All categories

3 years ago

Study the equation. x² + 6x = - 4

Mathematics

1 answer:

Zinaida [17]3 years ago

5 0

Answer:

x = -3+√5, -3-√5 (exact roots)

or x = -0.76, -5.24 to the nearest hundredth.

Step-by-step explanation:

x² + 6x = - 4

Completing the square:

(x + 3)^2 - 9 = -4

(x + 3)^2 = 5

x + 3 = +/-√5

x = - 3 + √5, - 3 - √5

You might be interested in

Use the given information to find the unknown value:y varies inversely with a. When x = 4, then y= 4. Find y when I = 2.Iyy =hel

Mashutka [201]

Inverse variation:

$y=\frac{k}{x}$

k is a constant

Use the given information (when x=4 y=4) to find the value of the constant:

$\begin{gathered} 4=\frac{k}{4} \\ \\ \text{Multiply both sides of the equation by 4:} \\ 4\times4=4\times\frac{k}{4} \\ \\ 16=k \\ \\ \\ k=16 \end{gathered}$

Then, the given relationship has the next equation:

$y=\frac{16}{x}$

Use the equation above to find y when x=2:

$\begin{gathered} y=\frac{16}{2} \\ \\ y=8 \end{gathered}$ Then, when x=2, y=8

3 0

7 months ago

Which expression is equvalent to 5(x+3)

FrozenT [24]

There are a few other ways to answer this but one way i know is 5x + 15

7 0

2 years ago

Read 2 more answers

If x=14, what is the value of 3(x + 5)?

gladu [14]

Answer:

Step-by-step explanation:

parentheses first then multiply by 3

5 0

2 years ago

There is a bag filled with 3 blue and 4 red marbles.

tresset_1 [31]

Using the hypergeometric distribution, it is found that there is a 0.4286 = 42.86% probability of getting 2 of the same colour.

The marbles are chosen without replacement, hence the <em>hypergeometric </em>distribution is used to solve this question.

<h3>What is the hypergeometric distribution formula?</h3>

The formula is:

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}$

$C_{n,x} = \frac{n!}{x!(n-x)!}$

The parameters are:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

In this problem:

There is a total of 3 + 4 = 7 marbles, hence N = 7.

Of those, 3 are blue, hence k = 3.

2 marbles will be taken, hence n = 2.

The probability of getting 2 of the same colour is the sum of P(X = 0), which is both red, with P(X = 2), which is both blue, then:

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}$

$P(X = 0) = h(0,7,2,3) = \frac{C_{3,0}C_{4,2}}{C_{7,2}} = 0.2857$

$P(X = 2) = h(2,7,2,3) = \frac{C_{3,2}C_{4,0}}{C_{7,2}} = 0.1429$

Hence:

$p = P(X = 0) + P(X = 2) = 0.2857 + 0.1429 = 0.4286$

0.4286 = 42.86% probability of getting 2 of the same colour.

You can learn more about the hypergeometric distribution at brainly.com/question/4818951

3 0

2 years ago

Three ways to make 26

Alik [6]

Answer:

13 times 2

52 divided by 2

20 plus 6

Step-by-step explanation:

6 0

2 years ago