Consider the system of equations
4 x+4 y=-12
3 x-4 y=-23

Part A: Solve the system. Show your work.
Part B: Use the solution to your equation to find the value of x-y. Show your work.
x-y=___

The phrase can be expressed as 3x-6, 3(x-2), x+2x-2-4, 4x-x+4-10 and x+x+x-2-2-2 and so on

It consists of several mathematical symbols organized in such a way that it can express mathematical concept.

Mathematical  phrase can be written in one or more different pattern to show the same expression.

As per question given, the phrase is expressed by

3x-6, where x is used to represent a number

the phrase can be written in 3(x-2)

other variable expressions of same phrase are x+2x-2-4

or 4x-x+4-10 or x+x+x-2-2-2

hence, a phrase can be written in one or more pattern to show same expression.

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Answer:

7 kg

Step-by-step explanation:

Newton's second law tells us that Force = Mass * Acceleration, also known as F = ma.

The downward acceleration due to gravity on Earth is usually taken to be 9.8 ms^-1.

Substitute the values into the equation:

68.6 = m * 9.8

Rearrange and simplify:

m = 68.6 / 9.8

m = 7 kg

The x-intercept of the given line having equation 2x–4y= -12 is -6

How to find x-intercept of a line?

An x-intercept is a point where the graph of a function or relation intersects with the x-axis of the coordinate system.

To find x-intercept of a line, put y = 0 in the given equation of line

According to the given question:

The equation of line is 2x - 4y = -12

Putting y = 0 in the above equation we get

2x - 4(0) = -12

        2x = -12

          x = -6

Therefore, x-intercept of the line 2x–4y= -12 is -6

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Answer: m = 22

Step-by-step explanation:

First, you subtract $2.50 from the total of $79.50 (because that is the static fee) to get $77.00. Now, because every mile is $3.50 and we want to find the number of miles, we divide $77 by $3.50 to get 22. (An easy way to do this mentally is to divide 77 by 7 and multiply by 2.) Therefore, m = 22.

Answer: C

Step-by-step explanation:

30 x 1.029

30.87

The given system of equations has a solution (16/11, 24/11), so they are consistent and independent.

The given system of equations are 4x+y=8 and x+3y=8.

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

Here, 4x+y=8 ----------(I) and x+3y=8 ----------(II)

Multiply equation (I) by 3, we get

12x+3y=24 ----------(III)

Now, subtract equation (II) from (III), we get

12x+3y-(x+3y)=24-8

11x=16

⇒ x=16/11

Substitute x=16/11 in equation (II), we get

16/11 +3y=8

⇒ 3y=8- 16/11

⇒ 3y=72/11

⇒ y=24/11

If equation as one solution, then they are consistent and independent.

Therefore, the given system of equations has a solution (16/11, 24/11), so they are consistent and independent.

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Answer:

[tex]y=2/11[/tex]

Step-by-step explanation:

[tex]\lim{t \to \pm \infty} R(t)=\lim_{ t \to \pm \infty} \frac{30t+525}{165t+7000} =\frac{30}{165}=\frac{2}{11}[/tex]

BY using the inequality,

(67 + 65 + 64 + 88 + 2x)/5 ≥ 73,

we find the score she must make on final exam to pass the courses with an average of 73 or higher is x>=80.

An inequality is a mathematical statement that shows that one quantity is greater than or less than another quantity.

The average, or mean, of a set of numbers is a measure of the central tendency of the set.

This inequality states that the average of Shureka's scores on the four tests and the final exam must be greater than or equal to 73 in order for her to pass the course. Solving for x, we find that x ≥ 80.

The meaning of the answer to part (a) is that Shureka must make a score of 80 or higher on the final exam in order to pass the course with an average of 73 or higher. In other words, if Shureka makes a score of 80 or higher on the final exam, her average score on the five tests will be 73 or higher, which is the minimum required to pass the course. If she makes a score lower than 80 on the final exam, her average score will be less than 73, and she will not pass the course.

