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3 years ago

Solve the system of equations.y= 2x + 4y = x2 + x - 2

Mathematics

1 answer:

bezimeni [28]3 years ago

3 0

Answer:

Step-by-step explanation:

$y=2x+4$

$y=x^2+x-2$

Both equations are solved for y so I'm just going to substitute

the 1st y (the 2x+4) into the second equation's y.

$2x+4=x^2+x-2$

I'm going to get everything on one side so I have 0=ax^2+bx+c.

Subtract 2x and subtract 4 on both sides:

$0=x^2-x-6$

Since the coefficient of x^2 is 1, all we have to do is find two numbers that multiply to be -6 and add up to be -1.

These numbers are -3 and 2.

So the factored form of our equation is:

$0=(x-3)(x+2)$

This means we have x-3=0 or x+2=0.

x-3=0

Add 3 on both sides:

x=3

x+2=0

Subtract 2 on both sides:

x=-2

So now we need to find y. I'm going to choose to use the easier equation:

y=2x+4.

If x=3, then y=2(3)+4=6+4=10. The ordered pair (3,10) is a solution.

If x=-2, then y=2(-2)+4=-4+4=0. The orded pair (-2,0) is a solution.

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Find the accumulated value of an investment of 12,000 at 8 % compounded semiannually for 11 years

AleksAgata [21]

The "compound amount" formula is A = P(1+r/n)^(nt),
where P=original investment, r=interest rate as a decimal fraction; n=number of compounding periods, and t=number of years.

Then A = $12000 * (1+0.08/2)^(2*11)
= $12000(1.04)^(22) = $28,439.03 (answer)

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3 years ago

George wants to purchase a gift for his father for Father’s Day that cost 67.25 if he has already saved 7/8 of the amount how mu

Arlecino [84]

Answer:

$58.84375, rounded ≈ $58.84

Step-by-step explanation:

You can do 67.25 x 7/8 (use a calc if you are lazy) = 58.84375

I'm guessing you don't need to round so I'm going to add both real and rounded answers

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2 years ago

What numbers are less than -0.625

Ivanshal [37]

Answer:

-8/5 = -1.6 (the smallest number here)

-5/8 = -0.625

your answer is A :)

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2 years ago

SUppose the total cost C(x) to manufacture a quantity x of insecticide (in hundreds of liters) is given by

Hitman42 [59]

Answer:

a) $C(x)$ is increasing in two regions: (i) $(+\infty, 8\,s)$ and (ii) $(10\,s,+\infty)$ .

b) $C(x)$ decreases in $(8\,s, 10\,s)$ .

Step-by-step explanation:

Let $C(x) = x^{3}-27\cdot x^{2}+240\cdot x +850$ , where $x$ is the quantity of insecticide, measured in hundreds of liters, and $C(x)$ is the total manufacturing cost as a function of the quantity of the insecticide, measured in US dollars. A possible approach to determine which regions of $C(x)$ are decreasing and increasing by means of the first derivative and graphing tools. The first derivative of the function is:

$C'(x) = 3\cdot x^{2}-54\cdot x+240$ (1)

Please notice that regions where C(x) is increasing has $C'(x) > 0$ , whereas $C'(x) < 0$ when $C(x) < 0$ .

We notice that $C(x)$ is increasing in two regions: (i) $(+\infty, 8\,s)$ and (ii) $(10\,s,+\infty)$ . Besides, $C(x)$ decreases in $(8\,s, 10\,s)$ .

6 0

3 years ago

Need help asap, the answer I picked I think is wrong but idk

BigorU [14]

Answer:

Reflected about the y-axis and then rotated 90° counterclockwise

Step-by-step explanation:

(x , y) to (-x , y) --> reflected over y-axis

then (-x , y) --> (-y, -x) -->90 degrees rotation counterclockwise

So answer is the last one

Reflected about the y-axis and then rotated 90° counterclockwise

8 0

3 years ago

Solve the system of equations.y= 2x + 4y = x2 + x - 2​

Solve the system of equations.y= 2x + 4y = x2 + x - 2