Which of the following are like terms?​

A set S spans R^2 if any element of R^2 can be written as linear combination of elements of S the set S spans R2.

(a) Given that S={ (1,-1),(2,1) }

Let (x,y) be the any element in R^2.

(x,y) = C1(1,-1)+C2(2,1)

(x,y) = (c1+2c2,-c1+c2)

x  =  c1+2c2

y  = -c1+c2

x+y = 3c2

c2= {x+y}/{3}

c1 = c2-y

= {x+y}/{3}-y

={x-2y}/{3}

So for any element (x,y) in R^{2} we have the constants c_1,c_2 so that (x,y) can be written as,

(x,y)= {(x-2y)}/{3}(1,-1) + {(x+y)}/{3}(2,1)

So S= { (1,-1),(2,1) } spans R^2.

(b) Given that S = { (1,1) }

Let (x,y) be the any element in R^2.

(x,y)=c_1(1,1)

(x,y)=(c_1,c_1)

x=c_1,y=c_1

If x,y are distinct then do not get a value of c_1 so that (x,y) = c_1(1,1).

So set S= { (1,1) } does not span R^2.

(c) Given that S= { (0,2),(1,4) }

Let (x,y) be the any element in R^2.

(x,y)=c_1(0,2)+c_2(1,4)

(x,y)=(c_2,2c_1+4c_2)

x=c_2

y=2c_1+4c_2

c_1={y-4c_2} / {2}

={y-4x} / {2}

So (x,y)= {(y-4x)}/{2}(0,2)+x(1,4)

So any element of R^2 can be written as written as linear combination of elements of Set S.

Hence set S={ (0,2),(1,4) } spans R^2.

Learn more about sets here :

https://brainly.com/question/28492445

#SPJ4

Answer:

3x^2 + 4x + 3

Step-by-step explanation:

we can use this information to find g(x) in terms of f(x).

substitute f(x) = 3x-1 into f(g(x)) = 9x^2 + 12x + 8, we get:

3g(x) - 1 = 9x^2 + 12x + 8

Now, we can solve for g(x) by isolating it on one side of the equation:

3g(x) = 9x^2 + 12x + 9

g(x) = 3x^2 + 4x + 3

therefore g(x) is equal to 3x^2 + 4x + 3

Answer:

30 + 4n

Step-by-step explanation:

Company X = 30 + 4n

Yes, the formula z = -b± √(b²-4ac)/2a is used to find the solutions (or roots) of a quadratic equation of the form az² + bz + c = 0. This is known as the Quadratic Formula.

What is the Quadratic Equation?

A quadratic equation is a type of polynomial equation of degree 2 in one variable (x), which can be written in the form of ax² + bx + c = 0, where a, b, and c are real numbers, and a is not equal to zero. The solutions or roots of this equation can be found by using the Quadratic Formula which is z = -b ± √(b²-4ac) / 2a.

The Quadratic formula is valid for any quadratic equation in standard form (ax² + bx + c = 0), where a, b, and c are real numbers, and a is not equal to zero. The two solutions are given by the formula are the roots of the equation, and they are always real and distinct, unless the discriminant b² - 4ac is negative, in which case the roots are complex numbers.

Hence, Yes, the formula z = -b± √(b²-4ac)/2a is used to find the solutions (or roots) of a quadratic equation of the form az² + bz + c = 0. This is known as the Quadratic Formula.

To learn more about the quadratic equation, visit:

https://brainly.com/question/1214333

#SPJ1

The probability that the student got a a a given that the student was in the afternoon class is 25/57

In math the term probability is defined as based on the possible chances of something to happen

Here we have given that  a test to a group of students, the grades by the two different classes are summarized.

and it can be written like the following;

                                a             b               c                   Total

Morning class         4             20              8                    32

Evening Class         13              5               7                   25

Total                        17             25              15                  57

Here we know that the total number of students is obtained as

=> 57

And the number of students who have been taking the afternoon class is calculated as,

=> 25

Then the probability the student got a a a given that the student was in the afternoon class is written as,

=> 25/57

To know more about Probability here.

https://brainly.com/question/11234923

#SPJ4

This is a system of equations problem. We can set up the following equations:

x = number of children admitted

y = number of adults admitted

1.25x + 7.20y = 1060 (the total amount of money collected)

x + y = 253 (the total number of people admitted)

To find the number of children admitted, we can use the second equation to solve for one of the variables in terms of the other.

x + y = 253

x = 253 - y

Now we can substitute this expression into the first equation:

1.25(253 - y) + 7.20y = 1060

Solving for y we get

y = 120

So there were 120 adults admitted.

