As an estimation we are told 5 miles is 8 km.
Convert 57.5 miles to km.

Answer: 4,000

Step-by-step explanation:

The solution is Option A.

The rate at which the swimming pool is being filled is 66.6 gallons per hour

What is an Equation of a line?

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the number of gallons be = y

Let the time taken be = x

The total volume of the pool = 15000 gallons

The pool is filled at constant rate

Now ,

The coordinate data is given as

The value of A = A ( 15 , 1000 )

The value of B = B ( 30 , 2000 )

The value of C = C ( 45 , 3000 )

Now , the rate at which the swimming pool is filled is given by the slope of the points in the line

So , the slope of the 2 points is given by the formula

Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 2000 - 1000 ) / ( 30 - 15 )

On simplifying the equation , we get

Slope m = 1000 / 15

Slope m = 66.66 gallons per hour

Therefore , the value of A is 66.6 gallons per hour

Hence ,

The rate at which the swimming pool is being filled is given by the slope of the line where slope m = 66.6 gallons per hour

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Answer:

0.0054054054

Also simplify to 0.005

Answer:

17÷3,145=0.00540

Answer:

50 degrees

Step-by-step explanation:

vertical angles are the same

angle LPM = 180-60-70

angle LPM = 180-130 = 50

angle LPM = angle KPN

50=angle KPN

Answer:

The number which should be added  with 49x square + 4y square to get a perfect square is 28xy

Step-by-step explanation:

We need to find the number which is to be added with 49x square + 4y square to get a perfect square.

The expression given is: [tex]49x^2+4y^2[/tex]

For the expression to be perfect square it should be of form: [tex]a^2+2ab+b^2=(a+b)^2[/tex]

Now, we are given [tex]49x^2+4y^2[/tex] and we need to find the middle term

So, solving:

[tex]49x^2+4y^2\\=(7x)^2+(2y)^2+2(7x)(2y)-2(7x)(2y)\\=7x^2+28xy+(2y)^2-28xy\\=(7x+2y)^2-28xy[/tex]

The number which should be added  with 49x square + 4y square ([tex]49x^2+4y^2[/tex]) to get a perfect square is 28xy

Answer:

x=−6 and y=7

Step-by-step explanation:

Step: Solve8x+5y=−13for x:

8x+5y=−13

8x+5y+−5y=−13+−5y(Add -5y to both sides)

8x=−5y−13

8x

8

=

−5y−13

8

(Divide both sides by 8)

x=

−5

8

y+

−13

8

Step: Substitute

−5

8

y+

−13

8

forxin3x+4y=10:

3x+4y=10

3(

−5

8

y+

−13

8

)+4y=10

17

8

y+

−39

8

=10(Simplify both sides of the equation)

17

8

y+

−39

8

+

39

8

=10+

39

8

(Add 39/8 to both sides)

17

8

y=

119

8

17

8

y

17

8

=

119

8

17

8

(Divide both sides by 17/8)

y=7

Step: Substitute7foryinx=

−5

8

y+

−13

8

:

x=

−5

8

y+

−13

8

x=

−5

8

(7)+

−13

8

x=−6(Simplify both sides of the equation)Step: Solve8x+5y=−13for x:

8x+5y=−13

8x+5y+−5y=−13+−5y(Add -5y to both sides)

8x=−5y−13

8x

8

=

−5y−13

8

(Divide both sides by 8)

x=

−5

8

y+

−13

8

Step: Substitute

−5

8

y+

−13

8

forxin3x+4y=10:

3x+4y=10

3(

−5

8

y+

−13

8

)+4y=10

17

8

y+

−39

8

=10(Simplify both sides of the equation)

17

8

y+

−39

8

+

39

8

=10+

39

8

(Add 39/8 to both sides)

17

8

y=

119

8

17

8

y

17

8

=

119

8

17

8

(Divide both sides by 17/8)

y=7

Step: Substitute7foryinx=

−5

8

y+

−13

8

:

x=

−5

8

y+

−13

8

x=

−5

8

(7)+

−13

8

x=−6(Simplify both sides of the equation)

Answer: The intersection between these 2 lines are (-6,7)

Source: Desmos Graphing Calculator (look it up its very helpful and gives answers)

Answer:

1.) 6 football tickets for $24

Step-by-step explanation:

The situation which leads to a unit cost of $6 per football ticket is; 6 football tickets for $24.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Multiplication is the mathematical operation is used to determine the product of two or more numbers.

