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FinnZ [79.3K]
2 years ago
5

Solve the system of equations:

Mathematics
1 answer:
bulgar [2K]2 years ago
5 0

Answer:

(2,2)

Step-by-step explanation:

2x+3y=10

x−2y=−2

​In order to solve by elimination, coefficients of one of the variables must be the same in both equations so that the variable will cancel out when one equation is subtracted from the other.

2x+3y=10,x−2y=−2

To make 2x and x equal, multiply all terms on each side of the first equation by 1 and all terms on each side of the second by 2.

2x+3y=10,2x+2(−2)y=2(−2)

Simplify.

2x+3y=10,2x−4y=−4

Subtract 2x−4y=−4 from 2x+3y=10 by subtracting like terms on each side of the equal sign.

2x−2x+3y+4y=10+4

Add 2x to −2x. Terms 2x and −2x cancel out, leaving an equation with only one variable that can be solved.

3y+4y=10+4

Add 3y to 4y.

7y=10+4

Add 10 to 4.

7y=14

Divide both sides by 7.

y=2

Substitute 2 for y in x−2y=−2. Because the resulting equation contains only one variable, you can solve for x directly.

x−2×2=−2

Multiply −2 times 2.

x−4=−2

Add 4 to both sides of the equation.

x=2

The system is now solved.

x=2,y=2

Correct choice is D) 2,2

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Write a polynomial that represents the length of the rectangle<br><br> help please !!
disa [49]

Answer:

\textsf{Length}=0.8x^2-0.7x+0.7\quad \sf units

Step-by-step explanation:

Area of a rectangle = width × length

Therefore, to find the length of the rectangle, we need to divide the area by the width.

Using long division:

\large\begin{array}{r}0.8x^2-0.7x+0.7\phantom{)} \\x+0.5{\overline{\smash{\big)}\,0.8x^3-0.3x^2+0.35x+0.35\phantom{)}}}\\-~\phantom{(}\underline{(0.8x^3+0.4x^2)\phantom{-b))))))))))))))}}\\0-0.7x^2+0.35x+0.35\phantom{)}\\ \underline{-~\phantom{()}(-0.7x^2-0.35x)\phantom{-b)))))}}\\ 0.7x+0.35\phantom{)}\\\underline{-~\phantom{()}(0.7x-0.35)}\\ 0\phantom{)}\end{array}

Therefore, the <u>length</u> of the rectangle is:

0.8x^2-0.7x+0.7

5 0
2 years ago
F(x) = 15,000(.84) shows the value of a car each year. Describe the following:
makvit [3.9K]

Answers:

  • a) 15000 represents the starting amount
  • b) The decay rate is 16%, which means the car loses 16% of its value each year.
  • c) x is the number of years
  • d) f(x) is the value of the car after x years have gone by

========================================================

Explanation:

We have the function f(x) = 15000(0.84)^x. If we plug in x = 0, then we get,

f(x) = 15000(0.84)^x

f(0) = 15000(0.84)^0

f(0) = 15000(1)

f(0) = 15000

In the third step, I used the idea that any nonzero value to the power of 0 is always 1. The rule is x^0 = 1 for any nonzero x.

So that's how we get the initial value of the car. The car started off at $15,000.

-------------

The growth or decay rate depends entirely on the base of the exponential, which is 0.84; compare it to 1+r and we see that 1+r = 0.84 solves to r = -0.16 which converts to -16%. The negative indicates the value is going down each year. So we have 16% decay or the value is going down 16% per year.

------------

The value of x is the number of years. In the first section, x = 0 represented year 0 or the starting year. If x = 1, then one full year has passed by. For x = 2, we have two full years pass by, and so on.

------------

The value of f(x) is the value of the car after x years have gone by. We found that f(x) = 15000 when x = 0. In other words, at the start the car is worth $15,000. Plugging in other x values leads to other f(x) values. For example, if x = 2, then you should find that f(x) = 10584. This means the car is worth $10,584 after two years.

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Answer:

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Step-by-step explanation:

18f = 33g

f/g = 33/18 = 11/6

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2 years ago
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