We can use the second equation to find the number of children admitted:

x + y = 253

x = 253 - y

x = 253 - 120

x = 133

So there were 133 children admitted.

Therefore,

There were 133 children admitted.

There were 120 adults admitted.

Answer:

128 children, 128 adults

Step-by-step explanation:

1.25  per child (c)

7.2 per adult (a)

a+c = 253 so c = 253-a

1.25c+7.2a=1060

2 equations 2 variables, solve

1.25 (253-a) + 7.2*a = 1.25*253 -1.25a + 7.2a =1060

sp 5.95a =1060- 1.25*253

so a =125

c = 253-125 = 128

Answer:

We can start solving the problem by using algebraic equations. Let x be the total number of stickers in the box at first.

According to the problem, Wenxuan took 8 more than of the total number of stickers, so he took x + 8 stickers.

The remaining stickers after Wenxuan took his share is x - (x+8) = x - x - 8 = -8 stickers.

Charlene took 7 more than of the remaining stickers, which is -8 + 7 = -1 stickers.

So, Charlene took x - (x+8) + 7 = -1 stickers.

Siti took the last 23 stickers, so the total number of stickers remaining is -1 - 23 = -24.

Now we can use this information to set up the equation:

x + (x+8) + (x-x-8+7) + (-1-23) = x

Solving for x we get x = 32

Therefore, there were 32 stickers in the box at first.

The distance between the Dog from the Home is 360.55 m and the direction of the Dog from Home is North-East.

In the inquiry,

The daring dog begins, let's say, at O.

He walks 300 meters east by 3 blocks.

then,

200 m / 2 blocks north

100 m East of 1 block

Block North = 100 meters.

200 m = 2 blocks west

So,

the separation between the Dog's initial location and ending position.

OE is supplied by,

By using Pythagoras' theorem to triangle OLE,

OE²=OL²+LE²

OE²=200²+300²

OE²=40000+90000

OE=360.55m

Therefore, the distance of the Dog from the Home is 360.55 m and the direction of the Dog from Home is North-East.

Know more about Pythagoras' theorem

https://brainly.com/question/343682

#SPJ4

A matrix is in the row-echelon form if:

1. The first nonzero element of each nonzero row (called the leading entry) is to the right of the leading entry of the row above it.

2. Each leading entry is 1 (also called a pivot).

3. Each element above and below a pivot is 0.

A matrix is in the reduced row-echelon form if it is in row-echelon form and also:

4. Each pivot is the only nonzero element in its column.

A matrix is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns. The numbers, symbols, or expressions in a matrix are called its entries or elements. Matrices are often used in linear algebra, a branch of mathematics that deals with vector spaces and linear transformations.

They can be used to represent systems of linear equations, perform operations such as matrix addition and multiplication, and solve systems of linear equations.

To know more about matrices refer to:

brainly.com/question/29132693

#SPJ4

The x-intercepts of this graph from least to greatest are x = -0.73, x = 1, and x = 2.73.

The local minimum of this graph is (0, -2).

The local maximum of this graph is (2, 2).

The intervals on which the function is decreasing are x < -0.73 and x > 1.

The intervals on which the function is increasing are 1 < x < 2.73.

The local minimum of a graph can be defined as the point on the graph of a function where it changes from a decreasing function to an increasing function, which is given by this ordered pair (0, -2).

Conversely, the local maximum of a graph can be defined as the point on the graph of a function where it changes from an increasing function to a decreasing function, which is given by this ordered pair (2, 2).

For any given function, y = f(x), if the output value is decreasing when the input value is increased, then, the function is referred to as a decreasing function.

In conclusion, we would use an online graphing calculator to plot the given function f(x) = x³ + 3x² - 2 in order to determine its key features.

Read more on function here: brainly.com/question/3990145

#SPJ1

Answer:

  -12,731

Step-by-step explanation:

You want to know what integer would be used to represent the value 12,731 feet below sea level.

Usually we measure elevation up from sea level. So, distances below sea level are usually represented with negative numbers. The integer corresponding to 12,731 feet below sea level would be ...

