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2 years ago

Find the distance between the two points (4,-5) and (-1,7) In units

Mathematics

1 answer:

viktelen [127]2 years ago

5 0

$\sqrt{ {(4 + 1)}^{2} + {( - 5 - 7)}^{2} } \\ {5}^{2} = 25 \\ { - 12}^{2} = 144 \\ 144 + 25 = 169 \\ \sqrt{169} = 13$

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Complete the steps to solve the polynomial equation x3 – 21x = –20. According to the rational root theorem, which number is a po

jeka94

Answer:

Zeroes : 1, 4 and -5.

Potential roots: $\pm 1, \pm 2, \pm 4, \pm 5, \pm 10, \pm 20$ .

Step-by-step explanation:

The given equation is

$x^3-21x=-20$

It can be written as

$x^3+0x^2-21x+20=0$

Splitting the middle terms, we get

$x^3-x^2+x^2-x-20x+20=0$

$x^2(x-1)+x(x-1)-20(x-1)=0$

$(x-1)(x^2+x-20)=0$

Splitting the middle terms, we get

$(x-1)(x^2+5x-4x-20)=0$

$(x-1)(x(x+5)-4(x+5))=0$

$(x-1)(x+5)(x-4)=0$

Using zero product property, we get

$x-1=0\Rightarrow x=1$

$x-4=0\Rightarrow x=4$

$x+5=0\Rightarrow x=-5$

Therefore, the zeroes of the equation are 1, 4 and -5.

According to rational root theorem, the potential root of the polynomial are

$x=\dfrac{\text{Factor of constant}}{\text{Factor of leading coefficient}}$

Constant = 20

Factors of constant ±1, ±2, ±4, ±5, ±10, ±20.

Leading coefficient= 1

Factors of leading coefficient ±1.

Therefore, the potential root of the polynomial are $\pm 1, \pm 2, \pm 4, \pm 5, \pm 10, \pm 20$ .

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3 years ago

A video club wants to reward its best members with a discount based on the member’s number of movie rentals and the number of ne

ivanzaharov [21]

Answer:

public class MovieRental

{

public static void main(String[] args)

{

Scanner in = new Scanner(System.in);

System.out.print("Enter the number of movie rentals: ");

int movieRentals = in.nextInt();

System.out.print("Enter the number of members referred to the video club: ");

int memberReferral = in.nextInt();

in.close();

double discountVal = Math.min(movieRentals + memberReferral, 75);

System.out.println("The discount is equal to: " + discountVal);

}

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2 years ago

1. Chip has $100 saved in his banking account. His dad has agreed to pay him $2.50 every day he cleans all the

elixir [45]

It will take 62 days

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3 years ago

Read 2 more answers

Which property can be used to expand the expression -2(3/4x+7)

geniusboy [140]

Answer:

B. the distributive property

Step-by-step explanation:

Distributive property can be used to expand the expression -2(3/4x+7).

When that property is used, we need to distrubute the monomial to the binomial which is the two terms.

$- 2( \frac{3}{4} x + 7) \\ \Longrightarrow \boxed{- 2( \frac{3}{4} x) + - 2(7)}$

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3 years ago

A line segment on a number line has its endpoints at -9 and 6. what is midpoint

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Midpoint formula = (-9 + 6) / 2 = -3/2

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