the graph y = arctan x is transformed to y = a arctan(b(x-c)) + d by a horizontal compression of 1/2 and translation of pi/3 units down. the new equation is:

Answer:

x = -6

Step-by-step explanation:

2-3(x+4) = 8

2 - 3x - 12 = 8

-3x - 10 = 8

-3x = 18

x = -6

Answer:

x = -6

Step-by-step explanation:

2 - 3 (x + 4) = 8

2 - 3x - 12 = 8

- 10 - 3x = 8

- 3x = 8 + 10

- 3x = 18

x = -18/3

x = -6

___________

hope this helps!

Reflections, rotations, and translations are all transformations that change the position and/or orientation of a geometric figure.

In mathematics, reflection is a transformation that flips a figure over a line called the line of reflection. This line acts like a mirror, reflecting the original figure onto the opposite side of the line.

Reflections, rotations, and translations are all transformations that change the position and/or orientation of a geometric figure.

Reflections (also known as flips) change the orientation of a figure by flipping it across a line of reflection, which acts like a mirror.

Rotations change the orientation of a figure by rotating it around a fixed point. The figure stays the same shape and size, but its position and orientation in space changes.

Translations (also known as slides) change the position of a figure by sliding it along a straight line without changing its orientation or shape.

All of these transformations are important in geometry and other fields, such as physics and computer graphics, and can be used to describe the motion and properties of geometric objects.

To learn more about reflection, visit the link:

https://brainly.com/question/26642069

#SPJ9

Answer: James' age now is 12 years old.

Answer:

Let x be the cost of 1 kg of mushrooms and y be the cost of 1 kg of turnips.

From the given information, we can form two equations:

2x + 2.5y = 8.55 (Equation 1)

3x + 4y = 13.10 (Equation 2)

To solve for x and y, we can use the method of elimination. Multiplying Equation 1 by 4 and Equation 2 by -2, we get:

8x + 10y = 34.20 (Equation 3)

-6x - 8y = -26.20 (Equation 4)

Adding Equation 3 and Equation 4, we get:

2x + 2y = 8

Simplifying this equation, we get:

x + y = 4 (Equation 5)

Now we have two equations: Equation 2 and Equation 5. We can solve for x and y using substitution or elimination. Here, we will use substitution.

From Equation 5, we can express x in terms of y as:

x = 4 - y

Substituting this expression for x into Equation 2, we get:

3(4 - y) + 4y = 13.10

Simplifying and solving for y, we get:

y = £1.50

Substituting this value for y into Equation 5, we can solve for x:

x + £1.50 = 4

x = £2.50

Therefore, the cost of 1 kg of mushrooms is £2.50 and the cost of 1 kg of turnips is £1.50.

a) The cost of 1 kg of turnips is £1.50.

b) The cost of 1 kg of mushrooms is £2.50.

The missing values that make this statement true are as

x² + 9x + 14,  x² - 3x - 10

x² - 2x - 15,   x² + 10x + 21

What is the quadratic equation?

A quadratic equation is a second-degree polynomial equation of the form ax² + bx + c = 0, where a, b, and c are constants and x is the variable. The term "quadratic" comes from the Latin word "quadratus," which means "square."

First, let Xa, Xb, Xc, Xd = each factor

Xd = each factor which shows In the graph

Then, we can know that

Xa, Xb are the roots of x² + ___x + 14

Xb, Xd are the roots of x²= 3x - __

Xc, Xd are the roots of x² - __x - 15

Xa, Xc are the roots of x² + 10x + __

Xa * Xb = 14           Xd = 15/10 +Xa

Xb+ Xd = 3            14/Xa + 15/10 +Xa = 3

Xc* Xd = - 15          140 + 29Xa/Xa(10+Xa)

Xa + Xc = -10x        140 + 29Xa = 30Xₐ + 3Xₐ²

Xb = 14/Xa             3Xₐ² + Xₐ² - 140 = 0

14/Xa + Xd = 3       Xa1 = -7   Xa2 = 20/3

Xd = -15/-3             Xb1 = -2   Xb2 = 21/10

Xc = -10 -X1            Xc1 = -3    Xc2 = -30/3

Xc1 = -3     Xc2 = -30/3

Xd1 = 5         Xd2=9/10

There are two kinds of answers.

