What are the 3 steps to solving a two step equation?

The value of next two terms are,

⇒ 0 and - 60

A relation between a set of inputs having one output each is called a function.

Given that;

The values are,

⇒ f (1) = 120,

⇒ f (2) = 60

And, The function is,

⇒ f (n) = f (n - 1) + ___

For n ≥ 2

Now,

Since, The values are,

⇒ f (1) = 120,

⇒ f (2) = 60

And, The recursive formula is,

⇒ f (n) = f (n - 1) + b

For n ≥ 2

Substitute n = 2;

⇒ f (2) = f (2 - 1) + b

⇒ 60 = f (1) + b

⇒ 60 = 120 + b

⇒ b = 60 - 120

⇒ b = - 60

So, The recursive formula is,

⇒ f (n) = f (n - 1) - 60

Substitute n = 3;

⇒ f (3) = f (3 - 1) - 60

⇒ f (3) = f (2) - 60

⇒ f (3) = 60 - 60

⇒ f (3) = 0

Substitute n = 4;

⇒ f (4) = f (4 - 1) - 60

⇒ f (4) = f (3) - 60

⇒ f (4) = 0 - 60

⇒ f (4) = - 60

Thus, The next two term are 0 and - 60.

Learn more about the function visit:

https://brainly.com/question/28793267

#SPJ1

The volume of the pyramid as calculated from the data given is found to be as 21.33 cubic units .

The distance from a corner to the center is 8 , and from the corner to the top of the pyramid is 8, because it is given that the tringles are equilateral.

so the height becomes,

√3a/2 = 4√3

The area of the hexagon is calculated using the formula ,

=3√3/2 x a²

=3√3/2 x 64

= 963√3

=332.553 square units.

Volume of a pyramid is calculated as ,

1/3 x base x height

= 1/ 3 x 8 x 8

= 1/3 x 64

=21.33 cubic units answer.

To learn more about pyramids

brainly.com/question/16527792

#SPJ4

The result of two Newton's technique iterations to approximation a function's zero using the provided starting guess is 1.5262!

Iteration describes carrying out a process repeatedly. To get a new value, start with an initial value and enter it into the iteration formula. To solve an equation using iteration, apply the new value for the subsequent substitution after that, and so on.

By Newton's Method, we have new guess of a zero of a function that are f(x), xn+1, and by using the previous guess, xn, like so-

xn+1 = xn - f(xn)/f'(xn)

and herethe case is [tex]f(x) = cos(x), and so f'(x) = -sin(x).[/tex]

Also, furthermore, [tex]cos(x)/(-sin(x)) = -cot(x).[/tex]

here, we have to simplify the formula to get a better guess for a zero to: xn+1 = xn + cot(xn)

[tex]x1 = 0.6, so x2 = 0.6 + cot(0.6) = 2.06170...\\And x3 = 2.06170... + cot(2.06170...) = 1.52615...\\Ans = 1.5262![/tex]

To know more about iterative formula visit:

brainly.com/question/29567951

#SPJ4

The solution for the rational equation (1/(x + 1)) - (1/(x + 2)) = 1/5 is specified by the option C.

C. x = -3.79, x = 0.79

A rational equation consists of a fraction that has a polynomial numerator denominator.

The specified equation can be expressed as follows;

[tex]\dfrac{1}{x + 1} - \dfrac{1}{x+2} = \dfrac{1}{5}[/tex]

Finding the common denominator for the right hand side expression, we get;

[tex]\dfrac{ (x + 2) - (x + 1)}{(x + 1) \times (x + 2)} = \dfrac{1}{5}[/tex]

[tex]\dfrac{1}{(x + 1) \times (x + 2)} = \dfrac{1}{5}[/tex]

[tex]\dfrac{1}{x^2+ 3\cdot x+ 2} = \dfrac{1}{5}[/tex]

