Prove: The square of an even number is even

Answers

Answer 1
Squares of even numbers are even, and are divisible by 4, since (2n)2 = 4n2. Squares of odd numbers are odd, and are congruent to 1 modulo 8, since (2n + 1)2 = 4n(n + 1) + 1, and n(n + 1) is always even.

Related Questions

Use the slope formula to fond the slope of the line that passes through the two points.

(13, -2) and (3, -2)

Answers

Answer:

Step-by-step explanation:

Notice that the y-component is the same, -2, in these two points.  That means y does not change as x changes, and therefore we conclude that the slope of the line connecting the two points is m = rise / run = 0.

                                      -2 - (-2)

Alternatively, use m = -------------- = 0

                                        3 - 13

The value of the slope in question is zero:  m = 0


[tex] \frac{25}{ \sqrt[3]{5} } [/tex]write ^ as a power of 5​

Answers

Answer:

[tex]5^{\frac{5}{3} }[/tex]

Step-by-step explanation:

Using the rules of exponent

[tex]\sqrt[3]{a}[/tex] = [tex]a^{\frac{1}{3} }[/tex]

[tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{(m-n)}[/tex]

[tex]\frac{25}{\sqrt[3]{5} }[/tex]

= [tex]\frac{5^2}{5^{\frac{1}{3} } }[/tex]

= [tex]5^{\frac{6}{3}-\frac{1}{3} }[/tex]

= [tex]5^{\frac{5}{3} }[/tex]

PLEASE HELP.
Directions: find x so that L || M. state the converse used

Answers

Answer:

  8. x=6; supplementary consecutive interior angles

  10. x = 4; no applicable theorem

Step-by-step explanation:

8.

The marked angles are "consecutive interior" angles. When their sum is 180°, the lines l and m will be parallel.

  (7x -15) +(24x +9) = 180

  31x = 186

  x = 6

Consecutive interior angles being supplementary will make the lines parallel.

__

10.

The sum of the remote interior angles of a triangle is equal to the exterior angle:

  28x = 48 +16x

  12x = 48

  x = 4

The above relation holds regardless of whether line l is parallel to line m. There is no applicable theorem or converse.

_____

Additional comment

Adding the marking shown in the attachment would make the converse of the alternate interior angles theorem applicable to problem 10.

Find two numbers x and y with a sum of 200 and a difference of 82

Answers

Answer:

Let x be the bigger number, and y be the smaller number.

[tex]x+y=200[/tex]

[tex]x=200-y[/tex]

Since the difference is 82,

[tex]x-y=82[/tex]

Substitute x in:

[tex](200-y)-y=82[/tex]

[tex]200-2y=82[/tex]

[tex]2y=200-82[/tex]

[tex]2y=118[/tex]

[tex]y=59[/tex]

[tex]x=200-59[/tex]

[tex]x=141[/tex]

Tarik filled his tank with 11 gallons of
premium gasoline. He paid $38.76. How
much did Tarik pay per gallon?

Answers

I think the answer is he payed $3.40

(5,3)(6,r) m=-1
Find the value of r so that the line that passes through the pair of points has the given slope

Answers

Answer:

Step-by-step explanation:

Slope is change in y over the change in x

(r - 3) / (6 - 5) = -1

(r - 3) / (1) = -1

r - 3 = -1

r = 2

AAAAAAAAA help please​

Answers

The answer is the first one BC ~ CD
Ok done. Thank to me:>

Which of the following tables does not represent a function?

Answers

Answer:

It's the 3rd option

Step-by-step explanation:

A function cannot have one value of 5 associated to more than one value on y

PLEASE HELP the information is below

Answers

Answer:

yellow: x=6

red: y=4

blue: y=-2

Step-by-step explanation:

Yellow is x=6
Red is y=4
Blue is y=-2

Find the distance between the points (-15,3) and (-9,8).