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Answer:

there is no solution to the equation

The area represents the aim tariff revenue the United States government collects is D. f

Tariffs are taxes levied by the government of a country or a supranational union on goods imported or exported. Import duties, in addition to being a source of revenue for the government, can also be a form of foreign trade regulation and policy that taxes foreign products in order to encourage or safeguard domestic industry.

Tariffs serve three primary functions: they generate revenue, they protect domestic industries, and they correct trade distortions (punitive function). The revenue function stems from the fact that tariff revenue provides governments with a source of funding. This was illustrated as f in the diagram.

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The total area of the shape will be;

⇒ 721 cm²

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Given that;

Two congruent parallelograms are joined along their base to make the shape below.

Now,

We know that;

2 identical parallelogram whose area = 2 (Base x Height)

And, 2 identical right triangle = base x height

And, 1 rectangle = length x width

So, We get;

In parallelogram;

Base = 15 cm

Height = 11 cm

Hence, We get;

Area = 2 (15 x 11)

       = 330 cm²

And, Area of two identical right triangle;

Base = 11 cm

Height = 11 cm

Hence, Area = 11 × 11

                    = 121 cm²

Area of rectangle = 18 x 15 = 270 cm²

Thus, The total area of shape will be;

⇒ 330 + 121 + 270

⇒ 721 cm²

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Answer:

Domain:  (−∞,∞)

Range:  (−∞,∞)

Step-by-step explanation:

This equation has no bounds of domain or range, so the answer to both is all real numbers.

Answer:  Based on the information you provided, it seems that the McQuires had a total of $793 in their account on Friday, and their wife wrote a check for $1,233.34 the next day. If this check cleared the bank, their account balance would be $793 - $1,233.34 = -$440.34.

Answer: 4 red and 12 blue

Step-by-step explanation: Answer to 9

We know that for every red rose, he plants 3 blue flowers. The rate is 1:3. If he grows 16, there will be 4 red roses and 12 blue ones. This is because the rate is 1:3 then there are 4 flowers in all. This is 1/4 of how much he wants to grow. So multiply each type of plant by 4. 1 times 4 is 4, so there are 4 red ones. 3 times 4 is 12, so there are 12 blue ones. Hope this helps!

Option A , if located in a method in the same class, will initialize the variable x to 11 i.e,  int x = function2(4, 5) + function1(1, 3).

function2(4, 5)  = 5-4 = 1

function1(1, 3) = 3+1 = 4

function2(4, 5) + function1(1, 3) = 5

On initializing the function with 11 ,

the output will be 5

A function is a set of statements that take inputs, do some specific computation, and produce output. The idea is to put some commonly or repeatedly done tasks together and make a function so that instead of writing the same code again and again for different inputs, we can call the function.

In simple terms, a function is a block of code that only runs when it is called.

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To paint , 7 rooms in white or yellow, 128 possible outcomes are there.

The Probability in mathematics is possibility of an event in time. In simple words how many times that incident is happening in any given time interval.

There are seven rooms in the house and each can be painted either yellow or white.

And probability of total number of different outcomes

= total number of options

So, total number of different outcomes = 2⁷

 Total number of different outcomes = 128

Therefore the total number of outcomes are 128.

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The complete question is;

A house has seven rooms. Each room can be painted white or yellow. How many possible outcomes are there?

Answer:

idek

Step-by-step explanation:

the answer is

a=p-3b-4c

The equation is 2x+3=9, x is the unknown number. After solving the equation, we get x=3.

A mathematical expression shows the equality between two terms.

In mathematics variables are used to denote any unknown number and equations are developed based on an expression. Finally, equations are solved, and unknown values are determined.

let, x is the unknown number. As per question the equation will be 2x+3=9

the equation is solved, and x is determined

2x=9-3

x=6/2

x=3

hence, x=3, 3 is the number.

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Answer:

[tex] \sf \: 2x + 3 = 9, \: x = 3[/tex]

Step-by-step explanation:

Given statement,

→ Sum of 2 times a number & 3 is 9.

