If f(x) = 4x² - x - 3, then what is the remainder when f(x) is divided by
x - 3?

Based on the graphs of functions f(x) and g(x) = f(x) + k, the value of k is: B. k = -2.

In Mathematics, the y-intercept of any graph such as a linear function, generally occur at the point where the value of "x" is equal to zero (x = 0).

Since the graph of the line for function f(x) passes through the ordered pairs (0, 1) and (2, 6), its y-intercept is given by:

y = f(0) = 1.

Since the graph of the line for function g(x) passes through the ordered pairs (0, -1) and (2, 4), its y-intercept is given by:

y = g(0) = -1.

From the information provided above, we have the following function:

g(x) = f(x) + k

g(0) = f(0) + k

Making k the subject of formula, we have:

k = g(0) - f(0)

k = -1 - 1

k = -2.

Read more on y-intercept here: brainly.com/question/19576596

#SPJ1

The total overhead variance is $7,000

What is variance?

Data points' variance from the mean is a measure of how they vary. A variance, according to Layman, is a measurement of how widely apart a collection of data (numbers) are from their mean (average) value.

Finding the predicted difference of departure from the actual number is what is meant by variance. As a result, variance is influenced by the data set's standard deviation.

Data is more dispersed from its mean the higher the variance value, and less dispersed from mean if the variance value is low or minimal. As a result, it is referred to as a measure of data dispersion from mean.

Total labor and overhead variance = 35000-14000 = 21000

Total overhead variance = 21000/(2+1)*1 = 7000  

Thus, total overhead variance is $7,000  

Learn more about Variance from the link below

https://brainly.com/question/13708253

#SPJ4

The solution of the equations 3x - 5y = 15 and x - 4y = 12 will be (0, -3).

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The system of equations is given below.

3x - 5y = 15         ...1

x - 4y = 12          ...2

From equation 2, then we have

x = 4y + 12  

Put in equation 1, then we have

3(4y + 12) - 5y = 15

12y + 36 - 5y = 15

7y = -21

y = - 3

Then the value of the variable 'x' is calculated as,

x = 4(-3) + 12

x = - 12 + 12

x = 0

The solution of the equations 3x - 5y = 15 and x - 4y = 12 will be (0, -3).

More about the solution of the equation link is given below.

https://brainly.com/question/545403

#SPJ1

Angle of the ladder with the floor is 74.5°.

We have given that,

base of the ladder from the wall, x₀ = 2.70 m

top of the ladder above the floor y = 5.13 m

speed of the spaceship = 0.85 c

and we have to find the angle ladder makes with the floor, θ.

From the given information we will construct a diagram.

From the diagram,

tanθ = y/x₀

tanθ = y / x₀√(1- V^2 / c^2)

we will substitute all the values,

tanθ = 5.13 / 2.70√(1-((0.85c)^2 / c^2))

        = 5.13 / 2.70√(1-(0.85^2))

        = 5.13 / 2.70√(1 - 0.7225)

        = 5.13 / 2.70√0.2775

        = 5.13 / 1.4223

tanθ = 3.606

    θ = tan⁻¹(3.606)

    θ = 74.5°

Therefore angle the ladder makes with the floor is 74.5°.

To know more about angle here

https://brainly.com/question/23210878

#SPJ4

The expression 5(x + 7) has a sum of two terms 5x and 35.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, an expression 5(x + 7).

Now distributing 5 to x and 7 we get 5x + 35.

So, The expression 5(x + 7) has the sum of two terms.

learn more about numerical expressions here :

https://brainly.com/question/29199574

#SPJ1

Answer:

x=mp-n

Step-by-step explanation:

Switch sides:

(n+x)/p=m

Then multiply both sides by p:

n+x=mp

Move n to the other side:

x=mp-n

Answer:

100000000000000000000000000

Step-by-step explanation:

Answer:

Step-by-step explanation:

i think the answer is 12

Michael's actual heart rate was about 2 beats per minutes less than the rate predicted by the line of best fit. The correct option is B

A scatterplot is a data visualization that depicts the relationship between two numerical variables. Each dataset member is plotted as a point whose x-y coordinates correspond to its values for the two variables.

