The graph of g(x), shown below in red, has the same shape as the graph of
f(x) = 2x, shown in blue. Which of the following is the equation for g(x)?

A. g(x) = 2(x-1) - 3
B. g(x) = 2(x+3) - 1
C. g(x) = 2(x-3) -1
D. g(x) = 2(x+1) - 3

The steps to find the inverse function are given in the development of the answer of this problem.

The inverse of a function y = f(x) is found exchanging x and y and isolating y.

In this problem, the function is:

[tex]f(x) = \sqrt{7x - 21}[/tex]

Then the steps to find the inverse function is given as follows:

[tex]y = \sqrt{7x - 21}[/tex]

[tex]x = \sqrt{7y - 21}[/tex]

[tex]x^2 = 7y - 21[/tex]

[tex]x^2 + 21 = 7y[/tex]

[tex]\frac{1}{7}x^2 + 3 = y[/tex]

[tex]\frac{1}{7}x^2 + 3 = f^{-1}(x)[/tex], where [tex]x \geq 0[/tex].

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The value of a₄₁ mean the expression in 4th row and 1st column will be 2. Then the correct option is B.

The complete question is attached below.

A matrix is a specific arrangement of items, particularly numbers. A matrix is a row-and-column mathematical structure. The [tex]\rm a_{ij}[/tex] element in a matrix, such as M, refers to the i-th row and j-th column element.

The matrix is given below.

[tex]\begin{bmatrix} 1&3&8&5&\\ 5&4&6&2\\6&7&1&8\\2&9&3&7&\\\end{bmatrix}[/tex]

Then the value of a₄₁ mean the expression in 4th row and 1st column will be 2.

Then the correct option is B.

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Answer:

x =  17.32 units

Step-by-step explanation:

In a right triangle tan (angle) = opposite leg / adjacent leg...

  for this triangle   tan 27° = 34 / x

      then x = 34 tan 27° = 17.32 units

The provided equation has no solution because the square of any number cannon is negative.

It is defined as the combination of constants and variables with mathematical operators.

The question is incomplete.

The complete question is:

Find a solution to the given equation

Please refer to the attached picture for the expression.

We have an expression:

[tex]\rm \dfrac{3}{\left(m+3\right)}-\dfrac{3}{\left(m-3\right)}=\dfrac{m^2+9}{\left(m^2-9\right)}[/tex]

3(m - 3) - 3(m + 3) = m² + 9

3m - 9 - 3m - 9 = m² + 9

m²  ≠ -27

As the square of any number cannot is negative, so no solution to the provided equation.

Thus, the provided equation has no solution because the square of any number cannon is negative.

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Answer:

D = No Solution

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

.....................

Answer:

Step-by-step explanation:

One equivalent can be obtain by distributing multiplication with 3 over subtraction 5-2i

3(5-2i) =

3·5 -3·2·i =

15 -6i or -6i +15

Answer:

x = 6.5

Step-by-step explanation:

* since it's a triangle ALL the angles inside should give you 180° * Equate everything to 180°

8x + 10x - 10°+ 10x + 8° = 180°( sum of angles on a triangle)

28x - 2° = 180° * group like terms*

28x = 182°

x = 6.5

Answer:

60

Step-by-step explanation:

60 because a regular hexagon has a exterior angle measure of 60.

A regular hexagon has 6 sides you divide 360 by 6 which is 60

Ans: 60

Answer:

y = -2x + 16

the y intercept is the y value at x = 0. On the graph there is a dot at 16 on x= 0, so the y intercept would be 16.

the only answer choice adding 16 sis y = -2x + 16

Answer:

18.88

Step-by-step explanation:

tan 42° = 17/x

x= 17/(tan 42°)

x = 17/(0.9004)

x = 18.88

Answer:

75 mm

Step-by-step explanation:

 To find the hypotenuse, use Pythagorean theorem

Hypotenuse² = base² + altitude²

                  c² = 21² + 72²

                      = 441 + 5184

                      = 5625

                 [tex]\sf c = \sqrt{5625}[/tex]

                    [tex]= \sqrt{75*75}\\\\\boxed{\bf c = 75 \ mm}[/tex]

Answer:

x = 9/4 + 1/4 √17 or x = 9/4 + −1/4 √17

/ = over

Step-by-step explanation:

a = 2, b=-9, c=8

x = −b±√b2−4ac/2a

x = −(−9)±√(−9)2−4(2)(8)/2(2)

x = 9±√17/4

x = 9/4 + 1/4 √17 or x = 9/4 + −1/4 √17

The graph of the linear function, considering the points in the domain, is given at the end of the answer.

