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Dvinal [7]
2 years ago
11

True or false. If a is any odd integer, then a^2 + a is even. Explain this.

Mathematics
1 answer:
Ainat [17]2 years ago
7 0

Answer:

True.

Step-by-step explanation:

We can represent an odd number by 2n + 1 where n = 0, 1, 2, 3, 5 etc.

Substituting:

a^2 + a = (2n + 1)^2 + 2n + 1

=  4n^2 + 4n + 1 + 2n + 1

= 4n^2 + 6n + 2

= 2(2n^2 + 3n + 1)

which is even because any integer multiplied by an even number is even.

This is also true if we use a negative odd integer:

We have 4n^2 + 4n + 1  - 1 - 2n

= 4n^2 + 2n

=  2(2n^2 + n(.

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Solve for m pls? I'd seriously appreciate it!
Vilka [71]

Answer:

m=-1

Step-by-step explanation:

Start by multiplying both sides by 2, this will get rid of the fraction on the left side and will result in the equation 12m+6=2m-4

Then, subtract 2m from both sides, which leaves the equation as 10m+6=-4

Then, subtract 6 from both sides, this results with the equation 10m=-10

Finally, divide both sides by 10, this will result in m=-1

3 0
3 years ago
Find x and y. <br><br> pls pls help
Anna [14]

Answer:

x = 65 , y = 64

Step-by-step explanation:

y - 16 and 2y + 4 are same- side interior angles and sum to 180° , that is

y - 16 + 2y + 4 = 180

3y - 12 = 180 ( add 12 to both sides )

3y = 192 ( divide both sides by 3 )

y = 64

then

2y + 4 = 2(64) + 4 = 128 + 4 = 132

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

2y + 4 is an exterior angle of the triangle , then

x + 67 = 132 ( subtract 67 from both sides )

x = 65

7 0
1 year ago
Elvis and $74 .50 a month.. how much does he earn to the nearest one penny.
sdas [7]

Answer:

Part A

12 months a year means

%74.5 x 12 = $894

Part B

4 weeks in a month means

$74.5 ÷ 4 = $18.625

But rounded to the nearest penny. . .

$18.62

because in the thousandths place was a 5 and you round up when there is a 5 or above

Part C

We will go with 31 days in a month, but I will also do 30 for you

$74.5 ÷ 30 = $2.48333

But rounded to the nearest penny. . .

$2.48

because you round down when there is anything less than a 4

$74.5 ÷ 31 = $2.40322580645

But rounded to the nearest penny. . .

$2.40

because you round down when there is anything less than a 4

3 0
3 years ago
An equation is shown below:
lisov135 [29]

Answer: x = 1

Step-by-step explanation:

5 ( 2x - 8 ) + 15 = -15 (write the equation)

5 ( 2x - 8 ) = -30 (subtract by 15 on both sides)

2x - 8 = -6 (divide by 5 on both sides)

2x = 2 (add 8 to both sides)

x = 1 (divide by 2 on both sides)

5 0
2 years ago
Read 2 more answers
The length of the top of a computer desk is 2 1/4 feet longer than it’s width. If it’s width measures y feet, express its length
Lera25 [3.4K]

Answer:

The length as an algebraic expression in y is  y   + (2\frac{1}{4} )  ft

Step-by-step explanation:

The measure of the width of the computer desk = y feet

The measure of the length of the desk = width + 2  1/4 ft

⇒Measure of Length = y   + (2\frac{1}{4} )   ft

Hence, the length as an algebraic expression in y is  y   + (2\frac{1}{4} )   ft

5 0
3 years ago
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