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3 years ago

Which of the following are identities?

Mathematics

2 answers:

podryga [215]3 years ago

6 0

Answer:

A. III only

Step-by-step explanation:

In mathematics, an identity is one of the characteristics of algebraic expressions.

Given variable a and b in an algebraic expression, an identity is defined as an equality that remains the same no matter the values that we choose for either variable a or b.

Identity in mathematics makes it very easy to solve algebraic expressions. The two sides of an identity in an algebra can easily be exchanged for each other.

In the above question, we are given 3 Options.

I) 3(5 + 2x) = 15 + 6x

II) y = x + 3

III) (x² - y²) = (x + y) (x - y)

Option I) 3(5 + 2x) = 15 + 6x

Is showing distributive property in mathematics.

Distributive property is :

a(b + c) = ab + ac

Option I is not an identity , therefore it is wrong.

Option II) y = x + 3 is just an algebraic expression.

Only Option III is an identity. This is because it follows the rule of

(a² - b²) = (a + b) (a - b)

We can prove and confirm this be solving the algebraic expression

(x + y) (x - y)

We expand the bracket

x² - xy +xy - y²

x² - y²

Therefore, option A is the correct option.

HACTEHA [7]3 years ago

6 0

Answer:

the answer is A

Step-by-step explanation:

try using math_way for help :)

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| 2p -1 | =45, what are the values of p?

Alex73 [517]

Answer:

p = 23 and p = -22

Step-by-step explanation:

| 2p -1 | =45

Absolute value equations have 2 solutions, one positive value and one negative

2p-1 = 45 and 2p-1 = -45

Add 1 to all sides

2p-1+1 = 45+1 and 2p-1+1 = -45+1

2p = 46 2p = -44

Divide by 2

2p/2 = 46/2 and 2p/2 = -44/2

p = 23 and p = -22

5 0

3 years ago

Read 2 more answers

A fast food restaurant executive wishes to know how many fast food meals adults eat each week. They want to construct a 98% conf

adelina 88 [10]

Answer:

$n=(\frac{2.326(1.1)}{0.07})^2 =1336.006 \approx 1337$

So the answer for this case would be n=1337 rounded up to the nearest integer

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

$\sigma=1.1$ represent the population standard deviation

n represent the sample size

Solution to the problem

The margin of error is given by this formula:

$ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (a)

And on this case we have that ME =0.07 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=(\frac{z_{\alpha/2} \sigma}{ME})^2$ (b)

The critical value for 98% of confidence interval now can be founded using the normal distribution. And in excel we can use this formula to find it:"=-NORM.INV(0.01;0;1)", and we got $z_{\alpha/2}=2.326$ , replacing into formula (b) we got:

$n=(\frac{2.326(1.1)}{0.07})^2 =1336.006 \approx 1337$

So the answer for this case would be n=1337 rounded up to the nearest integer

3 0

3 years ago

What is 3 5/8 + 6 1/2<br>

son4ous [18]

Answer:42

Because 5 Plus 8 is 13 plus 3 equals 16

3 0

3 years ago

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Julio works at an electronics store where he earns $11 an hour. Last week, he received a $120 bonus. How many hours did he work

ahrayia [7]

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3 years ago

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Sarita is selling lemonade in 400 milliliter bottles she made two batches of lemonade each batch made 16.3 liters of lemonade ho

Mrac [35]

Answer: She will have 200 milliliters of lemonade left after filling the bottles.

Step-by-step explanation:

Hi, since 1 liter = 1000 milliliters

For 16.3 liters: 16.3 x 1000 = 16,300 milliliters (1 batch)

She made 2 batches.

16,300ml x2 = 36,600 milliliters

We have the total amount of lemonade in two batches; we have to divide it by the capacity of each bottle (400 ml), to calculate how many bottles she can fill.

36,600 milliliters / 400 milliliters = 81.5 bottles

She can fill 81 bottles and she will have a leftover of half a bottle.

Since each bottle is 400 milliliters, half of it:

400/2 = 200 milliliters

She will have 200 milliliters of lemonade left after filling the bottles.

4 0

3 years ago