1) x² + 9x + 1x           Xa1 + Xb1 = -9

x² - 3x + 10           Xb1 * Xd1 = -10

x² - 2x - 15           Xc1 + Xd1 = 2

x² + 10x + 21           Xa1 * Xc1 = 21

2)

x² - (263/30)x + 14           Xa2 * Xb2 = 263/30

x² - 3x - (-189/100)           Xb2 * Xd2 = 189/100

x² - (413/30)x - 15           Xc2 + Xd2 = 413/30

x² + 10x + (1000/9)           Xa2 * Xc2 = 1000/9

Hence, the missing values that make this statement true are as

x² + 9x + 14,  x² - 3x - 10

x² - 2x - 15,   x² + 10x + 21

To learn more about the quadratic equation visit:

brainly.com/question/28038123

#SPJ1

Hence, there is only one answer, which is (-3, 3) as the two lines intersect in order to obtain the solution(s) to the system of equations.

A value or combination of values that satisfy an equation, inequality, system of equations, or system of inequalities are known as solutions in mathematics. Take the equation x2 - 3x + 2 = 0, for instance. This equation has a solution in the form of an x value that makes the equation true. The quadratic formula allows us to determine that this equation has two solutions, x = 1 and x = 2. According to this, a solution for a system of equations is a set of values that simultaneously satisfy every equation in the system. Mathematical problem-solving, which has many applications in areas like engineering, physics, economics, and more, is a crucial component of the subject.

given

We must identify the point(s) at where the two lines intersect in order to obtain the solution(s) to the system of equations depicted by the graph. The graph demonstrates that the lines cross at the location (-3, 3).

Hence, there is only one answer, which is (-3, 3) as the two lines intersect in order to obtain the solution(s) to the system of equations.

To know more about solution visit :-

https://brainly.com/question/16989201

#SPJ1

By answering the question using the information provided, we can conclude that in order to arrive at the general solution, we must take into account the scenario in which [tex]y-1\neq 0 , y \neq 1[/tex], by constructing equations.

Two equations are said to be equivalent when their bases and solutions line up. To create an equivalent equation, the same quantity, symbol, or expression must be added to or removed from both of the equation's two sides.

We can also create an analogous equation by multiplying or dividing both sides of an equation by a nonzero integer.

Solving differntial calculus

[tex](1+x)y'=( x+2) (y-1)[/tex]

We will first employ varying separation. The variables y and x will be placed on the opposite sides of the equation, and both sides will be integrated.

[tex](1+x)y'/(y-1) = (x+2)dx[/tex]

We will integrate both sides using the substitution[tex]u= y-1,\frac{du}{dy} =y'[/tex]

∫[tex](x+2)dx[/tex] =∫[tex](1+x)\frac{du}{u}[/tex]

㏑l[tex]u[/tex]l +[tex]x[/tex]㏑l[tex]u[/tex]l= [tex]\frac{1}{2} x^{2}+2x+c[/tex]

Substituting [tex]u= y-1[/tex]

㏑l[tex]y-1[/tex]l+ [tex]x[/tex]㏑l[tex]y-1[/tex]l= [tex]\frac{1}{2x^{2} } +2x+c[/tex]

Learn more about equations

brainly.com/question/2972832

#SPJ1

The complete question is: Find the general solution to the differential equation (1+x)y' = (x + 2)(y − 1).

Answer: 9x^2y

the gcf of -63 , 9 and 90 is 9

And the gcf of the variables is x^2 and y

So, 9x^2y

Texas' location and climate led to the development of the aviation industry.

What is the significance of Texas in the development of the aviation industry?

The development of the aviation industry in Texas can be attributed to its favorable geographical location and climate. Texas is located in the southern part of the United States, making it a strategic location for air travel between the east and west coasts of the country. Additionally, its warm and dry climate provided ideal conditions for flight testing and training.

Reason what led to the development of the aviation industry :

Texas has a long history of aviation, with the Wright brothers conducting one of their earliest flight demonstrations in the state in 1910. The establishment of military bases during World War II and the subsequent development of aircraft training facilities in Texas further fueled the growth of the aviation industry in the state. Additionally, the placement of the Johnson Space Center in Houston helped to establish Texas as a hub for aerospace research and development. However, it is Texas' favorable location and climate that truly made it a prime location for the aviation industry. Its central location made it a strategic location for air travel and logistics, while its warm and dry climate provided ideal conditions for flight testing and training. Today, Texas remains one of the top states for aviation and aerospace industries, with major airports, aircraft manufacturers, and research institutions located throughout the state.

