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3 years ago

Find the solution to the system of linear equations.

Mathematics

1 answer:

natali 33 [55]3 years ago

6 0

Answer:

x = -1 y = 2

Step-by-step explanation:

Notice that the coefficients of x are opposites of each other. That makes the problem so much easier to solve. All you have to do is add the two equations and the x terms will be eliminated.

2x - 4y = -10

- 5y = -10

y = 2 Substitute y = 2 into the first equation. 2x - 4(2) = -10

2x - 8 = -10

2x = -2

x = -1

It is always a good idea to check your results into the equations to see if they satisfy the equations.

You might be interested in

How many terms are in the expression <br> 5x^3-8x^2y+4xy-4

bazaltina [42]

Answer:

<h2>4 terms</h2>

Step-by-step explanation:

Term 1: 5x^3

Term 2: 8x^2y

Term 3: 4xy

Term 4: 4

8 0

3 years ago

Guys help please I am struggling

alina1380 [7]

9514 1404 393

Answer:

14.1 years

Step-by-step explanation:

Use the compound interest formula and solve for t. Logarithms are involved.

A = P(1 +r/n)^(nt)

amount when P is invested for t years at annual rate r compounded n times per year.

Using the given values, we have ...

13060 = 8800(1 +0.028/365)^(365t)

13060/8800 = (1 +0.028/365)^(365t) . . . . divide by P=8800

Now we take logarithms to make this a linear equation.

log(13060/8800) = (365t)log(1 +0.028/365)

Dividing by the coefficient of t gives us ...

t = log(13060/8800)/(365·log(1 +0.028/365)) ≈ 0.171461/0.0121598

t ≈ 14.1

It would take about 14.1 years for the value to reach $13,060.

8 0

3 years ago

Find the solution set of the inequality:<br> -3x + 8 < 15−3x+8<15

makkiz [27]

Answer:

x=(8/3, infinity)

Step-by-step explanation:

-3x+8<15-3x+8

-3x+8<-3x+23

8<23

15-3x+8<15

23-3x<15

-3x<-8

x>8/3

Therefore, x=(8/3, infinity)

3 0

3 years ago

What will the answer be?

Readme [11.4K]

To simplify:

Subtract 3 from 8 = 5
Reduce 2/4 = 1 / 2

And the answer is:
1 /2 d^5

8 0

4 years ago

You operate a gaming Web site, www.mudbeast.net, where users must pay a small fee to log on. When you charged $3 the demand was

Doss [256]

Answer:

A) The linear relation between price and demand is:

$d=-550x+2750$

The revenue R is:

$R=-550x^2+2750x$

B) The profit functionP is:

$P=-550x^2+2750x-30$

C) The largest monthly profit is obtained with a log-on fee of $2.5 per month. This corresponds to a profit of $3407.5.

Step-by-step explanation:

We have a site where the number of log-ons depends on our monthly fee. A linear relation is established between the price (log-on fee) and the number of log-ons.

We have two points for this linear relationship:

At price x=3, the demand is d=1100.
At price x=2.5, the demand is d=1375.

We will model the relation:

$d=mx+b$

We can calculate the slope m as:

$m=\dfrac{\Delta d}{\Delta x}=\dfrac{d_2-d_1}{x_2-x_1}=\dfrac{1375-1100}{2.5-3}\\\\\\m=\dfrac{275}{-0.5}=-550$

Then, replacing one point in the linear equation, we can calculate the intercept b:

$d_1=mx_1+b\\\\1100=(-550)\cdot 3+b\\\\1100=-1650+b\\\\b=1100+1650=2750$

Then, the linear relation between demand and price is:

$d=-550x+2750$

The revenue R can be expressed as the multiplication of the price and the demand:

$R=x\cdot d=x(-550x+2750)=-550x^2+2750x$

If we have a fixed cost of $30 per month, the profit P is:

$P=R-FC=-550x^2+2750x-30$

We can maximize the profit by deriving the profit function and making it equal to zero.

$\dfrac{dP}{dx}=0\\\\\\\dfrac{dP}{dx}=-550(2x)+2750(1)=0\\\\\\-1100x+2750=0\\\\x=\dfrac{2750}{1100}=2.5$

This corresponds to a profit of:

$P(2.5)=-550(2.5)^2+2750(2.5)-30\\\\P(2.5)=-550\cdot 6.25+6875-30\\\\P(2.5)=-3437.5+6875-30\\\\P(2.5)=3407.5$

5 0

3 years ago