Let the unknown number be,

→ [tex] \sf \pink{x}[/tex]

Forming the equation,

→ (2 × x) + 3 = 9

→ 2x + 3 = 9

Now the value of x will be,

→ 2x + 3 = 9

→ 2x = 9 - 3

→ 2x = 6

→ x = 6/2

→ [ x = 3 ]

Hence, the value of x is 3.

The number of banquets that can be formed is 6 and total number of flowers are 2+3=5.

What is the greatest common divisor?

the greatest common divisor of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers. For two integers x, and y.

We have given,

Petal and Leaf florists currently have 30 roses, 36 carnations, and 54 tulips

Since it is given that there are 75 rose and 45 lily flowers. Therefore,

Factorise 30 as follows:

30 = 2 × 3 × 5

Factorise 36 as follows:

36 = 2 × 2 × 3 × 3

Factorise 54 as follows:

54 = 2 × 3 × 3 × 3

We know that HCF is the highest common factor.

Since the common factor between the numbers 30, 36, and 54 is 2×3=6.

Hence, the number of banquets that can be formed is 6 and total number of flowers are 2+3=5.

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For the given matrix the additive inverse property is shown.

What is additive inverse of matrix?

The matrix that is created by changing the sign of each matrix element is known as the additive inverse. -(-A)=A is the notation for the additive inverse of the matrix A.

Rows and columns serve as a measure of a matrix's dimensions. Given that it has three rows and three columns, for instance, the matrix below has a dimension of 3 x 3. Three by three can be read off as the matrix's dimension. We consequently obtain the additive inverse of the matrix

M = - M.

Consider the given matrix,

[tex]\left[\begin{array}{ccc}-6&15&-2\\9&0&-3\end{array}\right] + \left[\begin{array}{ccc}6&-15&2\\-9&0&3\end{array}\right] = \left[\begin{array}{ccc}0&0&0\\0&0&0\end{array}\right][/tex]

Here each element in first matrix is negative of the element of second matrix.

That is each element is inverse of the element in second matrix.

And the addition of elements is 0.

Hence, for the given matrix the additive inverse property is shown.

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1. Average rate of change of function over the interval is d. -3/2

2. Average rate of change of function over the interval is 2. 12

3. Average rate of change of function over the interval is 1. -1

4. h(12) has the value of 61

What is the average rate of change of function?

The average rate of change function is defined as the average rate at which one quantity is changing with respect to something else changing.

Formula ----- A(x) = [tex]\frac{f(b)-f(a)}{b-a}[/tex]

Solution:

1.Given a = 2, b = 10

A(x) = [tex]\frac{f(10)-f(2)}{10-2}[/tex]

A(x) = [tex]\frac{-3-9}{8}[/tex]

∴A(x) = -[tex]\frac{3}{2}[/tex]

2. Given a= 3, b = 9

f(x) = x²

A(x) = [tex]\frac{9^{2}-3^{2} }{9-3}[/tex]

A(x) = [tex]\frac{72}{6}[/tex]

∴ A(x) = 12

3. Given a = 1, b = 7

f(x) = Given graph

f(7) = 0, f(1) = 6

A(x) = [tex]\frac{0-6}{7-1}[/tex]

A(x) = -1

4. Given h(5)= 12, a=5, b=9, A(x) = 7

To find: h(12)=?

A(x) = [tex]\frac{h(12)-h(5)}{12-5}[/tex]

7 = [tex]\frac{h(12)-12}{12-5}[/tex]

h(12) = 7×7 + 12

∴ h(12) = 61

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1. Average rate of change of function over the interval is d. -3/2

2. Average rate of change of function over the interval is 2. 12

3. Average rate of change of function over the interval is 1. -1

4. h(12) has the value of 61

What is the average rate of change of function?

The average rate of change function is defined as the average rate at which one quantity is changing with respect to something else changing.

Formula ----- A(x) = (f(b)-f(a))/b-a

Solution:

1.Given a = 2, b = 10

A(x) = -3-9/10-2

∴A(x) = -3/2

2. Given a= 3, b = 9

f(x) = x²

A(x) = 81-9/9-6

∴ A(x) = 12

3. Given a = 1, b = 7

f(x) = Given graph

f(7) = 0, f(1) = 6

A(x) = 0-6/7-1

A(x) = -1

4. Given h(5)= 12, a=5, b=9, A(x) = 7

To find: h(12)=?

