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Sorry I'm not CPhill.... but I'll try my best, too!

We know that in order to get a square of a binomial, we have to do (b/2)^2.

In this case, that will get us (22/2)^2 which is 121.

Therefore, we need to add 121 to each side, which will eventually get us (x+11)^2.

Hope this helped!

Hint:

Since Veronica earns 3% or 0.03 annual (per year) interest, the amount she earns in ten years will be (0.03)^10.

We can easily write an equation that shows how much Veronica wants to earn.

Hope this helped!

y  = (3x + 15)/4          x² + y²  =  36

Substituting:  x² + [ (3x + 15)/4 ]²  =  36

          x² + (9x² + 45x + 225) / 16  =  36

               16x² + 9x² + 45x + 225  =  576

                          25x² + 45x - 351  =  0

Using the quadratic formula:     x₁  =  [-9 + 12sqrt(3) ] / 5          or          x₂  =  [-9 - 12sqrt(3) ] / 5 

Substituting  x₁  into  y  = (3x + 15)/4  results in  y₁  =  [12 + 9sqrt(3) ] / 5

Substituting  x2  into  y  = (3x + 15)/4  results in  y2  =  [12 - 9sqrt(3) ] / 5

A  =  ( [-9 + 12sqrt(3) ] / 5 ,  [12 + 9sqrt(3) ] / 5 )

B  =  ( [-9 - 12sqrt(3) ] / 5  ,  [12 - 9sqrt(3) ] / 5 )

Now, to find the length of AB, place the values of  (x₁, y₁)  and  (x₂, y₂)  into the distance formula:

Distance  =  sqrt[ (x₂ - x₁)² + (y₂ - y₁)² ] 

Hint: 

Since you probably know what is needed for a line to be perpendicular, try to plug in the coordinates that you were given to one of the possible lines that are perpendicular to line 2x+3y=18.

Hope this helped!

Lets say thatV1= velocity of first train=50 ft/s

V2= Velocity of second train=30 ft/s

Then, the velocity of two trains moving in opposite directions is:

Vr= V1 + V2

From here we know that Vr= 50+30= 80 ft/s

Therefore, the distance is going to be 150ft

So the time taken= distance/ relative velocity

t=150/80

t=1.875 s

Hope this helped!

thanks

Let's call the lengths of the rectangular prism x, y, and z. The problem tells us that the sum of the edges is 40, so we can write:

x + y + z = 40

The problem also says that the surface area is 48. That means:

2(xy +yz + xz) = 48

Realize that if we square (x + y + z), that is equal to :

(x^2 + y^2 + z^2 + 2xy + 2xz + 2yz), or :

(x^2 + y^2 + z^2) + 2(xy + xz + yz)

(try expanding it out yourself if you want!)

(x^2 + y^2 + z^2 ) + 48 (since the surface area is 48. See how the substitution works?). 

This is then equal to 1600(40 ^2).

Subtracting 48 on both sides, we get:

(x^2 + y^2 + z^2) = 1552

What's important to realize here is that the question asks us for the space diagonal(the diagonal connecting opposite corners of the prism). The general formula for the length of a space diagonal in a rectangular prism is: sqrt(x^2 + y^2 + z^2). This can be derived from using pythagorean theorem if you really want to see for yourself. 

That means our desired diagonal length is sqrt(1552), which is simplifies to : 4sqrt(97) 

Hello, thank you, yes, the division by 3 applies only to the last term. But the problem is asking for the MAXIMUM possible value of a + b + c + d.

ABC, AB = BC = 25 and AC = 40. What is sin angle ACB?

cos(ACB) = 20/25 = 36.87°

sin(36.87°) = 0.6

Hint: 

Since we know what f(x) and g(x) is, try combining them and see what x value you will get. Then, it will be easy to see what c has to be.

Hope this helped!

thanks

The wave goes from 13   to  -13

Max height: 13 + 24 = 37ft

Minimum height: -13 + 24 = 11 ft

Here is the work:

The minimum height will be when the cos fxn = 1  

So when cos (?) is -1 (0 degrees)

Therefore, (pi)x/60 - 5pi/12 = 0

That will get us x=25.

The maximum height will be when -13 ( cos ( pix/60 - 5pi/12) = 13

There are two ways to write this. Go with whatever is easiest for you.