  -12,731 . . . . feet

Step-by-Step Explanation:

3rd term (a3) = -6

12th term (a12) = -3

We know, nth term of an AP = a1 + (n - 1)d, where d = common difference

a3 = a + (3-1)d = a + 2d = -6...(I)

a12 = a + (12-1)d = a + 11d = -3..(II)

Subtracting (II) from (I), we have

2d - 11d = -6 + 3

=> -9d = -3

=> d = 1/3

Therefore, a + 2×1/3 = -6

=> a + 2/3 = -6

=> a = -6-2/3 = -20/3

Therefore, 18th term

= a + (18-1)d

= -20/3 + 17/3

= -3/3

= -1

Answer:

-1

Hope it helps.

If you have any query, feel free to ask.

The value of a is 12. Therefore, the equation of the function is f(x) = 12|x|.

In algebra, an objective function function is one where the variables is inside the bars denoting absolute values. The absolute value is also referred to as the modulus function, and its most popular representation is f(x) = |x|, wherein x is a real number.

Finding x values that turn the equation inside the exact amount positive or negative into a constant is how absolute value equations are solved. Plot two for the negative and positive cases that intersect at the expression's 0 to graph exact value functions.

To find the value of a, we can use the point (1, 12) to set up the equation:

a = 12/|1| = 12

To know more about absolute value function visit:

https://brainly.com/question/10664936

#SPJ1

The total profit as the subject of formula is t = 3p

From the question, we have the following parameters that can be used in our computation:

p = t/3

Where

Individual Profit = p

total profit = t

Recall that, we have

p = t/3

Multiply both side of the equation by 3

So, we have

3p = t

Rewrite as

t = 3p

Hence, the solution is t = 3p

Read more about subject of formula at

https://brainly.com/question/657646

#SPJ1

Complete question

The equation p=t/3 is used to calculate the individual profit,p, made by each of three brothers operating a lemonade stand with total profit, t

make t the subject

The complete implementation of the function 'same diff ints' is written italic below.

Below is the implementation for the function same_diff_ints in Python:

def same_diff_ints(ints):

   for i in range(1, len(ints)):

       for j in range(i, len(ints)):

           if abs(ints[j] - ints[j-i]) == i:

               return True

   return False

The function takes in a list of integers as input and iterates through the list using nested for loops. The outer for loop iterates through the list starting at index 1, and the inner for loop iterates through the list starting at the outer loop's current index.

The function compares the absolute difference between the two elements at index j and j-i with the value of i. If the absolute difference between the two elements is equal to i, the function returns True. If no such pair of elements is found, the function returns False.

You can learn more about implementation of function on:

brainly.com/question/16260450

#SPJ1

The volume of the solid of revolution is  0

The volume of the solid of revolution obtained by rotating the region bounded by the curves x=0 and y=0 is zero since the area of the region is zero.

To calculate the volume of a solid of revolution, we use the formula V = ∫2dx, where r is the radius of the circle obtained by rotating the curve about the x-axis. Since the region bounded by the curves x=0 and y=0 has an area of 0, the radius r is also 0 and the integral becomes 0. Therefore, the volume of the solid obtained by rotating the region bounded by the curves x=0 and y=0 is 0.

Learn more about volume of the solid here:

https://brainly.com/question/12649605

#SPJ4

The given pair of linear equations is consistent.

What are Linear Equations?

An equation is said to be linear if the maximum power of the variable is consistent. Another name for it is a one-degree equation.

Equations are declarations of equality between two mathematical expressions containing one or more variables. A linear equation is one in which the maximum power of the variable is one. a real number equation of the form ax+by+c = 0, with real numbers a, b, and c with the highest power one variable x and y.

In our question, we can see:

a1 = -3 and a2 = 4

b1 = 3 and b2 = 4

c1 = 21 and c2 = 60

a1/a2 = -¾

b1/b2 = ¾

c1/c2 = 7/20

Since a1/a2 is not equal to b1/b2, therefore our pair of liner equation is consistent.

To learn more about consistent and inconsistent, visit: https://brainly.com/question/11117561

#SPJ4

Answer:

75,000

Step-by-step explanation:

We have to round up to nearest thousand ,so we need to check hundred place ...

If hundred place is equal or greater than 5 ,we need to add +1 to the number which is in thousand place , If it is less than 5 we don't need to do so ....

The set {1,2,3} is not a group under multiplication modulo 4, as it does not contain an identity element. However, the set {1,2,3,4} is a group under multiplication modulo 5.

