I need help with 1-4 please and thanks

The inverse of the function → f(x) = [tex]\sqrt{11x+12}[/tex] is

f⁻¹(x) = (x² - 12)/11

We have -

y = f(x) = [tex]\sqrt{11x+12}[/tex]

We have to find its inverse function.

Inverse of a function can be calculated by following the steps mentioned below -

Step 1 -  Replace 'y' with 'x' and vice - versa.

Step 2 - Rewrite the equation by solving for 'y'.

Step 3 - Replace 'y' with f⁻¹(x).

According to the question -

y = f(x) = [tex]\sqrt{11x+12}[/tex]

x = [tex]\sqrt{11y+12}[/tex]

x² = 11y + 12

x² - 12 = 11y

y = (x² - 12)/11

f⁻¹(x) = (x² - 12)/11

Therefore, the inverse of the function → f(x) = [tex]\sqrt{11x+12}[/tex] is

f⁻¹(x) = (x² - 12)/11

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Answer:

answer D is right. You need to substract,so that you can get x=2

Answer:

mark is right

Step-by-step explanation:

3+5x5 =13

Answer:

Mark is not correct , becouse squared number Is number which can be after "=" when you times same numbers for example: 4*4=16 so 16 is squared number,is this make sense?

Answer:

No solution

Step-by-step explanation:

-2 ( 4 - 3x ) - 6x = 10

→ Expand brackets

-8 + 6x - 6x = 10

→ Simplify

-8 = 10 ⇒ No solution

Answer:

Step-by-step explanation:

B)

x² + 6*x + 9 = x² + 2*x*3 +3² = (x + 3)²

The answer is -13k - 7

Answer:

1 - 3k - 8 + 10k

1 - 3k + 10k - 8

1 - 13k - 8

1 - 8 - 13k

-7 - 13k or -7 + (-13k)

Answer:

341 = 273k - 79 or 273k - 79 = 341

Answer: Question 1: 113 & Question 2: 27

Step-by-step explanation:

For question 1 you would add 35+32=67,then you subtract 180-67 to get 113  for your answer & question 2 you would subtract 155-128 to get 27 for the answer

Angles in a triangle add up to 180 degrees.

[tex]180-35-32=113[/tex]

Angles on a line add up to 180 degrees.

[tex]p=180-113=67[/tex]

Angles on a line add up to 180 degrees.

[tex]180-155=25[/tex]

Angles in a triangle add up to 180 degrees.

[tex]q=180-128-25=27[/tex]

we make a equation depending of the days

Where T is the total of pencils

In this equation we are going to subtract 50 pencils for each day from the original 2000

to know the days where are 950 pencils we replace the total by 950 and solve d

the number of days is 21

Here is the completed table:

x           /AM/

14          16

3            13

11           33

10           40

/AM/ + /AC/ = /AC/

(x + 2) + (3x - 9) = 6x - 21

4x - 7 = 6x - 21

6x - 4x = 21 - 7

2x = 28

x = 28 / 2

x = 14

/AM/ = 14 + 2 = 16

/AM/ + /MW/ = /AW/

(2X + 7) + (3x - 4) = 18

5x + 3 = 18

5x = 18 - 3

5x = 15

x = 15/5

x = 3

/AM/ = (2 X 3) + 7 =

= 6 + 7 = 13

x + x + x + x = 44

4x = 44

x = 44 / 4

x = 11

/AM/ = 11 x 3 = 33

/AG/ + /GM/ = /AM/

2(x + 10) = 3x + 10

2x + 20 = 3x + 10

20 - 10 = 3x - 2x

10 = x

/AM/ = (3 x 10) + 10

= 30 + 10

= 40

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The rate of change of the distance in feet below the sea level over time is: 8 ft/sec.

The rate of change of a linear relationship between variables x and y is calculated as:

Rate of change = change in y / change in x.

From the table given, we have:

Using any two points from the table, (0, 460) and (18, 604):

Rate of change of the linear relationship = change in y / change in x = (604 - 460)/(18 - 0)

Rate of change of the linear relationship = 144/18

Rate of change of the linear relationship = 8 ft/sec.

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The equation that could model the given situation is y = -x + 30.25. The correct option is B. y = -x + 30.25

From the question, we are to determine the equation that could model the given situation

The perimeter, P, of a rectangle is given by the formula,

P = 2(l + w)

Where P is the perimeter

l is the length

and w is the width

From the given information,

The perimeter of a rectangular room is 60.5 feet.

∴ P = 60.5 feet

Also,

x is the width of the room and y is the length of the room

That is,

l = y

and

w = x

Thus,

The equation becomes

60.5 = 2(y + x)

2(y + x) = 60.5

Divide through by 2

y + x = 30.25

y = -x + 30.25

Hence,

y = -x + 30.25 is the equation that might be used to model the circumstance.

