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3 years ago

I need help with this!

Mathematics

1 answer:

Viefleur [7K]3 years ago

4 0

Answer:

the answer is option E.

Step-by-step explanation:

it is in the form f/g (x).

we know f and g from the equation;

we can rewrite it as, (√(9-x^2)/(3x-1))

if you notice you cannot put any number less than -3 or greater than 3 in the numeror because if you do you get a negative root which is false. for instance if you put 4 or -4 in the numerator you get 9 - (4 or -4 square ) which is 9- 16 which is a negative number and you cannot take root of a negative number.

on the numerator if you put 1/3 as the value for x you will get zero in the denominator. and any number divided by zero is undefined so that cannot be.

this means that option E is the right one that satisfies the condition. it means the domain is [-3, 1/3) U (1/3, 3] .

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How many integers in the set {n ∈ Z | 1 ≤ n ≤ 700} are divisible by 2 or 7?

sukhopar [10]

$\large\begin{array}{l}\\\\ \textsf{This question gives us a set}\\\\ \mathsf{S=\{n \in\mathbb{Z}:~1\le n\le 700\}}\\\\ \mathsf{S=\{1,\,2,\,3,\,\ldots,\,699,\,700\}}\\\\\\ \bullet~~\textsf{Set of integers that are divible by 2 (even integers):}\\\\ \mathsf{A=\{n\in \mathbb{Z}:~n=2k,\,k\in\mathbb{Z}\}}\\\\ \mathsf{A=\{\ldots,\,-4,\,-2,\,0,\,2,\,4,\,\ldots\}}\\\\\\ \bullet~~\textsf{Set of integers that are divible by 7:}\\\\ \mathsf{B=\{n\in \mathbb{Z}:~n=7k,\,k\in\mathbb{Z}\}}\\\\ \mathsf{A=\{\ldots,\,-14,\,-7,\,0,\,7,\,14,\,\ldots\}} \end{array}$

___________

$\large\begin{array}{l}\\\\ \textsf{We want to know how many elements there are in the}\\\textsf{following set:}\\\\ \mathsf{S\cap (A\cup B)=(S\cap A)\cup(S\cap B)\qquad(i)} \end{array}$

____________

$\large\begin{array}{l}\\\\ \bullet~~\mathsf{S\cap A=\{n\in\mathbb{N}:~n=2k~~and~~1\le n\le 700,\,k\in\mathbb{Z}\}}\\\\ \mathsf{S\cap A=\{2,\,4,\,6,\,\ldots,\,698,\,700\}}\\\\ \mathsf{S\cap A=\{1\cdot 2,\,2\cdot 2,\,3\cdot 2,\,\ldots,\,349\cdot 2,\,350\cdot 2\}}\\\\\\ \textsf{So, there are 350 elements in }\mathsf{S\cap A:}\\\\ \mathsf{\#(S\cap A)=350.} \\\\\\ \bullet~~\mathsf{S\cap B=\{n\in\mathbb{N}:~n=7k~~and~~1\le n\le 700,\,k\in\mathbb{Z}\}}\\\\ \mathsf{S\cap B=\{7,\,14,\,21,\,\ldots,\,693,\,700\}}\\\\ \mathsf{S\cap B=\{1\cdot 7,\,2\cdot 7,\,3\cdot 7,\,\ldots,\,99\cdot 7,\,100\cdot 7\}} \\\\\\ \textsf{So, there are 100 elements in }\mathsf{S\cap B:}\\\\ \mathsf{\#(S\cap B)=100.} \end{array}$

____________

$\large\begin{array}{l}\\\\ \textsf{Therefore,}\\\\ \mathsf{\#\big[S\cap (A\cup B)\big]}\\\\ =\mathsf{\#\big[(S\cap A)\cup(S\cap B)\big]}\\\\ =\mathsf{\#(S\cap A)+\#(S\cap B)-\#\big[(S\cap A)\cap(S\cap B)\big]}\\\\ =\mathsf{350+100-50}\\\\ =\mathsf{450-50}\\\\ =\mathsf{400~elements.}\\\\\\ \textsf{There are 400 integers in S that are divisible by 2 or 7.} \end{array}$

If you're having problems understanding the answer, try to see it through your browser: brainly.com/question/2105863

$\large\begin{array}{l}\\\\ \textsf{Any doubts? Please, comment below.}\\\\\\ \textsf{Best wishes! :-)} \end{array}$

Tags: set theory divibilility divisible integers union intersection

3 0

3 years ago

5 is equal to what fraction?

KiRa [710]

5 equals 5/1. Simple as that.

8 0

3 years ago

Which equation results from adding the equations in this system?

Diano4ka-milaya [45]

Answer:

D. - 5x = - 10

Step-by-step explanation:

Given equations:

-8x+8y = 8
3x-8y=-18

Add together:

-8x + 8y + 3x - 8y = 8 - 18
- 5x = - 10

Correct option is D

7 0

3 years ago

Dustin bought a $2000 computer with a credit card.The minimum payment each month is $35.Each month 1% of the unpaid balance is a

yuradex [85]

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4 0

3 years ago

Read 2 more answers

A random sample of 12 men age 60-65 has a mean blood pressure of 142. 3 mmHg and a standard deviation of 20.8 mmHg. Construct a

Over [174]

Answer:

The 99% confidence interval = (126.93,157.67)

Step-by-step explanation:

The formula for Confidence Interval =

Mean ± z × Standard deviation /√n

Mean = 142. 3 mmHg

Standard deviation = 20.8 mmHg.

n = 12

Z score for 99% confidence interval = 2.56

Confidence Interval =

142.3 ± 2.56 × 20.8/√12

142.3 ± 2.56 × 6.0044427996

142.3 ± 15.371373567

Confidence Interval

= 142.3 - 15.371373567

= 126.92862643

≈ 126.93

142.3 + 15.371373567

= 157.67137357

≈ 157.67

Therefore, the 99% confidence interval = (126.93,157.67)

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3 years ago