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3 years ago

Can someone plz help me with this!

Mathematics

1 answer:

asambeis [7]3 years ago

3 0

Answer:

(arranged from top to bottom)

System #3, where x=6

System #1, where x=4

System #7, where x=3

System #5, where x=2

System #2, where x=1

Step-by-step explanation:

System #1: x=4

$2x+y=10\\x-3y=-2$

To solve, start by isolating your first equation for y.

$2x+y=10\\y=-2x+10$

Now, plug this value of y into your second equation.

$x-3(-2x+10)=-2\\x+6x-30=-2\\7x=28\\x=4$

System #2: x=1

$x+2y=5\\2x+y=4$

Isolate your second equation for y.

$2x+y=4\\y=-2x+4$

Plug this value of y into your first equation.

$x+2(-2x+4)=5\\x+(-4x)+8=5\\x-4x+8=5\\-3x=-3\\x=1$

System #3: x=6

$5x+y=33\\x=18-4y$

Isolate your first equation for y.

$5x+y=33\\y=-5x+33$

Plug this value of y into your second equation.

$x=18-4(-5x+33)\\x=18+20x-132\\-19x=-114\\x=6$

System #4: all real numbers (not included in your diagram)

$y=13-2x\\8x+4y=52$

Plug your value of y into your second equation.

$8x+4(13-2x)=52\\8x+52-8x=52\\0=0$

<em>all real numbers are solutions</em>

System #5: x=2

$x+3y=5\\6x-y=11$

Isolate your second equation for y.

$6x-y=11\\-y=-6x+11\\y=6x-11$

Plug in your value of y to your first equation.

$x+3(6x-11)=5\\x+18x-33=5\\19x=38\\x=2$

System #6: no solution (not included in your diagram)

$2x+y=10\\-6x-3y=-2$

Isolate your first equation for y.

$2x+y=10\\y=-2x+10$

Plug your value of y into your second equation.

$-6x-3(-2x+10)=-2\\-6x+6x-30=-2\\-30=-2$

<em>no solution</em>

System #7: x=3

$y=10+x\\2x+3y=45$

Plug your value of y into your second equation.

$2x+3(10+x)=45\\2x+30+3x=45\\5x=15\\x=3$

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The percentage of automobile consumers who are under 50 years of age decreased approximately linearly from 58.8% in 1980 to 50.5

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Using a linear function, we have that:

The percentage will be 47% during the year 2001.

The predicted percentage in 2005 is of 44.97%.

Given that, the percentage of automobile consumers who are under 50 years of age decreased approximately linearly from 58.8% in 1980 to 50.5% in 1995.

<h3>What is a linear function?</h3>

Linear functions are those whose graph is a straight line. The standard form of the linear function is f(x)=y= mx + b. A linear function has one independent variable and one dependent variable.

Where, m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.

b is the y-intercept, which is the value of y when x = 0 and can also be interpreted as the initial value of the function.

The percentage in 1980 is considered as the initial amount, so b = 58.8. In 15 years, the percentage decreased from 58.8% to 50.5%, hence the slope is given by: m = (50.5 - 58.8)/15 = 0.5533.

Thus, the percentage in t years after 1980 is P(t) = 58.8 - 0.5533t.

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47 = 58.8 - 0.5533t.

0.5533t = 11.8.

t = 11.8/0.5533

t = 21.3.

1980 + 21 = 2001, so the percentage will be 47% during the year 2001.

Now, 2005 is 25 years after 1980, so the percentage is P(25), given as follows: P(25) = 58.8 - 0.5533x25 = 44.97%.

More can be learned about linear functions at brainly.com/question/21107621.

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