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elena-14-01-66 [18.8K]
3 years ago
10

Determine whether the polynomial is a difference of squares and if it is, factor it.

Mathematics
1 answer:
ladessa [460]3 years ago
5 0

Answer:

(y - 4)(y + 4)

Step-by-step explanation:

y² - 16 ← is a difference of squares

Since y² and 16 are both squares separated by a difference , that is minus

A difference of squares factors as

y² - 16

= y² - 4²

= (y - 4)(y + 4)

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8x-3=3x+17<br> Solve for x
Olin [163]

Answer:

x = 4

Step-by-step explanation:

3 0
3 years ago
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Solve for x if the Perimeter = 26<br> 14-2x<br> 2x + 1<br> 3x - 1
sergejj [24]

Answer:

x = 4

Step-by-step explanation:

<em>Perimeter of triangle = sum of all sides</em>

Side 1: 14 - 2x

Side 2: 3x - 1

Side 3: 2x + 1

<em>Perimeter= side 1 + side 2 + side 3</em>

26 = 14 - 2x + 3x - 1 + 2x + 1

26 = 14 - 1 + 1 - 2x + 3x + 2x

26 = 14 + 3x

3x = 12

x = 12/3

x = 4

!!

3 0
3 years ago
Question is in screenshot. Please answer it correctly
fomenos

a) You need to sell 12 or 29 dresses.

b) Any number between 2 and 39 dresses will give a positive profit.

<h3>How many dresses must be sold in order to make a profit of 3000 euros?</h3>

Here we know that the profit, in euros, as a function of the number of dresses sold is:

P(x) = -11*x^2 + 450*x - 800

Now, if you want to find how many dresses you need to sell to have a profit of 3000 euros, then you need to solve:

P(x) = 3000 = -11*x^2 + 450*x - 800

So we need to solve the quadratic equation:

-11x^2 + 450x - 800 - 3000 = 0

-11x^2 + 450x - 3800 = 0

The solutions are given by Bhaskara's formula:

x = (-450 ± √(450^2 - 4*(-3800)*(-11))/2*(-11)

x = (-450 ± 187.9)/(-22)

We have two solutions that give the same profit:

  • x = (-450 + 187.9)/-22 = 11.9 that can be rounded to 12.
  • x = (-450 - 187.9)/-22 = 28.99 that can be rounded 29.

Then if you sell either 12 or 29 dresses, you will get a profit of 3000 euros.

b) To make a profit you need to sell more than P = 0, so let's solve that first:

P= 0 = -11*x^2 + 450*x - 800

The solutions are:

x = (-450  ± √(450^2 - 4*(-800)*(-11))/2*(-11)

x = (-450  ± 409)/(-22)

The smaller solution is:

x = (-450 + 409)/-22 = 1.86 that can be rounded to 2.

(because you can't sell 1.86 of a dress)

The other solution is:

x =  (-450 - 409)/-22 = 39

So, between 2 and 39 dresses, you will make a profit.

If you want to learn more about quadratic equations:

brainly.com/question/1214333

#SPJ1

6 0
1 year ago
A. After Lou poured 2 liters of water into a large jug, the jug
Finger [1]

Answer:

8 liters

Step-by-step explanation:

If the sum of 2 + x = 10,

then you subtract 10 - 2 = x,

to get x = 8

4 0
3 years ago
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You're a quality control manager in a fruit juice company. You want to choose
alekssr [168]

Answer:

246.

Step-by-step explanation:

a) The 95% confidence level two-tail confidence interval for the mean value of the key index of this batch is between 98.22 and 99.78

b) The minimum sample size to achieve this is 246.

Step-by-step explanation:

We have that to find our  level, that is the subtraction of 1 by the confidence interval divided by 2. So:

Now, we have to find z in the Ztable as such z has a pvalue of .

So it is z with a pvalue of , so  

Now, find the margin of error M as such

In which  is the standard deviation of the population(square root of the variance) and n is the size of the sample. So in this question,  

The lower end of the interval is the sample mean subtracted by M. So it is 99 - 0.78 = 98.22

The upper end of the interval is the sample mean added to M. So it is 99 + 0.78 = 99.78.

a) The 95% confidence level two-tail confidence interval for the mean value of the key index of this batch is between 98.22 and 99.78

(b) (5 points) If we want the sampling error to be no greater than 0.5, what is the minimum sample size to achieve this based on the same confidence level with part (a)

We need a sample size of n

n is found when  

Then

Rounding up

The minimum sample size to achieve this is 246.

7 0
3 years ago
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