All Answers 358468 Answers

Hi !  So....

3x^2 + 14 x + 8 = x^2 - 2x  + 6 

First, let's combine like terms : 

3x^2 + 14x + 2 = x ^2 - 2x 

 = 3x ^ 2 + 16x + 2 = x ^ 2 

 = 2x ^ 2 + 16 x + 2 

Now I am assuming that you know the quadratic equation:  ax ^ 2 + bx + c = 0 

Now we just plug the equation ( 2x^2 + 16x + 2 ) into the quadratic equation : 

Sorry, But it will be hard to type the quadratic equation step by step : 

But your final outcome will be : ( -4 + sqrt 15 )    or  ( -4 - sqrt 15) 

If you have trouble on this problem I suggest doing some basic research on the quadratic formula and how to recognize it. 

Thanks, 3515 is the right answer!

Hi! 

Replying back: By golly did this take long, here is your graph that I think is correct for the problem. Now the main key for making a sketch like that is to think about a concave quadrilateral. Especially about the common ones. Then after you have found it makes adjustments to your graph to make it follow the requirements. Hope you can do it from here !

IN THIS GRAPH G = P IN YOUR PROBLEM

no i was not given a graph. i was wondering if anyone has any idea how to draw one

Hi! 

I was just wondering if you were given a graph. If so could you possibly send it?

I drove to the beach at a rate of 40 miles per hour.  If I had driven at a rate of 50 miles per hour instead, then I would have arrived 45 minutes later.  How many miles did I drive?  

You mean 45 minutes earlier.  Obviously, if you drive faster, you get there faster.  

This problem makes use of

the following relationship:                   Distance = Velocity x Time 

                                                           D  =  V • T  

case 1                                                 D  =  (40) • (T)  

case 2                                                 D  =  (50) • (T – 45)  

Since the Distance, D, is the  

same for both cases, let's set       

the "V•T"s equal to each other.             (50)(T – 45)  =  (40)(T)  

                                                               50T – 2250  =  40T  

Subtract 40T from both sides                  10T – 2250  =  0  

Add 2250 to both sides                                       10T  =  2250  

Divide both sides by 10                                           T  =  225   (this is in minutes)  

Divide minutes by 60 to get hours                           T  =  225 min / 60 min/hr  =  3.75 hours  

Plug this T back into original equation                     D  =  (40 mi/hr) • (3.75 hr)  =  150 miles  

_.

Find the number of ways of arranging the numbers 1,2 ,3, 4, 5, 6, 7, 8, 9 in a row so that the product of any two adjacent numbers is even.  

For two numbers to have an even product, at least one of them must be even.  

That is, an odd number can never be adjacent to another odd number.  

So, odds and evens have to alternate, such as the example shown in the problem.  

Furthermore, since there are more odd numbers, the first number has to be odd.  

There are five odd numbers, and five positions into which they can be situated.  

So, there are 5 • 4 • 3 • 2 • 1 = 120 ways the odd numbers can be arranged.  

And, there are four even numbers, and four positions where they can be located.  

So, there are 4 • 3 • 2 • 1 = 24 ways that the even numbers can be arranged.  

Any even number arrangement can be combined with any odd number arrangement.  

Therefore, the number of possible mixes is 120 • 24 = 2880.   

_.

I have to paint one side of a wall.  The wall is 12 meters tall and 120 meters long.  Each gallon of paint covers 150 square feet. If a foot is approximately 0.3048 meters, then what is the smallest whole number of gallons I can buy and have enough paint to cover the whole wall? 

We're going to have to convert metric units to imperial units,  

so I think it's better to do it from the start.  Even though we'll  

have fractions to contend with, a calculator makes that easy.  

                                                                       12 m  

1 foot is 0.3048 meter, so the height is       –––––––––  =  39.3701 ft   

                                                                   0.3048 m/ft  

                                                                       120 m  

1 foot is 0.3048 meter, so the length is       –––––––––  =  393.7007 ft   

                                                                   0.3048 m/ft  

Area is height times length     (39.3701 ft)(393.7007 ft)  =  15,500.0359 sq ft  

1 gallon will cover 150 sq ft  

so divide that into the area               15,500.0359 sq ft  

                                                        –––––––––––––––  =  103.3335 gallons  

                                                           150 sq ft/gallon  

You can't buy just a third of a gallon of paint,  

so we have to round that up to whole gallons                       104 gallons  

^.

