Are the rational numbers closed under multiplication?

Answers

Answer 1

Answer:

Answer:

Yes, The rational numbers are closed under multiplication.

Step-by-step explanation:

A rational number is a number which can be expressed in the form of a fraction $(x)/(y)$ , where x and y are integers and y ≠ 0.

Now, closure property of multiplication states that if two rational numbers are multiplied then the product is also a rational number. Thus, if r and t are rational numbers, then

r×t = s, where s is the product of r and t

s is also a rational number.

Hence, the rational numbers are closed under multiplication.

This can be better explained with the help of an example $(3)/(4) * (2)/(5) = (6)/(20)$ ,

It is clear that $(6)/(20)$ is a rational number.

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Solve for x Write both solutions, seperated by a comma 4x^2+5x+1=0

Answers

Answer:

-1/4 , -1

Step-by-step explanation:

I solved it using Factorization method and Quadratic Equation .

Factorization Method

$4x^2+5x+1=0\nWrite +5x- as- a -difference(write+5x-using- two- numbers -in-which-their-sum-is ; 5-and-their-product-is ; 4)\n4x^(2) +4x+1x+1=0\nFactorize-out-common-terms\n4x(x+1)+1(x+1)=0\nFactor-out-(x+1)\n(4x+1)(x+1)=0\n4x+1 =0 \nx+1=0\n4x=0-1\nx =0-1\n4x =-1\nx =-1\n4x=-(1)/(4) \n\nAnswer = -1/4 , -1$

Quadratic Equation

$4x^2+5x+1=0\na = 4\nb =5\nc = 1\n\nx =(-b\±√(b^2 -4ac) )/(2a) \n\nx = (-(5)\±√((5)^2-4(4)(1)) )/(2(4)) \n\nx = (-5\±√(25-16) )/(8) \n\nx = (-5\±√(9) )/(8) \n\nx = (-5\±3)/(8) \n\nx =(-5+3)/(8) \n\nx = (-5-3)/(8) \n\nx = (-2)/(8) \n\nx = (-8)/(8) \n\nx = -(1)/(4) \nx=-1$

For the 405 highway that car pass through a checkpoint, assume the speeds are normally distributed such that μ= 61 miles per hour and δ=4 miles per hour. Calculate the Z value for the next car that passes through the checkpoint will be traveling slower than 65 miles per hour.

Answers

Answer:

$Z = 1$

Step-by-step explanation:

Z - score

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = (X - \mu)/(\sigma)$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 61, \sigma = 4$

Calculate the Z value for the next car that passes through the checkpoint will be traveling slower than 65 miles per hour.

This is Z when X = 65. So

$Z = (X - \mu)/(\sigma)$

$Z = (65 - 61)/(4)$

$Z = 1$

Ernie Rolph borrowed $6150 at 10% annual simple interest. If exactly 1 year later he was able to repay the loanwithout penalty, how much interest would he owe?
Ernie will owe $
in interest.

Show work!

Answers

Answer:

615

Step-by-step explanation:

6150 x 10%

6150 x 0.10 = 615

Answer:

615

Step-by-step explanation:

6150 ÷ 100 = 61.5

61.5 X 10 = 615

6150 X 0.1 = 615

Find the measure of angle b

Answers

Answer:

49 degrees

Step-by-step explanation:

You just subtract 41 degrees from 90 degrees because it's a right angle.

According to the Fundamental Theorem of Algebra, how many roots exist for the polynomial function?

Answers

Answer:

Step-by-step explanation:

Plz help i dont understand and if u can help i will mark brainliest!!

Answers

Answer:

Let fertilizer be F

and peat moss be P

since F is proportional to P

F = kP

where, k = constant of proportionality

k = F/P

putting in the values,

k = (3/4) /12

k = 3/4 * 1/12

k = 1/16

Therefore the constant of proportionality is 1/16.

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