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3 years ago

What is the answer to this in standard form y+4=2/3(x+7)

Mathematics

1 answer:

Mnenie [13.5K]3 years ago

3 0

Y=2/3x+2/3

I hope this helps!

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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: <em>set theory divibilility divisible integers union intersection</em>

3 0

3 years ago

Mark is building a custom wooden frame around his flower bed. The length of the frame is 5.45 feet ,and the width of the frame i

LUCKY_DIMON [66]

Answer:

17.84875

Step-by-step explanation:

5.45 x 3.275 = 17.84875

8 0

3 years ago

What equation can I use to get 6 with the numbers 9,2,10,7,6

alekssr [168]

Answer:

10+2-6=6

Step-by-step explanation:

If you don’t need to use all the numbers,

10+2-6=6

7 0

3 years ago

A passenger rode the subway 2 blocks west and then 10 south. If all the blocks are the same length what is the value of the slop

Nimfa-mama [501]

Answer:

The slope of the line is 5

Step-by-step explanation:

Great question, it is always good to ask away and get rid of any doubts that you may be having.

I have created an illustration which is attached below in order to help you understand the situation. As we are told the passenger rode the subway from point (0 , 0) to point (-2, 0). Then he rode the subway from point (-2, 0) to the final destination of point (-2 , -10). In order to find the value of the slope we need to use the slope formula which is

$Slope = \frac{y_{2}-y_{1} }{x_{2}- x_{1} }$

Now we just plug in the values of the starting point and final destination in order to find the slope of the line.

$Slope = \frac{(-10) - (0)}{(-2)-(0)}$

$Slope = \frac{-10}{-2}$

$Slope =5$

Finally we can see that the slope of the line is 5

I hope this answered your question. If you have any more questions feel free to ask away at Brainly.

6 0

2 years ago

7. Which of these polynomial functions gives the number of lights in a hexagonal rig (six sides) with n rows? (Hint: Look for a

morpeh [17]

Thank you for posting your question here at brainly. I hope the answer will help you. Feel free to ask more questions.
Below are the answers:

<span>7. C. H(n) = ½n^2 + n + 1
</span>8. D. As the number of rows increases, the hexagonal rig gets closer to having twice as many lights as the square rig.

3 0

3 years ago