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3 years ago

Which of the following is an example of the difference of two squares

Mathematics

1 answer:

True [87]3 years ago

8 0

Complete Question: Which of the following is an example of the difference of two squares?

A x² − 9

B x³ − 9

C (x + 9)²

D (x − 9)²

Answer:

A. $x^2 - 9$ .

Step-by-step explanation:

An easy way to spot an expression that is a difference of two squares is to note that the first term and the second term in the expression are both perfect squares. Both terms usually have the negative sign between them.

Thus, difference of two squares takes the following form: $a^2 - b^2 = (a + b)(a - b)$ .

a² and b² are perfect squares. Expanding $(a + b)(a - b)$ will give us $a^2 - b^2$ .

Therefore, an example of the difference of two squares, from the given options, is $x^2 - 9$ .

$x^2 - 9$ can be factorised as $x^2 - 3^2 = (x + 3)(x - 3)$ .

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if a cylinder has a volume of 75 cubic inches, what would be the volume of a cone with the same base and height? Explain

kumpel [21]

25 cubic inches because you know that every cone is a third of the volume of the cylinder with which it shares a height and base with.

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3 years ago

The length of a rectangle is 3 inches more than the width. The area is 10 square inches. Find the dimensions

mr_godi [17]

Answer:

Width = 2

Length = 5

Step-by-step explanation:

let A be the area of the rectangle

L be the length of the rectangle

w be the width of the rectangle

Formula: ‘area of a rectangle’

A = L × w

…………………………………………………

A = L × w

⇔ 10 = (w + 3) × w

⇔ 10 = w² + 3w

⇔ w² + 3w - 10 = 0

Solving the quadratic equation w² + 3w - 10 = 0 :

Δ = 3² - 4(1)(-10) = 9 - (-40) = 9 + 40 = 49

then √Δ = 7

$\Longrightarrow w=\frac{-b+\sqrt{\Delta } }{2a} =\frac{-3+7}{2} =2$

$or\ w=\frac{-b-\sqrt{\Delta } }{2a} =\frac{-3-7}{2} =-5$

-5 is not valid ,because w represents the width

which must be a positive number

Then w = 2

Conclusion:

Width = 2

Length = 2 + 3 = 5

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2 years ago

A study claims that the combination of vitamin C with vitamin E is more effective for preventing the flu than vitamin C alone. I

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1) In this study, the control group is the first group of 310 subjects that were instructed to take only 600 mg daily of vitamin C. (Option C; that is, group 1).

2) The study is not Blind (Option C).

In an experimental setup to test a theory, A control group is the set of experimental participants that the theory to be tested isn't applied upon.

In the case of testing a new treatment, the control group is the group that the new treatment isn't administered.

For this question, the experiment was set up to test the effectiveness of a combination of vitamin A and vitamin E in treating flu cases rather than using vitamin C alone. Group A is the only group that only the old treatment alone is applied to; group 1 participants received no dosage of the new combination of treatments to be tested involving vitamins A and E, unlike the two other groups.

It is obvious now why the experimental participants of group 1 are the control group.

2) A blind experiment/study is one in which the participants don't know which group they belong to, whether they are in the control group or the other experimental group. Like in this case, if this was a blind study, the participants wouldn't know which group they belonged to or which treatment is administered to them.

A double-blind experiment/study is one in which both the conductors of the experiment and the participants in the experiment wouldn't know which group any participant is in. The conductors wouldn't know which participants were in the control or treatment group and the participants too wouldn't have an idea whether they are in the control or treatment group.

To learn more about the vitamin visit: brainly.com/question/24324739

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Naomi earned $840 for working 40 hours last week. How much will she get paid this week if she only works 30 hours assuming she g

zloy xaker [14]

Answer:

Naomi will get paid $630 if she only works 30 hours this week.

Step-by-step explanation:

You divide 840 by 40 to see how much you get paid per hour.

Once you do that you get $21 per hour.

You multiply 21 by 30 to know how much you'd be paid for working 30 hours.

You get your final answer which is $630.

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