Real numbers a and b satisfy  

a + ab = 250  

a - ab = -240  

Enter all possible values of a, separated by commas.  

You probably will never find a simpler

problem in your algebra textbook, lol.  

                                                    a + ab  =    250   

                                                    a – ab  =  –240  

Just add the two together.  

                                                  2a          =      10    

Divide both sides by 2.  

                                                            a  =  5    

The problem didn't ask for b.  

_.

One ordered pair (a,b) satisfies the two equations ab^4 = 48 and ab = 72. What is the value of b in this ordered pair?    

To find b, consider                                                  ab⁴  =  48  

We will divide both sides by ab.  

Since ab=72, we will divide the left side  

by "ab" and the right side by its equal 72.  

                                                                              ab⁴         48  

                                                                             ——   =   ——  

                                                                              ab           72  

Note that ab⁴ = (ab) * (b³)  

Cancel ab out of the left side.  

Reduce 48/72 on the right side.  

                                                                               b³           2  

                                                                             ——   =   ——  

                                                                                1            3  

                                                                                 b   =   cube root of (2 / 3)  

_.

Find the coefficient of y^4 in the expansion of (2y-5+3y^2)^6.   

That's way too much multiplication to try to do manually.  

Fortunately, a useful tool has been provided for us, at   

https://www.symbolab.com/solver/expand-calculator

Per the "expand" tool on that page, the coefficient of y⁴ is 375.   

But don't take my word for it, go there and check it for yourself.  :-)  

Is it considered cheating, to use a tool to avoid the drudgery of endless     

multiplications?  I don't consider it cheating to use any tool that has been  

made available.  The abacus, the slide rule, the calculator, the computer.      

_.

That's right, because I clumsily misread the problem. 

It would have been nice if you'd said how it was wrong. 

I should have said x is to 18 as 2 is to 12    

(should have included the blue ones in the known ratio)   

                                                         x          2     

                                                       –––  =  –––     

                                                        18        12               

cross multiply                                  12x  =  36              

                                                           x  =  3     

_.

To find the possible values of ab, a+b, a, and b, we'll use the given equations and solve them simultaneously.

(a) Finding all possible values of ab:

From the equation a - b = 4, we can rewrite it as a = b + 4.

Substituting this value of a into the equation a^3 - b^3 = 0, we get:
(b + 4)^3 - b^3 = 0

Expanding the equation, we have:
(b^3 + 12b^2 + 48b + 64) - b^3 = 0

Simplifying the equation, we get:
12b^2 + 48b + 64 = 0

Dividing the equation by 4 to simplify it further, we have:
3b^2 + 12b + 16 = 0

Using the quadratic formula, we can solve for b:
b = (-12 ± √(12^2 - 4316))/(2*3)
b = (-12 ± √(144 - 192))/(6)
b = (-12 ± √(-48))/(6)

Since the discriminant is negative, there are no real solutions for b. Therefore, there are no possible real values for ab.

(b) Finding all possible values of a + b:

Given a - b = 4, we can rewrite it as a = b + 4.

Substituting this value of a into the equation a + b, we get:
(b + 4) + b = 2b + 4

So, the possible values of a + b are all real numbers of the form 2b + 4.

(c) Finding all possible values of a and b:

We have a - b = 4. By substituting the value of a from this equation into the equation a + b = 2b + 4, we get:
(b + 4) + b = 2b + 4

Simplifying the equation, we have:
2b + 4 = 2b + 4

This equation is true for all values of b. Therefore, there are infinitely many possible values for a and b that satisfy the given conditions.

In summary:
(a) There are no possible real values for ab.
(b) The possible values of a + b are all real numbers of the form 2b + 4.
(c) There are infinitely many possible values for a and b that satisfy the given conditions.