Therefore, option (d) is correct.

To know more about industry visit :

brainly.com/question/7721379

#SPJ1

Answer: 5kg

Step-by-step explanation:

If Ms. Walker has 15 kilograms of clay that she wants to distribute evenly among 3 students, all you need to do is divide 15 by 3. Doing so, we get:

15 kg / 3 = 5 kg

Therefore, each student will receive 5 kilograms of clay.

The mass of clay that each student will get is 5kg.

Here, the given questions ask for a solution that deals with the concept of  the basic principle of division. hence implementing the principle we can see that,

The given total amount of clay by Ms. walker is 15 kilograms(kg).

Furthermore, this total amount of clay needs to be divided equally between the  3 students.

Then, let the mass of clay given to each student equally be denoted by M in  the equation to find out the solution can be written as

M = Total amount of clay ÷ Total number of students

Then,

M = 15 ÷ 3

M = 5 kg

Therefore, The mass of clay that each student will get is 5kg.

To learn more about Simple Division,

https://brainly.com/question/941863

Answer:

0.167

Step-by-step explanation:

if you divide 30/180 it will get you a decimal of 0.166666667 but if you were to divide 180 by 30 you will get 6

technecaly your answer would be 0.166666667 but you only take the first number in the decimal which is 0.1 then take six 0.16 then add the 7 0.167

that should end up being your answer if i did the math right

Answer:

Step-by-step explanation:

5/12 * 6/15 =30/180

1/6=1/6

which is true, Right-hand side is equal to left-hand side

Answer:

Step-by-step explanation:

Let x be the original price of the television set.

The sale price is 28% off the original price, which means that the sale price is equal to 100% - 28% = 72% of the original price.

So we can write an equation based on this information:

0.72x = 435.60

Solving for x, we get:

x = 435.60 / 0.72

x ≈ $605

Therefore, the original price of the television set was approximately $605.

Answer: 41

Step-by-step explanation:

-26+z =1 5

       z= 15+26

       z= 41

Answer:

z = 41

Step-by-step explanation:

-26 + z = 15.                      | + 26
-26 + z + 26 = 15 + 26
z = 41

Answer:

28 people

Step-by-step explanation:

21 / 3 = 25

7 = 25%

25 x 4 = 100%

so

7 x 4 = 28

28 people are in the class

Answer:

Step-by-step explanation:

0.08*X >= 100000,   i.e.   X >= 100000%2F0.08 = 1,250,000 dollars.

Then each year he will draw 100000, but the bank will return  equal or even greater amount than 0.08*1250000 = 100000,

so his balance will only increase from year to year.

It is a rough estimation.

If we want to consider more realistic case, when he withdraws 100000 at the first day of the year and the bank compounds 8% at the end of the year,

then the unknown starting amount X must satisfy inequality

0.08*(X-100000) >= 100000,   which gives

0.08X - 0.08*100000 >= 100000,

0.08X > (1+0.08)*100000

x >= %28%281%2B0.08%29%2A100000%29%2F0.08 = 1350000.

Answer.  Having  $1,350,000 or more initially on the account provides the sough condition.

Answer:

$26421.76

Step-by-step explanation:

We have to calculate final value i.e. balance to earn $50,000 annually from interest.

[tex]= \dfrac{50,000}{0.08} = \$625,000[/tex]

Now, N = n × y  = 12 × 25 = 300

        I  = 8% =  APR = 0.08

       PV = 0  = PMT = 0

      FV = 625,000 = A

[tex]\text{A}=\dfrac{\text{PMT}\times[(1+\frac{\text{apr}}{\text{n}})^{\text{ny}}-1 }{\frac{\text{apr}}{\text{n}} }[/tex]

[tex]\text{PMT}=\dfrac{\text{A}\times(\frac{\text{APR}}{\text{n}}) }{[(1+\frac{\text{APR}}{\text{n}})^{\text{ny}}-1 }[/tex]

[tex]\text{PMT}=\dfrac{625,000\times(\frac{0.08}{12}) }{[(1+\frac{0.08}{12})^{12\times25}-1] }[/tex]

[tex]\text{PMT}=\dfrac{625,000\times(0.006667) }{[(1+\frac{0.08}{12})^{12\times25}-1] }[/tex]  

[tex]\text{PMT}=\dfrac{625,000\times(0.006667) }{[(1+0.006667)^{300}-1] }[/tex]

[tex]\text{PMT}=\dfrac{\frac{33335}{8} }{[1.006667^{300}-1]}[/tex]

[tex]\text{PMT}=\dfrac{\frac{33335}{8} }{6.34090515}[/tex]

Monthly payment (PMT) = $26421.7591469 ≈ $26421.76

$26421.76 is required monthly payment in order to $50,000 interest.

