Complete the two-column proof.
A
B
С

9514 1404 393

Answer:

  (2, 3, 5)  or  (1, 1, n) for n ≥ 1

Step-by-step explanation:

For some a, b, c, you want to show that ...

  (ab -1)/c is a whole number

  (ac -1)/b is a whole number

  (bc -1)/a is a whole number

__

A search of triples with numbers in the range of 1 to 100 gave these results:

  (1, 1, n) . . . for any n ≥ 1

  (2, 3, 5) . . . . apparently, the only non-trivial solution

__

Further comment

We can show that if you postulate the triple is (2, x, 2x-1), then the only non-trivial value for x is 3. This gives (2, 3, 5) as above.

This triple requires ...

  (2(2x -1) -1)/x = integer = (4x -3)/x = 4 -3/x

In order for 3/x to be an integer, we must have x=1 or 3. For x=1, the triple is (2, 1, 1). For x=3, the triple is (2, 3, 5).

Answer:

c

Step-by-step explanation:

asdfghj

Answer:

A. x = (k + c)/4

Step-by-step explanation:

In this question, they're asking for what x equals in terms of k.

You know that 4x - c = k

add c on both sides, you get:

4x = k + c

divide 4 on both sides to isolate the x variable, you get

x = (k + c)/4

It's a simple question when you think about it! If this helped, please mark it brainliest.....thank you....................

Answer:

y = 1/3x - 2

General Formulas and Concepts:

Pre-Algebra

Algebra I

Standard Form: Ax + By = C

Slope-Intercept Form: y = mx + b

Step-by-step explanation:

Step 1: Define

Standard Form:   x - 3y = 6

Step 2: Rewrite

Find Slope-Intercept Form

Answer:

1/3x-2

Step-by-step explanation:

Slope intercept form is y=mx+b

So change this to that form x-3y=6

-3y=-x+6 now divide both sides by -3

y=1/3x-2

Answer:

the thalia age be 19 years

Step-by-step explanation:

Let us assume her brother age be x

Now the thalia age be x - 3

Now the equation would be

x + x - 3 = 41

2x = 41 + 3

2x = 44

x = 22

thalia age be

= 22 - 3

= 19

Hence, the thalia age be 19 years

And, her brother age be 22 years

The same is to be considered

Answer:

f(x) = 19

Step-by-step explanation:

F(x) + -3(-5) +4

F (x) 15+4

F(x)= 19

Answer:

c = 289

Step-by-step explanation:

Given

x² + 34x

To complete the square

add ( half the coefficient of the x- term )² to x² + 34x

= x² + 2(17)x + 17²

= x² + 34x + 289 ( with c = 289 )

= (x + 17)² ← perfect square

The value of c that completes the square is 289.

The method "completing the squares", as per the name suggests, try to make the quadratic equation of the form such that the x variable is totally covered in single squared term, as the square of a linear expression in x.

The quadratic equation would look something like:

(px + q)^2 = s

where p, q and s are some constants.

We do so, so that we can then use square root and some other operations to get the variable 'x' on one side of the equation, and all the constants on the other side, being solution of the considered quadratic equation.

Expressing the quadratic equation in such form converts the form of the equation which contains 'x' with different powers in different term to a form which contains 'x' single time.

We are given that;

The function= x2+34x+c​

Now,

To find d, we can use the formula d = b/2, where b is the coefficient of x. In this case, b = 34, so d = 34/2 = 17.

To make x^2 + 34x + c a perfect square trinomial, we need to add (17)^2 to it. This is because (x + 17)^2 = x^2 + 34x + 289.

However, we also need to keep the value of the expression unchanged. So, if we add 289 to x^2 + 34x + c, we also need to subtract 289 from it.

Therefore, we have:

x^2 + 34x + c = (x^2 + 34x + 289) - 289 + c

= (x + 17)^2 - (289 - c)

To complete the square, we need to choose c such that 289 - c = 0. This means that c = 289.

Therefore, by completing the squares method the answer will be 289.

Learn more about completing the squares method here:

https://brainly.com/question/16800259

#SPJ2

Answer:

x = 3y + 1

Step-by-step explanation:

0-(-1) = 1

1-0 = 1

2-1 = 1

1-(-2) = 3

4-1 = 3

7-4 = 3

As x increases by 1, y increases by 3. At x = 0, y is already 1. Thus:

x = 3y + 1

Answer:

Slope-intercept Form:  [tex]y = 3x + 1[/tex]

Standard Form:  [tex]9x -3y = -3[/tex]

Point-slope Form:  [tex]y -7 = 3(x - 2)[/tex]

Step-by-step explanation:

Answer: 24 cubic meters

Step-by-step explanation:

Answer:

24 cubic meters

Step-by-step explanation:

Khan Academy

Answer:

2 pounds with is b. rhndgdmrgr k rgrnr

Answer:

2 pi, square root 38, 6 7/12 and 6.45%

Step-by-step explanation:

Answer:

6 7/12, 6.45, 6.28, 6.1

Step-by-step explanation:

6.29 is the one with the symbol and 6.1 is the square root

Please mark brainliest

Answer:

i don't understand what is this

Step-by-step explanation:

:(((((((((((((((

Answer:

m=-5 and b=7

Step-by-step explanation:

y=mx+b

so whatever is at m will be the slope and whatever at b is the y intercept

Answer:

Slope=m=-5/1  y-intercept=b=7

Step-by-step explanation:

Slope is always the number with the variable x so in this case -5 this is rise so the slope is (-5,1) because -5 is the only number therefore x represents 1. The y-intercept is always the number being added or subtracted by the slope or the number with x. If it is shown with subtraction then the y-intercept is negative.

