Write the formula for slope, for the point-slope
form of a line, and for the slope-intercept form of a
line.

Answers

Answer 1
Slope: M = rise/run = y2 - y1/x2 - x1

Point slope: y-y₁=m(x-x₁)

Slope-intercept: y = mx+b

Related Questions

How do you solve this?

Answers

∠1and∠2 form a linear pair, so by the Supplement Postulate, they are supplementary. That is, m∠1+m∠2=180°. m∠2+m∠3=180°.

What are the measures of ∠ 1 and ∠ 2?

We must determine the dimensions of angles 1 and 2. The geometric property can be used to: When two chords collide inside of a circle, the angle that is created is half the total of the intercepted arcs of the chords. In light of this, m1 = 50° and m2 = 130°.

According to the diagram, the angles 1 and 3 are vertical, and m1 = 90. Since their measurements are equivalent, m3 = 90 and 1 and 2 are additional. Angles 1 and 2 compliment one another. Two additional angles, the total of whose measurements equals 180 degrees.

The angles 1 and 2 complement one another. Because they have a similar side, angles 1 and 2 are neighbouring angles. Adjacent angles are two angles in a plane that do not share interior points but do share a vertex and a side.

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Addison has x pennies and y nickels. She has a minimum of 16 coins worth no more than $0.40 combined. Solve this system of inequalities graphically and determine one possible solution.
Inequality 1
Inequality 2

Answers

From the graph, a possible solution to the inequalities x + y ≥ 16 and 0.01x + 0.05y ≤ 0.4 is (15, 2)

What is an equation?

An equation shows how two or more numbers and variables are related to each other.

Let x represent the number of pennies and y represent the number of nickels. One penny = $0.01 and one nickel = $0.05

She has a minimum of 16 coins, hence:

x + y ≥ 16     (1)

Also:

It is no more than $0.40 combined, hence:

0.01x + 0.05y ≤ 0.4    (2)

From the graph, a possible solution is (15, 2)

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Darren is purchasing a car that costs $11,000. He is taking out a simple interest loan at an annual rate of 3%. If he makes monthly payments over a period of 5 years, how much is his monthly payment?

$183.33
$191.67
$198.05
$210.83

Answers

Darren makes $210.83 monthly payments over a period of 5 years. Therefore, option D is the correct answer.

What is the simple interest?

Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time.

Simple interest is calculated with the following formula: S.I. = (P × R × T)/100, where P = Principal, R = Rate of Interest in % per annum, and T = Time.

Given that, principal =$11,000, rate of interest =3% and time period = 5 years.

Now, S.I. =(11,000×3×5)/100

= $1650

Now, 11,000+1650 =$12650

In 5 years there are 60 months

So, 12650/60

= $210.83

Therefore, option D is the correct answer.

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list 3 values that would make this inequality true: 42 <_ y

Answers

Answer:

42, 50, 60

Step-by-step explanation:

42 is less than or equal to y.

That means y is greater than or equal to 42.

Answer: 42, 50, 60

Solve using methods 8148- 2077

Answers

8 148

- 2 077

______

6 07 1

_______

you cannot minus 7 from 4 so you borrow from the next number which is 1 then it will be 14-7 and 0-0

Luis drank 4 pints of juice from the carton. did luis drink closer to 9.5 cups or 7.5 cups of juice?

Answers

Answer:

Step-by-step explanation:

9.5

Question 1 When using the simple interest formula ( i = Prt ) the time t , is expressed inithe same period as the rate. True /False

Answers

The correct answer is true, When using the simple interest formula the time t, is expressed in the same period as the rate.

We can say that the answer is true due to the following reasons,

As we already know, the formula for simple interest is:

Simple Interest = Principal Amount * Rate of Interest * Time of interest

Here the Principal amount is the amount that is deposited and over which we will be receiving our interest.

We all know the rudimentary rule of solving any question is that the units and dimensions of the variables and values should be correct. It means that when we are solving any question where the unit being used is different from the required one, we need to perform unit conversion to get the necessary unit.

When it comes to Simple Interest, the variable unit is time, that is, it can be in hours, days, weeks, months, or years. The rate of interest is generally given in "per annum" which means 'per year.' Therefore we need the unit of time in the year or according to the unit in which rate is given to us.

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kaden used 2.25 cups of water in his lemonade mixute that serves 9 people how much more water is in one serving in christian lemonade

Answers

division

john stops at toy store a to buy 16 toy cars. Toy store A sells 6 toy cars for $4.20. John stops at toy store b and sees that they sell 4 toy cars for $3.80. How much money did John save by buying toy cars at toy store A?

Use the distributive property to multiply 7 x 9.
Enter your answer by filling in the boxes.
7x9=7x (5+ ? )
7x9=( ? x5)+(7x ? )
7x9= ? + ?
7x9= 63

Answers

The product of each addend times the third number (7 x 9 = 63) is the sum of two numbers multiplied by a third number.

What property is used to multiply?The distributive, commutative, associative, removes the neutral element, and associative properties of multiplication.Similar to 7 x 9 = 63, 7 x 9 = 7(4 + 5) = (7 x 4) + (7 x 5) = 28 + 35The associative quality of addition The amount remains unchanged when the order of the addends is changed. For instance, (2 + 3) + 4 = 2 + (3 + 4); (2 + 3) + 4 = 2 + ((3 + 4); Right parenthesis plus 2, plus, left parenthesis plus 3, plus, 4, equals 2, plus, right parenthesis plus.According to the commutative property of multiplication, changing the order of the elements has no impact on the final result. As an illustration, consider the following 4 × 3 = 3 × 4 4 x 3 = 3 x 4 = 4 x 3 = 3. Ab = ba when multiplying. Simply stated, this law adds that.

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Which ordered pairs are solutions to the system of equations (-2,1.6)(0,3 3/5)(2,5 3/5) y=-0.5x+0.6
Y=x+3 3/5

Answers

Result is x = - 2 and y = 1.6 so the ordered pair ( -2, 1.6) is the solution of the system equations.

What is equation?

It is a mathematical expression that shows the equalities between two or more terms. There are different types of equation such as linear equation, quadratic equation, exponential equation and so on.

Which is the solution of the systems of equations?

Given, the two systems of equation.

y = - 0.5x + 0.6

and y = x + 3³₅

rewrite the second equation and get y = x +18/5

                                                       5y = 5x + 18 ....  equation 2

                   the first equation is multiplied by 5 and we get.

                                               5y = - 2.5 x + 3

                                               5y = 5x +18

                                            -          -     -

                        we will now solve the above equations by addition method.

                                       0 = - 7.5 x - 15

                                    7.5 x = - 15

                                     x = -2

        putting the value of x in any equation, we get the value of y = 1.6

    x = - 2 and y =1.6

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7. Select the proper order from least to greatest for 2/3, 1/6, 1/8, 10-
O A. 1,3,9/10, 7-
O B. 1, 10, 76,2/3-
O C.3, %10, 6, 18.
O D., %10, 2/3, 18.

Answers

Therefore , the solution of the given problem of order comes out to be

1/8 < 1/6 < 2/3 < 10 .

Define order.

Thus putting things where they belong in accordance with some norm. The shapes in this image are arranged according to how many sides it have. Another illustration is to sort the integers 3, 12, 5, 2, and 9 from highest through lowest.

Here,

Given :

2/3 , 1/6 . 1/8 and 10

So ,

To form a proper order from least to greatest

Thus , ascending order:

So,

=> 1/8 < 1/6 < 2/3 < 10

Therefore , the solution of the given problem of order comes out to be

1/8 < 1/6 < 2/3 < 10 .

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NO LINKS!!

1. An arithmetic sequence that has t(28) = 6 and t(22) = 42. Write a rule to describe the sequence.

2. Kim invested $5000 in a Mutual fund at 7.6% compounded quarterly.
a. Write an equation to represent this situation
b. When will her investment be worth more than $10,000.

Answers

Answer:

[tex]\textsf{1.} \quad a_n=174-6n[/tex]

[tex]\textsf{2.\;a)} \quad A=5000\left(1.019\right)^{4t}[/tex]

   b)  9.25 years (to the nearest quarter)

Step-by-step explanation:

Question 1

[tex]\boxed{\begin{minipage}{8 cm}\underline{General form of an arithmetic sequence}\\\\$a_n=a+(n-1)d$\\\\where:\\\phantom{ww}$\bullet$ $a_n$ is the nth term. \\ \phantom{ww}$\bullet$ $a$ is the first term.\\\phantom{ww}$\bullet$ $d$ is the common difference between terms.\\\phantom{ww}$\bullet$ $n$ is the position of the term.\\\end{minipage}}[/tex]

Given terms of an arithmetic sequence:

[tex]a_{28}=6[/tex][tex]a_{22}=42[/tex]

Substitute the given values into the arithmetic sequence formula to create two equations:

[tex]\implies a_{28}=a+27d=6[/tex]

[tex]\implies a_{22}=a+21d=42[/tex]

Subtract the second equation from the first equation to eliminate a and solve for d:

[tex]\implies 6d=-36[/tex]

[tex]\implies d=-6[/tex]

Substitute the found value of d into one of the equations and solve for a:

[tex]\implies a+27(-6)=6[/tex]

[tex]\implies a-162=6[/tex]

[tex]\implies a=168[/tex]

Substitute the found values of a and d into the formula to create an equation for the nth term of the sequence:

[tex]\implies a_n=168+(n-1)(-6)[/tex]

[tex]\implies a_n=168-6n+6[/tex]

[tex]\implies a_n=174-6n[/tex]

Question 2

[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Compound Interest Formula}\\\\$ A=P\left(1+\frac{r}{n}\right)^{nt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $n =$ number of times interest is applied per year \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]

Given values:

P = $5000r = 7.6% = 0.076n = 4 (quarterly)

Substitute the given values into the compound interest formula to create an equation with respect to time, t:

[tex]\implies A=5000\left(1+\dfrac{0.076}{4}\right)^{4t}[/tex]

[tex]\implies A=5000\left(1.019\right)^{4t}[/tex]

To find when the value of the investment will be worth more than $10,000, substitute A = 10000 into the equation:

[tex]\implies 10000 < 5000\left(1.019\right)^{4t}[/tex]

[tex]\implies 2 < \left(1.019\right)^{4t}[/tex]

[tex]\implies \ln 2 < \ln\left(1.019\right)^{4t}[/tex]

[tex]\implies \ln 2 < 4t\ln\left(1.019\right)[/tex]

[tex]\implies \dfrac{\ln 2}{4 \ln\left(1.019\right)} < t[/tex]

[tex]\implies t > 9.20672924...[/tex]

Therefore, the investment will be worth more than $10,000 from 9.25 years (to the nearest quarter).

What is the range of y=|x-4|-2

Answers

Domain of  y=|x-4|-2 : (-∞, ∞) by -∞ < x < ∞

Range of y=|x-4|-2: [-2, ∞) by F(x) ≥ -2

What is meant by range of function?

When a function is applied to its entire set of outputs, the set of outputs it produces is known as its range. The set of things that really leave the function machine after you give it all the inputs is referred to as the range in the metaphor. The set of possible output values for a function is its range.

The range of values that can be plugged into a function is known as its domain. The x values for a function like f are contained in this collection (x). The collection of numbers that the function assumes is known as its range. Following the insertion of an x value, the function outputs this sequence of values.

Domain of  y=|x-4|-2 : (-∞, ∞) by -∞ < x < ∞

Range of y=|x-4|-2: [-2, ∞) by F(x) ≥ -2

Axis interception points of |x - 4| - 2:

X Intercepts: (2, 0), (6, 0), Y Intercepts: (0, 2)

Asymptotes of |x - 4| - 2 : None

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SOMEONE PLEASE HELP does anyone know the answers for

I can only attach one image

Exploring Congruent Triangles - Alternate Portfolio

Answers

So on solving the provided question we can say that here, in triangle ABC and XYZ;  by SSS property they are similar.

What is triangle?

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

here,

AB = XY

AC = XZ

BC = ZY

by SSS property, they are similar.

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The sum of three consecutive numbers is 150. Find them.

Answers

The sum of three consecutive numbers for 150 is 49,50,51.

Three consecutive numbers:  x+(x+1)+(x+2)

x+x+1+x+2= 150

3x+3 = 150

3x = 150-3

3x= 147

X = 147/3

49 =x

But we also need to find (x+1) and (x+2)

49+1= 50

49+2= 51

49+50+51 = 150

The three consecutive numbers are 49,50,51.

Meaning: Numbers that follow one another numbers sequentially are known as consecutive numbers. The difference between any two numbers is always 1. A series of numbers' mean and median are equal. If n is a number, then it follows that n, n+1, and n+2 are also numbers. Examples. 1, 2, 3, 4, 5.

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Which expression is equivalent to (1/512) ^1/3? PLEASE HELP

Answers

Option D is correct, [tex](\frac{1}{512}) ^{\frac{1}{3} }[/tex] is equivalent to [tex](\frac{1}{64}) ^{\frac{1}{2} }[/tex]

What is Expression?

An expression is combination of variables, numbers and operators.

Let us simplify using [tex]a^{\frac{n}{m} } =\sqrt[m]{a^{n} } :\sqrt[3]{\frac{1}{512} }[/tex]

Rewrite the expression using [tex]\sqrt[n]{ab} =\sqrt[n]{a} .\sqrt[n]{b} :\frac{1}{\sqrt[3]{512} }[/tex]

Factor and rewrite the radicand in exponential form :1/8

simplify using [tex]a^{\frac{n}{m} } =\sqrt[m]{a^{n} } :\sqrt{\frac{1}{64} }[/tex]

Rewrite their expression using  [tex]\sqrt[n]{ab} =\sqrt[n]{a}.\sqrt[n]{b} :\frac{1}{\sqrt{64} }[/tex]

Factor and rewrite the radicand in exponential form : 1/8

Hence, option D is correct, [tex](\frac{1}{512}) ^{\frac{1}{3} }[/tex] is equivalent to [tex](\frac{1}{64}) ^{\frac{1}{2} }[/tex]

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Solve the right triangle if the hypotenuse is 5 and one acute angle is 34°. Round answers to two decimal places.

Answers

The other two sides of the triangle are 2.795 and 4.095 respectively.

What is the triangle?

Generally, The right triangle is a right-angled triangle where one angle is 90 degrees.

If the hypotenuse is 5 and one acute angle is 34°, we can use trigonometry to find the other two sides of the triangle.

Using sine function, the side opposite to 34° angle is

=(sin 34°) * hypotenuse

= 0.559 * 5

= 2.7959

Using cosine function, the side adjacent to 34° angle is (cos 34°) * hypotenuse = 0.819 * 5

= 4.095

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the total cost, c, of renting a canoe for n hours can be represented by a system of equation.

Answers

The expression which represents the total cost of renting is C = nx.

What is an expression?

An expression is a mathematical phrase that can contain numbers, variables, and operators. It represents a value or a calculation, but it does not necessarily have an equal sign (=) to indicate that it is an equation.

Let us consider that, renting a Canoe for one hour is  $ x.

The total cost of renting is represented by C.

Since renting a Canoe for one hour is  $ x.

So that, for n hours, renting cost  = n*x

The total cost of renting, C= nx

Hence, the expression which represents the total cost of renting is C = nx.

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I missed the lesson today, I’m not exactly sure what to do for these.

Answers

Answer:

You graph them.

Go to desmos and put the equations in the calculator. It will graph them for you. Or you could graph them on paper, like the y-intercept is the amount you start with, like 11 or 2 in question 3. then you go two up and one to the side or 1 up and one to the side, depending on how many x there is. or how much the slope is. Like y=x+2 is where you start with (0,2) plot it and then you go one up, one to the side, and then repeat twice. Then plot the line. and in y=11-2x you plot (0,11) and then go down two, one to the side, and repeat twice. Then plot the line.

In question 4, y=3-2x, plot point (0,3) and then go two down, one to the side, and repeat twice. Plot the line. in y=1+2x, plot point (0,1) and then go two up, one to the side.

that's how you plot the slope equation.

Step-by-step explanation:

Match the vocabulary to the proper definition. 1. a number or a variable, or the product of a number and variable(s) variable 2. a number; a term containing no variables constant 3. an equation that uses variables to state a rule term 4. one term or multiple terms connected by an addition or subtraction sign expression 5. a letter or symbol used to represent an unknown number formula

Answers

1.)Monomial 2.) Constant term 3.) Formula 4.) Expression 5.)Variable.

What is a monomial?

A monomial is defined as an algebraic expression with one term, but it can have many variables and higher degrees. It can also be defined as the product of a number and variable(s).

Constant term is defined as the term that contains only a number with no variables.

A formula is defined as an equation that uses variables to state a rule term.

An expression is defined as one term or multiple terms connected by an addition or subtraction sign expression.

A variable a letter or symbol used to represent an unknown number formula.

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What is an equation of the line through (0, -3) with slope 25?

Answers

Answer:

y = (2/5)x - 3

Step-by-step explanation:

Brainliest pls

Answer: y = mx + b

y=-3  x=0 and m=2/5

-3 = (2/5)0 + b

Since 2/5(0) is 0, b must be -3

Step-by-step explanation: Since you know the slope and you know one point, all you have to do is plug the slope and the coordinates into the slope-intercept form and solve for b. You can check your answer by finding another point on the line and verifying that the equation works for that point, as well. Add the slope to the given point and you get ( 5 , -1 )

-1 = (2/5)5 - 3

-1 = 2 - 3 -1 = -1 So you know your answer is correct

Ellis drinks 12 ml of yogurt drink every day. The carton holds 1.5L. How many days will the carton last?

Answers

Answer:

125 days

Step-by-step explanation:

1.) First, you need to make the number equivalent!

1.5L=1500mL

2.) Then you need to divide 1500mL by how much she drinks every day!

1500mL divide by 12mL = 125 days

So the carton will last 125 days

:) Hope you have a good day!

Answer:

the carton will last for 125 days

Step-by-step explanation:

carton contain 1.5L

1.5L= 1.5×1000ml

= 1500ml

1day=12ml

1/12 ×1500 days = 1500ml

125 days = 1500ml

If Ellis drink 12ml of yoghurt everyday then the carton with 1.5L will last for 125 days.

Find the measure of the missing angles.

Answers

Answer:

<d=102°[Vertically opposite angles are equal]

<e=36°[Vertically opposite angles are equal]

<d+<f+<e=180°[Sum of angle on St.line supplementary]

or,102°+36°+<f=180°

or,<f=180°-102°-36°

:.<f=42°

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Write each expression without using exponents

5^2/3

4^-3/2




Answers

So, here on solving the provided question, we can say that  [tex]5^{2/3}[/tex] to write it without exponent = [tex]25^{1/3} = 1.70997594668[/tex] and [tex]4^{-3/2} = 64^{1/2} = 8[/tex]

what are exponents?

Exponentiation, often known as "b raised to the nth power," is a mathematical operation denoted by the symbol bn that involves two numbers: a base number, b, and an exponent, or power, n. Exponents show how many times a number has been multiplied by itself. As an illustration, 2-3 (written as 23) denotes: 2 x 2 x 2 = 8. 23 is not equivalent to 2 + 3 = 6. Recall that an integer raised to the power of one equals itself. A approach to express huge numbers as powers is through the use of exponents. Exponent, then, is the quantity that indicates how many times a number has been multiplied by itself. As an illustration, 6 is multiplied by 4 to provide 6 x 6 x 6 x 6. It may be expressed as 64.

here,

we have [tex]5^{2/3}[/tex] to write it without exponent = [tex]25^{1/3} = 1.70997594668[/tex]

and [tex]4^{-3/2} = 64^{1/2} = 8[/tex]

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Find the area of the figure pictured below

Answers

47 is the answer

27+20= 47 ft ^2
Answer for that is 47

What's the numerator for the following rational
expression?

Answers

The numerator for the following rational expression G/h + 8/h = ?/h will be g + 8.

What is a rational expression?

Simply put, a rational expression is the product of two polynomials. Or to put it another way, it is a fraction with polynomials as the numerator and denominator. A function whose value is determined by a rational expression is said to be rational.

Rational expressions resemble fractions with variable denominators and frequently, numerators as well. As you can see, there is h is denominator on both right hand side and left hand side. So, you can eliminate it and can consider all numerators as a whole at a time. Then, it will be: G+8 = G+8

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Complete question

What's the numerator for the following rational expression? G/h + 8/h = ?/h

A game includes spinning the spinner with 6 equal sections and then rolling a number
cube with numbers 1-6.
What is the probability of spinning yellow and having the number cube show an odd
number?

Answers

Because its a 1 in 6 chance to roll a five and a 1 in 4 chance to roll a yellow then you do 6 x 4 = 24.

What is probability?Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. Probability has been introduced in Maths to predict how likely events are to happen. The meaning of probability is basically the extent to which something is likely to happen. This is the basic probability theory, which is also used in the probability distribution, where you will learn the possibility of outcomes for a random experiment. To find the probability of a single event to occur, first, we should know the total number of possible outcomes.

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Write the equation of a line with a slope of -2 and a y-intercept of 5. Responses y = −2x −5y = −2x −5 y = 2x +5y = 2x +5 y = 2x −5y = 2x −5 y = −2x +5 i only have 5 mins pls hurry

Answers

The linear function f with the given values is y = -2x + 5

How to determine the linear function f with the given values.

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

a slope of -2 and a y-intercept of 5

A linear equation can be represented as

f(x) = mx + c

Where

m = slope

c = y-intercept

This means that

m = -2

c = 5

Substitute the known values in the above equation, so, we have the following representation

y = -2x + 5

Hence, the function is y = -2x + 5

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help im in dire need of assistance

Answers

Dividing 3x³ - 4x² - 9x + 15 by 3x + 5. will yield a quotient of x² - 3x + 2 and a remainder of 5 that is (x² - 3x + 2) + 5/(3x + 5).

Calculating for the quotient and remainder

Applying the long division method will require us to; divide, multiply, subtract, bring down the next number and repeat the process to end at zero or arrive at a remainder.

We shall divide the 3x³ - 4x² - 9x + 15 by 3x + 5 as follows;

3x³ divided by 3x equals x²

3x + 5 multiplied by x² equals 3x³ + 5x²

subtract 3x³ + 5x² from 3x³ - 4x² - 9x + 15 will result to -9x² - 9x + 15

-9x³ divided by 3x equals -3x

3x + 5 multiplied by -3x equals -9x² - 15x

subtract -9x² - 15x from -9x² - 9x + 15 will result to 6x + 15

6x divided by 3x equals 2

3x + 5 multiplied by 2 equals 6x + 10

subtract 6x + 10 from 6x + 15 will result to a remainder of 5

Therefore by the long division method, 3x³ - 4x² - 9x + 15 by 3x + 5 gives a quotient x² - 3x + 2 and a remainder of 5 and can be written as (x² - 3x + 2) + 5/(3x + 5).

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Kurtiss has a client who wants to invest in an account that earns 6%
interest, compounded annually. The client opens the account with an
initial deposit of $4,000, and deposits an additional $4,000 into the
account each year thereafter.
Assuming no withdrawals or other deposits are made and that the
interest rate is fixed, the balance of the account (rounded to the
nearest dollar) after the fifth deposit is

Answers

If a client of Kurtis's opens an account that earns 6% compounded annually and deposits $4,000 initially with additional deposits of $4,000 each year for 5 years, the account's balance (future value) will be $27,901.27.

What is the future value?

The future value is the amount of the present investments compounded into the future at an interest rate.

The future value can be determined using an online finance calculator as follows:

N (# of periods) = 5 years

I/Y (Interest per year) = 6%

PV (Present Value) = $4,000

PMT (Periodic Payment) = $4,000

Results:

Future Value (FV) = $27,901.27

Sum of all periodic payments = $20,000 ($4,000 x 5)

Total Interest = $3,901.27

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Answer:

$22,548

Step-by-step explanation:

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