A(x) = (f(b)-f(a))/b-a

7 = h(12) = 7×7 + 12

∴ h(12) = 61

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(a) The printer will print 3.5 pages per minute.

(b) It will plant 0.13 acres of seed per pound.

What is a unit rate?

A unit rate means a rate for one of something. We write this as a ratio with a denominator of one.

(a) If a color printer prints 14 pages in 4 minutes.

   So it will print = 14/4

                           = 3.5 pages per minute

(b) If it takes 23 pounds of seed to completely plant a 3 - acre field

  So it can plant = 3/23

                           = 0.13 acres per pound.

Hence,

(a) The printer will print 3.5 pages per minute.

(b) It will plant 0.13 acres of seed per pound.

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Option B is the graph best represents the most reasonable distribution of the differences.

Any variable whose value is uncertain or any function that values each result of an experiment is referred to be a random variable. Discrete (having definite values) or continuous random variables are also possible (any value in a continuous range).

As a result, the random variables are so-called because it is impossible to determine their value with certainty; instead, we can only guess, and this estimate is known as the probability that a random variable will have a given value.

Here we assume the random variable X denotes the difference between the outcomes of rolling the two dice.

here the number of rolls is 500. As we know by central limit theorem every distribution approaches to normal distribution irrespective of the parent distribution. Since Normal is symmetric about the mean the most reasonable distribution is the second figure.

Option B is the correct answer.

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The complete question is as follows:

The equation which has an axis of symmetry with the equation x = 3 as required in the task content is; y = x² - 6x +3.

It follows from the task content that the equation which has an axis of symmetry; x = 3 be determined among the answer choices.

By expressing the equation; y = x² - 6x +3 in vertex form; y = ( x - h )² + k; where the axis of symmetry is given by; x = h; we have that;

y = ( x - 3 )² - 6

On this note, it can be concluded that the axis of symmetry of the considered equation; y = x² - 6x +3 is; x = 3.

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Answer:3.9

Step-by-step explanation:

Divide -19.50 by 5

=3.9

Answer:

Step-by-step explanation:

You want the (a) post-order, and (b) pre-order list of visited vertices in a traversal of the tree described by {root, left, center, right}: {d, f, {b, i, h, e}, {a, {c, g}}}.

A tree is traversed in post-order by visiting the left branch, center branch, and right branch before the root. This is accomplished recursively.

For the given tree, the root 'd' has left branch 'f' which has no branches. That means node 'f' is reported first.

The middle branch goes to 'b' which has three branches. Those are reported before their root 'b'.

The right branch from root 'd' goes to 'a', which has branch 'c' going to 'g'. So, 'g' is reported, then 'c', then 'a'.

Finally, 'd' is reported.

Hence, the post-order traversal is f, i, h, e, b, g, c, a, d.

The pre-order traversal reports the root node, then the left, center, and right nodes, recursively. The vertices are effectively visited in the order in which we have defined the tree above: d, f, b, i, h, e, a, c, g.

do 180-32=148 and then do 148÷2=74

452 ÷ 21 is equal to [tex]$21 \frac{11}{21}$[/tex].

What is  Quotient?

When we divide a number, the result we ultimately obtain is the quotient. Division is a mathematical operation that involves dividing items into equal groups. It is represented by the symbol (÷). For instance, three groups of 15 balls each need to be equally split. Therefore, the division formula is 15 3 = 5 when we divide the balls into three equal groups. Here, the quotient is 5, so. This implies that there will be 5 balls in each group.

[tex]$\frac{452}{21}=21$[/tex] Remainder 11

Convert to mixed number: Quotient= [tex]$\frac{\text { Remainder }}{\text { Divisor }}$[/tex]

[tex]$\frac{452}{21}=21 \frac{11}{21}$[/tex]

[tex]$=21 \frac{11}{21}$[/tex]

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