MATHEMATICS HIGH SCHOOL

All of the following numbers are composite numbers except:

15
17
18
14

Answers

Answer 1

Answer: 15, 18 and 14 are composite except 17 which is prime

Answer 2

Answer:

your answer is B=17

hope I helped you

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The number( √5 +2)(√5 - 2) is a. an irrational number b. a rational number c. not a natural number d. none of these

Answers

Answer:

The number (√5 + 2)(√5 - 2) can be simplified using the difference of squares formula, which states that (a + b)(a - b) = a² - b². In this case:

(√5 + 2)(√5 - 2) = (√5)² - 2² = 5 - 4 = 1

So, the number (√5 + 2)(√5 - 2) is equal to 1, which is a rational number because it can be expressed as a ratio of two integers (1/1). Therefore, the correct answer is:

b. a rational number

Final answer:

The expression ( √5 +2)(√5 - 2) can be simplified using the difference of squares formula. The result is a rationalnumber, making option b. a rational number the correct answer.

Explanation:

The expression ( √5 +2)(√5 - 2) can be simplified using the difference of squares formula. The difference of squares formula states that a^2 - b^2 = (a + b)(a - b). In this case, a = √5 and b = 2. Plugging these values into the formula, we have (√5)^2 - 2^2 = ( √5 +2)(√5 - 2) = 5 - 4 = 1.

Since 1 is a rational number (it can be expressed as a fraction), the correct answer is b. a rational number.

Learn more about Simplifying algebraic expressions here:

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Decrease from 126 ounces to 48 ounces percent

Answers

Answer: There is 61.9% decrease in the value from 126 ounces to 48 ounces.

Step-by-step explanation:

Original value=126 ounces

New value = 48 ounces

Difference = 126-48 = 78 ounces

So, Percentage of decrease value is given by

$(Difference)/(Original)* 100\n\n=(78)/(126)* 100\n\n=61.9\%$

So , there is 61.9% decrease in the value from 126 ounces to 48 ounces.

Answer:

Decrease in percentage = 61.9%

Step-by-step explanation:

Decrease from 126 ounces to 48 ounces percent

First find out the amount of decrease. Subtract the number to find the amount of decrease

$126-48=78$

now find out which percentage is 78

percentage = $(78)/(126) \cdot 100=61.9$

Decrease in percentage = 61.9%

Evaluate $\rm (3^2+1)/(3^2-1)+(5^2+1)/(5^2-1)+(7^2+1)/(7^2-1)+\ldots+(101^2+1)/(101^2-1) =$
With step by step explanation !

Answers

It's easier to deal with the symbolic sum (in sigma notation),

$\displaystyle\sum_(k=1)^(50)((2k+1)^2+1)/((2k+1)^2-1)$

Expanding the terms in the fraction, computing the quotient, and decomposing into partial fractions gives

$((2k+1)^2+1)/((2k+1)^2-1) = (4k^2 + 4k + 2)/(4k^2 + 4k)$

$=\frac12*(2k^2 + 2k + 1)/(k^2 + k)$

$=\frac12\left(2+\frac1{k(k+1)}\right)$

$=\frac12\left(2 + \frac1k - \frac1{k+1}\right)$

and it's the latter two terms that reveal a telescoping pattern.

In case you need more details about the partial fraction decomposition, we are looking for coefficients a and b such that

$\frac1{k(k+1)}=\frac ak+\frac b{k+1}$

$1 = a(k+1) +bk =(a+b)k+a$

which gives a = 1, and a + b = 0 so that b = -1.

Our sum has been rearranged as

$\displaystyle\frac12\sum_(k=1)^(50)\left(2+\frac1k-\frac1{k+1}\right)=\sum_(k=1)^(50)1+\frac12\sum_(k=1)^(50)\left(\frac1k-\frac1{k+1}\right)=50+\frac12\sum_(k=1)^(50)\left(\frac1k-\frac1{k+1}\right)$

The remaining telescoping sum is

1/2 [(1/1 - 1/2) + (1/2- 1/3) + (1/3- 1/4) + … + (1/48- 1/49) + (1/49- 1/50) + (1/50 - 1/51)]

and you can see how there are pairs of numbers that cancel, so that the sum reduces to

1/2 [1/1 - 1/51] = 1/2 [1 - 1/51] = 1/2 × 50/51 = 25/51

So, our original sum ends up being

$\displaystyle\sum_(k=1)^(50)((2k+1)^2+1)/((2k+1)^2-1) = 50 + (25)/(51) = \boxed{(2575)/(51)}$

Solve the equation for the indicated variable
x - 3y for y

Answers

Answer:y=x/3

Step-by-step explanation:

x-3y=0

or,x=3y

y=x/3

Which mistake did Columbus make in the expedition that led him to the Americas? A.
He miscalculated the size of the earth and thought he had reached Asia.

B.
He thought the language of the people he met was Chinese and didn't realize he was in the Americas.

C.
He did not bring enough supplies, so he had to stop in the Americas instead of going all the way to Asia.

D.
He did not realize how bad storms could be and got so far off course that he reached the Americas instead of Asia.

Answers

The real answer is either A. Or from what I've been taught, Columbus thought that he could sail around the world to reach to India and did NOT know there were other lands. And he landed in America and he thought it was India.

Can someone please help me ASAP?

I will give brainliest if it’s correct