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Answer:

D $376.20

Step-by-step explanation:

The monthly membership fee at a gym increased by 10% this year. Last year, the cost of a monthly membership was $28.50. What is the total yearly cost for a membership at the gym this year?

A $307.80

C $334.20

B $319.20

D $376.20

28.50 × 1.10 = $31.35 per month this year

there are 12 months per year so:

$31.35 × 12 =  $376.20

Answer:

Step-by-step explanation:

First, convert hour into seconds:

Now find the distance:

The standard normal distribution  becomes smaller.

What is standard deviation?

As the number of degrees of freedom for a t distribution increases, the difference between the t distribution and the standard normal distribution

becomes smaller.

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In order to find the quadratic equation, let's use the standard form of a quadratic equation:

Using the point (0, 2) from the table, we have:

Now, using the points (-1, -2) and (1, 22):

Adding both equations, we can solve for a:

Therefore the equation is y = 8x² + 12x + 2

The statements that are true are:

Statement A: Figure A was reflected from the third quadrant to the second quadrant

Statement B: Triangle DEF was reflected over the x-axis

The False statements are:

Statement C: The image of DEF is in quadrant 3

Statement D: The reflection of A can be represented by (-x, y)

Statement E: The reflection of DEF can be represented by (-x, y)

A linear equation is a mathematical form of a line segment the point (6,5) satisfies the equation y = 2/3x + 1 so it is the solution of the equation but (9,8) is not the solution.

A straight line on the coordinate plane is represented by a linear function.

The formula for a linear function is f(x) = ax + b, where a and b are real values.

As per the given linear equation, y = 2/3x + 1

To be a point of its solution the point must satisfy the given equation.

Substitute (6,5)

5 = (2/3)6 + 1

5 = 2(2) + 1 = 5

Therefore, the (6,5) is the solution of the equation.

Substitute,(9,8)

(2/3)9 + 1 = 7

8 ≠ 7

So,(9,8) is not the solution of the equation.

Hence "A linear equation is a mathematical form of a line segment the point (6,5) satisfies the equation y = 2/3x + 1 so it is the solution of the equation but (9,8) is not the solution".

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1. The sum for the algebraic expression 4j+k, -3k+7, 5-2j, and j+k-8 is 3j-k+4

2.The sum for the algebraic expression 5x^2-9x+3 and -2x^3+4x^2+7 is -2x³+9x²-9x+10

The addition of two or more numbers or quantities taken with regard to their signs according to the rules of addition in algebra.

First we will find the sum of 4j+k, -3k+7, 5-2j, and j+k-8

0i + 4j  + k  +  0

0i + 0j  - 3k +  7

0i - 2j  + 0k  +  5

0i +  j  +  k-  8

So the sum of 4j+k, -3k+7, 5-2j, and j+k-8 is 3j-k+4

First we will find the sum of 5x²-9x+3 and -2x³+4x^2+7

0x³ +  5x² - 9x + 3

-2x³ + 4x² + 0x+ 7

So the sum of 5x²-9x+3 and -2x³+4x²+7 is -2x³+9x²-9x+10

Therefore, the sum of the given algebraic expressions 4j+k, -3k+7, 5-2j, and j+k-8 is 3j-k+4 and 5x²-9x+3 and -2x³+4x²+7 is -2x³+9x²-9x+10.

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Answer:

Answer down below!

Step-by-step explanation:

Answer: 310000000

Step-by-step is provided in the picture below!

To calculate the surface area of a sphere, you have to use the following formula:

Where "r" is the radius of the sphere.

We know that the diameter of the sphere is d = 60 inches and that the radius is half the diameter, then the radius can be determined as follows:

Once the radius is calculated, you can determine the surface area of the sphere:

The surface area of the sphere is 3600π in², expressed as a decimal value, the surface area is equal to 11309.73 in²

The maximum remaining life span of Halley's Comet is 76000 years.

The  formula for calculating maximum remaining life span of Halley's Comet is    [tex]L = \frac{M}{m} \times t[/tex]

M =  mass of comet = [tex]1 X 10^{11}[/tex] tons

m = Mass of material lost =[tex]1 X 10^{8}[/tex] tons

t=orbital period =  76 years

Equating values in the equation

L = [tex]\frac{1 X 10^{11}}{1 X 10^{8}} \times76[/tex]

L = 76000 years

life span, is the  time between the birth and death of an organism. It is normal for all organisms to die. Some die after  a short existence, like  the nymph fly, which returns to adult life  in a day, and others, like  the wrinkled fly, which live for thousands of years. It seems that the lifespan limits  of each species are ultimately determined  by heredity. Locked in the code of the genetic material are instructions that determine the age at which a species cannot survive even under the most favourable conditions. And many environmental factors reduce this upper age limit.

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real number can be a complex number but a complex number can not be a real number, verified.

the lengths of the complex number and its conjugate are equal but the converse is not necessarily true., verified.