Frequency Distribution Table is down below.

Class Count Cumulative Frequency Table

160 - 180 3 3

181 - 201 5 8

202 - 222 14 22

223 - 243 14 36

244 - 264 10 46

265 - 285 2 48

286 - 306 1 49

307 - 327 1 50

Total 50     100

Here its peak is in between 202 to 243 frequency range. There are three extreme values that are 270, 295 and 325 pounds weight.

Median lies in the interval 223-243 and mean also lies in that interval. Maximum values lies in between 200 - 225 interval.

The distribution is left skewed.

Learn more about frequency distribution on;

https://brainly.com/question/17114842

#SPJ1

Answer:

Step-by-step explanation:

To calculate the amount of money Nathaniel needs to deposit today to fund this gift for his descendants, we can use the present value formula for a perpetuity:

Present Value = Annual Payment / Discount Rate

In this case, the annual payment is R380 000 and the discount rate (expected rate of return) is 6.45% in decimals, or 0.0645 as a fraction. So we can plug these values into the formula:

Present Value = R380 000 / 0.0645

This gives us a present value of approximately R5,899,225.68. Therefore, Nathaniel would need to deposit R5,899,225.68 today into the trust fund to provide R380 000 a year forever for his descendants, assuming a 6.45% expected rate of return.

We can claim that after answering the above question, the As a result, angles the regular polygon has ten sides.

An angle is a shape in Euclidean geometry that is made up of two rays, known as the angle's sides, that meet at a point in the middle known as the angle's vertex. Two rays may combine to generate an angle in the plane in which they are located. An angle is formed when two planes collide. They are known as dihedral angles. In plane geometry, an angle is a potential configuration of two rays or lines that share a termination. The English term "angle" derives from the Latin word "angulus," which means "horn." The vertex is the point at where the two rays, also known as the angle's sides, converge.

The interior angle of a regular polygon with n sides is calculated as follows:

(n-2) * 180° / n = interior angle

The internal angle of the polygon is presented to us as 144°. When we plug this into the formula, we get:

144° = (n - 2) * 180° / n

144° * n = (n - 2) * 180°

144° * n = 180° * n - 360°

144° * n + 360° = 180° * n

360° = 36° * n

n = 10

As a result, the regular polygon has ten sides.

To know more about angles visit:

https://brainly.com/question/14569348

#SPJ1

Answer:

<AOB = 112

<AOD = 68

<DOC = 112

Hoped this helped

: )

The domain is all real numbers, The range is all real numbers and There is one y-intercept is true from the given option in context of all linear functions. option B. The domain is all real numbers, C. The range is all real numbers , and E. There is one y-intercept is right choice.

All linear functions have a domain that includes all real numbers, a range that includes all real numbers, and exactly

one y-intercept.

The rate of change of a linear function is non-zero only if the function is not constant (i.e. its slope is not zero).

However, there are linear functions that have a slope of zero, such as the function f(x) = 2, which is a horizontal line.

This means that statement A is not true of all linear functions.

Furthermore, there are linear functions that have no x-intercept (if the line is parallel to the x-axis) or that have more

than one x-intercept (if the line intersects the x-axis more than once).

Therefore, statement D is also not true of all linear functions.

The correct answers to this question are B. The domain is all real numbers, C. The range is all real numbers , and E. There is one y-intercept.

for such more question on linear functions

https://brainly.com/question/9753782

#SPJ11

The true statement about the parallelogram is (c) Yes, because adjacent sides are congruent.

Given that

Figure ABCD is a parallelogram

Such that

Side lengths = 5 cm

This means that

The figure is a square

As a general rule

All squares can be classified as rhombus

This is because a rhombus is a quadrilateral with all four sides of equal length and square is a type of rhombus in which all four sides are equal in length

Hence, the true statement is (c)

Read more about rhombus at

https://brainly.com/question/12918359

#SPJ1

To determine the profit earned from selling 250 shares worth $4.50 each with a 7% fee charged by the stock broker, we need to calculate the total revenue earned and the total cost incurred.

