Find a solution to the linear equation y=6x−18 by filling in the boxes with a valid value of x and y.

Answer:  second option Let (2a +1) be an odd number. Let (2b +1) be a different odd number. Because the sum of these two numbers, 2(a + b + 1), is a multiple of 2, it is an even number.

B.  Let (2A + 1) and  (2B + 1) are different odd numbers. sum of these odd number is 2(A+ B +1) is a multiple of 2.

Whole numbers in mathematics can also be divided into even and odd numbers. There isn't a single number that can be both even and odd, making odd and even numbers distinct sets of numbers. A number can be either even or odd. Odd numbers are ones that are not entirely divisible by two, whereas even numbers are entirely divisible by two.

Let (2A + 1) and  (2B + 1) are different odd numbers. the sum of these odd numbers is 2(A+ B +1) is a multiple of 2. furthermore, let 2a and 2b be two even numbers so the sum of those two will also be an even number. Therefore the sum of two odd numbers is always even.

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Answer:

[tex]y = \frac{x}{2}[/tex]

Step-by-step explanation:

Functions:

Functions have the following format:

y = f(x)

In which y is the output, x is the input, and f is the relation between them.

In this question:

The output is half of the input x. This means that:

[tex]y = \frac{x}{2}[/tex]

Functions can be represented using equations and mathematical statements

The function rule is y = 0.5x

The statement is given as:

The output is half of the input x."

Let the output be y.

So, we have:

y = 0.5 * x

Evaluate the product

y = 0.5x

Hence, the function rule is y = 0.5x

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Answer:

Maximum length and breadth of the box is 6.32 cm and the height of the box is 3.16 cm

Step-by-step explanation:

Surface area of box

[tex]4xy+x^2=120\\\Rightarrow y=\dfrac{120-x^2}{4x}[/tex]

Volume of box is

[tex]V=x^2y\\\Rightarrow V=x^2\times \dfrac{120-x^2}{4x}\\\Rightarrow V=\dfrac{120x-x^3}{4}\\\Rightarrow V=30x-\dfrac{1}{4}x^3[/tex]

Differentiating with respect to [tex]x[/tex]

[tex]\dfrac{dV}{dx}=30-\dfrac{3}{4}x^2[/tex]

Equating with zero

[tex]30-\dfrac{3}{4}x^2=0\\\Rightarrow x^2=\dfrac{30\times 4}{3}\\\Rightarrow x^2=40\\\Rightarrow x=6.32[/tex]

Double derivative of the volume

[tex]\dfrac{d^2V}{dx^2}=-\dfrac{6x}{4}=-\dfrac{6\times 6.32}{4}=-9.48<0[/tex]

So, the volume is maximum at [tex]x=6.32[/tex]

[tex]y=\dfrac{120-x^2}{4x}=\dfrac{120-40}{4\times \sqrt{40}}\\\Rightarrow y=3.16[/tex]

So, the maximum length and breadth of the box is 6.32 cm and the height of the box is 3.16 cm.

Answer:

450cm3 or 450 cube cm.

Step-by-step explanation:

Formula = Length x Width x Height

So,

5 x 7.5 x 12 = 450cm3

Answer:

Step-by-step explanation:

10

Answer:

Let say the four number x, y, a and b

(X+y+a+b) ÷4=9 equation 1(we divide by 4 is because It says average)

So let say x=7 and so let insert this equation

(7+y+a+b)÷4=9

7+y+a+b=9×4

7+y+a+b=36(then shift 7)

Y+a+b=36-7

Y+a+b=29

So the sum of 3 number is 29

The sum of the other numbers is 29

Since the average of 4 numbers is 9. Then the total value of the numbers will be:

= 4 × 9

= 36

Since one of the numbers is given as 7, then the value of the remaining numbers will be:

= 36 - 7

= 29

In conclusion, the sum of the remaining numbers is 29. Therefore, the correct option is C.

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Answer:205

Step-by-step explanation:This is an hexogon so you would do

720-118-112-131-154

Answer:

y=2x+5

0=2x+5

-2x=5

x=-2.5

Answer:

See step-by-step explanation

Step-by-step explanation:

Table

To eat out  ( x )                      cost  150 $    and  need   3 hours

To go to the theater ( y )      cost   100 $   and need    3 hours

Therefore Budget constraint:

150 * x  + 100 * y   ≤  12000

And  time constraint is:

3 * x  +  3* y  ≤ 300

General constraints     x ≥ 0    y ≥ 0  and must be integer

Answer:

78

Step-by-step explanation:

Hope this helped. Pls mark brainliest

Answer:

78

Step-by-step explanation:

3(9+13+4)

9+13+4 = 26

3(26) = 78

Answer:

Original price: $

75

Discount percentage:  

20

%

Results

Discount:  

$15.00

Final Price:  

$60.00

Step-by-step explanation:

Answer:

94/18

Step-by-step explanation:

Answer:

400

Step-by-step explanation:

9514 1404 393

Answer:

  360 cm³

Step-by-step explanation:

The volume is the product of the given dimensions:

  V = LWH

  V = (12 cm)(6 cm)(5 cm) = 360 cm³

Answer:

Please check the explanation.

