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A system of equations has infinitely many solutions. If 2y - 4x = 6 is one of the equations, which could be the other

Serjik [45]

Answer:

-y = -2x - 3

Option 3

Step-by-step explanation:

When equations are equivalent, they will have infinitely many solutions.

If you want to find an equivalent equation, you can multiply/divide every term in the equation by the same number. You can also rearrange the equation.

Since the options mostly have "y" by itself, start by rearranging to isolate "y" in the given equation.

Move all the other numbers to the right of the equal sign except for "y". To move a number, apply its reverse operation to the entire equation.

Do reverse operations in reverse BEDMAS order.

2y - 4x = 6 Move "-4x" first. It's reverse is +4x.

2y - 4x + 4x = 6 + 4x

2y = 6 + 4x Move the "2" in 2y. Divide the whole equation by 2.

2y/2 = 6/2 + 4x/2

y = 3 + 2x Rearrange to look like the answer choices.

y = 2x + 3

This equation looks like option 3 except every term has a different negative/positive.

y = 2x + 3 -y = -2x - 3

We can multiply every term by -1.

y = 2x + 3

y*-1 = 2x*-1 + 3*-1

-y = -2x + (-3) Negative and positive make a negative

-y = -2x - 3 Same as option 3

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3 years ago

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A box with a square base and open top must have a volume of 296352 c m 3 . We wish to find the dimensions of the box that minimi

mestny [16]

Answer:

Base Length of 84cm
Height of 42 cm.

Step-by-step explanation:

Given a box with a square base and an open top which must have a volume of 296352 cubic centimetre. We want to minimize the amount of material used.

Step 1:

Let the side length of the base =x

Let the height of the box =h

Since the box has a square base

Volume, $V=x^2h=296352$

$h=\dfrac{296352}{x^2}$

Surface Area of the box = Base Area + Area of 4 sides

$A(x,h)=x^2+4xh\\$Substitute h=\dfrac{296352}{x^2}\\A(x)=x^2+4x\left(\dfrac{296352}{x^2}\right)\\A(x)=\dfrac{x^3+1185408}{x}$

Step 2: Find the derivative of A(x)

$If\:A(x)=\dfrac{x^3+1185408}{x}\\A'(x)=\dfrac{2x^3-1185408}{x^2}$

Step 3: Set A'(x)=0 and solve for x

$A'(x)=\dfrac{2x^3-1185408}{x^2}=0\\2x^3-1185408=0\\2x^3=1185408\\$Divide both sides by 2\\x^3=592704\\$Take the cube root of both sides\\x=\sqrt[3]{592704}\\x=84$