Solve the quadratic equation by completing the square. 3x2 - 6x - 4 = 0

Mathematics

1 answer:

Akimi4 [234]3 years ago

7 0

Answer:

-0.53, 2.53 to the nearest hundredth.

Step-by-step explanation:

3x^2 - 6x - 4 = 0

3(x^2 - 2) - 4 = 0

3 [ ( x - 1)^2 - 1] = 4

3(x - 1)^2 - 3 = 4

3(x - 1)^2 = 7

(x - 1)^1 = 7/3

x - 1 = +/- √(7/3)

x = +/- √(7/3) + 1

x = 2.53, -0.53.

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Household incomes are normally distributed with a mean of $47,500 and a standard deviation of $12,500. What is the probability o

Romashka [77]

Answer:

Option C: 15.87 is the correct answer

Step-by-step explanation:

Given

Mean = $47500

SD = $12500

We have to find the probability of having $60000 or more

So,

x = $60000

The z-score will be:

$z-score = z = \frac{x-mean}{SD}\\z = \frac{60000-47500}{12500}\\= \frac{12500}{12500}\\= 1$

Looking in the z-score table, we get

P(Z<60000) = 0.8413

In order to find the probability P(Z>60000) => 1-P(Z<60000)

= 1-0.8413

=0.1587

Converting into percentage: 0.1587*100 = 15.87%

Hence,

Option C: 15.87 is the correct answer

4 0

3 years ago

Help ASAP please

hoa [83]

Answer: Each multiple choice question is worth 5 points.

Step-by-step explanation: You can find this answer by using the equation "14m + 24 = 16m + 14" and then solving for "m". To find what "m" is, you must first subtract 14m from both sides, leaving "24 = 2m + 14". Next, you subtract 14 from both sides, leaving "10 = 2m". Finally, you divide both sides by 2, which will give you "m = 5". Thus meaning each multiple choice question is worth 5 points.

To check this, simply fill in for "m" and solve each side. 14 * 5 + 24 = 94 and 16 * 5 + 14 = 94. 94 = 94, so "m = 5" is correct.

I hope this helps!

8 0

4 years ago

Which relation is a direct variation that contains the ordered pair (2, 7)? y = 4x – 1 y = StartFraction 7 Over x EndFraction y

Vanyuwa [196]

Answer:

The relation $y=\frac{7}{2}x$ or y = seven-halves x is a direct variation that contains the ordered pair (2,7).