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Aleksandr-060686 [28]
3 years ago
9

What is the domain, range, and function of y=absolute value of x-3 +2

Mathematics
1 answer:
olga55 [171]3 years ago
5 0
y=|x-3|+2\\\\Domain:x\in\mathbb{R}\\\\Range:y\in[2;\ \infty)\ because\ |x-3|\geq0\ and\ +2

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Let n be the smallest positive integer that is a multiple of 75 and has exactly 75 positive integral divisors, including itself
Juli2301 [7.4K]

Answer:

n=2^4 3^4 5^2 =32400 and then we have:

\frac{n}{75}=\frac{2^4 3^4 5^2}{3 5^2}=432

Step-by-step explanation:

From the info given by the problem we need an integer defined as the smallest positive integer that is a multiple of 75 and have 75 positive integral divisors, and we are assuming that 1 is one possible divisor.

Th first step is find the prime factorization for the number 75 and we see that

75=3 5^2

And we know that 3 =2+1 and 5=3+2 and if we replace we got:

75 = (2+1)(4+1)^2 = (2+1)(4+1)(4+1)

And in order to find 75 integral divisors we need to satisify this condition:

n= a^{r_1 -1}_1 a^{r_2 -1}_2 *...... such that a_1 *a_2*....=75

For this case we have two prime factors important 3 and 5. And if we want to minimize n we can use a prime factor like 2. The least common denominator between 2 and 4 is LCM(2,4) =4. So then the need to have the prime factors 2 and 3 elevated at 4 in order to satisfy the condition required, and since 5 is the highest value we need to put the same exponent.

And then the value for n would be given by:

n=2^4 3^4 5^2 =32400 and then we have:

\frac{n}{75}=\frac{2^4 3^4 5^2}{3 5^2}=432

8 0
3 years ago
Express the sum in the simplest form.
olga nikolaevna [1]
The answer would be the third one because you cannot change the denominator and you can only add the numerators
5 0
3 years ago
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Write an expression to represent: 3 minus the quotient of x and 4
alisha [4.7K]

The expression representing the sentence is $3 -\frac{x}{4}.

We have a sentence - "3 minus the quotient of x and 4".

We have to determine the expression that represents the sentence.

<h3>Express the statement - "The difference of x and y is equal to an irrational number" in the form of expression.</h3>

The expression representing the above statement is -

x - y = π.

According to the question, we have -

3 minus the quotient of x and 4.

Using the Division Algorithm -

x = 4q + r

Substituting r = 0 by introducing decimals in the quotient, we get -

q = $\frac{x}{4}

Therefore -

$3 -\frac{x}{4}

Hence, the expression representing the sentence is $3 -\frac{x}{4}.

To solve more questions on Expression modelling, visit the link below-

brainly.com/question/20876878

#SPJ2

8 0
1 year ago
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What type of word a relationship does this analogy show
Trava [24]

Answer:

part/whole

Step-by-step explanation:

jazz is only a part of music, music is the whole thing and also lave tube would be a part of a bigger thing which is the cave

7 0
3 years ago
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What is the slope of the table x= 2, 0, -2, -4 y= 6, 1, -4, -9
Murrr4er [49]

Answer:

The slope of the table is m=\frac{5}{2}   or  m=2.5

Step-by-step explanation:

we know that

The formula to calculate the slope between two points is equal to

m=\frac{y2-y1}{x2-x1}

we have the following ordered pairs

(2,6),(0,1),(-2,-4) and (-4,-9)

take two points

(2,6) and (-4,-9)

substitute in the formula

m=\frac{-9-6}{-4-2}

m=\frac{-15}{-6}

simplify

m=\frac{5}{2}

6 0
3 years ago
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