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3 years ago

9

Randy buys gas at a store that charges $3 per gallon. Sarah buys gas at a different store. The table shown here gives the cost w

hen she buys 3, 4, and 5 gallons of gas.
Is gas more expensive at Randy’s store or Sarah’s store?

1 answer:

marin [14]3 years ago

5 0

Where is the table??

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(100 Points) What's does X equal in the equation (4 * 2) - 4 = x ?

icang [17]

Answer:

4

Step-by-step explanation:

(4 * 2) - 4 = x

8 - 4 = x

x = 4

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2 years ago

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What are the coordinates of the vertices of the triangle under the translation (x, y) mc011-2.jpg (x + 1, y - 4)?

Dima020 [189]

Original
(-1,1) (-4,1) (-4, 4)

<span> translation (x, y) to (x + 1, y - 4)
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answer
(0, -3), (-3, -3), (-3, 0)

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3 years ago

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

sukhopar [10]

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

___________

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

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

____________

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

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

SportsBounceCo makes only boxes that have sides that are measured in whole inches, like the boxes you have been describing so fa

stepan [7]

Answer:

No

Step-by-step explanation:

Look at the surface area of the box formular : S = 2lw + 2lh + 2wh

When l : length. w: with and h: hight

As we often considered strange, you can always multiply a whole number by a whole number and always get a whole number, and there is no decimal number about the 3 dementions like the boxes you have been describing so far. So It is impossible.

6 0

3 years ago

7 times a number is 8 less than the square of that number. Find the negative solution.

charle [14.2K]

Answer:

-1

Step-by-step explanation:

The required relation is ...

7n = n^2 -8

0 = n^2 -7n -8 . . . . put in standard form

0 = (n -8)(n +1) . . . . factor

Solutions are n=8 and n=-1.

The negative solution is -1.

7 0

2 years ago