===========================================

Work Shown:

Because we have similar triangles, we can form the proportion below to isolate x.

(AC)/(BC) = (CD)/(AC)

(15)/(20) = (x)/(15)

15*15 = 20x .... cross multiply

225 = 20x

20x = 225

x = 225/20

x = (5*45)/(5*4)

x = 45/4

Answer:

Step-by-step explanation:

5 and 4 mutually prime numbers, therefore we need to find their LCM.

Next time they will both exercise on the 20th days, which is January 20

Answer:

Two non zero vectors, a and b are parallel when they are scalar multiples of each other such that a = c·b where c is a scalar quantity.

Therefore, in order to find a vector that is parallel to the vector, b = (-2, -1), we multiply the vector, b by a scaler quantity

Step-by-step explanation:

Given that the vector b = (-2, -1) can be written as follows;

b = -2·i - j, we have;

[tex]\left | b \right |[/tex] = √((-2)² + (-1)²) = √5

Therefore, we have;

The coordinates of the endpoint of the vector are (-2, 0) and (0, -1)

Therefore, the slope of the vector = (-1 - 0)/(0 - (-2)) = -1/2

The slope of parallel vectors are equal, which gives the slope of the parallel vector = -1/2 = (λ × (-1 - 0))/(λ ×(0 - (-2))

Therefore, a parallel vector is obtained from a vector by multiplying with a scaler product.

Answer: 24-150

Step-by-step explanation:

-6(-4 + 25)

24-150

Answer:

-126

Step-by-step explanation:

First, you multiply the -6 by -4

-6 * -4 = 24

Because a negative times a negative equals a positive.

So you now have 24

Second, you multiply the -6 times 25

-6 * 25 = -150

Because a negative times a positive is a negative.

So now you have -150

Third, you add up the two numbers together

24 + -150 = -126

Answer:

Step 1: Distribute 1.2 to 6.3 and –7x

Step 2:  Combine 3.5 and 7.56

Step 3:  Subtract 11.06 from both sides

Step-by-step explanation:

Given the expression  3.5 + 1.2(6.3 – 7x) = 9.38, we are to write the possible steps involved in solving the equation

3.5 + 1.2(6.3 – 7x)

Step 1: Distribute 1.2 to 6.3 and –7x

3.5 + 1.2(6.3 – 7x) = 9.38

3.5 + 1.2(6.3) + 1.2(-7x) = 9.38

3.5 + 7.56 - 8.4x = 9.38

Step 2:  Combine 3.5 and 7.56

11.06 - 8.4x = 9.38

Step 3:  Subtract 11.06 from both sides

11.06 - 8.4x - 11.06 = 9.38 - 11.06

-8.4x = -1.68

Step 3=4: Divide both sides by -8.4

-8.4x/-8.4 = -1.68/-8.4

x = 0.2

Hence the three steps are

Step 1: Distribute 1.2 to 6.3 and –7x

Step 2:  Combine 3.5 and 7.56

Step 3:  Subtract 11.06 from both sides

Answer:

y- intercept = - 5, slope = 8

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + b ( m is the slope and b the y- intercept )

y = 8x - 5 ← is in slope- intercept form

with slope m = 8 and y- intercept b = - 5

Answer: slope: 8, intercept: (0, −5)

Step-by-step explanation:

Find the Slope and y-intercept

y = 8x − 5

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

y = mx + b

Find the values of m and b using the form y = mx + b.

m = 8

b = −5

The slope of the line is the value of m, and the y-intercept is the value of b.

Slope: 8

intercept: (0, −5)

Answer:

f(-4) = 4

Step-by-step explanation:

Fro the graph attached,

We have to calculate the value of the function at x = -4.

As we can find from the graph at the input value x = -4, output value of the function is f(-4) = 4

Therefore, f(-4) = 4 will be the answer.

amount he earned for selling all of the oranges =

$0.5 x 100 = $50

% profit = ((50 - 40)/40) x 100% = 25%

Therefore, he made a 25% profit

Answer:

c five hours

Step-by-step explanation:

i did the math

Answer:

The width is 3cm

Step-by-step explanation:

Since the area of the rectangle is 27cm² and the length is 9cm you can just divide 27 by 9 to find out the width of the rectangle

Answer:

width = 3 cm

Step-by-step explanation:

area of rectangle = length× breadth

27 = 9 × breadth

27/9 = breadth

3 cm = breadth

hope this will help you and plzzz mark my answer as brainlist plzzzz vote me also....

Answer:

----------------------------------------------------

Information

----------------------------------------------------

Amount = $400

Interest rate = 4% a year

----------------------------------------------------

Equation

----------------------------------------------------

Total amount = 400 + 0.04(400)

Total amount = 400 + 16

Total amount = $416

----------------------------------------------------

Answer: Total Amount = 400 + 0.04(400)

----------------------------------------------------

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

right now the good doctor and criminal minds

Answer:

Sara could list the factors of 18 and 30 and then find the greatest value that the lists have in common. The length of the longest equal-sized pieces that she can cut from both boards with no wood left over, is 3 inches. She will be able to cut 6 pieces from the 18-inch board and 10 pieces from the 30-inch board. She will have enough wood to cut 10 equal-sized pieces for her club project.

Hope this helps you Merry Christmas!!!!

Answer:

1

Step-by-step explanation:

They ask how many ducks there are they never said what they are made out of so the rubber duck counts. there is no other ducks so there is only 1 which is your rubber ducky.