On each of the eighteen days, Michael swam 2,000 yards. The scatterplot above depicts his swim time and heart rate after each swim. The data's best fit line is also shown.

From the graph the actual heart rate=150

but calculated heart rate from best fit line=148

Difference between actual and calculated=150−148=2

Option B is correct.

Learn more about scatterplot on:

https://brainly.com/question/6592115

#SPJ1

V = 4/3 r3, where V is the volume and r is the radius, is the formula for a sphere's volume. A sphere's radius is equal to half of its diameter.

Given data :

radius = 3x²

volume of sphere =  V = 4/3 π r³

v = 4 x π x (3x²)[tex]{3}[/tex] / 3

= 4π.[tex]x^{5}[/tex]

volume of cube = side3

= (x²)[tex]^{3}[/tex]

Learn more about sphere's volume refer to :

https://brainly.com/question/22807400

#SPJ1

The proper way that you can prove that the square of an odd number is always one more than a multiple of eight is by using an example.

An example is a term that refers to a tool that is intended to explain, illustrate, or prove a general statement. When we want to explain a procedure we can give an example (that we have previously chosen) to seek to clarify the understanding of a phenomenon or process.

To prove that the square of an odd number is always a multiple of eight, the first step is to find the square of any odd number. Subsequently, we must subtract 1 from the result. Finally we must divide the previous result by 8 and it must give us an exact number (not a decimal).

3 * 3 = 9

9 - 1 = 8

8 / 8 = 1

123 * 123 = 15,129

15,129 - 1 = 15,128
15,128 / 8 = 1,891

9 * 9 = 81

81 - 1 = 80

80 / 8 = 10

Learn more about mathematical examples in: https://brainly.com/question/25829795

#SPJ1

Answer:

x^2 + 10

Step-by-step explanation:

The equation that can be used to describe g(x) in terms of f(x), considering the transformations, is given as follows:

A. g(x)=-f(x+2)+1.

From the image given at the end of the answer, the function f(x) is given as follows:

f(x) = x².

The transformations to obtain function g(x) are given as follows:

Meaning that option A gives the correct option to describe the function g(x) as a function of the function f(x).

The functions are given by the image presented at the end of the answer.

More can be learned about transformations at https://brainly.com/question/28725644

#SPJ1

Using polar coordinates, the result for integral is - 0.448[tex]\pi[/tex]

What is polar co-ordinates?

In arithmetic, the polar coordinate system may be a two-dimensional organization within which every purpose on a plane is set by a distance from a indicator and an angle from a reference direction.

Main body:

The most used relation for polar coordinates is:

[tex]x^{2} +y ^{2} =r^{2}[/tex]

An integral in Cartesian coordinates is converted to polar using:

[tex]\int\int{f(x,y)} \, dA = \int\int{ f(r, \beta )d\beta[/tex]

In this problem:

f(x,y) = sin [tex]x^{2} +y^{2}[/tex]

thus

f(r,[tex]\beta[/tex]) = sin[tex]r^{2}[/tex]

Region between the circles with center at the origin and radii 1 and 3, thus the inner limits of integration are r =1  and r =3.

First quadrant, thus, the outer limits of integration are: [tex]\beta[/tex] = 0,[tex]\beta[/tex] = [tex]\pi /2[/tex].

