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The sum of five consecutive positive integers is 2020. Find the largest of these numbers.  

Divide 2020 by 5 and get 404. 

That's your middle number.  Now go two numbers to the left and two numbers to the right. 

402 + 403 + 404 + 405 + 406  =  2020 

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okay, thank you!

The total of the interior angles of any polygon is (n – 2) • 180^o where n is the number of sides. 

The total of the interior angles of this (and every) pentagon is 540^o so set up the addition. 

z + 2z + 117 + 64 + (2z –6) = 540 

5z + 175 = 540  

5z = 540 – 175

z = 73^o  

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See the answers here:  https://web2.0calc.com/questions/someone-please-help-me_8

Let the hourly rate of company B = 1/B

Then, the hourly rate of company A =1 /(B + 5)

1/B + 1 / (B+5) = 1/8, solve for B

Solve for B:
1/B + 1/(B + 5) = 1/8

Bring 1/B + 1/(B + 5) together using the common denominator B (B + 5):
(2 B + 5)/(B (B + 5)) = 1/8

Cross multiply:
8 (2 B + 5) = B (B + 5)

Expand out terms of the left hand side:
16 B + 40 = B (B + 5)

Expand out terms of the right hand side:
16 B + 40 = B^2 + 5 B

Subtract B^2 + 5 B from both sides:
-B^2 + 11 B + 40 = 0

Multiply both sides by -1:
B^2 - 11 B - 40 = 0

Add 40 to both sides:
B^2 - 11 B = 40

Add 121/4 to both sides:
B^2 - 11 B + 121/4 = 281/4

Write the left hand side as a square:
(B - 11/2)^2 = 281/4

Take the square root of both sides:
B - 11/2 = sqrt(281)/2 or B - 11/2 = -sqrt(281)/2

Add 11/2 to both sides:
B = 11/2 + sqrt(281)/2 or B - 11/2 = -sqrt(281)/2

Add 11/2 to both sides:

B = 11/2 + sqrt(281)/2 =13.882 =~13.9 hours for Co. B to finish the Job alone.

13.9 + 5 =~18.9 hours for Co. A to finish the Job alone                                                     

45 - 21 = 24

24 / 4 = 6 - This is the common difference

The sequence = 21, 27, 33, 39, 45

1 - Let the number of five-dollar bills =F

Then, the number of ten-dollar bills  =33 - F

5F + 10*[33 - F] =260

5F + 330 - 10F    =260

- 5F =260 - 330

- 5F = - 70

F = - 70 / - 5

F = 14 - Number of 5-dollar bills

33 - 14 = 19 - Number of 10-dollar bills

Check: [14 x $5  +  19 x  $10] =$70 + $190 =$260

2 - Let the number of Human heads = H

Then, the number of dog heads         =36 - H

H x 2 legs each + [36 - H] * 4 legs each = 102 legs

2H  + 144 - 4H = 102

 - 2H = 102 - 144

- 2H = - 42

H =- 42 / -2 =21 - Number of Humans at the Fair.

36 - 21 = 15 - Number of dogs at the Fair.

Check: [21 x 2 legs + 15 x 4 legs] =42 + 60 =102 legs at the Fair.

Thanks!

Thank youuuu!

If you graph these coordinates, you will find it is a 5 x 6 rectangle. Thus the area is 30.

Thank you sooo much! 

SA = 2(hl+hw+lw)

It doesn't matter which specifically is the height or width or length in this case.

1.8 x 0.5 = 0.9

1.8 x 0.5 = 0.9

0.5 x 0.5 = 0.25

2(0.9 + 0.9 + 0.25) = 2(1.8 + 0.25) = 2(2.05)

2 x 2.05 = 4.1, which is the surface area.

Just count them:  [5240, 4365, 3490, 2615, 1740, 865, -10, -885, -1760, -2635]

Since it is a square, all four sides are equal. Since the perimeter of the square is 144, 144/4 = 36 is the side length of one side of the big square. One of the sides is divided into 4 equal parts, so 36/4 = 9. This means one rectangle has a length of 36, and a width of 9. 

Perimeter: 36+36+9+9 = 90.

Thank you, all three of you. I appreciated it very much.

Im so sorry XO=4!

Sorry for my mistake

Thanks Melody!

It's been answered here::::: https://web2.0calc.com/questions/help-pls_51443#r2

Dividing by 0 is undefined. You can imagine it this way:

You have 0 friends and you have 10 cookies. Now, how many cookies does each friend get? You may think the answer is 0, but it acctually is not! This is because you have NO friends, so therefore there is no way to get an answer. 

Now, if you say that you have 10 friends and 0 cookies, each friend will get 0 cookies. This time, we are not dividing by 0, but 0 is divided by us. See the difference?

To complete the square, we see that the second number in the square must be -1. So, "taking" a 1 from the 4, we get:

(x-1)^2+y-5=0

Now, we can see that if we take the y to the other side, we get the equation in vertex form. So, this will become:

(x-1)^2-5=-y

Divide both sides by -1:

-(x-1)^2+5=y

Since this is in vertex form, we see that the vertex is at (1, 5)

We can graph this on desmos: https://www.desmos.com/calculator

And we see that our answer is correct.

So, the vertex is at (1, 5)

That question is for that guest who cannot solve that simple question. 

Yes! If you need to find the area of an incircle, you need only a radius of that circle. But if you need to find the area of a circumcircle, you need to find the lengths of both radii. 

You're very welcome!

 Let the percentage of 7 L of acid solution =P
7*P/100 + 0.15*3 =0.29*[7 + 3]
0.07P + 0.45 =2.9
0.07P =2.9 - 0.45 =2.45
P =[2.45 / 7 ]  x 100
P = 35 % - Percentage of acid in the 7 L solution.