The linear function is defined by:

y = -2x - 5.

Considering the domain, the points are given as follows:

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Answer: Writing an equation in function form. You want to remove the x term from the side y is on and move it to the other side of the equal sign. To do this either add or subtract the x term from both sides. Next divide by the coefficient of the y term. Now your equation is in function form.

explanation: like 57 * Y =142500

what is the number for Y if u don't know u could divided 142500 by 57 and it equals? 2500;) hope I helped

The answer is B

When there is a solid point that means it is included in the graph, so you'd use a greater/less than or equal to symbol (the one with a line under). If it's an unfilled point then it means that it is not included in the graph, so you'd use a greater/less than sign.

The x² equation is less than 2 while the linear equation is greater than or equal to 2.

We know it's the x² equation that is less than two because it has a curve in it.

Answer:

90°

Step-by-step explanation:

right angle - 90°

.....

Answer:

65

Step-by-step explanation:

Answer:

A and C

Step-by-step explanation:

solving the equations

A

x² - 4 = 0 ( add 4 to both sides )

x² = 4 ( take square root of both sides )

x = ± [tex]\sqrt{4}[/tex] = ± 2 ← required solution

B

x² = - 4 ← has no real solutions

C

4x² = 16 ( divide both sides by 4 )

x² = 4 ( take square root of both sides )

x = ± [tex]\sqrt{4}[/tex] = ± 2 ← required solution

D

2(x - 2)² = 0 , then

x- 2 = 0 ( add 2 to both sides )

x = 2 ← not the required solution

Answer:

Answer A and C

Step-by-step explanation:

Let us solve the equations one by one and let us check whether the answers are matching with the answers given in the questions.

A) x² - 4 = 0

   ( x² - 2² ) = 0

   ( x -2 ) ( x + 2 ) = 0

   ∴ x - 2 = 0                   or           x + 2 = 0

      x = 2                                       x = -2               ( Matched )

B) x² = -4

  x = ±√-4  ← no real solutions                    (Not matched )

B)   3x² + 12 = 0

      3 ( x² + 4 ) = 0

      3 ( x² + 2² ) = 0 ← no real solutions      (Not matched)

C) 4x² = 16

Divide both sides by 4.

 x² = 4

 x = ±√4

 ∴ x = 2         or        x = -2       (Matched)

 D) 2 ( x - 2 )² = 0    

      (2x - 4)² = 0

      4x² - 16x + 16 = 0

Divide the whole equation by 4.

   x² - 4x + 4 = 0

 x² - 2x - 2x + 4 = 0

x ( x - 2 ) - 2 ( x - 2 ) = 0

( x - 2 ) ( x - 2) =

∴ x - 2 = 0          or        x - 2 = 0

  x = 2                            x = 2                 ( Not matched )

Answer:

(-2, -4)

Step-by-step explanation:

You can complete the square of the equation to get

y+(4/2)^2 = x^2+4x+(4/2)^2

y+4 = x^2 + 4x + 4

y+4 = (x+2)^2

y = (x+2)^2 - 4

This gives the form y = a(x-h)^2 + k where (h, k) is the vertex of the equation. You can also arrive at the same conclusion by making some observations of the equation. (x+2)^2 minimum value is going to be 0 since and negative values resulting from x+2 is going to become positive because of the square. So the minimum value is when x+2 is 0 or when x is equal to -2 and when it's at that minimum value of 0 it's going to have 4 subtracted from it which gives the vertex of (-2, -4)

Step-by-step explanation:

2/5 oz. for 1 cup

40 oz for x cups

2/5x = 40

x = 100 cups

The transformation is non-rigid because the side lengths are not preserved.

The drop-down menus and the image of the triangles are not given.

However, the question can still be solved using the available parameters.

The given parameters are:

Pre-image: 6, 10, 8

Image: 3, 5, 8

See that the side lengths of the image and the pre-image are not the same

This means that the transformation is a non-rigid transformation

Hence, the complete statement is the transformation is non-rigid because the side lengths are not preserved.

