Find the slope of the line that passes through the point (0,-3) and (4,5)



Answer 1
Answer: It depends which pair goes first but the formula is Y2-y1 over x2-x1
Answer 2

Answer: m=2

(0,-3) = (x1,y1)

(4,5) = (x2,y2)

Slope = (y2-y1)/(x2-x1)

          = (5-(-3))/(4-0)

          = (5+3)/(4)

          = (8)/(4)

          = 2

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8000 dollars a month equals what in one year? how long till you reach a million dollars?


If you earn $8000 a month in year you will earn $96000. You will hit the 1 million mark after 125 months or 10 years and 5 months

8000 dollars in one month... 12 months in a year... 12 x 8000 is 96000. An equation would be y=8000x, x being amount of time in months and y being the total amount of dollars. So then...

-------------   --------
    8000       8000

125=x... 25 months.

candy box is made from a piece of cardboard that measures 45 by 24 inches. Squares of equal size will be cut out of each comer. The sides will then be folded up to form a rectangular box. What size square should be cut from each corner to obtain maximum volume? inches should be cut away from each corner to obtain the maximum volume. A square with a side of length (Round to the nearest hundredth as needed.)



Each square should have 5 inches of side and area = 25 square inches.

Step-by-step explanation:

Candy box is made that measures 45 by 24 inches.

Let the squares of equal size x inches has been cut out of each corner.

The sides will then be folded up to form a rectangular box.

Now we have to find the size of square that should be cut from each corner to obtain maximum volume of the box.

Now the box is with length = (45 - 2x) inches

and width = (24 - 2x) inches

and height = x inches

Volume of the candy box = Length × width × height

V = (45 - 2x)(24 - 2x)(x)

V = x(1080 - 48x -90x + 4x²)

  = x(1080 - 138x + 4x²)

  = 4x³ - 138x² + 1080x

Now we will find the derivative of volume and equate it to zero.


12(x² - 23x + 90) = 0

x² - 23x + 90 = 0

x² - 18x - 5x + 90 = 0

x(x - 18) - 5(x - 18) = 0

(x - 5)(x - 18)=0

x = 5, 18

Now for x = 18 Width of the box will be = (24 - 2×18) = 24 - 36 = -12

Which is not possible.

Therefore, x = 5 will be the possible value.

Therefore, square having area 25 square inches should be cut out from each corner to get the maximum volume of candy box.

Final answer:

The size of the square that should be cut away from each corner to obtain the maximum volume for a box made from a cardboard measuring 45 by 24 inches is 3 inches.


To find the size of the square that should be cut from each corner to obtain the maximum volume, we should first make an equation for the volume of the box. If x is the length of the side of the square, then the dimensions of the box are (45-2x) by (24-2x) by x, thus the volume of the box V is (45-2x)(24-2x)x.

By using calculus, we can find the derivative of this function, set it to zero and solve, this will give the critical points where the maximum and minimum volumes will be.

The derivative is found to be -4x^2 + 138x - 1080. Setting this to zero and solving, we find that x = 3 and x = 90 are the critical points for the maximum and minimum volumes. Since we cannot cut corners more than 24 inches (this would make the width negative), x = 3 inches is the only feasible solution.

So, 3 inches should be cut away from each corner to obtain the maximum volume.

Learn more about Optimization here:


Consider the set S of primes less than 15. List the set S . (Input this as a list with no spaces, use commas.) How many subsets does the set have


9514 1404 393


  S = {2, 3, 5, 7, 11, 13}

  2^6 = 64 subsets

Step-by-step explanation:

The list of primes less than 15 is ...

  S = {2, 3, 5, 7, 11, 13}


A set with n unique elements has 2^n unique subsets, including the empty set and the full set. This set of 6 elements has 2^6 = 64 subsets.

Question 2

Determine which triangle appears to be acute.


Number 2. Because I am in college
number two because it has at least one acute angle

6) Write an equation and solve: Twice a number, increased by 3 is 7.A) 2
B) 5
D) 20




Step-by-step explanation:

2×x + 3=7




divide both sides by the coefficient of x which is 2



Please help me solve this!



Step-by-step explanation:

a) AB=2AM


If M is the midpoint of AB, then AM = MB

Since AM=MB MB=2AM

Therefore AB=2AM


sincs M is midpoint of AB.

then AM=BM....(1)

and also AM+BM=AB

AM+AM=AB from (1)..AM=BM