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2 years ago

Hurry please!

Mathematics

1 answer:

chubhunter [2.5K]2 years ago

7 0

Answer:

The slope of the given line and a line parallel to it is

Explanation:

Given:

−

is the standard form of a linear equation.

A line parallel to this line has the same slope. To determine the slope, solve for

to change the equation to slope-intercept form:

where:

is the slope and

is the y-intercept.

−

Subtract

from both sides.

−

Divide both sides by

−

Simplify.

−

The slope of the given line and a line parallel to it is

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Simplify 6 sqrt -20 Enter your answer in simplest form in the box

Ksivusya [100]

Answer:

12sqrt5i

Step-by-step explanation:

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3 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

On a shopping trip, Peter spent 1/3 of his money for a jacket and another $5 for a hat. If peter still had 1/2 of his money left

katen-ka-za [31]

Let x be the money he had originally.
x/3+5=x/2
5=x/6
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So he had $30 originally.

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4 years ago

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VMariaS [17]

Since in a pass code, the placement of the digits is important, therefore this means that to solve for the total number of possibilities we have to make use of the principle of Permutation. The formula for calculating the total number of possibilities using Permutation is given as:

P = n! / (n – r)!

where,

n = is the total amount of numbers to choose from = 20

r = is the total number of digits needed in the passcode = 4

Therefore solving for the total possibilities P:

P = 20! / (20 – 4)!

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Answer:

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