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3 years ago

Complete the square leave your answer in root form. 2x² - 6x - 3 = 0

Mathematics

2 answers:

nexus9112 [7]3 years ago

6 0

Answer:

x = 1.5 ± √3.75

Step-by-step explanation:

There are several variations of completing the sqaure.

This is the one I use.

-------------------------------------

2x² - 6x - 3 = 0

add 3 to both sides

2x² - 6x = 3

the x² coefficient must be 1

so divide both sides by 2

x² - 3x = 1.5

use half the x coefficient (-3/2 = -1.5) as the complete the square term

(x - 1.5)² = 1.5 + (-1.5)²

(x - 1.5)² = 1.5 + 2.25

(x - 1.5)² = 3.75

Take the square root of both sides

x - 1.5 = ± √3.75

add 1.5 to both sides

x = 1.5 ± √3.75

ira [324]3 years ago

6 0

Answer:

x = 1.5 + √3.75 ; x = 1.5 - √3.75

Step-by-step explanation:

2x² - 6x -3 = 0

Add 3 to both sides

2x² - 6x = 3

Divide the entire equation by the coefficient of x²

$\dfrac{2x^{2}}{2}-\dfrac{6x}{2}=\dfrac{3}{2}\\$

x² - 3x = 1.5

Divide the coefficient of x by 2 and then square it and add to both sides.

3/2 = 1.5

1.5² = 2.25

Add 2.25 to both sides

x² - 3x + 2.25 = 1.5+2.25

(x - 1.5)² = 3.75

Take square root,

x - 1.5 = ±√3.75

x = 1.5 ± √3.75

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How to solve 3-k-4-k=k+11 with a multiple step equation

Ket [755]

Answer:

Step-by-step explanation:

3-k-4-k=k+11

Collecting like terms

-k - k - k = 11 +4 - 3

-3k = 12

Dividing each term by -3

k = 12/-3

k = -4

7 0

3 years ago

What is the best estimate for the product 289 and 7? Make it clear to understand : )

xxMikexx [17]

Hey friend!
Let's figure this out!

The best estimate for the product 289 and 7 is 2,900.

290 x 10 = 2,900.

You must round the multiplicand and multiplier to come up with the best estimate.

Hope this helps!

4 0

4 years ago

A CBS News/New York Times survey found that 97% of Americans believe that texting while driving should be outlawed (CBS News web

Murrr4er [49]

Answer:

a) $P(X\geq 8)=0.0317+0.228+0.737=0.9972$

b) $P(X>95) =1-P(X$

Step-by-step explanation:

Previous concepts

A Bernoulli trial is "a random experiment with exactly two possible outcomes, "success" and "failure", in which the probability of success is the same every time the experiment is conducted". And this experiment is a particular case of the binomial experiment.

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

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

The complement rule is a theorem that provides a connection between the probability of an event and the probability of the complement of the event. Lat A the event of interest and A' the complement. The rule is defined by: $P(A)+P(A') =1$

Part a

We want this probability:

$P(X\leq 12)$

$P(X\geq 8)=P(X=8)+P(X=9)+P(X=10)$

$P(X=8)=(10C8)(0.97)^8 (1-0.97)^{10-8}=0.03174$

$P(X=9)=(10C9)(0.97)^9 (1-0.97)^{10-9}=0.2287$

$P(X=10)=(10C10)(0.97)^{10} (1-0.97)^{10-10}=0.7374$

$P(X\geq 8)=0.0317+0.228+0.737=0.9972$

Part b

We need to check if we can use the normal approximation , the conditions are:

$np=100*0.97=97>10$ and $n(1-p)=100*(1-0.97)=3$

On this case the second condition is not satisfied, but the problem says that we can use it. So then if we apply the normal approximation to the binomial distribution in our case:

$X \sim N(\mu=97,\sigma=1.706)$