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Answer: £20 doubling at the end of each year for 5 years

From the question, Stephen would want to select one option which gives the highest amount of profit. I mean, even if you were to select one, you would obviously try calculating all the 4 choices to see which one makes you earn the most money. Now let's conduct the workout and see which one will earn us the most £ in 5 years:

Option 1:
[tex](500*\frac{5}{100} ) + 500 ---- > 1yr\\= 25 + 500 \\ = 525\\\\(525*\frac{5}{100} ) + 525 ----- > 2yrs\\= 26.25 + 525\\= 551.25\\\\(551.25 * \frac{5}{100}) + 551.25 - - - > 3yrs\\ = 27.563 + 551.25\\= 578.813\\\\(578.813 * \frac{5}{100}) + 578.813 - - > 4 yrs\\ = 28.941 + 578.813\\ = 607.754 \\\\(607.754 * \frac{5}{100}) + 607.754 - - > 5 yrs\\ = 30.388 + 607.754\\ = 638.142 \\[/tex]

ans: £ 638.142

Option 2:

[tex]1 year = 12 months\\5 years : 5*12 = 60 months\\\\10*60 = 600[/tex]

ans: £ 600

Option 3:

[tex](550*\frac{3}{100}) + 550 - - - - > 1yr\\= 16.5 + 550\\= 566.5 \\\\(566.5 * \frac{3}{100}) + 566.5 - - - > 2 yrs\\ = 16.995 + 566.5\\= 583.495\\\\(583.495 * \frac{3}{100}) + 583.495 - - > 3 yrs\\ =17.505 + 583.495\\= 601\\\\(601 * \frac{3}{100}) + 601 - - - - - - > 4 yrs\\= 18.03 + 601\\= 619.03\\\\( 619.03* \frac{3}{100}) + 619.03 - - - - > 5 yrs\\= 18.571 + 619.03\\= 637.601[/tex]

ans: £ 637.601

Option 4:

[tex]20*2= 40 - - - - > 1yr\\40 * 2= 80 - - -- > 2 yrs\\80*2 = 160 - - - > 3 yrs\\160*2 = 320 - - - > 4 yrs\\320*2= 640 - - - > 5yrs[/tex]

ans: £ 640

Out of all the calculated answers, you can see that option 4 has the highest amount. So that's it. By the way, I might do some incorrections in some calculations because I am not good at long maths, but yes i hope I did it all right!

∩_∩
(„• ֊ •„)♡
┏━∪∪━━━━┓
   hope it helped
┗━━━━━━━┛

Answer:

[tex]x=1[/tex] ± [tex]i\sqrt{19}[/tex]

Step-by-step explanation:

First off let's state the quadratic formula

Quadratic formula

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

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

For this question our quadratic equation is

[tex]x^2+20=2x[/tex]

Now before we can apply the quadratic formula we first have to set the equation equal to zero. We do this my moving everything to one side and setting it equal to zero.

In this case, we simply move the 2x to the other side making it negative and setting the equation equal to zero.

[tex]x^2-2x+20=0[/tex]

From here we plug in the values to the quadratic equation.

Now incase you don't know

[tex]a =[/tex] Coefficient of [tex]x^2[/tex] value

[tex]b=[/tex] Coefficient of [tex]x[/tex] value

[tex]c=[/tex] The Constant

Now plug in values

[tex]a=1[/tex]

[tex]b=-2[/tex]

[tex]c=20[/tex]

To get the values of x using the quadratic formula we have the plug in the values, we also have to both subtract and add the [tex]\sqrt{b^2-4ac}[/tex] to [tex]-b[/tex]

Plug in values into formula

[tex]\frac{2+\sqrt{(-2)^2-4(1)(20)} }{2(1)}[/tex]

[tex]\frac{2+\sqrt{-76} }{2}[/tex]

[tex]\frac{2+\sqrt{-1} *\sqrt{76} }{2}[/tex]

[tex]\frac{2+i *\sqrt{76} }{2}[/tex]

[tex]\frac{2+i *\sqrt{4(19)} }{2}[/tex]

[tex]\frac{2+i *\sqrt{2^2(19)} }{2}[/tex]

[tex]\frac{2+2i \sqrt{19} }{2}[/tex]

[tex]x=1+i\sqrt{19}[/tex]

Now repeat the steps except subtract from -b rather than add to it.

Final Answer

[tex]x=1[/tex] ± [tex]i\sqrt{19}[/tex]

BTW

± = plus and minus

Lets try to figuring out the definition of it.

1. Planning for the distribution of one's estate after death is Estate planning.

2. Trust: an estate, or other property or money, given to a person or institution to manage.

3. Compound interest: figured on the amount of money in the savings account plus the amount of interest already earned.

4. Dividend: a share of money earned as profits by a company and distributed to its stockholders.

5. Checking account: account allows you to write an instruction to the bank, as a check, to make a payment from that account.

6. Will a legal document that describes how your estate should be distributed upon.

8. Purchasing a bond is like loaning money to the company for interest.

9. Club accounts: accounts are set up to save for specific purchases.

11. Mutual fund: instrument in which you purchase a part of a collection of investments.

12. A debit card can be used like a credit card, but money is deducted directly from bank account.

13. Automatic Teller Machine: permits the customer to make transactions by using a special computer terminal.

14. Adjusted balance: balance after adding the outstanding deposits and subtracts the outstanding checks to the balance on the statement.

15. Certificate of deposit (CD) is a sum on deposit usually for a given period of time at a fixed interest rate.

18. A trust created while a person is still alive is called a Living Trust.

19. Intestate: without a will.

20. Interest is the fee a bank pays you to keep your money.

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Answer:

1. Planning for the distribution of one's estate after death is Estate planning.

2. Trust: an estate, or other property or money, given to a person or institution to manage.

3. Compound interest: figured on the amount of money in the savings account plus the amount of interest already earned.

4. Dividend: a share of money earned as profits by a company and distributed to its stockholders.

5. Checking account: account allows you to write an instruction to the bank, as a check, to make a payment from that account.

6. Will a legal document that describes how your estate should be distributed upon.

8. Purchasing a bond is like loaning money to the company for interest.

9. Club accounts: accounts are set up to save for specific purchases.

11. Mutual fund: instrument in which you purchase a part of a collection of investments.

12. A debit card can be used like a credit card, but money is deducted directly from bank account.

13. Automatic Teller Machine: permits the customer to make transactions by using a special computer terminal.

14. Adjusted balance: balance after adding the outstanding deposits and subtracts the outstanding checks to the balance on the statement.

15. Certificate of deposit (CD) is a sum on deposit usually for a given period of time at a fixed interest rate.

18. A trust created while a person is still alive is called a Living Trust.

19. Intestate: without a will.

20. Interest is the fee a bank pays you to keep your money.

Step-by-step explanation:

If 3 ft = 1yard

?        = 16 yards?

Thats [tex]\frac{16 yards * 3ft}{1yard}[/tex]

The common values cancel each other out and you'll have 48 feet :)

Answer: 2

Step-by-step explanation:

By the geometric mean theorem,

[tex]\sqrt{8k}=4\\\\8k=16\\\\k=\boxed{2}[/tex]

Based on the data, it is found that "being female" and "earning over $50,000" are not independent events. the correct answer is option D.

Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Two events, A and B are independent, if:

P(A [tex]\cap[/tex] B) = P(A) P(B)

In this problem, the events are:

Out of the 1000 people, 450 are female, hence:

P(A) = [tex]\dfrac{450}{1000}[/tex] = 0.45

850 earn over $50,000, hence:

P(B) = [tex]\dfrac{850}{1000}[/tex] = 0.85

375 are women who earn over $50,000, hence:

P(A [tex]\cap[/tex] B)  = [tex]\dfrac{375}{1000}[/tex] = 0.375

The multiplication of the probabilities is:

P(A [tex]\cap[/tex] B)  = 0.45(0.85} = 0.3825

Therefore based on the data, it is found that "being female" and "earning over $50,000" are not independent events. the correct answer is option D.

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The area of a 2D form is the amount of space within its perimeter. The surface area of the prism is 232 in².

The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm2, m2, and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.

The surface area of the prism is,

Surface area = 2 [(2 × 8)+(8 × 10)+(2 × 10)]

                      = 232 in²

Hence, the surface area of the prism is 232 in².

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[tex]\textsf {Simplifying the exponents :}[/tex]

[tex]\mathsf {\frac{3x^{-6}y^{-3}}{15x^{2}y^{10}}}[/tex]

[tex]\mathsf {\frac{1}{5x^{(2+6)}y^{(10+3)}}}[/tex]

[tex]\mathsf {\frac{1}{5x^{8}y^{13}}}[/tex]