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3 years ago

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Q8 Q2.) What are the lot's dimensions?

1 answer:

Triss [41]3 years ago

7 0

Equation for perimeter is 2L +2W

perimeter of the lot is 390 ft

so we have 390 = 2L +2w

divide all terms by 2:

195 = L + W

rewrite this as L = 195-W ( eq.1)

cost of fence for the length = 36 per foot so we have 36L
cost of fence for width = 6 per foot so we have 6W

the fence was 1 length and 2 sides
so we have 36l + 6w +6w = total cost

total cost is 4980

so we have 4980 = 36L + 6w +6w

combine like terms:

4980 = 36L +12w

replace L with eq1 from above:

4980 = 36(195-w) +12w

distribute:

4980 = 7020 -36w +12w

combine like terms:

4980 = 7020-24w

subtract 7020 from both sides:

-2040 = -24w
divide both sides by -24:

-2040 / -24 = 85
width = 85 feet

using eq1 L = 195 - 85

Length = 110 feet

lond = 110 feet
short = 85 feet

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Solve each system of equations (systems with 3 variables)

Natasha2012 [34]

Answer:

x = 2 , y = 5 , z = -1 You are correct!!!

Step-by-step explanation:

Solve the following system:

{9 x + 3 y - 4 z = 37 | (equation 1)

4 x + 3 y + 7 z = 16 | (equation 2)

x - 5 y + 8 z = -31 | (equation 3)

Subtract 4/9 × (equation 1) from equation 2:

{9 x + 3 y - 4 z = 37 | (equation 1)

0 x+(5 y)/3 + (79 z)/9 = (-4)/9 | (equation 2)

x - 5 y + 8 z = -31 | (equation 3)

Multiply equation 2 by 9:

{9 x + 3 y - 4 z = 37 | (equation 1)

0 x+15 y + 79 z = -4 | (equation 2)

x - 5 y + 8 z = -31 | (equation 3)

Subtract 1/9 × (equation 1) from equation 3:

{9 x + 3 y - 4 z = 37 | (equation 1)

0 x+15 y + 79 z = -4 | (equation 2)

0 x - (16 y)/3 + (76 z)/9 = (-316)/9 | (equation 3)

Multiply equation 3 by 9/4:

{9 x + 3 y - 4 z = 37 | (equation 1)

0 x+15 y + 79 z = -4 | (equation 2)

0 x - 12 y + 19 z = -79 | (equation 3)

Add 4/5 × (equation 2) to equation 3:

{9 x + 3 y - 4 z = 37 | (equation 1)

0 x+15 y + 79 z = -4 | (equation 2)

0 x+0 y+(411 z)/5 = (-411)/5 | (equation 3)

Multiply equation 3 by 5/411:

{9 x + 3 y - 4 z = 37 | (equation 1)

0 x+15 y + 79 z = -4 | (equation 2)

0 x+0 y+z = -1 | (equation 3)

Subtract 79 × (equation 3) from equation 2:

{9 x + 3 y - 4 z = 37 | (equation 1)

0 x+15 y+0 z = 75 | (equation 2)

0 x+0 y+z = -1 | (equation 3)

Divide equation 2 by 15:

{9 x + 3 y - 4 z = 37 | (equation 1)

0 x+y+0 z = 5 | (equation 2)

0 x+0 y+z = -1 | (equation 3)

Subtract 3 × (equation 2) from equation 1:

{9 x + 0 y - 4 z = 22 | (equation 1)

0 x+y+0 z = 5 | (equation 2)

0 x+0 y+z = -1 | (equation 3)

Add 4 × (equation 3) to equation 1:

{9 x+0 y+0 z = 18 | (equation 1)

0 x+y+0 z = 5 | (equation 2)

0 x+0 y+z = -1 | (equation 3)

Divide equation 1 by 9:

{x+0 y+0 z = 2 | (equation 1)

0 x+y+0 z = 5 | (equation 2)

0 x+0 y+z = -1 | (equation 3)

Collect results:

Answer: {x = 2 , y = 5 , z = -1

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ivann1987 [24]

Given:

Two values of a linear function are f (6) = 8 and f (9) = 3.

To find:

The linear function.

Solution:

According to the question f (6) = 8 and f (9) = 3, it means the function passes through (6,8) and (9,3).

If a linear function passes through two points then the equation is

$y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)$

So, the equation of linear function is

$y-8=\dfrac{3-8}{9-6}(x-6)$

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Add 8 on both sides.

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Function form is,

$f(x)=-\dfrac{5}{3}(x)+18$

Therefore, the required linear function is $f(x)=-\dfrac{5}{3}(x)+18$ .

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3 years ago