Answers

(-15,3)(-9,8)

Distance:-

[tex]\\ \sf\longmapsto \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

[tex]\\ \sf\longmapsto \sqrt{(-9+15)^2+(8-3)^2}[/tex]

[tex]\\ \sf\longmapsto \sqrt{(6)^2+(5)^2}[/tex]

[tex]\\ \sf\longmapsto \sqrt{36+25}[/tex]

[tex]\\ \sf\longmapsto \sqrt{61}[/tex]

[tex]\\ \sf\longmapsto 7.32units[/tex]

Given info:- Find the distance between the points (-15,3) and (-9,8).

Explanation:-

Distance formulae:

Distance = √{(x₂ - x₁)² + (y₂ - y₁)²}

Let's figure out the distance between two points A = (-15,3) and B = (-9,8).

From those points,

x₁ = -15

x₂ = -9

y₁ = 3

y₂ = 8

Using them in the formula,

Distance btw AB = √[{(-9 - (-15)}² + (8 - 3)²]

= √[(-9 + 15)² + (8 - 3)²]

= √[(6)² + (5)²]

= √[(6*6) + (5*5)]

= √[36 + 25]

= √[61] Units.

Therefore, the distance between A(-25,3) and B(-9,8) is √(61) units.

Bella conducted a scientific experiment. For a certain time, the temperature of a compound rose
3
1
3
3
3
1

degrees in
15
15 minutes. What was the rate, in degrees per hour, that the temperature of the compound rose?

Answers

Answer: 13 1/3 degrees per hour

Explanation: 10/3 x 4 = 40/3

40/3 = 13 1/3

Round 2,913 to the nearest ten

Answers

Answer:2,910

Step-by-step explanation:

Answer:

2910

Step-by-step explanation:

We round the number up to the nearest ten if the last digit in the number is 5, 6, 7, 8, or 9.

We round the number down to the nearest ten if the last digit in the number is 1, 2, 3, or 4.

If the last digit is 0, then we do not have to do any rounding, because it is already to the ten.

Zander was given two functions: the one represented by the graph and the function f(x) = (x + 4)2. What can he conclude about the two functions?

They have the same vertex.
They have one x-intercept that is the same.
They have the same y-intercept.
They have the same range.

Answers

Answer:

C.They have the same y-intercept.

Step-by-step explanation:

Edge 2021

The conclusion about the two functions is (c) they have the same y-intercept.

What are functions?

Functions are used to represent equation, graphs and tables

The equation of the function is given as:

[tex]f(x) = (x + 4)^2[/tex]

Set x = 0, to calculate the y-intercept

[tex]f(0) = (0 + 4)^2[/tex]

Evaluate

[tex]f(0) = 16[/tex]

From the complete question, the graph crosses the y-axis at y = 16

This means that both functions have the same y-intercept

Hence, the true statement about the functions is (c) they have the same y-intercept.

Read more about functions at:

https://brainly.com/question/15602982

Evaluate - 2c + d for c = -9 and d = 4.

Please help.​

Answers

Answer:

-14

Step-by-step explanation:

2c + d

We are given the values of c and d:

c = -9

d = 4

We substitute in these values

2(-9) + 4 = ?

2 times -9 is -18

-18 + 4 = -14

2c + d = -14

I need to know the answer

Answers

Answer:

2 x 6 = 12

6 x 2 = 12

12 ÷ 6 = 2

12 ÷ 2 = 6

Step-by-step explanation:

Frank had 5/9 acres of land. He planted 2/3 of this land with corn. How many acres did he plant with corn ?

Answers

Answer:

22/45

Step-by-step explanation:

i literally just looked it up and that's what it gave me i pretty sure its right

Azad wants to Buy a book he has 25,000 dinars which is 9000 dinars less than she needs does the book cost 34,000 Dinars or 16,000 dinars

Answers

Answer: 34,000 Dinars

Step-by-step explanation: As 25,000 + 9000 is 34,000

Help help help please good luck be honest

Answers

Answer:

A'(-6,4) B'(2,2) C'(-2,-2)

Step-by-step explanation:

The dilation is by 2. This just means you multiply each number by two. FOr example, for point a, multiply -3 by 2 and 2 by 2 to get (-6, 4).

