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Danny's car can drive 32 miles on each gallon of gas. He has an 18 gallon tank thank is 3/4 of the way full. How many miles can he drive on the gas he has? 

He has  18 (3/4)  =  51/4  =  27/2  = 13.5 gallons of gas....so......

13.5  gallons *  32  miles / gallon =  432  miles

We have this :

y  = −2(x + 6) (x + 2) (x  − 3) (x − 5)   + b

And when x = 0, y  = −360

So

−360  = (−2) (6)(2)( −3) ( −5)  + b

−360 = −360 + b    →   b = 0

So....the function is  

y  = −2(x + 6) (x + 2) (x  − 3) (x − 5)

y  =  -2 x^4 + 74 x^2 - 48 x - 360

Here's .the  graph :  https://www.desmos.com/calculator/svpexeicjl

NinjaAnswer: Can you please explain your answer?

4/9

Thanks CPhill!!

Nice, Ninja.....!!!!!

The answer is 11

Equation 1: 3g+24=3(g+8)

3g+24=3(g+8)--------Simplify

3g+24 = 3g + 24------Subtract 3g + 24 from each side(you might relieze that there are infinitly many solutions from this step)

0 = 0 ---------Infinitly many solutions

Equation 2:  5c+9=5c-12

 5c+9=5c-12--------Subtract 5c from each side

9 =-12  ---------------Since 9 doesn't equal -12 then there are no solutions 

Equation 1 has infinitly many solutions

Equation 2 has no solutions

if you mean 5^x = sqrt(5) then:

x = 1/2

Because square roots are numbers raised to the 1/2 power.

Hope that helped

The symbol to the left of the C. Thats a division symbol

12m + 4n = 480------Divide both sides by 4

3m + n = 120---------Subtract n

3m = 120 - n---------Isolate m by dividing both sides by 3

m = (120 - n)/3 -------Simplify if you want

m = 40 - n/3

m = -n/3 =40

The answer is B

Any questions??

(3^8) / (3^5)

3 ^ 8-5

3^3

27

Or plug into web2.0 calc

Very nice, Isabelle.....!!!!

Yes it depends on what kind of calculator you're using. There's a graphing calc online as well. :)

B is the answer.

Simplifying 12m + 4n = 480 Solving 12m + 4n = 480 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-4n' to each side of the equation. 12m + 4n + -4n = 480 + -4n Combine like terms: 4n + -4n = 0 12m + 0 = 480 + -4n 12m = 480 + -4n Divide each side by '12'. m = 40 + -0.3333333333n

\(16x-12x-15=2x+9\)

\(4x-15=2x+9\)

\(2x=24\)

\(x=12\)

Yes, go back to your first post, I also answered your questions.

See your earlier post for the answers

Use the arctangent here

arctan ( −1.5)   +  180°  = x   =    −56.31°  + 180 =  123.69°

A- as you can see here, your function f is a referential equation: f(x)=x²

You can notice from the graph, let's call it the graph of the function g, is got by a translation of all the points of the graph of the  referential function f(x) = x² by a vector v(-2,2)

So, according to a theorem, the graph of a function \(x \rightarrow f(x+a)+b \)is got by a translation of the graph of \(x\rightarrow f(x)\)by using the vector v(-a,b)

As a result our function is \(g(x)=(x+2)²+2\)

g(-1) graphically = 3

g(-1) algebrically: g(-1) = (-1+2)²+2 = 1+2 = 3

Hard to see this but I think we have 

a)    g(x)  = ( x + 2)^2  + 2

c)   g(−1 )   =  ( −1   + 2) ^2  + 2   =   1^2   + 2   =  3

Here's the graph  :  https://www.desmos.com/calculator/cacudo2xos

Could you send another correctly tilted pic??

Then I could do it.

Since each child can be male or female with equal likelihood, there are 2^6 = 64 possible ways in which the genders of the children can be determined. The only way in which Mr. Jones won't have more sons than daughters or more daughters than sons is if he has exactly 3 of each, which can occur in 6C3 = 20 ways. Using the concept of complementary counting gives us that there are 64-20=44 ways in which he can have more children of one gender than the other out of a total of 64 possible ways, for a final probability of 44/64 = 11/16 .

Thanks for your additonal comment.

My initial question could have been answered with a yes or no but you answered it with a question.  This required me to try to understand based on your question.  I was quite willing to do that in order to enable my understanding the subject better.

In reading about this subject elsewhere, I am pretty sure mention was made that systems of numbers (maybe 'systems' is the wrong word) evolved to accomodate issues in mathematics which could not be resolved using previously existing knowledge.  Negative numbers were one such development, imaginary numbers another.  To understand your answer/question, then, I concluded you were speaking from this perspective, ie there are different systems.

If someone were to ask me now if both 2 and (-1 + i (3^.5) are equal to each other, I would say each is a cube root of 8, they are not equal to each other, and I will continue to attempt to learn why they are not equal to each other..

I dont see it. i think he is typing it.