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2 years ago

14

contractor wishes to build 9 houses, each different in design. In how many ways can he place these houses on a street if 6 lots

are on one side of the street and 3 lots are on the opposite side?

1 answer:

Tju [1.3M]2 years ago

5 0

The houses can be placed in 362,880 ways.

<u>Step-by-step explanation:</u>

The 9 houses are each in different design.

The each lot can place any of the 9 houses.

The 1st lot can place anyone house of all the 9 houses.
The 2nd lot can place one of remaining 8 houses.
The 3rd lot can place one of remaining 7 houses.

Similarly, the process gets repeated until the last house is placed on a lot.

<u>From the above steps, it can be determined that :</u>

The number of ways to place the 9 houses in 9 lots = 9!

⇒ 9×8×7×6×5×4×3×2×1

⇒ 362880 ways.

Therefore, the houses can be placed in 362880 ways.

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1 year ago

An equivalent expression for 16x − 8 is _____ . The _____ Property is used to generate this expression.

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2 years ago

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Match each pair of points to the equation of the line that is parallel to the line passing through the points.

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The formula to calculate the slope between two points is equal to

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we will proceed to calculate the slope in each case, to determine the solution of the problem

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Substitute the values in the formula

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$m=\frac{-7}{2}$

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therefore

<u>the answer Part A) is</u>

$B(5,2)\ C(7,-5)$ ------> $y=-3.5x-15$

<u>Case B)</u> Point $D(11,6)\ E(5,9)$

Find the slope DE

Substitute the values in the formula

$m=\frac{9-6}{5-11}$

$m=\frac{3}{-6}$

$m=-0.5$

so

The equation $y=-0.5x-3$ is parallel to the line passing through the points $D(11,6)\ E(5,9)$

therefore

<u>the answer Part B) is</u>

$D(11,6)\ E(5,9)$ ------> $y=-0.5x-3$

<u>Case C)</u> Point $F(-7,12)\ G(3,-8)$

Find the slope FG

Substitute the values in the formula

$m=\frac{-8-12}{3+7}$

$m=\frac{-20}{10}$

$m=-2$

so

Any linear equation with slope $m=-2$ will be parallel to the line passing through the points $F(-7,12)\ G(3,-8)$

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Find the slope HI

Substitute the values in the formula

$m=\frac{9-4}{8-4}$

$m=\frac{5}{4}$

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The equation $y=1.25x+4$ is parallel to the line passing through the points $H(4,4)\ I(8,9)$

therefore

<u>the answer Part D) is</u>

$H(4,4)\ I(8,9)$ ------> $y=1.25x+4$

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Find the slope JK

Substitute the values in the formula

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The equation $y=5x+19$ is parallel to the line passing through the points $L(5,-7)\ M(4,-12)$

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$L(5,-7)\ M(4,-12)$ ------> $y=5x+19$

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1 year ago

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