We have been given a condition as; a unit cost of $6 per football ticket.

Meaning that;

The cost of one football ticket is 6 dollar

Then The cost of 12 football ticket  = 12 x 6 dollar

                                                  = 72

Therefore, the situation which leads to a unit cost of $6 per football ticket is; 12 football tickets for $72.

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Answer:

f=8/3

Step-by-step explanation:

Answer:

vegetarians= 28

chickens= 44

Step-by-step explanation:

let the number of vegetarians be x

and chickens be y

So

x+2.7y=119.6----------1

x+y=72--------------2

from 2, x= 72-y

put x= 72-y in 1

72-y+2.7y=119.6

-y+2.7y=119.6-72

1.7y=47.6

divide both sides by 1.7

y=47.6/1.7

y=28

put y=28 in 1

x+28=72

y= 72-28

y=44

Answer:

x = 16/5

Step-by-step explanation:

9x – 6 = 4x + 10 <-- Combine like terms on one side

5x = 16 <-- Isolate x

x = 16/5

Answer: 3.2

Step-by-step explanation:

(9x - 6) = 4x + 10

9x - 6 = 4x + 10

9x = 4x + 16

5x = 16

x = 3.2

The answer is:

8 miles

Answer:

6.4 .

Step-by-step explanation:

this was on my test

Answer:

$1200

Step-by-step explanation:

Let the initial amount that you invested be $ x.

We are told that the new balance after investing $500 is $1760.

Thus, the balance you had before the deposit $500 us;

$1760 - $500 = $1260

So, when the amount invested was $x, the balance was $1260.

Since this money earned 5% interest on the amount you initially

Thus;

$1260 = initial deposit + (5% of inital deposit)

Thus;

x + (5% * x) = 1260

x + (0.05x) = 1260

1.05x = 1260

x = 1260/1.05

x = $1200

Answer:

A

Step-by-step explanation:

Edge

The trigonometric functions y = arcsinx and y = arccosx have a domain of [–1, 1] option (A) is correct.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

It is given that:

The domain of a trigonometric function is [-1, 1]

As we know,

The range of the sin x and cos x functions is [-1, 1]

The inverse of the above trigonometric functions are:

arc sin x and arc cos x

The range of sin x and cos x becomes domain.

So the domain of y = arcsinx and y = arccosx is [-1, 1].

Thus, the trigonometric functions y = arcsinx and y = arccosx have a domain of [–1, 1] option (A) is correct.

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Answer:

Below

Step-by-step explanation:

A perfect number is one whose proper divisors add up to that number.

For example, 6 is a perfect number because

Its proper divisors 1, 2 and 3 and 1+2+3 = 6.

First list prime factors:

3364 = 2 * 2 * 29 * 29

Proper divisors are 1, 2, 4, 29, 58, 116, 841, 1682

Sum of these = 2733.

So, 3364 is not a perfect number.

4489 = 67 * 67

Divisors are 1 and 67.

Sum = 68.

So, 4489 is not a perfect number.

4358 =2 * 2179

Divisors are 1 , 2 and 2179.

Sum = 2182.

So, 4358 is not a perfect number.

Answer:

hum I think it is a bisect

Step-by-step explanation:

h(x) = 3. g(x) + 5

x= -1 h(x) = 3×8 + 5= 29

x= 0h(x) = 3×5 + 5= 20

x= 2 h(x) = 3×1 + 5= 8

x= 5 h(x) = 3×-5 + 5= -10

[tex]h(x) = 3*g(x)+5[/tex]

When x = -1.

Substitute x = -1 in both h(x) and g(x).   | As shown in the table, when x = -1, g(x) = 8 |

h(-1) = 3*8+5 = 24+5 = 29

h(0) = 3*5+5 = 15+5 = 20

h(2) = 3*1+5 = 3+5 = 8

h(5) = 3*(-5)+5 = -15+5 = -10

Answer:

1) It has a y-intercept of 4

2) A, the rate of change represents how fast the boys run every hour.