Not all complex numbers are real numbers, despite the fact that every complex number is a real number.

In fact, determining whether the complex number z = a + bi is real is one of the complex conjugate's most useful applications. If and only if z = a + 0i, a complex number is real. In other words, a complex number is real if it contains an imaginary part.

Mathematical proof:

Let z = a+bi, where a and b = real numbers.

Let z* =complex conjugate of z.

Then the magnitude (absolute value) of z is:

|z| = √(a²+b²).

And the value of z* is:

|z*| = √[a²+(-b)²] = √(a²+b²).

So |z| = |z*|.

This Completes the Proof.

what are real numbers?

its a quantity whose decimal expansion has an endless range. In contrast to the natural numbers 1, 2, 3,... that result from counting, real numbers are utilised in measurements of continuously altering quantities such as size and time.

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Answer: These linear functions can be represented by two lines y = 5x and y' = 5x' + 3

So when we shift line y = 5x by 3 units up on the y-axis then a new graph of

y = 5x + 3 will be formed.

Therefore, Option A is the answer.

Answer:

  5 and -3

Step-by-step explanation:

You want two integers that have a sum of 2 and a product of -15.

Solving a problem like this can often be done fairly quickly by listing the factor pairs that make up the product. Only the pairs need be listed that have a sum with the same sign as the sum you're looking for.

Divisors of 15 are 1, 3, 5, and 15. You want a negative product with the largest factor being positive:

  -15 = 15(-1) = 5(-3)

The sums of these factor pairs are 14 and 2. The latter pair is the one of interest.

The two integers are 5 and -3.

__

Additional comment

The desired relations can be expressed as a quadratic equation. It generally works well to solve it by completing the square.

If one of the numbers is x, the other is 2-x. Their product is -15:

  x(2 -x) = -15

  2x -x^2 = -15 . . . . . eliminate parentheses

  x^2 -2x = 15 . . . . . . make the leading coefficient positive

Complete the square by adding the square of half the x-coefficient

  x^2 -2x +1 = 15 +1

  (x -1)^2 = 16

  x -1 = √16 = 4 . . . . . . take the square root

  x = 5 . . . . . . . . . . . add 1

  2-x = 2 -5 = -3 . . . . the other number

Answer:

y=-1/3x+7

Step-by-step explanation:

put it in y-y1=m(x-x1)

perpendicular means the slope is opposite

slope is -1/3

y-9=-1/3 (x+6)

y-9=-1/3x -2

+9           +9

y=-1/3x +7

The description of the error in finding the slope and y-intercept, of the graph of the equation is given by the option:

To be in slope-intercept form, the equation needs to be solved for y, not x

The equation in slope-intercept form is,  [tex]\displaystyle{y = -\frac{1}{4} \cdot x[/tex]

The slope-intercept form of the equation of a straight line is an equation of the form, y = m·x + c

The slope-intercept form of a straight-line equation is of the form, y = m·x + c, where:

m = The slope of the equation

c = The y-intercept

The given equation is x = -4·y

The given equation is not in the slope and intercept form given that the subject of the equation is x, rather than y

The error is therefore, in making x, the subject of the equation rather than y, that is the equation needs to be solved for y, not x

The correction of the error is performed as follows:

x = -4·y

-4·y = x

[tex]\displaystyle{y = \frac{x}{-4} = -\frac{1}{4} \cdot x[/tex]

Which gives: [tex]\displaystyle{y = -\frac{1}{4} \cdot x[/tex]

The slope of the graph of the equation is [tex]-\frac{1}{4}[/tex], the y-intercept, c, is 0

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There is a requirement of 176 packets of economy blend and 96 packets of a superior blend to make maximum profit for the week.

Using the given data, calculate the x number of packages of the economy blend as well as the y number of packages of the superior mix.

3x + 11y =1584

6x + 4y = 1440

From the graph of these two equations, three extreme points are deduced: (240,0), (0,144), and (176,96).

The maximum (2x +4y) is the goal function.

Determine the aim function's value at all these extreme points,

The objective function value for (240,0) is 2 × 240 = 480

The objective function value for (0,144) is 4 × 144 = 576

The value of the objective function for (176,96) is 2 × 176 + 4 × 96 = 736

∴ The optimal point is (176,96) where x = 176 and y = 96.

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The Bank discount and proceeds of the given information is:

$2365.27 and $47634.73 respectively.

Given the face value is $50,000

Discount rate = 13%

No.of term days = April 5 to August 14

= 131 days.

Bank discount = ?

Proceeds = ?

First calculate the bank discount using the formula:

Bank discount = face value × discount rate × time

Bank discount = $50,000 × 0.13 × 131/360

= 50,000×0.13×0.36388

= $2365.27

now calculate the proceeds using the formula :

Proceeds = face value - bank discount

= 50,000 - 2365.27

= $47634.73

Hence the bank discount and proceeds are $2365.27 and $47634.73 respectively.

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