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3 years ago

A first number plus twice a second number is 11. Twice the first number plus the second totals 16. Find the numbers.

Mathematics

1 answer:

satela [25.4K]3 years ago

4 0

<h3><u>The first number, x, is equal to 7.</u></h3><h3><u>The second number, y, is equal to 2.</u></h3>

x + 2y = 11

2x + y = 16

We can subtract 2y from both sides of the first equation to get a value for x.

x = 11 - 2y

Because we have a value for x, we can plug it into the second equation.

2(11 - 2y) + y = 16

Distributive property.

22 - 4y + y = 16

Combine like terms.

22 - 3y = 16

Subtract 22 from both sides.

-3y = -6

Divide both sides by -3.

y = 2

Now that we have a value for y, we can plug it into either equation to solve for x.

x + 2(2) = 11

x + 4 = 11

Subtract 4 from both sides.

x = 7

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Answer:

$x=-7$

Step-by-step explanation:

We have been given an equation $y=2x^2+28x+96$ . We are asked to find the zeros of equation by factoring and then find the line of symmetry of the parabola.

Let us factor our given equation as:

$2x^2+28x+96=0$

Dividing both sides by 2:

$x^2+14x+48=0$

Splitting the middle term:

$x^2+6x+8x+48=0$

$(x^2+6x)+(8x+48)=0$

$x(x+6)+8(x+6)=0$

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Using zero product property:

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$x+8=0\text{ (or) }x+6=0$

$x=-8\text{ (or) }x=-6$

Therefore, the zeros of the given equation are $x=-8\text{ (or) }x=-6$ .

We know that the line of symmetry of a parabola is equal to the x-coordinate of vertex of parabola.

We also know that x-coordinate of vertex of parabola is equal to the average of zeros. So x-coordinate of vertex of parabola would be:

$\frac{-8+(-6)}{2}=\frac{-14}{2}=-7$

Therefore, the equation $x=-7$ represents the line of symmetry of the given parabola.

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