All categories

3 years ago

Which of the following values "completes the square," or creates a perfect square trinomial, for x2 + 6x + ___?

1 answer:

7 0

To create a perfect square trinomial, halve the x coefficient, square it, and then add that value.

In the case of x² + 6x, we would have 6 to get 3, then square 3 to get 9.
We would add 9 to make a perfect square trinomial.
<u>
</u><u>Why this works</u>
A perfect square trinomial is designed to factor to some value (x+n)².
When you FOIL this you get x² + 2nx + n².
As you can see, if you wanted to find the value of that n², you could take that x coefficient 2n, halve it to get n, and then square it to get n²!

You might be interested in

27. 8 minus the product of 9 and r

Tems11 [23]

8-9r is the answer to this

6 0

3 years ago

An Airliner has a capacity for 300 passengers. If the company overbook a flight with 320 passengers, What is the probability tha

TEA [102]

Answer:

The probability is $P(X >300 ) = 0.97219$

Step-by-step explanation:

From the question we are told that

The capacity of an Airliner is k = 300 passengers

The sample size n = 320 passengers

The probability the a randomly selected passenger shows up on to the airport

$p = 0.96$

Generally the mean is mathematically represented as

$\mu = n* p$

=> $\mu = 320 * 0.96$

=> $\mu = 307.2$

Generally the standard deviation is

$\sigma = \sqrt{n * p * (1 -p ) }$

=> $\sigma = \sqrt{320 * 0.96 * (1 -0.96 ) }$

=> $\sigma =3.50$

Applying Normal approximation of binomial distribution

Generally the probability that there will not be enough seats to accommodate all passengers is mathematically represented as

$P(X > k ) = P( \frac{ X -\mu }{\sigma } > \frac{k - \mu}{\sigma } )$

Here $\frac{ X -\mu }{\sigma } =Z (The \ standardized \ value \ of \ X )$

=> $P(X >300 ) = P(Z > \frac{300 - 307.2}{3.50} )$

Now applying continuity correction we have

$P(X >300 ) = P(Z > \frac{[300+0.5] - 307.2}{3.50} )$

=> $P(X >300 ) = P(Z > \frac{[300.5] - 307.2}{3.50} )$

=> $P(X >300 ) = P(Z > -1.914 )$

From the z-table

$P(Z > -1.914 ) = 0.97219$

$P(X >300 ) = 0.97219$

8 0

3 years ago

Zen deposited some money in a savings account. The graph below shows the value of Zen's investment y, in dollars, after x months

kifflom [539]

The y-intercept of 1000 in the graph is at the point where x is equal to 0.

At $x=0$ , it means no month have passed. It is the initial point where Zen deposited the money.

What is the amount (y axis)? 1000!

So y represents the initial deposit of Zen, which is 1000.

ANSWER: Answer choice D (Amount of money Zen deposited in the savings account)

6 0

3 years ago

Read 2 more answers

A number is chosen at random from 1 to 25. Find the probability of selecting an odd number or multiples of 5. *

Ymorist [56]

Answer:

Odd number: 13/25 (52%)

Multiples of 5: 5/25 (20%)

Step-by-step explanation:

There are 13 odd numbers between 1 and 25 so you have a 13/25 chance which is 52% (13/25 = 0.52). There are 5 multiples of 2 between 1 and 25 so you have a 5/25 chance which is 20% (5/25 = 0.2).

8 0

3 years ago

Use the Distributive Property to find the Product 4 and 2/5 × 10

arlik [135]

Distributive Property ( A number, n, is multiplied to the expression in parentheses)

$4( \frac{2}{5} \times 10) = \\ 4( \frac{20}{5} ) = \\ 4(4) = 16$

5 0

3 years ago