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Andrews [41]
3 years ago
11

Suppose x, y and z are integers. Prove that, if 3x−y + 5z is even, then at least one of x, y or z is even.

Mathematics
1 answer:
Elden [556K]3 years ago
4 0

Given:

x, y and z are integers.

To prove:

If 3x-y+5z is even, then at least one of x, y or z is even.

Solution:

We know that,

Product of two odd integers is always odd.          ...(i)

Difference of two odd integers is always even.          ...(ii)

Sum of an even integer and an odd integer is odd.      ...(iii)

Let as assume x, y and z all are odd, then 3x-y+5z is even.

3x is always odd.          [Using (i)]

5z is always odd.          [Using (i)]

3x-y is always even.       [Using (ii)]

(3x-y)+5z is always odd.       [Using (iii)]

3x-y+5z is always odd.

So, out assumption is incorrect.

Thus, at least one of x, y or z is even.

Hence proved.

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The ratio of boys to girls in a sophomore class of 460 students is 11:12. find the number of boys.
lukranit [14]
11 : 12.....11 + 12 = 23

boys : 11/23 * 460 = 5060/23 = 220 <===
girls : 12/23 * 460 = 5520/23 = 240
7 0
3 years ago
What is addition and subtraction
choli [55]

\huge\text{Hey there!}

\huge\textsf{What is addition \& subtraction?}

\huge\textbf{What is addition?}

\bullet\large\textbf{ Well, \underline{addition} simply means when you're ADDING}\\\large\textbf{2 or more numbers from each other to get the result of}\\\large\textbf{a number.}

\huge\textbf{Random notes}

\star\large\textbf{ Usually, you start working with addition when you're in}\\\large\textbf{pre-kindergarten (pre-k also known as head-start)}\\\\\star\large\textbf{ When, you're adding you are going upward.}\\\\\star\large\textbf{ Addition sometimes come after you learn how to count}\\\large\textbf{the basic numbers and so forth because adding never}\\\large\textbf{ends if you really think about.}

\huge\textbf{Example:}

\heartsuit\large\textbf{ 2 \boxed{\bf +} 5 = 7}\\\\\\\heartsuit\large\textbf{ You got the result of 7 because you started at 2 \& went}\\\larg\textbf{up 5 spaces to your right on your number and you landed}\\\large\textbf{on 7.}

\huge\textbf{What is subtraction?}

\bullet\large\textbf{ Well, subtraction simply means you're taking away. Often}\\\large\textbf{people call it take aways.}

\huge\textbf{Random notes:}

\star\large\textbf{ Usually, you start working with subtraction when you're}\\\large\textbf{in pre-kindergarten (pre-k also known as headstart)}\\\\\star\large\textbf{When you're subtracting you are doing downward.}\\\\\star\large\textbf{You focus more on subtraction when you're counting}\\\large\textbf{backwards.}

\huge\textbf{Example:}

\heartsuit\large\textbf{ 7 \boxed{\bf -} 5 = 2 }\\\\\\\heartsuit\large\textbf{ 7 \boxed{\bf -} 2 = 5}\\\\\\\heartsuit\large\textbf{ For equation \#1. you begin at 7 and go BACK 5 spaces}\\\large\textbf{and you should have landed on 2.}\\\\\\\heartsuit\large\textbf{ For equation \#2. you begin at 7 \& go BACK 2 spaces}\\\large\textbf{and you should have landed on 5.}

\huge\textsf{KEEP IN MIND:}

\circ\large\textsf{ Addition OPPOSITE is subtraction \& subtraction OPPOSITE is}\\\large\textsf{addition.}

\huge\text{Good luck on your assignment \& enjoy your day!}

~\frak{Amphitirite1040:)}

4 0
2 years ago
Read 2 more answers
A car traveled 180 miles at a constant rate. Write an equation that would
Mnenie [13.5K]

Answer:

180/t = r

Step-by-step explanation:

In this question, we would have to write an equation that represents the scenario given.

We know that the car traveled 180 miles at a constant rate.

We would use the y = mx + b format for the equation, but replacing the variables with "r" and "t"

We know that 180 will be our y-variable, since that would be the base of the equation:

180 = ???

And to find how long/fast it will take the car, we would need to multiply the rate of speed "r" and time "t" in order to get our distance.

Plug it into the equation:

180 = rt

With this set up, you can find the rate of speed of the car when you know the time.

You would simply solve it as:

180/t = r

7 0
3 years ago
A carpenter purchased 50 ft of redwood and 80 ft of pine for a total cost of $285. A second purchase, at the same prices, includ
Marizza181 [45]

Hey there!!

Let us take the price of the redwood as ' x ' and pine as ' y '

Then , we take it into an equation. We get,

50x + 80y = 285 -------------- ( 1 )

80x + 50y = 339 -------------- ( 2 )

Now, multiply the first equation with 8 and the second equation with 5

400x + 640y = 2280

400x + 250y = 1695

Now subtract the second equation from the first

390y = 585

y = 585 / 390

y = $1.5

Now substitute this into any equation

50x + ( 80 ) ( 1.5 ) = 285

50x + 120 = 285

50x = 165

x = 165 / 50

x = $3.3

Redwood = $3.3

Pine = $1.5

Hope helps!



6 0
3 years ago
Lydia and Claudia have the same number of charms in their collections. Lydia started with 6 charms and bought 3 more packs. Clau
serious [3.7K]

Answer:

E. 3x + 6 = 2x + 9

Step-by-step explanation:

The total number of charms that Lydia has in term of x

6 + 3x

The total number of charms that Claudia has in term of x

9 + 2x

Since they have the same number of charms, we can set these 2 equations above equals to each other

6 + 3x = 9 + 2x

x = 9-6 = 3

So E is the correct answer

7 0
3 years ago
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