Inverting both sides of the above equation, we get the following quadratic equation;

x² + 3·x + 2 = 5

x² + 3·x + 2 - 5 = 0

x² + 3·x - 3 = 0

The quadratic formula indicates that we get;

x = (-3 ± √(3² - 4×1×(-3))) ÷ (2 × 1)

x = (-3 + √(21)) ÷ 2 and x = (-3 - √(21)) ÷ 2

x ≈ 0.79 and x ≈ -3.79

The correct option is option C

C. x = -3.79, x = 0.79

Learn more on quadratic equations here: https://brainly.com/question/17105224

#SPJ1

so hmmm we look at hmm x³ + x² - 8x - 6 so how do squeak out a factor out of it, well, using the rational root test and using our p/q checking for factors, we find that likely factors can be ± 6/1 and ±(3, 2, 1) / 1, anyhow so we check some of those and hopefully without boring you to death we find that -3 works, we can always use the remainder theorem to check if that's true, by simply plugin in f(-3) and if it's indeed a factor, that'd give us 0, well, f(-3) = -27 + 9 +24 +6 = 0, holly smokes!! is a factor.

well, all that jazz means that -3 is a factor, namely the factor is really x = -3 or x + 3 = 0 so the factor is (x+3) and for our synthetic division we'll use the -3 version, Check the picture below.

so we end up with the factors of (x+3)(x²-2x-2), now for the 2nd factor what we can do to break it up is use the quadratic formula

[tex]~~~~~~~~~~~~\textit{quadratic formula} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{-2}x\stackrel{\stackrel{c}{\downarrow }}{-2} \qquad \qquad x= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a}[/tex]

[tex]x= \cfrac{ - (-2) \pm \sqrt { (-2)^2 -4(1)(-2)}}{2(1)} \implies x = \cfrac{ 2 \pm \sqrt { 4 +8}}{ 2 } \\\\\\ x= \cfrac{ 2 \pm \sqrt { 12 }}{ 2 }\implies x=\cfrac{2\pm\sqrt{2^2\cdot 3}}{2}\implies x=\cfrac{2\pm 2\sqrt{3}}{2}\implies x=1\pm\sqrt{3} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill {\Large \begin{array}{llll} (x+3)(x-1+\sqrt{3})(x-1-\sqrt{3}) \end{array}}~\hfill[/tex]

now, just to clarify, all those are real roots, and the last two come from simply setting x = 1 ± √3 to 0 to get the factors.

The answer is $112.70  The Question is a simple Sales tax rate calculating problem.

Multiplying the purchase price by the sales tax rate will provide the sales tax. Don't forget to round the sales tax rate from percent to decimal. The price of the purchase is increased after the sales tax has been calculated. The entire cost is what the client pays as a result.

Sales tax rate = Sales tax percent / 100.

Sales tax = List price x Sales tax rate.

Given,

Rate of sandwich is = $4. 00

Rate of drink is = 94$

The rate of a meal that Her grandson ordered is =$6. 35.

What was the total price of all three items when 8% sales tax was added?

Total price of all three items without tax = 4 + 94 + 6.35

= $104.35

Total price of all three items with tax = (100% + tax) * Price

= (100% + 8%) * 104.35 = 108% * 104.35

= 1.08 * 104.35 = 112.698

≅ $112.70

The estimation to check if the result is reasonable by putting the answer in the original equation.

E.g. x + 4 = 10; x = 10 - 4

We get that x = 6

Plug in x = 6 in x + 4 = 10.

6 + 4 = 10.

To know more about sales tax problems visit:

brainly.com/question/9437038

#SPJ4

Parallelogram M'N'P'Q' is larger than parallelogram MNPQ because MN and M'N' have lengths of 2 and 5 respectively, and parallelogram MNPQ is dilated by a factor of 5/2 to give parallelogram M'N'P'Q'.

A parallelogram is a straightforward quadrilateral in Euclidean geometry that has two sets of parallel sides. In a particular kind of quadrilateral known as a parallelogram, both sets of opposite sides are parallel and equal. There are four different kinds of parallelograms, including three unique kinds. Parallelograms, squares, rectangles, and rhombuses are the four different shapes. Having two sets of parallel sides makes a quadrilateral a parallelogram. In a parallelogram, the opposing sides and angles are both the same length. On the same side of the horizontal line, the interior angles are additional angles as well. 360 degrees is the total number of interior angles.

