If g(x) = 2x – 9, determine g(4) – g(1)

The rational root theorem and factor theorem helps you in solving polynomial equation as they help in solving the question and finding the roots of it.

A mathematical expression made up of coefficients and uncertainty that only makes use of additions, subtractions, multiplications, and positive integer powers of variables is known as a polynomial. The formula x2 4x + 7 denotes a single indeterminate x polynomial. An expression in mathematics known as a polynomial is made up of variables (also known as indeterminates) and coefficients that may be added, subtracted, multiplied, and raised to negative integer powers of non-variables. An algebraic statement with variables and coefficients is called a polynomial. An expression can only contain the operations addition, subtraction, multiplication, and non-negative integer exponents. Polynomials are the name for these expressions.

here,

The rational root theorem and factor theorem helps you in solving polynomial equation as they help in solving the question and finding the roots of it.

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Answer:

  10 ft

Step-by-step explanation:

You have a photo of a palm tree in which the tree is 6 inches tall. The scale of the photo is 1.5 in : 2.5 ft, and you want the know the height of the actual tree.

The heights of things in the photo are presumed to be related to their actual height by the given scale factor.

  actual height / photo height = 2.5 ft / (1.5 in)

  actual height / 6 in = (2.5 ft)/(1.5 in)

Multiplying by 6 in gives ...

  actual height = (2.5 ft)(6/1.5) = 10 ft

The actual palm tree is 10 feet tall.

__

Additional comment

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Answer:

x = 1, 12

Step-by-step explanation:

Given the equation:

[tex]\displaystyle{(x-1)(x-12)=0}[/tex]

This can be set as:

[tex]\displaystyle{x-1 = 0 \ \, \text{or} \ \, x - 12 = 0}[/tex]

Solve equations like linear, add both sides by 1 for x - 1 and add both sides by 12 for x - 12:

[tex]\displaystyle{x-1 +1= 0+1\ \, \text{or} \ \, x - 12+12 = 0+12}\\\\\displaystyle{x= 1\ \, \text{or} \ \, x = 12}[/tex]

Instead of using "or" for conjunction, we can simply write the solution as x = 1, 12 (or you can also write x = 12, 1)

Additional Info

If you see the equation in form of [tex]\displaystyle{(ax+b)(cx+d)=0}[/tex] then you can just simply solve like linear separately and combine solutions together as one.

Therefore the solution to the given question is option d)128.78 for this particular equation.

Many different definitions exist for a mathematical equation. In algebra, a statement that mathematically establishes the equality of two mathematical expressions is known as an equation.. Consider the equation 3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the symbol "equal." Mathematical variables are used in even the most fundamental and straightforward algebraic equations.

Here,

=> v/9.4 = 13.7

Consider the equation 3x + 5 = 14, in which the terms 3x + 5 and 14 are separated by the word "equal." Even the simplest and most easy algebraic equations need mathematical variables.

=> v = 13.7*9.4

=> v= 128.78

Therefore the solution to the given question is option d)128.78 for this particular equation

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Answer:

0.00497512437

Step-by-step explanation:

calcuator

Answer: 0.00497512437

Step-by-step explanation:

To divide a decimal number by a whole number, long divide as you would with two whole numbers, but put the decimal point in the answer at the same place it is at in the dividend. If it does not divide evenly, add a 0 to the end of the dividend and continue dividing until there is no remainder.

The length of the side of the given square is 12.3 inches approx.

Due to the fact that this particular group of numbers makes up a square, they are known as square numbers (or squared numbers).

Finding the area of a square is easy because they all have equal sides. Just "square" (multiply by itself) one of their sides!

So, we have:

The area of the square is 151 in².

Area formula: s²

Now, calculate the length of the side as follows:

A = s²

151 = s²

s = √151

s = 12.3 approx

Therefore, the length of the side of the given square is 12.3 inches approx.

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Therefore , the solution of bar graph is estimated number of the pizza sold on 30 days = 1200

A bar graph is a graphical depiction of information, amounts, or numbers using bars or strips. They are employed to contrast and compare various data types, frequencies, or other measurements of various categories of data.

Here,

Given : The data set from the bar chart is

20, 30, 40, 35, 25

Total number of pizza sold on a day = 20 + 30 + 40 + 35 + 25= 150

Number of pizza of type T3 sold on a day = 40

Estimated number of pizza sales (T3) on 30 days = 40

150×4500= 1200

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Good models are expected to reflect the number of books sold between zero and w numbers of weeks where w is defined.

What is a domain?

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.

Here, we have

Given: The function f gives the number of copies a book has sold w weeks after it was published. The equation f(w) = 500 * 2^w defines this function.

The following are all domains for which the average rate of change could be a good measure of the number of books sold:

0 ≤ w ≤ 2

0 ≤ w ≤ 7

0 ≤ w ≤ 10

Hence, good models are expected to reflect the number of books sold between zero and w numbers of weeks where w is defined.

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Answer: 6/7 / 2/9 = 3/1 or 3 ✅

PLEASEEEE GIVE BRANLIEST

Step-by-step explanation:

To divide two fractions, you can invert the second one (the one being divided by) and then multiply the two fractions.

So:

(6/7) / (2/9) = (6/7) * (9/2)

To multiply the fractions, you just multiply the numerators together and multiply the denominators together.

(6/7) * (9/2) = (69)/(72)

= 54/14

So the final answer is 54/14.

You can also simplify the fraction by dividing the numerator and denominator by their greatest common factor.

54/14 = 3/1

So the final answer is 3/1 which is 3.

The angles EBI and BCJ are complementary. Show that the corresponding angles are congruent by transforming angle EB1 to angle BCJ. Orient point C at angle BCJ by 180 degrees. reflecting from line BCJ over angle BC Angle BCJ is translated by the directed line segment from C to B.

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Answer:-3x-1

Step-by-step explanation:

First we remove the parentheses and we will get 6x+2-9x-3

second, we combined like term 6x and -9x can combine and 2 and -3 can combine we will get 6x-9x and -1

third, we mix it together and can get -3x-1

We can answer any quadratic equation using the quadratic formula. The first step is to change the equation's form to ax2+bx+c=0, where a, b, and c are the coefficients. The formula is then updated with these coefficients:

[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

We observed that many real-world scenarios can be represented by quadratic equations. Let's study about the many ways to solve quadratic equations now that we are familiar with what they are.

Three basic approaches can be used to resolve quadratic equations:

(1) The use of factors

(2) Using the square approach to finish

(3) Formula for a Quadratic Equation

The two approaches mentioned above are ineffective for some equations. Such equations call for a more robust approach. A technique that is applicable to all quadratic equations.

This is the formula for a quadratic equation in general. It is described as follows: The value of x is determined by the following equation if the quadratic equation ax2 + bx + c = 0 is true:

[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

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Answer:

Step-by-step explanation:

6.56

Answer:

53

Step-by-step explanation:

[tex]\frac{477}{9}[/tex]

    53

9[477]

 -45

     27

    -27

       0  

i and iv are correct  in a 45° - 45° - 90° triangle?|. The legs are congruentII. The length of the hypotenuse is twice the length of the shorter leg.

in 45 -45-90 triangle the legs are both 1 units in length and the hypotenuse is sqrt 2

sqrt2 ^2 = 1^2+1^2

this denotes our measurement is true

if the legs ofa right triangle are a and b and the hytponuse is c then

a²+b²=c²

lets say

a>b

so

longer leg is 4ft longer than shorter

a=4+b

hypotnuse is 8ft longer than shorter

c=8+b

teh equation in terms of b and solve

a²+b²=c²

subsitute

(b+4)²+b²=(b+8)²

b²+8b+16+b²=b²+16b+64

2b²+8b+16=b²+16b+64

minus (b²+16b+64) from both sides

b²-8b-48=0

what 2 numbers multiply to get -48 and add to get -8?

-12 and 4

(b-12)(b+4)=0

set equal to 0

b-12=0

b=12

b+4=0

b=-4

false, can't have negative length

b=12

so

a=4+b

a=4+12

a=16

c=8+b

c=8+12

c=2

shorter leg: 12ft

longer leg: 16ft

hypotonuse: 20ft

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Sam's rationale for the third step based on logarithm properties would be logb(b^x+y), power rule of exponents. Thus, the correct answer is C.

The first step of Sam's proof is to show that logb(MN) is equal to logb(b^x.b^y), which is a substitution of MN for b^x.b^y. This is based on the product property of logarithms, which states that logb(MN) = logb(M) + logb(N) for any positive numbers M and N and any base b, as long as b doesn't equal 1.

The third step of her proof is to simplify logb(b^x.b^y) further by applying the power rule of exponents, which states that:

So, by substituting b^(x+y) for b^x.b^y, we get:

So, in short, the justification of the third step is based on the power rule of exponents, and it shows that logb(b^x.b^y) can be simplified further to logb(b^x+y).

The answer choice A, logb(b^xy), power rule of exponents, is incorrect because it implies that the third step is to multiply x and y instead of adding them.

This question should be provided with answer choices, which are:

The correct answer is C.

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Answer: its c

Step-by-step explanation:

cop a hoodie at moneymotivated.us thanks

The minimum and maximum possible volume for a rectangular right prism are 1221.875 and 1603.125 cubic inches.

In this problem we must determine the minimum possible and maximum possible volumes for a rectangular right prism, whose volume formula including length uncertainties is shown below:

V = (w ± Δw) · (l ± Δl) · (h ± Δh)

Where:

Please notice that minimum possible volume is found when all "±" operators are replaced by "-" operators and that maximum possible volume is found when all "±" are replace by "+" operators. Given that statement does not mention the value of every length uncertainty, we assume that Δw = Δl = Δh = 0.5 in.

If we know that w = 12 in, l = 13 in, h = 9 in and Δw = Δl = Δh = 0.5 in, then the minimum and maximum possible volumes are:

Minimum possible volume

V = (12 in - 0.5 in) · (13 in - 0.5 in) · (9 in - 0.5 in)

V = (11.5 in) · (12.5 in) · (8.5 in)

V = 1221.875 in³

Maximum possible volume

V = (12 in + 0.5 in) · (13 in + 0.5 in) · (9 in + 0.5 in)

V = (12.5 in) · (13.5 in) · (9.5 in)

V = 1603.125 in³

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On solving the provided question,  annual rate is 2% while doing calculations through simple interest.

Borrowers must pay simple interest to lenders as a fee for a loan. Compound interest is not taken into account while calculating it; just the principal is used. Simple interest is applicable to all loans. It is also the form of interest that banks give their customers on their savings accounts. Simple interest can be calculated using a simple formula. Simply multiply the loan's principal by the interest rate and the period to get the total. Although some mortgages employ this calculation approach, this type of interest typically relates to auto loans or short-term loans.

Let the annual rate be x%

Principal Amount (p)= $600

Annual Rate (r) = x % (Assumed)

Time (t) = 5 years

Simple Interest (I) = $60

Use the simple interest formula given below:

SI = p×r×t/100

r = 60 ×100/600× 5

r = 2%

Thus, the annual rate of interest is 2 %.

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Question:

April took out a $600 loan from the bank. At the end of 5 years, she pays back the principal, plus $60 simple interest. What was the interest rate? Enter your answer in the box.

Interior angles on the same side The same-side interior angles are additional if a transversal connects two parallel lines.

A triangle, which is a polygon, has three sides and three vertices. One of geometry's basic shapes is it. A triangle with the vertices A, B, and C is referred to as Triangle ABC. A unique plane and triangle are discovered in Euclidean geometry when the three points are not collinear. Having three sides and three corners, a triangle is a polygon. The triangle's corners are defined as where the three sides meet one another end to end. 180 degrees is the sum of the angles in a triangle.

given

The Isosceles Triangle Theorem's opposite is also accurate.

A triangle's opposite sides are congruent if two of the triangle's angles are.

Each right angle exists when two angles are complementary and congruent. Interior angles on the same side The same-side interior angles are additional if a transversal connects two parallel lines.

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a) Melissa's monthly payment for the promissory note is $133.10.

b) The total monthly payment amounts to $6,388.80.

c) The total finance charge is $388.80, which is the difference between the total payment and the promissory note amount.

The monthly payment represents the equal periodic payment made to settle the loan and the finance charge.

Using an online finance calculator, we can compute the monthly payment, total payments, and finance charges.

N (# of periods) = 48 months (4 years x 12)

I/Y (Interest per year) = 3.11%

PV (Present Value) = $6,000

FV (Future Value) = $0

Results:

PMT (Monthly Payment) = $133.10

Sum of all periodic payments (Total Payments) = $6,388.80

Total Interest (Finance Charge) = $388.80

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Answer: All Real Numbers Except "-8" (R - {-8})

Step-by-step explanation:

The domain of a function is all possible x values that the function can be defined with.

This means that if a value does not create any indeterminate situation, we can consider this value is in the domain of a function.

For this function, "-8" is not in the domain of the function because the denominator of a rational fraction cannot be zero in any case. This creates an indeterminate situation, therefore we do not consider "-8" in the domain of the function.

But for the other values, there is no problem since the denominator cannot be zero without x = -8.

In this rule, we have to find the value of any of the variables either first or second and substitute its value in the other equation.

It is best to use the substitution method when equations are either given in form or can be gain into the form of x = ay + b and y = mx + n.

A procedure to answer a system of linear equations in more than two variables algebraically is the substitution method. In this process, we find the value of any one of the variables by alienating it on one side and taking every other term on the other side of the equation.

Then we substitute that first value in the second equation.

The substitution method is one of the algebraic processes to answer simultaneous linear equations. It implies substituting the value of any one of the variables from one equation into the other equation.

And at last, we can put the value of y in any of the given equations to find x.

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D) Moving Expenses is an adjustment allowed by the IRS.

The IRS allows certain deductions or adjustments to income for individuals who meet certain qualifications. Some examples of these deductions or adjustments include medical expenses, certain taxes, and certain work-related expenses.

Moving expenses are also an adjustment allowed by the IRS, if you move due to change in your job or business location, or because you start a new job or business. You can deduct certain expenses of moving to the area where you will be working, such as the cost of getting yourself and your household goods to your new home, and lodging during the move.

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The addition and subtraction of the fractions gives 9/(x+3)²(x-3)²

A fraction can be described as one part of a whole number, element or variable.

In mathematics, there are different types of fractions which includes;

From the information given, we have the fractions;

1/(x -3)² - 2/x² - 9 + 1/(x+3)²

Note that with the knowledge of difference of two squares;

x² - 9 is equivalent to (x+3)(x-3) = (x-3)²

Now, let's take the lowest common multiple

(x+3)² -2(x+3)(x-3) +(x-3)²/ (x+3)²(x-3)²

expand the bracket

x²+3x+3x+9 -2x² -6x +6x +9 + x² -3x -3x - 9/ (x+3)²(x-3)²

Add like terms

9/(x+3)²(x-3)²

Hence, the value is 9/(x+3)²(x-3)²

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The area of the circle, considering it's diameter of 5.35, is given as follows:

22.48 units squared.

The area of a circle of radius r is given by π multiplied by the radius squared, as follows:

A = πr²

The diameter for the circle in this problem is given as follows:

5.35.

The radius is half the diameter, hence it's length is given as follows:

r = 0.5 x 5.35

r = 2.675.

Hence the area of the circle is given as follows:

A = π x (2.675)²

A = 22.48 units squared.

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Down Below

Angle bisector

An angle bisector is a line segment, ray, or line that divides an angle into two congruent adjacent angles.

Line segment OC bisects angle AOB above. So, ∠AOC = ∠BOC which means ∠AOC and ∠BOC are congruent angles.

Bisecting an angle with compass and ruler

In geometry, it is possible to bisect an angle using only a compass and ruler. To do so, use the following steps:

Things to know about an angle bisector

If a point lies anywhere on an angle bisector, it is equidistant from the 2 sides of the bisected angle; this will be referred to as the equidistance theorem of angle bisectors, or equidistance theorem, for short.

In the figure above, point D lies on bisector BD of angle ABC. The distance from point D to the 2 sides forming angle ABC are equal. So, DC and DA have equal measures.

Conversely, if a point on a line or ray that divides an angle is equidistant from the sides of the angle, the line or ray must be an angle bisector for the angle.

Based on the equidistance theorem, it can be seen that when the two sides that make up an angle are tangent to a circle, the line segment or ray formed by the angle's vertex and the circle's center is the angle's bisector.

In the diagram above, the two sides of the angle are tangent to the circle and, DC and DA are the distances from the center of the circle to the sides. DC and DA are also the radii of the circle. Since all radii of a circle have equal measure, line BD bisects the angle.

Angle bisector theorem

For a triangle, like the one in the diagram below, if the bisector of angle A intersects side BC at point D, the ratio of the lengths of AB to AC equals the ratio of the length BD to DC. This can be written as: [tex]\frac{AB}{AC}=\frac{BD}{DC}[/tex]

The point at which the three interior angle bisectors intersect is known as the incenter of the triangle. Referencing the diagram below, the three bisecting rays intersect at point D. Point D is the incenter of the triangle and is a point that is equidistant from the three sides of the triangle.

Extra:

I hope this helped at all.

We get the Polynomials  quotient and remainder as 2x+7 and 5 respectively.

An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.

A polynomial is an equation made up of coefficients and indeterminates that uses only the addition, subtraction, multiplication, and powers of positive-integer variables.

Polynomial long division is an extended variant of the well-known mathematical operation known as long division. It is an algorithm for dividing a polynomial by another polynomial of the same or lower degree. Due to the fact that it breaks down a more difficult division issue into simpler ones, it may be completed quickly by hand.

The polynomials are

2X^2 - X +16

and

x - 3

Dividing  by 2X^2 - X +16 BY x-3 = 2x + 7

We get the quotiant and remainder as 2x+7 and 5 respectively.

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  n = -6 is the value of n in the expression .

What does a mathematical expression mean? 

A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation. This mathematical operation may be addition, subtraction, multiplication, or division.

                 Any combination of a number, a variable, and operation symbols is considered an expression. Two expressions are combined to form an equation, which is joined by the equal sign.

   (Xⁿ)  =  (X⁻⁸)(X²)

  (Xⁿ)  = X⁻⁸⁺²

  (Xⁿ)   = X⁻⁶

  n = -6

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