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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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In Ryan Corporation, the first shift produced 5 1/2 times as many lightbulbs as the second shift. If the total lightbulbs produc

Andru [333]

Answer:

13750

Step-by-step explanation:

Let 'x' be the number of bulbs produced in second shift

Number of bulbs produced in 1st shift= 5.5x

Total number of bulbs= 5.5x+x

16250=5.5x+x

x=2500

Number of bulbs produced in shift 1= 5.5×2500

= 13750

7 0

3 years ago

Melanie connected a brown garden hose, a green garden hose, and a black garden hose to make one long hose. The brown hose is 10.

natta225 [31]

Answer:

35.65 feet

Step-by-step explanation:

Melanie connected a brown garden hose , a green garden hose and a black garden hose to make one long hose

The brown hose is 10.75 feet

The green hose is 16.4 feet

The black hose is 8.5 feet

Therefore the farthest distance that the one hose can reach can be calculated as follows

= 10.75 + 16.4 + 8.5

= 35.65 feet

Hence the farthest distance that one hose can reach is 35.65 feet

3 0

3 years ago

Express p in terms of q if

Irina-Kira [14]

$p=x^2+\dfrac{1}{x^2}\\\\p=\dfrac{x^4}{x^2}+\dfrac{1}{x^2}\\\\p=\dfrac{x^4+1}{x^2}\qquad(*)$

$q=x+\dfrac{1}{x}\\\\q=\dfrac{x^2}{x}+\dfrac{1}{x}\\\\q=\dfrac{x^2+1}{x}\qquad\text{square both sides}\\\\q^2=\left(\dfrac{x^2+1}{x}\right)^2\\\\q^2=\dfrac{(x^2+1)^2}{x^2}\qquad\text{use}\ \ (a+b)^2=a^2+2ab+b^2\\\\q^2=\dfrac{(x^2)^2+2(x^2)(1)+1^2}{x^2}\\\\q^2=\dfrac{x^4+2x^2+1}{x^2}\\\\q^2=\dfrac{x^4+1}{x^2}+\dfrac{2x^2}{x^2}\\\\q^2=\dfrac{x^4+1}{x^2}+2\qquad\text{subtract 2 from both sides}\\\\q^2-2=\dfrac{x^4+1}{x^2}\\\\\text{From (*) we have}\\\\\boxed{p=q^2-2}$

8 0

3 years ago

Mandy used the graph to write the equation of the line it represents. She took these steps. 1. y−intercept = (0, 2) 2. Slope = r

Katyanochek1 [597]

Based on the information given about the equation, y will be 0.5x + 2.

<h3>How to illustrate the equation?</h3>

From the information given, it should be noted that the equation of the line it represents was given and the y intercept is = (0, 2).

The function to represent y will be:

y = mx + b

y = (1/2)x + 2

y = 0.5x + 2

In conclusion, y = 0.5x + 2.

Learn more about equations on:

brainly.com/question/2972832

#SPJ1

3 0

2 years ago

Recycling one glass bottle can save enough energy to power an oven for 7.5 minutes. A glass bottle weighs 500 grams. Glass used

musickatia [10]

This is a units conversion problem: you have time and you want to convert that to money. Any units conversion problem involves multiplication by 1 in various forms. When you are given 7.5 min = 1 bottle = 500g, you know that (500 g)/(7.5 min) = 1 because the numerator and denominator are equal. (Of course, you are aware that 500 g = 0.500 kg.) The idea is to choose the forms of 1 that cause units you don't want to cancel, leaving only the units you do want.

$6\,h\times \dfrac{0.500\,kg}{7.5\,min}\times \dfrac{60\,min}{1\,h}\times \dfrac{5\,p}{1\,kg}\\\\=\dfrac{6\cdot 0.500\cdot 60\cdot 5\,p}{7.5\cdot 1\cdot 1}=120\,p$

The glass for recycling that would save enough energy to power an oven for 6 hours costs 120p.

3 0

3 years ago