To make parallelogram M'N'P'Q, parallelogram MNPQ was enlarged.

Points include M(2, 2), N(4, 2), P(3, 3), and Q. (1,-3)

M'(5, 5), N'(10, 5), P'(8, 7), and Q' (3,-7)

A) First, determine Minnesota's length:

|MN| = 2

|M'N'| = 4

To know more about parallelograms visit:

https://brainly.com/question/29147156

#SPJ4

The exact value of secθ in simplest radical for is 1.083

Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.

We are Given θ is an angle in standard position.

Its terminal side passes through the point (12, -5).

To find the exact value of secθ in simplest radical form.

When θ is an angle in standard position and its terminal side passes through the point (x,y), then the exact value of secθ is:

So, we have x = 12 and y = -5 which is in the first quadrant.

Therefore,

r² = x² + y²

r² = ( 12 )² + ( -5 )²

r² = 144 + 25

r² = 169

r = 13

Then,

sec θ = 1/cosθ

sec θ = [ 1/(x/r) ]

sec θ = r/x

sec θ = 13/12

sec θ = 1.083

Learn more about trigonometric;

https://brainly.com/question/21286835

#SPJ1

Answer:

x=0

Step-by-step explanation:

The general form of the equation of y-axis is x = 0. hence, the equation of line parallel to the y-axis is given by the equation: x = k.

The true statements after a dilation of scale factor 3 are,

∠A corresponds to ∠A' and Triangle ABC is similar to triangle A'B'C'.

Two-dimensional figures can be transformed mathematically in order to travel about a plane or coordinate system.

Dilation: The preimage is scaled up or down to create the image.

Reflection: The picture is a preimage that has been reversed.

Rotation: Around a given point, the preimage is rotated to create the final image.

Translation: The image is translated and moved a fixed amount from the preimage.

Given, The points of ABC are (negative 3, 3), (- 1, 1), and (- 3, 1).

The points of A'BC' are (- 9, 9), (- 3, 3), and (- 9, 3) after a dilation of 3, (x, y) ⇒ (3x, 3y).

We know dilation maintains the similarity of the dilated figures.

Therefore, The statements that are true,

∠A corresponds to ∠A' as dilation maintains similarity.

Triangle ABC is similar to triangle A'B'C'.

learn more about transformations here :

https://brainly.com/question/13176891

#SPJ1

Answer:

Options A,B,C,E

Step-by-step explanation:

A form of reasoning called induction is the process of forming general ideas and rules based on your experiences and observations.

The process of welcoming newly hired employees and assisting them in adjusting to their new positions and working surroundings is known as induction. Beginning a new work can be stressful, so new hires require assistance adjusting to their new environment.

The action or process of inducting someone to a position or organization.

We have given that,

A form of reasoning called is the process of forming general ideas and rules based on your experiences and observations.

As a result, the process of formulating general hypotheses and rules based on your observations and experiences is known as induction.

learn more about induction here:

brainly.com/question/24672369

#SPJ1

Answer:√17

              √81

                √27

This 3 numbers are irrational number

Answer:

17 and 27 are irrational

Step-by-step explanation:

This is how you construct a parent graph - it is the simplest form of the function, and has a basic shape.

The most basic form of a function is a parent function. Its essential shape is not changed in any manner. In mathematics, some graphs are frequently seen. Because of this, the graphs of quadratic functions, square roots, absolute values, cubics, and cube roots are among the original, widespread functions that are referred to as parent graphs.

For instance, you should still be able to identify the parabola that has undergone various transformations when you view a u-shaped graph that has been inverted and stretched vertically.

We can take a few examples to understand this concept further.

Hence, this is how you construct a parent graph - it is the simplest form of the function, and has a basic shape.

To learn more about parent graphs, visit the link:

brainly.com/question/20333814

#SPJ4

Answer:

Didn't move the 12 on the other side of the equal sign to make

2x^2 + 5x - 12 = 0

the other steps error city.