WLOG 

realize for two numbers to sum up to 100, one must be < 50 (as 50 isn't prime)

There are 6 prime numbers less than 50 that satisfy our condition

And these 6 prime numbers could be placed in the x coord or the y coord

So 6*2= 12 

Lets begin with the problem by find the slope of line b.

We know that if a line is perpendicular to another line the its slope hase an opposite sine (+ turns to -), and its the recipricol of it.

So, based of this piece of knowledge we know that the slope of line c is \(-2\), so the slope of line b is \(1/2\).

With this piece of info we can easily find the slope of line a!

Parallel lines have equal slope so now we know the slope of line a is \(1/2\) as well!! 

Now lets find the equation of line a using point-slope form!

Point-Slope Form: y=m(x-x₁)+y₁

We know it goes through the point \((1,2)\) so we can use this as our point, and we can use \(1/2\) as our slope!
Now we have the equation of line a!:

\(y=1/2(x-1) +2\)

\(y=1/2x+3/2\)

Great! But, this isn't our answer, but... we can use this equation to find our answer!! 
To find the y-intercept of a certain line, we must replace x with \(0 \)! That's super easy!

\(y = 1/2(0)+3/2\)
\(y = 3/2\)

So our answer is \((0,3/2)\)!!! 

Hope this helped!

Other users, if you see a mistake please reply with your answer! I make mistakes!!

As you can see in the sqaure roots we can extract the x^2's, as \sqrt{x^2} = x, we can do the same with the 4 and our equation(s) become:

2x + x = 6 + 3x  (1)

-2x + x = 6 + 3x  (2)

2x - x = 6 + 3x  (3)

-2x - x = 6 + 3x  (4)

!! Notice the signs as (-2)^2 = (2)^2, and the prblem is asking us to find all values of x !!

Solving the equations we get that x=:

(1): x = no solution

(2): x = -3/2

(3): x = -3

(4): x = -1

So our answer is -3, -1, and -3/2! 

Hope this helped!

Other user, if you see a mistake please reply with your answer! I make mistakes!!

let's just say they all have one worker. A is 5 times more then B = 5 

C is 3 times more then B = 3 

Meaning A have 5/3 more workers then C

To have something that has infinite solutions we need both sides of a equation to be the exact same. Now lets use this to our advantage. 

Let us simply the system of equations via substitution : 

3a + 2b = 2 

 = 3a = 2 - 2b

Now we can substitute that into the second equation : 

6a + 2b = k + 3a + mb 

= (2 - 2b) x 2 + 2b = k + ( 2 - 2b ) + mb 

= 4 - 4b + 2b = k + 2 -2b + mb 

= 4 - 2b  =  k + 2-2b + mb 

Now after this, we will start moving variables : 

4 = 2 + mb + k

2 = mb + k 

Now you may feel stuck at this point but we will need to use guess and check to find the answer : 

Since 2 is such a small number I would assume in this problem that some variable would be equal to 0

Using substituion we can find the m = 0 and k = 2 

Hope this helps!

Bosco summed it up really nicely, for me the key to these types of problems / where to start is by trying to make everything related to a single variable : 

For example:  since warehouse A and Warehouse B are relating themselves to Warehouse C then I would say :

Warehouse A = 5 ( Warehouse B)

Warehouse C = 3 ( Warehouse B)

Warehouse A has 5 times as many employees as Warehouse B, and Warehouse C has 3 times as many employees as Warehouse B. Warehouse A has how many times as many employees as Warehouse C?   

                                              A  =  5B      (eq 1)   

                                              C  =  3B      (eq 2)   

Multiply (eq 1) by 3               3A  =  15B    

Multiply (eq 2) by 5               5C  =  15B    

Therefore                             3A  =  5C   

                                               A  =  (5 / 3) C   

_.

Hi!

3a + 4b = 5a - 6b + 24 - 3a 

First let's simplify : 

3a + 6b + 4b = 5a -3a + 24 

= 3a + 10 b = 2a + 24 

Now let us move everything that isn't A onto 1 side : 

3a - 2a  = 24 + (-10 b)

a = (-10) b + 24 

That would be your answer 

We are not here to do all your homework for you, cheater.

youngwolf is just trying to cheat on homework.