Second way: cos ( pi x / 60 - 5pi/12)   = -1      pi x/60 - 5pi/12 =   pi      

Both will get you  x = 85 minutes =  9: 25

Hope this helped!

A rectangular prism has a total surface area of 48. Also, the sum of all the edges of the prism is 40. Find the length of the diagonal joining one corner of the prism to the opposite corner.

Let's start off and name the angle between the hour and minute hand x, representing the number of degrees between the hands. Next, let's look at the minute hand first. After exactly an hour, the minute hand does not change its position(since after one hour, it comes back to where it was previously). As for the hour hand however, its position differs by exactly "1 hour tick", which is equivalent to 30 degrees (360 / 12 hours). What that implies is that x would have to equal x + 30, which is clearly impossible. However, we can think about the problem in a different way: by looking at the acute angle only between the hands, that would indeed be possible. Assuming that x + 30 is greater than 180(since if it wasn't, that wouldn't be possible), we can write the following equation:

x = 360 - (x+30) 

, with the right hand side coming from the fact that the obtuse angle of x + 30 must have an acute counterpart, of which both add up to 360. 

Then, we can simplify to:

x = 330 - x

or:

2x = 330

x = 165.

This gives us our only answer of 165 degrees

Um..... I can't see the table. I'd love to help, though.

The equation would be

Rate x=time y= job

1/10x+1/4 y =1/2  

1/10y+1/4 x = 1     

Now, solve for x and y.

Hope this helped!

Okay. Here is another way to put it.

a^2=k/b^3.

So that means that 49=k/27.

Therefore, k would be 1323.

So, a^2=1323/(6^3).

       a^2=1323/216.

Therefore, a^2 would be equal to 6.125

Thanks!! This really helped!

This is kind of nitpicky but "pie" is not correct mathematically speaking; that's the food pie(the one that you eat). The correct way to spell it mathematically is "pi" but that's just something on the side. Getting to the problem at hand:

the circumference given is 15pi centimeters. The definition of the circumference of a circle is equal to: 2pi * r , with r being the radius. If we use that in the context of our problem, that gives us:

2 * pi * r = 15 * pi. Dividing by pi on both sides, we get:

2r = 15

r = 15/2

Now that we have our radius, we can find the area. The area of a circle is equal to: pi * r^2

Since we already have the radius, the area of the circle is equal to:

pi * (15/2)^2, which expands out to:

225/4 * pi

Circumference = pi * d    where d = diameter

circumference/pi = d      

circumference/2pi  = radius

Area = pi r^2   = pi   *( circumference/2pi)^2

                       = pi ( 15pi/2pi)^2

                       = pi * (15/2)^2    = 225/4  pi =56.25 pi  cm²

First, there are 5 + 6 + 4 +3 + 2 = 20 marbles total in the bag.

the probability of getting a brown, an orange, and another orange is equivalent to:

the probability of a brown * the probability of 2 oranges.

The probability of a brown marble is just (5 choose 1), or 5 ways to choose it.

Next, the number of ways to get 2 orange marbles is just (2c2), or 1.

Finally, the total number of ways to choose three marbles(our divisor) is (20 choose 3), since you're picking 3 out of 20 total 

This gives us: 

(5c1) * (2c2) / (20c3) =

5 / 1140 = 

1/228

This is just combining like terms. Think about it. if you have a constant, you look for other constants, and then add or subtract as indicated in the problem. You do the same with linears and squares; it's just addition and subtraction. 

Start by looking at the constant terms of both equations, which are g and -16. We know that when we multiply the two polynomials together, the constant terms of the new equaion is only affected by the constant terms of the previous equations. In other words, g * (-8) = -16. This means that g = 2. Next, to find the value of h, we can look at the coefficient of "d" in the product. we know that the coefficient of d in the product comes from multiplying a linear "d" with a constant. That means that (-3d) * (-8) + hd * g = 14d. This expands to:

24d + hd*g = 14d, and subtracting on both sides, we get:

hd * g = -10 d

Remember that we already found that g = 2, giving us

hd * 2 = -10 d

hd = -5d 

h = -5.

Since the problem asks for g + h, we get :

2 - 5 = -3