It is 9 kilometers from Charlie's house to the nearest mailbox. How far is it in meters?
Be sure to include the correct unit in your answer.

Answers

Answer:

Step-by-step explanation:

9,000 meters

Katie is 1.83 m tall. George is 9 cm shorter than Katie. How tall is George?
Give your answer in cm

Answers

Answer:

174 cm

Step-by-step explanation:

1.83 m to cm is 183.

So, 183 cm - 9 cm = 174cm

Hope you understand ^^

Answer:

174 cm

Step-by-step explanation:

1 meter is equal to 100 centimeter so 1.83m times 100 is equal to 183cm. so 183 cm-9cm=174 cm

Can someone help me solve these problems?

Answers

Answer:

Step-by-step explanation:

1) add all angles to 180

2) exterior angle = P + Q

i can add remaining ones also

you will receive a golden cookie and 30 points if you help me

Answers

Answer:

A: -5/4 ; B: -0.5 ; C: 2

Step-by-step explanation:

Its the number line which shows.

Answer:

B = -0.5

A= -5/4

C= 2

Brainlest

Step-by-step explanation:

If 12 cats can kill 12 mice in 12 hours, how many hours will it take for 2021 cats to kill 2021 mice

Answers

Step-by-step explanation:

168 hours I guess

have a food day

Eloise's math tutor used algebra tiles to model 3n + 4 - n + 5. What is the simplified form of this expression?

Answers

Answer:

2n + 9

Step-by-step explanation:

3n - n + 4 + 5 = 2n + 9

Chris rented a truck for one day. There was a base fee of $14.99, and there was an additional charge of 75 cents for each mile driven. Chris had to pay
$167.24 when he returned the truck. For how many miles did he drive the truck?
M miles

Answers

Answer:

Chris drove the truck 203 miles.

Step-by-step explanation

So, first I subtracted the base free cost of the amount he paid and got $152.25. Then, I divided $152.25/0.75 and got 203. S0, that's how I got the answer. I subtracted the base free because we know he had to pay that initially and then I just divided the rest of the money he had to pay by 0.75 because he was charge 0.75 per mile driven.

Write an equation for the line with a slope 3 and Y intercept -2

A. y=-3x -2

B. y= 1/3 x -2

C. y= 3x - 2
with explanation pls

Answers

Answer:

C. y=3x-2

Step-by-step explanation:

Well we know the equation: y=mx+b

The slope is m, so m= 3

And the y-intercept is b, so b= (0,-2) or b=-2

Then,

Subsitute everything in:

y= 3x -2

I hope this helped :)

Anthony is in a hot air ballon that has taken off and is floating above its launching point. Leroy is standing on the ground, 8 METERS away from the launching point. If Anthony and Leroy are 10 meters apart, how high up is Anthony?

Answers

since the base of the triangle is 8 and 10 is the hypotenuse, you would do b= 10^ -8^2 which gives you 6

Solve for r.

17r+6r+16r+17r–19r=12
r=

Answers

Step 1 (Combine like terms) you are left with 37r=12 divide by 37 on both sides and get r=12/37

Answer: R= 4

Step-by-step explanation:

FOR step by step explanation ask me by my mail , Thanks !

Write 12 as a product of primes. Use index notation when giving your answer

Answers

[tex]12 = 2 \times 2 \times 3[/tex]

or

[tex]12 = {2}^{2} \times 3[/tex]

- BRAINLIEST answerer

Equations
So I’m having trouble with this pls explain step by step
Here’s the question

W+2=12

Pls explain

Answers

Answer:

w = 10

Step-by-step explanation:

To find the value of w, you need to isolate w on one side.

You can start by subtracting 2 from both sides. What you do to one side of the equation, you have to do to both.

12 - 2 = 10

So now w is isolated and is equal to 10.

w = 10

You can check your work by replacing w with 10 in the equation.

10 + 2 = 12

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