Step-by-step explanation:

2x^2 + 5x - 12 = 0

(2x - 3)(x + 4)= 0

2x - 3 = 0

2x = 3

x = 3/2

x + 4 = 0

x = -4

The expanded form in terms of the sums of powers to tens of 237.45 is [tex]2 \times 10^2+3 \times 10^1+7 \times 10^0+4 \times 10^{-1}+5 \times 10^{-2}[/tex]

As per the given data the given decimal number is 237.45.

Here we have to determine the expanded form in terms of the sums of powers to tens.

Expanded Form: In its extended sense, A number is divided up into its place values, then expanded to represent the value of each digit.

Then N can be written in expanded in for terms of 10 is

[tex]$$\Rightarrow N=a \times 10^2+b \times 10^1 + c \times 10^0+d \times 10^{-1}+e \times 10^{-2}$$[/tex]

Let the given number 237.45 is denoted by N.

N = 237.45

First, write the expanded form of a number before the decimal place.

Then using [tex]$\circledast$[/tex], we have

[tex]& N=2 \times 10^2+3 \times 10^1+7 \times 10^0+4 \times \frac{1}{10}+5 \times \frac{1}{10^2} \\[/tex]

[tex]& N=2 \times 10^2+3 \times 10^1+7 \times 10^0+4 \times 10^{-1}+5 \times 10^{-2} \\[/tex]

237.45 = [tex]2 \times 10^2+3 \times 10^1+7 \times 10^0+4 \times 10^{-1}+5 \times 10^{-2}[/tex]

Therefore the expanded form of 237.45 is [tex]2 \times 10^2+3 \times 10^1+7 \times 10^0+4 \times 10^{-1}+5 \times 10^{-2}[/tex].

For more questions on expanded form

https://brainly.com/question/20875957

#SPJ4

Which of the following expressions represents 237.45 written in expanded form in terms of the sums of powers to tens

A. [tex]$2 \times 10^2+3 \times 10^1+7 \times 10^0+4 \times 10^{-1}+5 \times 10^{-2}$[/tex]

B. [tex]$237 \times 100+45 \times 1 / 1000$[/tex]

C. [tex]$2 \times 10^2+3 \times 10^1+7 \times 10^0-4 \times 10^1-5 \times 10^2$[/tex]

D. 200+30+7+0.4+0.05

The first blank is skewed left, the second blank is median, and the third blank is 9 is correct options.

A distribution that is left-skewing has a lengthy left tail.

Distributions that are negatively skewed are also known as left-skewed distributions.

This is due to the number line having a significant negative tail.

Additionally, the peak is to the left of the mean.

The right tail of a right-skewed distribution is lengthy.

It's a widespread misperception that "peakness" is defined by the distribution's peak.

To put it another way, a peak that leans left indicates a left-skewed distribution.

Hence, The first blank is skewed left, the second blank is median, and the third blank is 9 is correct options.

learn more about the median click here:

brainly.com/question/19243813

#SPJ4

Therefore , the solution of the given problem of function comes out to be  f(x) = 2871 thousands.

A science called mathematics studies numbers, its variations, arithmetic and the local tissue, shapes, and both their existing and projected places. The relationship between a group of inputs, which each have a corresponding output, is described by a function. A function is a collection of inputs that together produce a single, recognizable output with each input. A city, municipality, or scope—often referred to as a realm—is assigned to each function. Usually, the letter f is used to represent functions (x). The input has an x in it.

Here,

Given :

=>  f(x) = 225(1.29)×

After 10 year number of years x =10

=> f(x) = 225(1.29)¹⁰

=> f(x) = 12.76 * 225

=>  f(x) = 2871 thousands.

Therefore , the solution of the given problem of function comes out to be  f(x) = 2871 thousands.

To know more about function visit:

https://brainly.com/question/28193995

#SPJ1

No, 8 15 17 is not a right angle triangle. A right angle triangle is a triangle in which one of the three angles is equal to 90 degrees.

To determine if a triangle is a right angle triangle, we can use the Pythagorean theorem. This states that in a right angle triangle, the sum of the squares of the two shorter sides (a and b) will equal the square of the longest side (c).

In this case, the length of the sides are 8, 15 and 17. We can calculate the sum of the squares of the two shorter sides, which is 8² + 15² = 144 + 225 = 369. However, the square of the longest side (17²) is 289. Since 289 is not equal to 369, this means that 8 15 17 is not a right angle triangle.

Learn more about right angle triangle here:

https://brainly.com/question/3772264

#SPJ4

The system of equations, in standard form, modeling the relationship between cost of gespils (x) and cost of alabers (y) is -

8x + 9y = 117

3x + 8y = 67

Given is that Farmers Lirn and Rew both bought gespils and alabers for their farms. Lirn bought 8 gespils and 9 alabers for $117. Rew bought 3 gespils and 8 alabers for $67.

We can write the system of equations as -

8x + 9y = 117

3x + 8y = 67

Where -

cost of gespils → (x)

cost of alabers → (y).

Therefore, the system of equations, in standard form, modeling the relationship between cost of gespils (x) and cost of alabers (y) is -

8x + 9y = 117

3x + 8y = 67

To solve more questions on expressions, visit the link below -

brainly.com/question/1041084

#SPJ1

The kilogram of fruits sold each day are 135 kg, 110 kg and 70 kg

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

Day 2 = Day 1 - 25

Day 3 = 2/7 * (Day 1 + Day 2)

Total weights = 315

Next, we use the following representations

x = Day 1, y = Day 2 and z = Day 3

So, we have the following equations

y = x - 25

z = 2/7(x + y)

x + y + z = 315

Substitute y = x - 25 in z = 2/7(x + y) and x + y + z = 315

z = 2/7(x + x - 25) = 2/7(2x - 25)

x + y + z = 315 ⇒ x + x - 25 + z = 315

So, we have

z = 2/7(2x - 25)

2x + z = 340

Substitute z = 2/7(2x - 25) in 2x + z = 340

2x + 2/7(2x - 25) = 340

So, we have

7x + 2x - 25 = 1190

Evaluate the like terms

9x = 1215

Divide by 9

x = 135

So, we have

y = x - 25 = 135 - 25 = 110

z = 2/7(x + y) = 2/7 *(135 + 110) = 70

Hence, the amounts are 135 kg, 110 kg and 70 kg

Read more about equations at

https://brainly.com/question/2972832

#SPJ1

Answer:

1376x-736

Step-by-step explanation:

Take 32 and multiply it by 43. By multiplying vertically, distribute the multiplication of 3 (from 43) times both the 2 and 3 of 32 (right to left)

3 x 2=6; 3 x 3=9:

32

x

43

--------

96

Then, distribute the multiplication of 4 (from 43) times both the 2 and 3 of 32 (right to left) and leave a zero under the last number of your previous answer while moving the distribution of numbers forward.

4 x 2=8; 4 x 3=12

32

x

43

--------

   96

+

1280   <----(this is the zero you must leave under your previous set)

After distributing each number of 43 to each number of 32 while multiplying, add your answers together vertically from right to left and bring down the x:

  96

+

1280

----------

1376x

Now do the same for 32 x -23 after learning vertical multiplication to get -736

Your final answer put together is 1376x-736

Answer:

+ - × ÷

Step-by-step explanation:

addition, subtraction, multiplication and division

The correct answer is option A: the optimal corner point won't change.

The optimal corner point is the point where the objective function reaches its maximum value, with the constraints of the problem being satisfied. If the slope of the objective function stays between the slopes of the binding constraints, it means that the current optimal corner point will remain unchanged.

This is because if the objective function's slope is within the slopes of the binding constraints, then the set of points where the objective function reaches its maximum value will be the same. Therefore, the optimal corner point will not change.

Learn more about Slopes here:

https://brainly.com/question/3493733

#SPJ4

There are 15 different books and 3 each can be arranged on a shelf i.e., there are 15/3 i.e., 5 shelves to arrange the book in the the display case.