Answer:

x=3

Step-by-step explanation:

Answer:

Step-by-step explanation:

1. Slope = (y2-y1) / (x2-x1) = -3-0/ -1-4= -3/-5= 3/5 (d)

2.

Compare to the equation y= mx+b, where m is the slope

3y = 15x+9 divide by 3 each term

y = 15x/3 +9/3

y= 5x + 3 so slope is 5 ( a)

3.

use first the equation point- slope y-y1 =m (x-x1) and rearange it to be in slope-intercept form y=mx +b

y-y1 =m (x-x1)

y-2 = -3( x-1)

y = 2-3x+3

y= -3x +5 ( c)

4.

if the point y- intercept is at (0, 3) then the y-intercept is b=3

y= mx+b

y = 2x +3 (a)

5.

the equation point- slope y-y1 =m (x-x1), find the slope m= (y2-y1) / (x2-x1)

m= 3-12/ 1+2 = -9/3 = -3

y-1 = -3(x-3) is (a)

6.

y-intercept is at -4  ( yet the graph is off a bit -tell your teacher)

slope m = 1

so the equation is y=mx+b and here is y=x -4 (c)

7.

the slope is m= (y2-y1) / (x2-x1) si pich any two points from the table and calculate the slope

for example (0, 3) and (1, 0)

m = (3-0)/ (0-1) = 3/-1 = -3 (d)

1. Slope = (y2-y1) / (x2-x1) = -3-0/ -1-4= -3/-5= 3/5 (d)

2.

Compare to the equation y= mx+b, where m is the slope

3y = 15x+9 divide by 3 each term

y = 15x/3 +9/3

y= 5x + 3 so slope is 5 ( a)

3.

use first the equation point- slope y-y1 =m (x-x1) and rearange it to be in slope-intercept form y=mx +b

y-y1 =m (x-x1)

y-2 = -3( x-1)

y = 2-3x+3

y= -3x +5 ( c)

4.

if the point y- intercept is at (0, 3) then the y-intercept is b=3

y= mx+b

y = 2x +3 (a)

5.

the equation point- slope y-y1 =m (x-x1), find the slope m= (y2-y1) / (x2-x1)

m= 3-12/ 1+2 = -9/3 = -3

y-1 = -3(x-3) is (a)

6.

y-intercept is at -4  ( yet the graph is off a bit -tell your teacher)

slope m = 1

so the equation is y=mx+b and here is y=x -4 (c)

7.

the slope is m= (y2-y1) / (x2-x1) si pich any two points from the table and calculate the slope

for example (0, 3) and (1, 0)

m = (3-0)/ (0-1) = 3/-1 = -3 (d)

Answer:

Step-by-step explanation:

Here is a guide to help:

Best of luck!

Answer: (9,21)

Step-by-step explanation:

R180 (3,-7) = (-(3),-(-7)) = (-3,7)

D3​ (−3,7) = (3 x −3, 3 x 7) = (−9,21)

Answer: John grew 4 and 3/4 inches in one year.

Step-by-step explanation:

Start by subtracting  64.375 (64 and 3/8) by 59.625 (59 and 5/8).

Type your numbers into a calculator (both ways can be put into your calculator, but decimals are easier for you to type)

Get your final answer of 4.75.

Hope this helps!

Answer:

3x4/8×4-1x2/16x2

12/32-2/32=10/32

hope it helped

Answer:

the expected population after 3 years is 863.7009

Step-by-step explanation:

The computation of the expected population after 3 years is shown below

P = P_0 × e^rt

where,

r = 21% = 0.21

t = 3 years

P_0 = 460

Now place these values to the above formula

P = 460 × exp(0.21 × 3)

= 863.7009

hence, the expected population after 3 years is 863.7009

We simply applied the above formula so that the correct value could come

And, the same is to be considered

Answer:

650 pieces of paper

Step-by-step explanation:

each piece is 0.0075 so all you need to do is divide 4.875 by 0.0075

Answer:

i think they both scored the same

Answer:

Colton did.

Step-by-step explanation:

Jack's score was 80%.

Colton got a score of 83.33...

I got Colton's score by solving 10/12.

Answer:

$2 per soda

Step-by-step explanation:

6/3= 2

Answer: 8

Step-by-step explanation:

hope this helped :)

Answer:

8

Step-by-step explanation: