VERY HARD MATH Question.?

Question

The hunt is on. The 3 finalists in a competition are Sue, Jim and Vinny. They are each starting from a different location in the city. The reach the treasure, all three finalists take different routes.

Sue's route can be modeled by the equation 7x-4y= -14

Jim's route can be modeled by the equation 4(x+4)-3(y-3)=12

Vinny's route can be modeled by the equation 4x+ky=-6

Eventually all 3 finalists would find the location of the treasure.

a) Where is the treasure located?

b) The equation for Vinny's route is missing a coefficient. Explain how you would find the value of the missing coefficient.

c) What is the complete equation for Vinny's route?

PLEASE SHOW ALL YOUR STEPS!

Answer 1

Obvious HW problem:
But, if you don't want to do it yourself . . .

Since they all end up at the treasure, they must all be at the same point (sometime). Thus Sue and Jim must be at the same point. What points are they at together? Well, that can be found by simutaniously solving their equations:

7x-4y=-14
4(x+4)-3(y-3)=12 <==> 4x-3y=-13

or
21x-12y=-42
16x-12y=-52

subtracting the second:
5x=10 or x=2

inserting into 2nd equation:
4(2)-3y=-13 or 3y=13+8=21, or y=7.

Therfore the treasure is at (2,7).

2nd part:

Vinny must also be at this point. Thus (2,7) must be a solution for 4x+ky=-6. By inserting 2,7 in for x,y and solving for k, you find the solution.

3rd part:

actually doing the second part. 4(2)+k(7)=8-3k=-6. Thus 7k=-6-8=-14 and k=-2

Vinny's complete equation is
4x-2y=-6

Answer 2

x = 2
y = 7
k = -2

Took me about 10 minutes...

1. Get Sue's equation to equal either x or y. I chose x.
7x - 4y = -14
x = (-14 + 4y) / 7

2. First simplify and distribute Jim's equation...
4 (x + 4) - 3(y - 3) = 12
4x + 16 - 3y + 9 = 12
4x - 3y + 25 = 12

3. Plug in our x from Sue into Jim's equation.

4[(-14 + 4y) / 7] - 3y + 25 = 12

4. Using algebraic procedures...

4[(-14 + 4y) / 7] - 3y + 25 = 12
-25 from 12
4[(-14 + 4y) / 7] - 3y = -13
Distribute the fraction...
(-56 + 16y / 7) - 3y = -13
Find the least common denominator which is 7, sooo...
(-56 + 16y / 7) - 3y(7/7) = -13
(-56 + 16y / 7) - (21y / 7) = -13
Add like-terms for numerator...
-56 + 16y - 21y = -56 - 5y

So we have so far...
(-56 - 5y / 7) = -13

I cross multiply...
(-56 - 5y / 7) = -13/1

-56 - 5y = -91
-5y = -91 + 56
-5y = -35
y / -5 = -35 / -5
y = 7

5. Now that we have y, plug in y for Sue's equation...

7x - 4(7) = -14
7x - 28 = -14
7x = -14 + 28
7x = 14
7x / 7 = 14 / 7
x = 2

6. Now that we have both x and y, we can now find the missing coefficient for Vinny's equation by plugging in for x and y...

4(2) +(7)k = -6
8 + 7k = -6
7k = -14
7k / 7 = -14 / 7
k = -2

The location of the treasure is at point (2, 7), and is -2 below ground or zero.

Answer 3

a)

We need to find the intersection of the three equations. We can use Sue's and Jim's equations to solve x and y.

Sue's equation is 7x-4y=-14
Jim's equation
4(x+4)-3(y-3) = 12
4x+16-3y+9 = 12
4x-3y = 12-16-9
4x-3y = -13

Use elimination to determine x
-3(7x-4y) = (-3)(-14)
-21x+12y = 42

4(4x-3y) = 4(-13)
16x-12y = -52

-21x+12y + 16x +12y = 42 - 52
-5x = -10
x = 2

Now solve for y using Sue's equation where x = 2
7(2)-4y=-14
14 - 4y = -14
-4y = -28
y = 7

Therefore the location of the treasure is at (2, 7)

b)

Now that we know x and y.. and we know that Vinny's route must also cross the treasure, then we can plug in the x and y of 2, 7 and solve for k to get the coefficient.

4(2)+k(7)=-6
8 + 7k = -6
7k = -14
k = -2

c)
Since we know k, Vinny's complete equation must be 4x-2y = -6 but we should simplify it by dividing by 2 to get 2x-y=-3

Answer 4

actually the question is... what happened to sue... Notice she's not even a finalist... being that her mother raised her in a broken household Sue considered this school competition an out. while on her field trip, sue decided to find treasures of her very own and met a slick hustler by the name of Sal at a local pool hall. now being that the route she took was 7x-4y=-14.... she unfortunately lost her virginity somewhere around 4y, made a wrong turn at 7x and ended up somewhere between Denver and Cincinatti.

Vinny's missing coefficient is obviously herreditary, because his mother left his father when she found out about his un-coefficientness as well...

Jim is another story all together!

Answer 5

Here are some hints...

Solve each equation for y

Determine where Sue's and Jim's routes intersect.

Determine the k for Vinny's route that intersects this same point...this is where the treasure is.

See how far that help gets you.

Answer 6

a million+a million=2 moreover, someone with a procedures too a lot time on their fingers wanting to tutor it... "The information begins from the Peano Postulates, which outline the organic numbers N. N is the smallest set gratifying those postulates: P1. a million is in N. P2. If x is in N, then its "successor" x' is in N. P3. there is not any x such that x' = a million. P4. If x isn't a million, then there's a y in N such that y' = x. P5. If S is a subset of N, a million is in S, and the implication (x in S => x' in S) holds, then S = N. then you ought to outline addition recursively: Def: allow a and b be in N. If b = a million, then outline a + b = a' (employing P1 and P2). If b isn't a million, then allow c' = b, with c in N (employing P4), and outline a + b = (a + c)'. then you ought to outline 2: Def: 2 = a million' 2 is in N by employing P1, P2, and the definition of two. Theorem: a million + a million = 2 information: Use the first part of the definition of + with a = b = a million. Then a million + a million = a million' = 2 Q.E.D. be conscious: there is yet another formula of the Peano Postulates which replaces a million with 0 in P1, P3, P4, and P5. then you ought to regulate the definition of addition to this: Def: allow a and b be in N. If b = 0, then outline a + b = a. If b isn't 0, then allow c' = b, with c in N, and outline a + b = (a + c)'. you even ought to outline a million = 0', and a pair of = a million'. Then the information of the theory above is slightly distinct: information: Use the second one part of the definition of + first: a million + a million = (a million + 0)' Now use the first part of the definition of + on the sum in parentheses: a million + a million = (a million)' = a million' = 2 Q.E.D." Wow, he might want to be a actual hit with the girls...!! :)

Answer 7

a) solve for (x,y) using Sue's and Jim's equations. There will be: (1) a infinite number of solutions; (2) zero solutions; or (3) exactly one solution. If it's not 3, you're in trouble.
b) "substitute (x,y) that you found in 'a)' into Vinny's route equation and solve for k"
c) substitute (x,y) that you found in 'a)' into Vinny's route equation and solve for k. Replace this into the equation for the answer.

Answer 8

a) (2,7)
4(x+4) - 3(y-3) = 12
4x + 16 - 3y + 9 = 12
4x - 3y + 25 = 12
4x - 3y = -13
Your two equations are
7x - 4y = -14
4x - 3y = -13
Multiply the first equation by 3 and the second equation by -4
21x - 12y = -42
-16x +12y = 52
Add the two equations together
5x = 10
x = 2
Replace x with 2 in either one of the original equations.
7(2) - 4y = -14
14 - 4y = -14
-4y = -28
y = 7
b) k = 2
Replace x with 2 and y with 7 in Vinny's equation.
4(2) + k(7) = -6
8 + 7k = -6
7k = -14
k = -2
c) 4x - 2y = -6
Replace k with -2

Answer 9

im not going to work out your hw for you
however
rearrange each equation to be y= ax+b
so sue's becomes
y= -7/4x-14/4
then plot using graphing calculator and entering in the equation to fin the point of intersection for jim and sue. Vinnys will go through this point as well, use the coordinates of the points and plug them into her equation to get the complete equasion for her.

Answer 10

Try asking your math teacher because the answer i got didn't look right and i did it three times