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4 years ago

Identify the x-intercepts by factoring and solving m^3 + 4m^2 - 6m -24 = 0

Mathematics

1 answer:

Tpy6a [65]4 years ago

7 0

Answer:

m = -4 or m = sqrt(6) or m = -sqrt(6)

Step-by-step explanation:

Solve for m:

m^3 + 4 m^2 - 6 m - 24 = 0

The left hand side factors into a product with two terms:

(m + 4) (m^2 - 6) = 0

Split into two equations:

m + 4 = 0 or m^2 - 6 = 0

Subtract 4 from both sides:

m = -4 or m^2 - 6 = 0

Add 6 to both sides:

m = -4 or m^2 = 6

Take the square root of both sides:

Answer: m = -4 or m = sqrt(6) or m = -sqrt(6)

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Answer:

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Step-by-step explanation:

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3 years ago

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3 years ago

Read 2 more answers

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

8 0

3 years ago

The factors of a quadratic function are 2x-3 and x-3. what is the axis of symmetry of this function?

Crank

F : R -> R, f(x) = ( 2x - 3)( x - 3 ) => f(x) = 2x^2 - 9x + 9;
The axis of symmetry is x = - b / (2a) => x = 9 / 4.

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3 years ago

Please hurry I will mark you brainliest

pishuonlain [190]

Answer:

Here's the answers

Step-by-step explanation:

1. When two variables are in relation with a formula or a variable is related by the sum of two or more variables, then it is a partial variation. X = KY + C (where K and C are constants) is a straight line equation which is an example of partial variation.

2. The formula y=kxn y = k x n is used for direct variation. The value k is a nonzero constant greater than zero and is called the constant of variation.

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3 years ago