Step-by-step explanation:

We know that a function is a relation where each input or x-value of the X set has a unique y-value or output of the Y set.

In other words, we can not have duplicated inputs as there should be only 1 output for each input.

In our case, we need to determine the value of x so that we can have repeated or duplicated inputs or x-values because duplicated inputs mean the relation would not be a relation.

Given

{(0, 1), (x, 0), (3, 5), (2, 6)}

Now, if we put x = 3, the relation would become:

{(0, 1), (3, 0), (3, 5), (2, 6)}

Here, x = 3 is repeated twice, and we can not have duplicated inputs as there should be only 1 output for each input.

Therefore,

For the value of x = 3, the relation would not be a function.

Note: The same can be said about the values of x = 0, or x = 2 because then the the dupilcated values be x = 0 or x = 2 respectively.

9514 1404 393

Answer:

  see below

Step-by-step explanation:

Adding 3 to x shifts the function's graph 3 units to the left. That makes the graph look like the one attached.

Answer:

quotient: 9y

sum: 4³+8

variable is y

Answer:

27000

Step-by-step explanation:

Answer:

its 27,000

Step-by-step explanation:

hope it helps ;)

Answer:

remember that you start in the [ ] and work your way out

Step-by-step explanation:

Answer:4

Step-by-step explanation:

Given:

The three vertices of parallelogram DEFG are D(-4, - 2), E(-3, 1) and F(3, 3).

To find:

The coordinates of vertex G.

Solution:

Let the coordinates of vertex G are (a,b).

We know that, diagonal of parallelogram bisect equal other. It means, the midpoints of both diagonals are same.

Midpoint formula:

[tex]Midpoint=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)[/tex]

Two diagonals of the parallelogram DEFG are DF and EG.

[tex]\text{Midpoint of DF}=\text{Midpoint of EG}[/tex]

[tex]\left(\dfrac{-4+3}{2},\dfrac{-2+3}{2}\right)=\left(\dfrac{-3+a}{2},\dfrac{1+b}{2}\right)[/tex]

[tex]\left(\dfrac{-1}{2},\dfrac{1}{2}\right)=\left(\dfrac{-3+a}{2},\dfrac{1+b}{2}\right)[/tex]

On comparing both sides, we get

[tex]\dfrac{-3+a}{2}=-\dfrac{1}{2}[/tex]

[tex]-3+a=-1[/tex]

[tex]a=-1+3[/tex]

[tex]a=2[/tex]

And,

[tex]\dfrac{1+b}{2}=\dfrac{1}{2}[/tex]

[tex]1+b=1[/tex]

[tex]b=1-1[/tex]

[tex]b=0[/tex]

Therefore, the coordinates of vertex G are (2,0).

The coordinates of vertex G of parallelogram DEFG is: (2, 0).

Recall:

The given vertices of parallelogram DEFG are:

D(-4, - 2), E(-3, 1) and F(3, 3)

Let (x, y) = coordinates of vertex G.

DF and EG are diagonals of parallelogram DEFG, therefore:

Find midpoint of D(-4, - 2) and F(3, 3) using  [tex](\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})[/tex]:

 [tex](\frac{-4 + 3}{2}, \frac{-2 + 3}{2}) = (\frac{-1}{2}, \frac{1}{2})[/tex]

Find midpoint of E(-3, 1) and G(x, y) using  [tex](\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})[/tex]:

 [tex](\frac{-3 + x}{2}, \frac{1 + y}{2})[/tex]

Make the midpoint of DF equal to the midpoint of EG, then solve for x and y.

[tex]\frac{-1}{2}, \frac{1}{2} = \frac{-3 + x}{2}, \frac{1 + y}{2}[/tex]

[tex]\frac{-1}{2} = \frac{-3 + x}{2}[/tex]

[tex]2(-1) = 2(-3 + x)\\\\-2 = -6 + 2x\\\\-2 + 6 = 2x\\\\4 = 2x\\\\\mathbf{x = 2}[/tex]

[tex]\frac{1}{2} = \frac{1 + y}{2}[/tex]

[tex]2(1) = 2(1 + y)\\\\2 = 2 + 2y\\\\2 - 2 = 2y\\\\0 = 2y\\\\\mathbf{y = 0}[/tex]

Therefore, the coordinates of vertex G of parallelogram DEFG is: (2, 0).

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Answer:

14 ft

Step-by-step explanation:

Let x represent the number of segments of the divided wood beam

Let y represent the total length of the wood beam.

Given that each segment measures 3.5, the equation to express this scenario is given as

y = 3.5x

Thus, to find the length of the wood beam, substitute x = 4 into the equation.

We would have:

y = 3.5(4)

y = 14

Length of the wood beam = 14 ft

Answer: They charge the same amount.

Step-by-step explanation:

Answer:

4 2/3

Answer:

The coefficient in the first term is 4

The constant is 6

There are 4 terms in this expression

The variable in the third term is y

Step-by-step explanation:

The constant is 6 because it is the only term without a variable, therefore the one term that will stay the same/remain constant.

The first term is 4x^2, the second term is -5x, the third term is 3y, and the fourth term is 6.

The variable in the first term is x^2, therefore the coefficient of x^2 is 4.

Answer:

b & e

Step-by-step explanation:

tell me if I am right :)