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So since we are trying to find the value of the expression, does that mean that the Y value is the answer?

\(\text{For this problem the simplest route is just completing the square}\\ y=x^2+8x = \\ x^2 + 8x + 16 - 16 = \\ (x+4)^2 - 16\\ \text{This is a minimum at }x=-4 \text{ and the minimum is }y=-16\)

Definitely not positive integers... because of the +8x

Negatives can't be too small because of the \(x^2\) will turn it into a positive integer.

Because I'm am not the best at math, I will just use a guess and check to solve.

1. We are trying to find the peak at which the value will be on the verge of becoming bigger.

    Substituting -3 for x we will get : -15

    Substituting -4 for x we will get : -16

    Substituting -5 for x we will get : -15

So the answer SHOULD be -16? I'm not sure someone check this.

Formula for picking r items from n set: \(\frac{n!}{r!(n-r)!}\)

Since you are trying to find the combinations for a ten question test with 4 true and 6 false, you can just think it as picking 4 items from a set of 10 or picking 6 items from a set of 10.

Note: There are the same amount of combinations picking 4 items from a set of 10 is the same thing as picking 6 items from a set of 10

Now use the formula.

Good job.....hadn't occure to me !

oh ok

See here: https://web2.0calc.com/questions/what-is-0-48-expressed-as-a-fraction-in-simplest_1#r3​

There are a 100 integers between 1-100, inclusive. Since 50 is \(2*5^2\), it has \((1+1)(1+2)=(2)(3)=6\) factors. Thus, the answer is \(\frac{6}{100}=\boxed{\frac{3}{50}}. \)

144 minutes

(I am pretty sure)

The diameter of a conical paper cup is 3.4 inches, and the length of the sloping side is 4.53 inches, as shown in the figure. How much water will the cup hold? (Round your answer to two decimal places.)

Turn the paper cup upside down.  This is just to make it easier for me. 

Draw a line from the point of the cone down to the middle of the circular base.

In two dimensions, that line is one side of a right triangle whose base is 1.7 inches and hypotenuse is 4.53 inches

Use Pythagoras' Theorem to determine the third side.  This will be the height of the cone.

                                                              4.53² = h² + 1.7²   

rearrange terms for my convenience     h² = 4.53² – 1.7²

do the arithmetic                                    h² = 20.52 – 2.89 = 17.63    

                                                              h = sqrt(17.63) = 4.20

you have the radius of the cone

and its height; use the formula               V = (1/3) * pi * r² * h

plug in the values                                   V = (1/3) * 3.14 * 2.89 * 4.20

do the arithmetic                                     V = 12.70 inch³

.

multiply both sides by x+4

to get

x = -9(x+4) / (x+3)     Multiply both sides by x + 3 to get

x (x+3) = -9 (x+4)    expand

x^2 + 3x = - 9x - 36

x^2 + 12x + 36 = 0    factor

(x+6)(x+6) = 0           two roots   at   x = -6

When the ball hits the ground   h = 0

so set the equation = 0 and solve for 't'

0 = -4.9t^2-3.5t + 2.4       solve for t    (quadratic formula)          Let me know what you find!

6x+8=x+35 how do i solve??

                                                 6x + 8 = x + 35

subtract x from each side          6x – x + 8 = x – x + 35

that gives you                            5x + 8 = 35

subtract 8 from each side          5x + 8 – 8 = 35 – 8

that gives you                            5x = 27

divide both sides by 5                 x = 27/5

                                                    x = 5.4 

5.4

subtract x from both sides to get

5x + 8 = 35     now subtract 8 from both sides

5x = 27     divide by 5

x = 27/5 = 5 2/5

Diagram?    Need angle of sloping side or height to determine volume...

A triangular region is bounded by the two coordinate axes and the line given by the equation 2x + y = 6. What is the area of the region, in square units?

The x-axis and the y-axis form two legs of the triangle, and the line 2x + y = 6 forms the third side. 

use the equation 2x + y = 6     to determine the points where the third side joins each of the other two

at x = 0     you get y = 6          That's the height of the triangle.  (the distance up the y-axis)

at y = 0     you get x = 3          That's the base of the triangle.  (the distance out the x-axis)

Area of a triangle = half the base times the height

A = (1/2)*(3)*(6) = (1/2)*(18)

A = 9 units²

.

1  - C

2  -  B

3 -   A

And some more :

https://web2.0calc.com/questions/help-due-tomorrow_4

Here's some :

https://web2.0calc.com/questions/permutations_15

I interpret this question to mean the probability of the experiment ending exactly on the fifth throw. Melody has calculated the probability that it could end on any throw from the second to the fifth (I think!).

If my interpretation is correct, then the fourth and fifth throws must be 4s, and the third throw must be not4.   This means the possible combinations for the first two throws are (1) 4 followed by not4, (2) not4 followed by 4, (3) not4 followed by not4.

Putting all this in probability terms we have p = (1/6²)(5/6)[ (1/6)(5/6) + (5/6)(1/6) + (5/6)(5/6) ]

or p = 175/7776 ≈ 0.0225

This is borne out by a MonteCarlo simulation (which also confirms Melody’s calculation using her interpretation of the question).

1.  The common difference is (1/2)

Recursive

a_n  =  (1/2)a_n-1, a1  = 80

2.  Here: https://www.desmos.com/calculator/dzbwv2cbw4

3. Recursive...tedious....find the first 99 terms....the 100th term = (1/2) * 99th term

                                                     0

(1/56)x^8 + (1/21)x^7 - (1/2)x^2  ]       =

                                                    -2  

                                                         -2

- [ (1/56)x^8 + (1/21)x^7 - (1/2)x^2 ]             =

                                                         0

- [ (1/56)(-2)^8  + (1/21)(-2)^7 - (1/2)(-2)^2 ]  =   74/21  units^2

1.  a_n  = a_n-1  - 4,  a₁  = 11 

2. Here :  https://www.desmos.com/calculator/xnzwqsnu8u

3. Probably wouldn't want to use the recursive formula to find the 100th term......we would have to find the first 99 terms and then subtract 4 from the 99th term.....extremely tedious....!!!