A group is a set of elements which is closed under an operation and contains an identity element. In order to be a group, the set must satisfy the four group axioms: closure, associativity, identity, and invertibility. The set {1,2,3} does not satisfy the group axioms under multiplication modulo 4, since it does not contain an identity element, and thus is not a group.

On the other hand, the set {1,2,3,4} is a group under multiplication modulo 5, since it contains an identity element (1) and is closed under multiplication. The other group axioms are also satisfied, as the operation is associative, and each element has an inverse (for example, the inverse of 1 is 4). Therefore, {1,2,3,4} is a valid group under multiplication modulo 5.

Learn more about set here

https://brainly.com/question/12979762

#SPJ4

The length of the ladder used in the question is; 6.974 ft

The 3 main trigonometric ratios are;

sin x = opposite/hypotenuse

cos x = adjacent/hypotenuse

tan x = opposite/adjacent

Now, since the ladder makes an angle of 35 degrees with the wall, it means the ladder will be the hypotenuse of the right angle triangle and the distance from the base of the wall to the base of the ladder will be labelled as h = 4 will be the opposite side of the triangle. Thus;

4/hypotenuse = sin 35

hypotenuse = 4/sin 35

hypotenuse = 4/0.5736

Hypotenuse = 6.974 ft

Read more about trigonometric ratios at; https://brainly.com/question/13276558

#SPJ1

Projects that adopt agile methodology are not prone to the typical rapid changes that occur throughout the system development lifecycle, The statement is False.

The methodology is defined as to the overarching strategy and rationale of your research project.

It involves studying the methods used in your field and the theories or principles behind them, in order to develop an approach that matches your objectives.

Agile project management methodology is commonly used for software development projects. It has greater adaptability to frequently changing scopes. Adopt Agile because they want to increase speed to market, meet customer demand, or increase team productivity.

To know more about Methodology:

https://brainly.com/question/12325081

#SPJ4

The number of cans to be added to 18 gallon tank is given by equation

A = 2.25 cans

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number of cans for 18 gallon tank be A

Now , the equation will be

The number of cans per 8 gallons = 1 can

So , the number of cans for 1 gallon = number of cans per 8 gallons / 8

On simplifying the equation , we get

The number of cans for 1 gallon = 1/8

The number of cans for 1 gallon = 0.125 can

And ,

The number of cans for 18 gallons A = 18 x number of cans for 1 gallon

Substituting the values in the equation , we get

The number of cans for 18 gallons A = 18 x 0.125

The number of cans for 18 gallons A = 2.25 cans

Hence , the number of cans is 2.25 cans

To learn more about equations click :

https://brainly.com/question/19297665

#SPJ1

The domain and the range of y = 12x - 36 are the set of all real numbers

From the question, we have the following parameters that can be used in our computation:

y = 12x - 36

There is no restriction on the input values, x

So, the domain of y = 12x - 35 is all real numbers, since there is no restriction on the input (x).

The range of y = 12x - 35 is also all real numbers, since the output (y) can be any real value, depending on the input (x).

This can be seen by considering that for any real number x, the output y = 12x - 35 will also be a real number.

Read more about domain and range at

brainly.com/question/2264373

#SPJ1

Complete question

What is the Domain of y = 12x - 36

x > 3 ,

-3 ≤ x ≤ 3,

all real numbers

Also, determine the range

The volume of the solid obtained by rotating the region bounded by the given curves about the specified line about x-axis is 3.93740 and y=-1 is 5.0740

We have to find the volume of given curve about x-axis

we have [tex]$\mathrm{y}=\mathrm{e}-\mathrm{x}^2,[/tex] y=0, x=-5, x=5

(a).

The volume of solid of revolution about the x-axis using disk method is evaluated as:

Volume V=[tex]\pi \int_{\mathrm{x}=-5}^{\mathrm{x}=5} \mathrm{y}^2 \mathrm{dx}$[/tex]

[tex]$$\begin{aligned}& \mathrm{V}=\pi \int_{\mathrm{x}=-5}^{x=5}\left(\mathrm{e}^{-\mathrm{x}^2}\right)^2 \mathrm{dx} \\& \mathrm{V}=\pi \int_{\mathrm{x}=-5}^{x=5} \mathrm{e}^{-2 \mathrm{x}^2} \mathrm{dx} \\& \mathrm{V}=\pi \sqrt{\frac{\pi}{2}}=3.93740 .\end{aligned}$$[/tex]

V=3.93740

we use the formula

(b). The volume of solid of revolution about the y= - using washer method is:

[tex]$$\begin{aligned}& \text { volume } \mathrm{V}=\pi \int_{\mathrm{x}=-5}^{\mathrm{x}=5} \mathrm{y}^2-{ }^2 \mathrm{dx} \\& \mathrm{V}=\pi \int_{\mathrm{x}=-5}^{\mathrm{x}=5} \mathrm{y}^2 \quad 2 \mathrm{y}-{ }^2 \mathrm{dx} \\& \mathrm{V}=\pi \int_{\mathrm{x}=-5}^{\mathrm{x}=5} \mathrm{y}^2 2 \mathrm{ydx} \\& \mathrm{V}=\pi \int_{-5}^5 \mathrm{e}^{-2 \mathrm{x}^2} 2 \mathrm{e}^{-\mathrm{x}^2} \mathrm{dx} \\& \mathrm{V}=\pi \sqrt{\frac{\pi}{2}} .77245 \\& \mathrm{~V}=5.0740\end{aligned}$$[/tex]

Therefore, the The volume of solid of revolution about the y= - using washer method is 5.0740

For more such questions on disk method

https://brainly.com/question/28184352

#SPJ4

Answer:

150 students in total

Step-by-step explanation:

30 students is 20%

20% x 5 = 100%

30 x 5 = 150 students

The 1x8 vector resulting from multiplying each entry of x by 4.x4 = [4*x1, 4*x2, 4*x3, 4*x4, 4*x5, 4*x6, 4*x7, 4*x8]

For example, if x = [1, 2, 3, 4, 5, 6, 7, 8], x4 would be [4, 8, 12, 16, 20, 24, 28, 32]. This can be represented mathematically as x4 = [4x1, 4x2, 4x3, 4x4, 4x5, 4x6, 4x7, 4x8] which is the same as 4*x = [4x1, 4x2, 4x3, 4x4, 4x5, 4x6, 4x7, 4x8]. By multiplying each entry of x by 4, we can create a new vector x4 with every entry multiplied by 4.Multiplying each entry of a 1x8 vector x by 4 can be expressed as multiplying the vector by the scalar 4, resulting in a 1x8 vector x4. For example, if x = [1, 2, 3, 4, 5, 6, 7, 8], then x4 = [4, 8, 12, 16, 20, 24, 28, 32].

Learn more about vector here:

https://brainly.com/question/29740341

#SPJ4

Answer: c) 130

Step-by-step explanation:

x+8+42=180

x=180-50

x=130

Answer:

A, C

Step-by-step explanation:

A)

(120 ∙ 8) ∙ 5 = 120 ∙ (8 ∙ 5)

Multiply 8 and 5 first to get 40.

Then 40 × 120 = 4800

C)

(17 + 75) + 25 = 17 + (75 + 25)

Add 75 and 25 first to get 100.

then 17 + 100 = 117

Answer/Step-by-step explanation:

Starting with:

8r + 5p + 7



There are three terms. 8r is a term; 5p is a term; 7 is a term. See how the terms are separated by + or -

r and p are variables. Most often the variable is a letter, that way it can stand for an unknown value. It can vary.

5 is the coefficient of p. Its the number right next to the p. (They are multiplied together)

7 is the constant. Constant means unchanging, right? So 7 is a plain old number, it doesn't change like a variable can. A plain number with no variable is a constant.

As per the given confidence interval, the proportion of all city residents who would respond very supportive or somewhat supportive of the proposal is 336 ± 0.197

The term confidence interval is defined as the statistical measure used to indicate the range of estimates within which an unknown statistical parameter is likely to fall.

Here we have given that the random sample of 1,018 city residents were asked to rate their level of support for a proposal being considered by the city council.

Here we have also know that the percent of confidence interval is 95%.

Here we also identified the following values,

Total population = 1,018

Very supportive population = 336

Somewhat supportive population = 387

Not supportive population= 295

Then the value of confidence interval is calculated as,

Proportion of positive results = P = x/N = 0.3301

Lower bound = 0.3012

Upper bound = 0.3599

Therefore, it can be written as,

=> 336 ± 0.197

Complete Question:

A random sample of 1,018 city residents were asked to rate their level of support for a proposal being considered by the city council. Based on the responses, which of the following is a 95% confidence interval for the proportion of all city residents who would respond very supportive of somewhat supportive of the proposal?

To know more about Confidence interval here.

https://brainly.com/question/24131141

#SPJ4