MATHEMATICS MIDDLE SCHOOL

4x + 12 = -7y
-y + 12 = 4x
Solve with elimination

Answers

Answer 1
Answer: Take the second equation and flip it around so the y on the left ends up on the right and the 4x on the right ends up on the left.  This makes all negatives positive and all positives negative.   -4x   + 12  = y 

Then add the first equation to the second equation 
4x   +12   = -7y
-4x   + 12  = y    this eliminates the x's
          24 = - 6y            then divide by - 6
           - 6     - 6
         - 4    = y

So if you know that y = negative 4, you can substitute into either equation.  I pick the second one because I am a lazy person.  
  -y  + 12  = 4 x
-(-4) + 12 = 4 x     combine your numbers
     16      = 4 x        then divide by 4
       4      =  x
So your solution is: x = 4 and y = -4 or this is also written (4, -4)

Does that work for you?
Answer 2
Answer: \begin{cases}4x + 12 = -7y \n -y + 12 = 4x \end{cases} \n \n\begin{cases}4x + 7y = -12 \n -4x-y =-12 \end{cases} \n+ ------- \n6y=-24\ \ /:6\n \ny=-(24)/(6)\n \ny=-4

4x+12=-7y\n \n 4x+12=-7*(-4)\n \n4x=28-12\n \n4x=16\ \ /:4\n \nx=(16)/(4)\n \n x=4 \n \n \begin{cases}x=4 \n y=-4 \end{cases}

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Find the point B on AC such that the ratio of AB to BC is 2:3

Answers

Answer:

B(4, - 3 )

Step-by-step explanation:

We have A(2, - 7) and C(7, 3 )

Using the section formula to calculate the coordinates of B

x_(B) = (3(2)+2(7))/(2+3) = (6+14)/(5) = (20)/(5) = 4

y_(B) = (3(-7)+2(3))/(2+3) = (-21+6)/(5) = (-15)/(5) = - 3

Hence B(4, - 3 )

Answer:

2 1/5, 1/5

Step-by-step explanation:

khan academy

Standard showerhead in Andrew's house dispenses 8 gallons of water per minute. Andrew changed this shower head to an energy-saving one. The equation shows the amount of water dispensed, y, as a function of the number of minutes, x, for the new shower head.y = 3x

How much water does Andrew save each day with the change in shower heads if he uses the shower for 8 minutes each day?
5 gallons
16 gallons
24 gallons
40 gallons

Answers

40 gallons water  Andrew save each day with the change in shower heads if he uses the shower for 8 minutes each day

What is equation?

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

According to questions, standard showerhead in Andrew's house dispenses 8 gallons of water per minute. Andrew changed this shower head to an energy-saving one.

The equation shows the amount of water dispensed, y, as a function of the number of minutes, x, for the new shower head.

y=3x

Following, this pattern, the equation for the previous shower head is y=8x

Amount of water dispensed previously

=3×8=24

Amount of water dispensed after change in shower

=8×8=64

Total water  Andrew save each day with the change in shower

=64-24=40 gallons

Hence, we can conclude that 40 gallons water  Andrew save each day with the change in shower heads if he uses the shower for 8 minutes each day.

Learn more about equation here:

brainly.com/question/21105092?referrer=searchResults

#SPJ2
Slope is the rate of change.
y=3x.
3 is the slope here, and it means that the new shower head dispenses 3 gallons per minute.
Following, this pattern, the equation for the previous shower head is y=8x.
From this point, there are two ways to solve this:
Way 1: Input x, which in this case is 8 minutes, into each equation, and then find the difference with subtraction.
y=3x
y=3*8
y=24
So the new shower head dispenses 24 gallons in eight minutes.
y=8x
y=8*8
y=64
Therefore, you can conclude that the old shower head dispensed 64 gallons in eight minutes.
To figure out how much he saves, subtract the values:
64-24= 40 gallons.
Way 2) Find the difference before substitution:
y=8x-3x
y=5x
Substitute for x.
y=5*8
y=40 gallons
Therefore, the answer is D. 40 gallons. I hope this helped :)

Even more easy questions

Answers

Answer:

In the first box, the fraction is 1 and 1/4. In the second box, the fraction is 2 and 3/4. In the third box, the fraction is 3 and 3/4.


Step-by-step explanation:

Answer:

In the first box, the fraction is 1 and 1/4. In the second box, the fraction is 2 and 3/4. In the third box, the fraction is 3 and 3/4.

Step-by-step explanation:

16x²-81=0 solve the following quadratic equation

Answers

16x^2-81=0\n\n(4x)^2-9^2=0\n\n(4x-9)(4x+9)=0\iff4x-9=0\ \vee\ 4x+9=0\n\n4x=9\ \vee\ 4x=-9\n\nx=(9)/(4)\ \vee\ x=-(9)/(4)


or\n\n16x^2-81=0\n\n16x^2=81\ \ \ \ /:16\n\nx^2=(81)/(16)\n\nx=\pm\sqrt(81)/(16)\n\nx=-(√(81))/(√(16))\ \vee\ x=(√(81))/(√(16))\n\nx=-(9)/(4)\ \vee\ x=(9)/(4)
16x^2-81=0
(4x-9)(4x+9)
x=9/4 or x=-9/4

To become a member of an ice skating rink, you have to pay a $30 membership fee.The cost of admission to the rink is $5 for members, and $7 dollars for nonmembers. After how many visits to the rink is the total cost for members, including for membership fee, the same total cost for nonmembers?

Answers

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Answers

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