All categories

3 years ago

Write the quadratic equation whose roots are 3 and -1, and whose leading coefficient is 5.

Mathematics

1 answer:

Assoli18 [71]3 years ago

6 0

Answer:

5x² - 10x - 15 = 0

Step-by-step explanation:

Given that the roots are x = 3 and x = - 1, then the factors are

(x - 3) and (x + 1) and the quadratic is the product of the factors, that is

f(x) = a(x - 3)(x + 1) ← a is a multiplier

Here a = 5, thus

f(x) = 5(x - 3)(x + 1) ← expand factors using FOIL

= 5(x² - 2x - 3) ← distribute parenthesis by 5

= 5x² - 10x - 15

Thus equation is

5x² - 10x - 15 = 0

You might be interested in

What is the slope of a horizontal line

Step2247 [10]

Answer:

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

Given two points M & N on the coordinate plane, find the slope of MN , and state the slope of the line perpendicular to MN .

telo118 [61]

Answer:

Problem 1) $m = \dfrac{1}{4}$ $slope_{perpendicular} = -4$

Problem 2) $m = \dfrac{1}{3}$ $slope_{perpendicular} = -3$

Step-by-step explanation:

$slope = m = \dfrac{y_2 - y_1}{x_2 - x_1}$

$slope_{perpendicular} = \dfrac{-1}{m}$

Problem 1) M(9,6), N(1,4)

$slope = m = \dfrac{6 - 4}{9 - 1} = \dfrac{2}{8} = \dfrac{1}{4}$

$slope_{perpendicular} = \dfrac{-1}{\frac{1}{4}} = -4$

Problem 2) M(-2,2), N(4,-4)

$slope = m = \dfrac{4 - 2}{4 - (-2)} = \dfrac{2}{6} = \dfrac{1}{3}$

$slope_{perpendicular} = \dfrac{-1}{\frac{1}{3}} = -3$

4 0

3 years ago

The probability that a new car battery functions for more than 10,000 miles is .8, the probability that it functions for more th

MAXImum [283]

Answer:

There is a 50% probability that its total life will exceed 20,000 miles.

Step-by-step explanation:

To solve this question, we use the following formula:

$P(A|B) = \frac{P(A \cap B)}{P(B)}$

In which P(A|B) is the probability of A happening, given that B has happened, $P(A \cap B)$ is the probability of A and B happening, and P(B) is the probability of B happening.

In this problem, we want:

The probability of the total life of the car battery exceeding 20,000 miles, given that it exceeded 10,000 miles.

$P(A \cap B)$ is the probability of exceeding 20,000 and 10,000 miles. It is the same as the probability of exceeding 20,000 miles(If it exceeded 20,000 miles, necessarily it will have exceeded 10,000 miles). So $P(A \cap B) = 0.4$