth vertex is (7/3,1)

8 0

3 years ago

Of the 1200 people who attended the Friday night football game, 57% were high schoolers. How many students attended the game?

Brilliant_brown [7]

Answer:

684

Step-by-step explanation:

Using proportions (equivalent ratios), we can find the number of students that make up the 57% out of the total number of people:

$\frac{57}{100}=\frac{x}{1200}$

Cross-multiply: 100x = (57)(1200) or 100x = 68,400

Divide: 100x/100 = 68,400/100

Solve for x: x = 684 students

5 0

4 years ago

The graph of which function has a minimum located at (4, –3)?

valentinak56 [21]

Answer:

None of the options is the answer to the question

Step-by-step explanation:

we know that

The equation of a vertical parabola into vertex form is equal to

$f(x)=a(x-h)^{2}+k$

where

(h,k) is the vertex of the parabola

case A) we have

$f(x)=x^{2}+4x-11$

In this case the x-coordinate of the vertex will be negative

therefore

case A is not the solution

case B) we have

$f(x)=-2x^{2}+16x-35$

This case is a vertical parabola open downward (the vertex is a maximum)

The vertex is the point $(4,-3)$ <u>but is not a minimum</u>

see the attached figure

therefore

case B is not the solution

case C) we have

$f(x)=x^{2}-4x+5$

Convert into vertex form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$f(x)-5=x^{2}-4x$

Complete the square. Remember to balance the equation by adding the same constants to each side

$f(x)-5+4=(x^{2}-4x+4)$

$f(x)-1=(x^{2}-4x+4)$

Rewrite as perfect squares

$f(x)-1=(x-2)^{2}$

$f(x)=(x-2)^{2}+1$ --------> vertex form

The vertex is the point $(2,1)$

therefore

case C is not the solution

case D) we have

$f(x)=2x^{2}-16x+35$

Convert into vertex form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$f(x)-35=2x^{2}-16x$

Factor the leading coefficient

$f(x)-35=2(x^{2}-8x)$

Complete the square. Remember to balance the equation by adding the same constants to each side

$f(x)-35+32=2(x^{2}-8x+16)$

$f(x)-3=2(x^{2}-8x+16)$

Rewrite as perfect squares

$f(x)-3=2(x-4)^{2}$

$f(x)=2(x-4)^{2}+3$ --------> vertex form

The vertex is the point $(4,3)$

therefore

case D is not the solution

The answer to the question will be the function

$f(x)=2x^{2}-16x+29$

7 0

4 years ago

Read 2 more answers

Two sevenths of the height of a sailboats tallest mast is 8 feet. How many feet high is the sailboats tallest mast

Rudik [331]

Answer:

The answer is 28 ft

Step-by-step explanation:

Since two sevenths of the height of a sailboats tallest mast is 8 feet, we keep adding two sevenths until we get its tallest mast.

2/7 = 8 ft

4/7 = 16 ft

6/7 = 24 ft

(Adding 1/7 which is 4 feet)

we get 7/7 = 28 ft

5 0

3 years ago

Which number line shows the solution to<br> 11x + 14 < –8?

GalinKa [24]

Answer:

D

Step-by-step explanation:

11x + 14 < -8

Cancel the addition by subtracting

11x + 14 - 14 < -8 - 14

11x < -22

11x / 11 < -22/11

x < -2

Therefore, the answer is D

8 0

3 years ago