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3 years ago

According to the rational root theorem, which is a factor of the polynomial f(x)=3x^3-5x^2-12x+20?

Mathematics

1 answer:

MakcuM [25]3 years ago

4 0

Answer:

(x-2), (x+2), (3x-5)

Step-by-step explanation:

Factors of 3: ±1, ±3

Factors of 20: ±1, ±2, ±4, ±5, ±10, ±20

Possible factors of the polynomial: ±1, ±2, ±3, ±4, ±5, ±10, ±20, .... (there's a lot more but you probably do not need to list them all)

Pick a number to divide the polynomial by (I picked 2)

(3x³-5x²-12x+20)÷(x-2) = 3x²+x-10

So (x-2) is a factor of f(x) = 3x³-5x²-12x+20

Factor 3x²+x-10 = (3x-5)(x-2) these are the other factors of f(x) = 3x³-5x²-12x+20

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Tatami mats are used as a floor covering in japan. One possible layout uses four identical rectangular mats and one square mat,

Maksim231197 [3]

a) Given

Total area = 81 feet squared.

Let the area of the square mat = x feet.

From question, area of the rectangular mat is twice that of square mat.

So, the area of the rectangular mat $= 2 x$ feet.

Now,

Total area = 81 feet squared

Then,

$4(2 x) + x = 81\\ \\ 9 x = 81\\ \\ x = \frac{81}{9}\\ \\ x = 9\\$

Hence the area of the one rectangular mat = 2*9 = 18 feet squared

b) Let the width of the rectangular mat = y feet.

Then length of the mat = 2 y feet.

Area of the rectangle $= 2 y* y = 2 y^{2}$

and area of rectangle = 18 feet squared.

So,

$2 y^{2} = 18\\ y^{2} = 9\\ y= \pm3\\$

Width can not be negative.

Hence, the width of the rectangular mat = 3 feet

and length of the rectangular mat = 3*2 = 6 feet

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3 years ago

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Orlov [11]

Given:

The base of the given triangle has two part:

Left( left side of the hypotenuse) = 25

Right ( right side of the hypotenuse) = x

The altitude (h) = 60

To find the value of x.

Formula:

By Altitude rule we know that, the altitude of a triangle is mean proportional between the right and left part of the hypotenuse,

$\frac{left}{altitude} =\frac{altitude}{right}$

Now,

Putting,

left = 25, altitude = 60 and right = x we get,

$\frac{25}{60} =\frac{60}{x}$

or, $(25)(x )=(60)(60)$ [ by cross multiplication]

or, $x = \frac{3600}{25}$

or, $x = 144$

Hence,

The value of x is 144.

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Natalka [10]

Answer:

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Step-by-step explanation:

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3 years ago

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Find the midpoint of the segment between the points (17,−11) and (−14,−16)

Viefleur [7K]

Answer:

(1.5, -13.5)

Step-by-step explanation:

Midpoint Formula: $(\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )$

Simply plug in our coordinates into the formula:

x = (17 - 14)/2

x = 3/2

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Find the maxmium area of a rectangular plot of land which can be enclosed by rope of length 60 metres

mario62 [17]

Answer:

225 m²

Step-by-step explanation:

If W is the width of the rectangle, and L is the length, then:

60 = 2W + 2L

A = WL

Use the first equation to solve for one of the variables:

30 = W + L

L = 30 − W

Substitute into the second equation:

A = W (30 − W)

A = 30W − W²

This is a parabola, so we can find the vertex using the formula x = -b/(2a).

W = -30 / (2 × -1)

W = 15

Or, we can use calculus:

dA/dW = 30 − 2W

0 = 30 − 2W

W = 15

Solving for L:

L = 30 − W

L = 15

So the maximum area is:

A = WL

A = (15)(15)

A = 225

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3 years ago