Total revenue earned from selling 250 shares at $4.50 per share:

Revenue = 250 x $4.50 = $1,125

Total cost incurred for buying and selling the shares, including the 7% fee charged by the broker:

Cost = 2 x 250 x $4.50 x 0.07 = $157.50

Here, we are multiplying the number of shares (250) by the price per share ($4.50) to get the total value of the shares. Then we multiply this by 2, since we need to account for both the buying and selling transactions, and then multiply by the broker fee rate of 7% (0.07) to get the total cost incurred.

Therefore, the profit earned from the sale of 250 shares is:

Profit = Revenue - Cost

Profit = $1,125 - $157.50

Profit = $967.50

Hence, the profit earned from selling 250 shares worth $4.50 each with a 7% fee charged by the stock broker is $967.50.

To know more about profit:

https://brainly.com/question/30091032

#SPJ9

The total balance after four years when compounded continuously is $12,615.24.

A technique of calculating interest on a loan or investment where interest is compounded an endless number of times annually is called continuous compounding. Continuous compounding is a method of growing an investment or debt over time by continually adding interest earned over a relatively brief period of time to the principal. In financial computations where interest is earned or charged continuously, such in the bond or mortgage markets, continuous compounding is frequently utilised.

The compound interest is given as:

[tex]A = Pe^{(rt)}[/tex]

Substituting the values:

[tex]A = 12000 * e^{(0.0125 * 4)}\\A = 12000 * e^{(0.05)}[/tex]

A = 12000 * 1.05127

A = 12615.24

Therefore, the total balance after four years is $12,615.24.

Learn more about compound interest here:

https://brainly.com/question/14295570

#SPJ1

The equivalent fraction for 2/3 is 8/12.

Equivalent fraction of a given fraction is got by multiplying or dividing its numerator and denominator by the same whole number. For example, if we multiply the numerator and denominator of 2/3 by 4 we get. 2/3 = 2×4 / 3×4 = 8/12 which is an equivalent fraction of 2/3.

The intercepts of the line are:

x-intercept: (3, 0)

y-intercept: (0, 1)

What are the intercepts?

To find the x-intercept, we need to find the point where the line intersects the x-axis. This occurs when the y-coordinate of the point is zero. From the given information, we know that the line passes through the point (3, 0), so this point must be the x-intercept.

Therefore, the x-intercept is (3, 0).

To find the y-intercept, we need to find the point where the line intersects the y-axis. This occurs when the x-coordinate of the point is zero. We can find the equation of the line using the two given points (0, y) and (3, 0):

Slope of the line = (y2 - y1) / (x2 - x1)

= (0 - y) / (3 - 0)

= -y / 3

Using the point-slope form of the equation of a line, y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line, we can write:

y - 0 = (-y/3)(x - 3)

Simplifying this equation, we get:

y = (-y/3)x + 1

Multiplying both sides by 3, we get:

3y = -yx + 3

Adding yx to both sides, we get:

yx + 3y = 3

This is the equation of the line in standard form. To find the y-intercept, we set x = 0:

0 + 3y = 3

Solving for y, we get:

y = 1

Therefore, the y-intercept is (0, 1).

Hence, the intercepts of the line are:

x-intercept: (3, 0)

y-intercept: (0, 1)

To know more about the intercepts, visit:

https://brainly.com/question/29113022

#SPJ1

Step-by-step explanation:

given quadratic equation is

simplification,

by using,

[tex]y^\frac{1}{2} -6y^\frac{1}{4} +8=0

\\ y^\frac{1}{2} -6y^\frac{1}{4} = - 8 \\

[/tex]

[tex]square[/tex]

[tex] \\ {(y^\frac{1}{2} -6y^\frac{1}{4})}^{2} = {(- 8)}^{2}[/tex]

[tex]y + 36 {y}^{ \frac{1}{2}} \: [/tex]

Reason:

We cannot divide by zero. This means the denominator cannot equal zero. If it was zero, then,

2x+10 = 0

2x = -10

x = -10/2

x = -5

Follow that chain in reverse to see that x = -5 causes the denominator 2x+10 to be zero. This is why we kick -5 out of the domain. Any other x value is valid.

Answer:

Option (C)

-0.46 brother

Answer:

Option (C)

-0.46

Step-by-step explanation: