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2 years ago

Use substitution to write an equivalent quadratic equation. (3x + 2)2 + 7(3x + 2) – 8 = 0

Mathematics

2 answers:

ANEK [815]2 years ago

6 0

Let z = 3x+2. Then, by substitution, your equation is
.. z^2 +7z -8 = 0

_____
This equation can be factored as
.. (z +8)(z -1) = 0
.. x = -8 or +1
Then
.. 3x +2 = -8 or +1
.. 3x = -10 or -1
.. x = -10/3 or -1/3

nirvana33 [79]2 years ago

3 0

CORRECT ANSWER : u^2+7u-8=0, where u=3x+2

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The sum of two numbers is 9. And the sum of their reciprocals is 1/2.find the numbers

Musya8 [376]

Set up a system of equations:

x + y = 9
1/x +1/y = 1/2

The easiest way to solve would be substitution.
x + y = 9 can be solved for y:

y = 9 - x

Then plug this into the second equation and solve for x:

1/x + 1/(9-x) = 1/2
(9-x) + x = x(9-x)/2
9 = (9x-x²)2
18 = 9x - x²
x² - 9x + 18 = 0
(x-6)(x-3) = 0
x = 6, 3

You can check your answer by plugging the two numbers back into both of the equations:

6 + 3 = 9
1/6 + 1/3 = 1/2

The two numbers are 6 and 3.

7 0

2 years ago

Dexter has a fish tank shaped like a rectangular prism. It has a volume of 480 in^3 . The height of the tank is 8 inches taller

ella [17]

Answer:

the height=12; the length=10; the width=4.

Step-by-step explanation:

1) the formula of the described volume is length*width*height=480 (in.³).

2) according to the condition the height=8+width; the length=6+width.

3) if to substitute all the values into the formula, ⇒ (6+width)*(8+width)*width=480.

(width)³+14(width)²+48width-480=0.

4) if to resolve the equation, the width=4.

The length=6+4=10; the height=8+4=12 (in.).

4 0

3 years ago

Sean is taking drivers ed. And the instructor asked him to stay within 2 miles of the posted speed limits. The current speed lim

Aleonysh [2.5K]

Answer:

{x| 43 ≤ x ≤ 47} where x = Sean's speed (in mph)

Step-by-step explanation:

Sean is taking driver's ed. The instructor asked him to stay within 2 miles of the posted speed limits. The current speed limit is 45 mph.

So, the maximum speed which Sean can reach is, (45 + 2) mph

=47 mph

and, the minimum speed which Sean can reach is, (45 - 2) mph

=43 mph

so, {x| 43 ≤ x ≤ 47} where x = Sean's speed (in mph)

3 0

3 years ago

At least 96.00% of the data in any data set lie within how many standard deviations of the mean? Explain how you arrived at yo

zheka24 [161]

The answer assumes that the question is about the normal distribution.

Answer:

96% of the data in any data set normally distributed is 2.05 standard deviations above and below the mean.

Step-by-step explanation:

The key to solving this question is having into account that exists the standard normal distribution that permits obtaining any probability from any normally distributed data, doing the following transformation:

$\\ z = \frac{x-\mu}{\sigma}$

That is, in this case, we subtract a given value x from the population mean and then divide the result by the population standard deviation. This is a z-score, and this value is associated with the probability for a standard normal distribution, with a population mean = 0 and population standard deviation = 1.

Fortunately, for the standard normal distribution, there is associated a ubiquitous standard normal table for possible values of z and the corresponding probability. Then, knowing that the data are normally distributed and having both distribution parameters, namely, the population mean and population standard deviation, we can consult any standard normal table to find the probabilities for any data distributed following the normal distribution.

However, even without previously know the values of the normal parameters, the standard normal distribution can tell us how many standard deviations from the mean are 96.00% of the data for every normally distributed population.

<h3>Solving the question</h3>

Having all this information at hand, we know that the z-score value tells us how many standard deviations from the mean are the data normally distributed. As a result, we can determine how many standard deviations below and above the population mean represent the 96.00% of the cases for this normal distribution consulting a cumulative standard normal table from the mean.

If we divide 96.00/2 = 48, that is, 0.48, we need to find the z-score for this probability consulting a cumulative standard normal table from the mean. The values for a z-score for that probability is z=2.05, approximately. So, since the normal distribution is also symmetrical, those values are above and below the mean, that is, z =2.05 (above) and z=-2.05(below).

Thus, 96% of the data in any data set normally distributed is 2.05 standard deviations above and below the mean.

5 0

3 years ago

Evaluate 10m+n/4 wnen m=5 and n=16

solmaris [256]

Hi!

Let's put the values in the equation.

10 · 5 + 16 ÷ 4 = ?

Using PEMDAS...

Multiplication
50 + 16 ÷ 4 = ?

Division
50 + 4 = ?

Addition
54

The answer is 54

Hope this helps! :)

4 0

3 years ago

Read 2 more answers