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3 years ago

Find the greatest common factor of 15x^2 y^3 and -20x^3 yz

Mathematics

1 answer:

natali 33 [55]3 years ago

6 0

$15x^2y^3=\boxed{5x^2y}\cdot3y^2\\\\-20x^3yz=\boxed{5x^2y}\cdot(-4xz)\\\\GCF(15x^2y^3;\ -20x^3yz)=\boxed{5x^2y}$

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4 years ago

A factory is to be built on a lot measuring 210 ft by 280 ft. A local building code specifies that a lawn of uniform width and e

Tresset [83]

Answer:

Width of lawn = 35 ft

Dimensions of factory = length: 210 ft, width: 140 ft

Step-by-step explanation:

The total area of the lot can be calculated as:

$A_{lot} = 210 * 280\\A_{lot} = 58800 ft^{2}$

Since, the area of factory should be equal to area of lawn:

$A_{lot} = A_{factory} + A_{lawn}\\58800 = 2 A_{factory or lawn}\\\\A_{factory or lawn} = \frac{58800}{2}\\A_{factory or lawn} = 29400 ft^{2}$

Now, let 'x' be the width of lawn, the dimensions of factory can be written as:

$(210-2x)\\(280-2x)\\$

Since, area is equal to length x width:

$(210-2x)*(280-2x) = 29400\\Simplifying:\\210*280 - 210*2x - 2x*280 + 4x^{2} = 29400\\58800 - 420x - 560x +4x^{2} = 29400\\4x^{2} - 980x +58800 = 29400\\4x^{2} - 980x + 29400 = 0\\$

Divide whole equation by 4,

$x^{2} - 245 + 7350 = 0\\$

Solving above quadratic equation, we get,

$x = 210\\x = 35\\$

x = 35 seems realistic width of the lawn.

Now, finding the dimension of factory:

$(210-2x) = 210 - 2(35) = 140 ft\\(280-2x) = 280 - 2(35) = 210ft$

We can also reconfirm the area of factory by multiplying the above two lengths:

140 * 210 = 29400 ft

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3 years ago

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Oduvanchick [21]

Answer:

80 students applied

Explanation:

24 ÷ 30 × 100

= 0.8 × 100

= 80

i hope this helps! :D do comment if you need any clarification.

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