To learn more about arrange3 books on a shelf refers to:

brainly.com/question/15836110

#SPJ4

https://brainly.com/question/11495883

Hello there!

Answer:

$400'000

Step-by-step explanation:

Estate -- $2.4 million or $2'400'000

Springfield University will receive: 10% * $2'400'000 = 0.1 * $2'400'000 = $240'000

First Church of Springfield will receive: 15% * $2'400'000 = 0.15 * $2'400'000 = $360'000

Wife will receive $600'000

Total: $240'000 + $360'000 + $600'000 = $1'200'000

Children will receive at total: $2'400'000 - $1'200'000 = $1'200'000

So each child will receive: $1'200'000 / 3 = $400'000

Answer: Each child of Homer Simpson gets $400000.

Step-by-step explanation:

Homer Simpson left 10% of his estate, or (10/100)  x $2.4 million

= $ (10/100)x2400000= $240000

$240,000 to Springfield University.

He left 15% of his estate, or (15/100) x $2.4 million = $(15/100)2400000

= $360000

So 360,000 to the First Church of Springfield.

So in total, he left $240,000 + $360,000 + $600,000 = $(240000+360000+600000)

=$1200000

 $1,200,000 to organizations and his wife.

That means the remainder of the estate, $2.4 million - $1,200,000

= $2400000-1200000

= $1200000

1,200,000, was divided among his three children. So each child received $1,200,000 / 3 = $1200000/3

=$400000

Answer: $400000.

Answer:

y = 2x

Step-by-step explanation:

y = mx + b

m = 2

y-intercept = b = 0

y = 2x + 0

y = 2x

Answer:

Step-by-step explanation:

hello follow me on zepeto if this helps

16 is 33.3333% of 48. 33 is the whole number hope you get a

The degree of a constant polynomial (such as 7) is zero.

The variable's highest power in a polynomial expression is the polynomial's degree.

A polynomial is a mathematical expression made up of more than two algebraic terms, particularly the sum (or difference) of several terms that each contain a different power of a single or several variables (s).

It is a monomial combination that is linear. Since the polynomial can be conceived of as 7x0, the degree of a constant polynomial (such as 7) is zero.

Normally, the degree of the zero polynomial (zero) is regarded as being undefinable.

A polynomial function with a degree of 7 is known as a septic function (also known as a 7th degree polynomial). 

To more about Polynomials here:

https://brainly.com/question/20121808#

#SPJ4

Due to the fact that they obscure bimodality or any multimodality, boxplots are best reserved for distributions with a single mode.

The distribution is said to be symmetrical when the box's whiskers are roughly the same on both sides and the median is in the centre of the box. The distribution is positively skewed if the whisker is shorter on the lower end of the box and the median is closer to the bottom of the box (skewed right).

Due to the fact that they obscure bimodality or any multimodality, boxplots are best reserved for distributions with a single mode.

There is just one peak in a unimodal distribution, two peaks in a bimodal distribution, and three or more peaks in a multimodal distribution. If the data is skewed or symmetric, such information can also be used to characterise the histogram's structure.

Therefore, the correct answer is option b) Unimodal.

To learn more about Unimodal refer to:

https://brainly.com/question/30125628

#SPJ1

The required correct option for the given question is uni-modal.

The distribution is said to be symmetrical when the box's whiskers are roughly the same on both sides and the median is in the center of the box. The distribution is positively skewed if the whisker is shorter on the lower end of the box and the median is closer to the bottom of the box (skewed right).

Due to the fact that they obscure bi-modality or any multi-modality, box-plots are best reserved for distributions with a single mode.

There is just one peak in a uni-modal distribution, two peaks in a bimodal distribution, and three or more peaks in a multi-modal distribution. If the data is skewed or symmetric, such information can also be used to characterize the histogram's structure.

Therefore, the correct answer is option b) Uni-modal.

To learn more about Uni-modal refer to:

brainly.com/question/30125628

#SPJ1