The polar integral is:

I = [tex]\int\limits^3_1 {sinr^{2} r} \, dr[/tex]

Using substitution:

u =[tex]r^{2}[/tex] ⇒ du = 2rdr⇒ dr = du /2

I = 1/2[tex]\int\ {sin u} \, du[/tex]

 = -[tex]cos r^{2[/tex] /2     where limits are 3, 1

Applying the fundamental theorem of calculus:

I = [tex]-cos 5^{2} /2[/tex][tex]-cos1^{2}/2[/tex]

I = - 0.996

Then, the outer integral is:

O =[tex]\int\limits^\pi _0 {-0.996} \, d\beta[/tex]

O=  - 0.448[tex]\pi[/tex]

Hence the result for integral is - 0.448[tex]\pi[/tex]

to know more about polar co-ordinates, visit:

https://brainly.com/question/14965899

#SPJ4

Hamiltonian due to interaction of spin magnetic field:

H = -u.B

H = α/√2[tex]\left[\begin{array}{ccc}1&1\\1&-1\\\end{array}\right][/tex]

What is a matrix?

In mathematics, a matrix (multiple matrices) is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, and used to represent mathematical objects or properties of such objects. The

matrix represents a linear mapping without additional information and allows explicit computation in linear algebra. The study of matrices is therefore a large part of linear algebra, and most properties and operations in abstract linear algebra can be expressed in matrices. For example, matrix multiplication represents the construction of linear maps.

Not all matrices are related to linear algebra. This is especially true for graph theory, occurrence matrices, and adjacency matrices. This article focuses on matrices in the context of linear algebra. Unless otherwise stated, all matrices either represent linear maps or can be considered linear maps.

Square matrices (matrices with the same number of rows and columns) play an important role in matrix theory. Square matrices of a given dimension form non-commutative rings, one of the most common examples of non-commutative rings. The determinant of a square matrix is ​​the numerical value associated with the matrix that underlies the study of square matrices. For example, a square matrix has nonzero determinant and is invertible only if the eigenvalues ​​of the square matrix are the roots of the polynomial determinant.

To know more about matrices, check out:

https://brainly.com/question/12661467

#SPJ4

The relations which are functions as required to be identified in the task content are;

It follows from the task content that the relations which are functions among the given answer choices are to be identified.

Since the definition of a function is such that; a function is a special kind of relation in which case only one output value is assigned to each input values.

Put simply, a function has only one output value for each input value.

Therefore, it follows from the definition above that the relations which are functions among the given answer choices are as listed above.

Read more on relations and functions;

https://brainly.com/question/19191518

#SPJ1

Answer:

The correct option is C

Step-by-step explanation:

Answer:

Step-by-step explanation:

78 sin

(+0

Answer:

7

Step-by-step explanation:

649-531=118

We know that there are 118 more guests per hour.

Divide 826 by 118 to get 7.

Answer: 7

Step-by-step explanation:

The first line of the table is 2 and 236 if you divide 236 by 2 you get 118

Then after that you times it by any number after 5.5 until you get 826.

When he saved $80 in March, he saved $112 in April because he intended to save 140% more than he did.

In essence, percentages are fractions with a 100 as the denominator. We place the percent sign (%) next to the number to indicate that the number is a percentage. Percentage, a relative number showing hundredth parts of any amount, is a relative measure that indicates how many questions on a test you correctly answered out of 100 (75/100). Since one percent (symbolized as 1%) is equal to one tenth of anything, 100 percent stands for everything, while 200 percent refers to double the amount specified. By dividing the total by the amount you wish to convert to a percentage. You would divide 2 by 5 in this case as 2 divided by 5 equals 0.4. The result of multiplying 0.4 by 100 is 40, or 40%.

Here,

Amount of money he saved in march=$80

Amount of money he wish to save in April,

=140%*80

=$112

He saved $112 in April when he saved $80 in March and he wanted to save 140% more than what he saved in March.

To know more about percent,

https://brainly.com/question/16797504

#SPJ4

Answer:

Domain: {9, 13, 21}

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Worth of furnishings = $1580

Tax rate = 4.5%

Tax = 4.5% × $1580 = 0.045 × $1580 = $71.10

Amount paid = $1580 + $71.10 = $1651.10

Since the decorator's fee was 12% of the purchases. This will then be calculated as:

y = kx

where,

y = decorators fee

k = percentage of decorators fee on purchases

x = amount paid

y = 12% × $1651.10

= 0.12 × $1651.10

= $198.132

Answer:

less than

Step-by-step explanation:

when you divide by a bigger number the smaller the quotient will be

Hopes this helps please mark brainliest

Step by step solution is above

Work Shown:

[tex](x_1,y_1) = (-5,-3) \text{ and } (x_2,y_2) = (8,-1)\\\\m = \text{slope} = \frac{\text{rise}}{\text{run}} = \frac{\text{change in y}}{\text{change in x}}\\\\m = \frac{\text{y}_{2} - \text{y}_{1}}{\text{x}_{2} - \text{x}_{1}}\\\\m = \frac{-1 - (-3)}{8 - (-5)}\\\\m = \frac{-1 + 3}{8 + 5}\\\\m = \boldsymbol{\frac{2}{13}}\\\\[/tex]

A slope of 2/13 means we go up 2 units and to the right 13 units. If starting at (-5,-3) and following this movement pattern of "up 2, right 13", then we arrive at (8,-1).

For the given exponential function, the value of f(3) would be f(3) = 41.472.

What is an exponential function?

The exponential function is a mathematical function that is represented by f(x)= e^x. Unless otherwise specified, the term refers to a positive-valued function of a real variable, though it can be extended to complex numbers or generalized to other mathematical objects such as matrices or Lie algebras.

The given function would be [tex]f(x)=ab^x[/tex].

The growth factor is b = 2.4

            [tex]f(0) = ab^0\\\\a=3\\[/tex]

Now find f(3),

                [tex]f(3)=3.(2.4)^x\\\\ f(3) = 3*(2.4)^3\\\\\f(3) = 41.472[/tex]

Hence, the value of f(3) would be f(3) = 41.472.

To learn more about an exponential function, visit:

https://brainly.com/question/2456547

#SPJ4

The response variable in this study is

Yield of crop.

"Information available from the question"

In the question:

A study is conducted to determine if one can predict the yield of a crop based on the amount of fertilizer applied to the soil.

Now, According to the question:

Let's know:

What is called fertilizer?

A fertiliser is a natural or artificial substance containing chemical elements (such as Nitrogen (N), Phosphorus (P) and Potassium (K)) that improve growth and productiveness of plants. Some synonyms include the terms "enrichment" or "plant nutrient".

The answer is:

Yield of crop.

Learn more about Fertilizer at:

https://brainly.com/question/891813

#SPJ4

The complete question is this:

A study is conducted to determine if one can predict the yield of a crop based on the amount of fertilizer applied to the soil. The response variable in this study is

Answer:

attached in the file

The probabilty that the first card is 7 and the second card is 6 numbered would be 0.0059.

What is probability?

Probability is a branch of mathematics that deals with numerical descriptions of how likely an event is to occur or how likely a proposition is to be true. The probability of an event is a number between 0 and 1, where 0 indicates the event's impossibility and 1 indicates certainty.

It is given that there is a deck of 52 cards.

So sample space (n) = 52.

Now in the first draw, 7 numbered card should be drawn

and there are four 7 numbered cards in a deck of 52 cards

so probability of drawing a 7 numbered card will be = 4/52 = 2/26

Now in the second draw, 6 numbered cards should be drawn

and there are four 6 numbered cards in a deck of 52 cards but already one card is drawn so there will be 51 cards remaining in the deck.

so probability of drawing a 6 numbered card will be = 4/51

Hence the probability that the first card is 7 and the second card is 6 numbered will be = 2/26 * 4/51

                             = 0.076 * 0.078

                             = 0.0059

Hence, the probabilty that the first card is 7 and the second card is 6 numbered would be 0.0059.

To learn more about probability in mathematics, visit:

https://brainly.com/question/24756209

#SPJ4