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3 years ago

Solve the system of equations using the substitution method.

Mathematics

1 answer:

ANTONII [103]3 years ago

5 0

The solution of system of equations is: x = 1.6 and y = 1.2

Step-by-step explanation:

Given equations are:

$y = 2-\frac{1}{2}x\ \ \ \ Eqn\ 1\\x-3y = -2\ \ \ eqn\ 2$

Putting $y = 2-\frac{1}{2}x$ in equation 2

$x - 3(2-\frac{1}{2}x) = -2\\x - 6 + \frac{3}{2}x = -2\\x +\frac{3}{2}x = -2+6\\\frac{2x+3x}{2} = 4\\\frac{5x}{2} = 4\\5x = 4 * 2\\5x = 8\\x = \frac{8}{5}\\x = 1.6$

Putting x = 1.6 in equation 2

$1.6-3y = -2\\-3y = -2-1.6\\-3y =- 3.6$

Dividing both sides by -3

$\frac{-3y}{-3} = \frac{-3.6}{-3}\\y = 1.2$

Hence,

The solution of system of equations is: x = 1.6 and y = 1.2

Keywords: Linear equations, variables

Learn more about linear equations at:

#LearnwithBrainly

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I need help! ASAP!! please and thank you

Neko [114]

Answer: The walking path around it.

Step-by-step explanation:

Remember the Pythagorean's theorem, for a triangle rectangle with catheti A and B, and with hypotenuse H, we have:

A^2 + B^2 = H^2

H = √(A^2 + B^2)

Here, A + B is the total distance for the path, while the hypotenuse is the distance for the bridge

Here we can see that:

A = 1170 ft

B = 520 ft

Then:

H = √( (520 ft)^2 + (1170 ft)^2) = 1280.4 ft

Now, let's compute the costs.

For the bridge, we know that each foot costs $11, then for 1280.4 ft the cost is:

Cost of the bridge = (1280.4)*$11 = $14,084.4

And for the walking path, the cost is $6 per foot, then the total cost of the path is:

Cost of the path = (520 ft + 1170 ft)*$6 = $10,140

We know that the bridge is preferred if it is within the range of $1500 for the path's cost.

This range is:

($10,140 - $1,500, $10,140 + $1,500) = ($8,640, $11,640)

Here we can see that the cost of the bridge does not belong to this range, (is higher) so the option we should recommend is the walking path around.

8 0

3 years ago

Please helppp!!!!!!! And please show your work so i can know what to do next time i have this same problem !

solmaris [256]

Answer: The answer is $152.25

Step-by-step explanation:

First you multiply 0.07 by 163.71 to get 11.4597.

The you subtract 163.71 from 11.4597.

Then that's your answer. I hope this helped!

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3 years ago

Am I correct? (Perfect Square Form)

natka813 [3]

Answer:

$(x -3 )^2 = 10$

Step-by-step explanation:

Given

$x^2 - 6x - 1 = 0$

Required: Express as a perfect square

$x^2 - 6x - 1 = 0$

Add 10 to both sides

$x^2 - 6x - 1 +10= 0+10$

$x^2 - 6x +9= 10$

Expand

$x^2 - 3x - 3x+9= 10$

Factorize:

$x(x - 3) - 3(x - 3)= 10$

Factorize:

$(x -3 )(x - 3) = 10$

$(x -3 )^2 = 10$

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3 years ago

William has been contracted to paint a school classroom. The classroom is 20 m long, 15 m wide and 5 m high. There are four wind

valina [46]

Answer:

Step-by-step explanation:

l -> length

b -> width

h -> height

Find the area of four walls and ceiling. then subtract the area of four windows and a door form that area.

Area of four walls + <u>ceiling</u> = 2( lh + bh) +<u>lb</u>

= 2*(20*5 + 15*5) + 20*15

= 2( 100 + 75) + 300

= 2* 175 + 300

= 350 +300

= 650 sq m

Area of window = 2 *3 = 6 sq.m

Area of four windows = 4*6 = 24 sq.m

Area of door = 2 * 1 = 2 sq.m

Area of four walls excluding 4 windows and door = 650 - 24 - 2 = 624 sq.m

Cost of painting = 624 * 6.50

= $ 4056

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3 years ago

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Bezzdna [24]

Answer:

Step-by-step explanation:

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3 years ago