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3 years ago

Multiply (sqrt 10 + 2 sqrt 8) (sqrt 10 -2 sqrt 8)

Mathematics

2 answers:

sveta [45]3 years ago

8 0

$(\sqrt{10} + 2\sqrt{8})(\sqrt{10} - 2\sqrt{8}) = -22$

Solution:

Given that we have to multiply the given expression

Given is:

$(\sqrt{10} + 2\sqrt{8})(\sqrt{10} - 2\sqrt{8})$

We have to multiply the above expression

Apply the difference of two squares formula

$(a+b)(a-b) = a^2-b^2$

Similarly for,

$(\sqrt{10} + 2\sqrt{8})(\sqrt{10} - 2\sqrt{8})$

We have,

$a = \sqrt{10}\\\\b = 2\sqrt{8}$

Thus the equation becomes,

$(\sqrt{10} + 2\sqrt{8})(\sqrt{10} - 2\sqrt{8}) = (\sqrt{10})^2 - (2\sqrt{8})^2\\\\Simplify\\\\(\sqrt{10} + 2\sqrt{8})(\sqrt{10} - 2\sqrt{8}) =(\sqrt{10} \times \sqrt{10}) - (2\sqrt{8} \times 2\sqrt{8})$

Use the below rule,

$\sqrt{a} \times \sqrt{a} = a$

Therefore, the above equation becomes,

$(\sqrt{10} + 2\sqrt{8})(\sqrt{10} - 2\sqrt{8}) =10 - 4 \times 8\\\\(\sqrt{10} + 2\sqrt{8})(\sqrt{10} - 2\sqrt{8}) = 10 - 32\\\\(\sqrt{10} + 2\sqrt{8})(\sqrt{10} - 2\sqrt{8}) =-22$

Thus upon multiplying the given expression, solution is -22

sergiy2304 [10]3 years ago

5 0

Answer:

-22

Step-by-step explanation:

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Point K is on line JL. given JL =4x, JK= 2x+3, and KL=x, determine the numerical length of kl

balandron [24]

Hi! I'm happy to help!

Our total line is JL (4x), and it is split into two parts: JK, and KL. We have our values, and we know that JK+KL=JL, so we can substitute our values and solve for x:

4x=(2x+3)+(x)

4x=3x+3

To solve for x, we have to isolate it on one side of the equation.

First, let's subtract 3x from both sides so that we can isolate x:

4x=3x+3

-3x -3x

x=3

So, our x=3, which means that KL=3.

I hope this was helpful, keep learning! :D

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3 years ago

An advertising company is designing a new logo that consists of a shaded triangle inside a parallelogram.What is the area, in sq

tatyana61 [14]

<h2>Explanation:</h2><h2 />

The complete question is shown in the figure below. As you can see one square units is well shown in the graph. So we can conclude that the distance between two consecutive points is 1 unit. If so, then we can calculate the area of the parallelogram as follows:

$A=b\times h \\ \\ A:Area \\ \\ b:Base \\ \\ h:Height \\ \\ \\ CB=b \\ \\ AB=h$

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3 years ago

Find the value of k such that lim-->4 (x^2+x-k)/(x-4) exists

7nadin3 [17]

Answer:

k=20

Step-by-step explanation:

when x approaches 4, the denominator x-4 approaches 0

if the denominator is 0, it means that this is invalid

if the function is a number over 0 when x=4, it represents a vertical asymptote, which means no limit

so the only way possible to let there be a limit is to let the function be 0/0 when we plug in x=4

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3 years ago

Richard has just been given an l0-question multiple-choice quiz in his history class. Each question has five answers, of which o

myrzilka [38]

Answer:

a) 0.0000001024 probability that he will answer all questions correctly.

b) 0.1074 = 10.74% probability that he will answer all questions incorrectly

c) 0.8926 = 89.26% probability that he will answer at least one of the questions correctly.

d) 0.0328 = 3.28% probability that Richard will answer at least half the questions correctly

Step-by-step explanation:

For each question, there are only two possible outcomes. Either he answers it correctly, or he does not. The probability of answering a question correctly is independent of any other question. This means that we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

Each question has five answers, of which only one is correct

This means that the probability of correctly answering a question guessing is $p = \frac{1}{5} = 0.2$

10 questions.

This means that $n = 10$

A) What is the probability that he will answer all questions correctly?

This is $P(X = 10)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 10) = C_{10,10}.(0.2)^{10}.(0.8)^{0} = 0.0000001024$

0.0000001024 probability that he will answer all questions correctly.

B) What is the probability that he will answer all questions incorrectly?

None correctly, so $P(X = 0)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{10,0}.(0.2)^{0}.(0.8)^{10} = 0.1074$

0.1074 = 10.74% probability that he will answer all questions incorrectly

C) What is the probability that he will answer at least one of the questions correctly?

This is

$P(X \geq 1) = 1 - P(X = 0)$

Since $P(X = 0) = 0.1074$ , from item b.

$P(X \geq 1) = 1 - 0.1074 = 0.8926$

0.8926 = 89.26% probability that he will answer at least one of the questions correctly.

D) What is the probability that Richard will answer at least half the questions correctly?

This is

$P(X \geq 5) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)$

In which

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 5) = C_{10,5}.(0.2)^{5}.(0.8)^{5} = 0.0264$

$P(X = 6) = C_{10,6}.(0.2)^{6}.(0.8)^{4} = 0.0055$

$P(X = 7) = C_{10,7}.(0.2)^{7}.(0.8)^{3} = 0.0008$

$P(X = 8) = C_{10,8}.(0.2)^{8}.(0.8)^{2} = 0.0001$

$P(X = 9) = C_{10,9}.(0.2)^{9}.(0.8)^{1} \approx 0$

$P(X = 10) = C_{10,10}.(0.2)^{10}.(0.8)^{0} \approx 0$

$P(X \geq 5) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) = 0.0264 + 0.0055 + 0.0008 + 0.0001 + 0 + 0 = 0.0328$

0.0328 = 3.28% probability that Richard will answer at least half the questions correctly

8 0

3 years ago

I just need to make sure my answer is correct :)

vampirchik [111]

Answer:

Its positive

Step-by-step explanation:

3x - 5 = -3

3x = 2

x = 2/3

2/3 is positive

5 0

3 years ago