Consider this function.
ƒ(=) =-3x + 3
Which graph represents the inverse of function??

Answer:

-2

Step-by-step explanation:

[tex]2(3-4) +3(3)-3^2\\= 2(-1) + 3(3) -3^2\\= -2 + 9 - 9\\= -2[/tex]

The error from Jorge's arithmetic operation on the given algebraic expression is that he distributed it incorrectly.

An algebraic expression is a mathematical equation that is made up of variables together with arithmetic operations.

From the given expression, we have:

4x - x + 2 + 6 = 6x + 16

Add similar elements together;

3x + 8 = 6x + 16

Using distributive property, subtract 8 from both sides:

3x + 8 - 8 = 6x + 16 - 8

3x = 6x + 8

Simplify

3x-6x = 8

-3x = 8

Divide both sides by -3

-3/-3x = -8/3

x =  -8/3

So from Jorge's calculation, because he distributed incorrectly, we can conclude that could be his error.

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The only option that meets the root theorem is option b.

The polynomial function is:

[tex]f(x) = 2x^2 - 4x + 9[/tex]

The rational root theorem says that if a root is a rational number, then the leading coefficient must be divisible by the denominator of the rational number and the constant term must be divisible by the numerator.

In this case, the constant is 9, and the only option such that the constant is divisible by the numerator is option b: 3

Where 3 is a rational number:

3 = 3/1

The numerator is 3 (which divides 9) and the denominator is 1 (which divides the leading coefficient 9. (notice that it meets the theorem, but it is not an actual root).

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The correlation between variables (r) = 0.959, and signifies a positive relationship between the variables.

The correlation of two pairs of data values tells about the degree of movement(along or opposite) that can occur in one of the data values when other data value is increased or decreased respectively.

The pertinent data are:

Period Fertilizer Sales Number of Mowers Sold

1 1.6 12.0

2 1.3 10.0

3 1.8 13.0

4 2.0 15.0

5 2.2 15.0

6 1.5 11.0

7 1.6 12.0

8 1.4 10.0

9 1.8 13.0

10 1.4 10.0

11 1.9 15.0

12 1.4 11.0

13 1.7 14.0

14 1.4 13.0

To determine the correlation between the two variables

Regression equation ( y ) = a + bx

y = dependent variable ( mower )

x = independent variable ( fertilizer)

a = intercept point ( y-axis and regression line )

b = slope ( regression line )

From the given data;

N = 14 ,    Σ x = 22.8,  

Σy = 131,   Σy^2 = 1269,

Σx^2 = 38.18,      (Σx)^2 = 519.84

Σxy = 219.8,       (Σy)^2 = 17161

Hence, The correlation between variables (r) = 0.959, and signifies a positive relationship between the variables.

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Answer:

20°

Step-by-step explanation:

Measure of QR is 180 - 108 = 72°

 then using     intercepted arc - external angle theorem:

angle RPQ then equals  1/2 ( 108 - 72) = 20 °

Answer:

£11.50

Step-by-step explanation:

7litres of petrol cos t £3.50. The cost of 1 liter will be:

= £3.50/7

= £0.50

The cost of 23 litres of petrol of the same grade will be:

= £0.50 × 23

= £11.50

An expression is defined as a set of numbers, variables, and mathematical operations. The given statement can be modeled as (3m+7)/27 < n.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The given statement "The quotient of 7 more than three times a number m and the number 27 less than n" can be modeled as an algebraic expression as shown below.

(3m+7)/27 < n

Hence, the given statement can be modeled as (3m+7)/27 < n.

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The surface area of the triangular prism is 480 square inches and net A is the correct net of the prism

When a triangle is, stretch it out to produce a stack of triangles, one on top of the other. A triangular prism is a name given to this novel 3D object.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have given a triangular prism with its net.

After analyzing the correct net will be net A because the inner rectangle length should be 14 in not 13 in.

The surface area of the triangular prism:

[tex]= 2[\dfrac{1}{2}(5\times12)]+ 5\times 14+ 12 \times 14+ 13\times 14[/tex]

After solving:

The surface area = 480 square inches.

Thus, the surface area of the triangular prism is 480 square inches and net A is the correct net of the prism

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The number of cups of lemonade, y that can be made with any number of cans of frozen lemonade concentrate, x is y=6x.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Given that with a single can of frozen lemonade concentrate 6 cups of lemonade can be made. Therefore, the number of cups that can be made with x number of cans is,

Number of cups that can be made, y = 6x

Hence, the number of cups of lemonade, y that can be made with any number of cans of frozen lemonade concentrate, x is y=6x.

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Answer:

x = 37

Step-by-step explanation:

Answer:

(x - 9)(x^2 + 18x + 81).

Step-by-step explanation:

Use the difference of cubes factorization, which claims that a^3 - b^3 = (a - b)(a^2 + ab + b^2)

x^3 - 729 = (x - 9)(x^2 + 18x + 81)

Answer:[tex](x-9) (x^{2} +9x + 81)[/tex]

Step-by-step explanation:

Answer:

a. 700

b. 1000

c. 80

d. 700

e.

Answer:

57 square units

Step-by-step explanation:

Area is = Length x Width

Given:

f(x)= 4x + 3    Length

g(x)=2x-5      Width

x = 4

============

Width

g(x)=2x-5

g(4)=2(4)-5

g(4)= 3

Length

f(x)= 4x + 3

f(4) = (4)(4) + 3

f(4) = 19

Area = (length)*(width)

Area = f(x)*g(x) for x = 4

Area = (f(4))*(g(4))

Area = (19)*(3)

Area = 57 square units

Answer:

x = 55 degrees

Step-by-step explanation:

The sum of the internal angles of a triangle results in 180°

x + 50° + 75° = 180°

x + 125° =180°

x = 180° - 125°

x = 55°

Answer:

x < 13 and x > -13

Step-by-step explanation:

Split the absolute value equation into 2 equations to account for the positive and negative answers possible with absolute values.

Write the positive value first by removing the absolute value symbol.

x < 13

Flip the inequality and make the 13 negative for the other side.

x > -13

The values of x does f(x) = 0 will be -4,0,2.Option A is corect.

A diagram depicting the relationship between two or more variables, each measured along with one of a pair of axes at right angles.

The graph shows the cubic polynomial equation found as;

⇒(x+4)(x)(x-2)

The points f(x) = 0 is;

⇒(x+4)(x)(x-2)

⇒(-4+4)(0)(2-2)

⇒0

The values of x does f(x) = 0 will be -4,0,2.

Hence, option A is corect.

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Step-by-step explanation:

please give this answer brainlist answer

Answer:

$75

[It is easy to say $60, but don't forget to add Samuel to the total]

Step-by-step explanation:

There are 5 people in total:

1  Samuel

4 friends

5 people who can spend up to $15 each.

(5 people)*($15/person) = $75 total spent on supplies

Answer:

r = - 3.25, p = -1.5

Step-by-step explanation:

→ Rearrange p - 2r = 5

p = 5 + 2r

→ Substitute into 6p - 4r = 4

6 ( 5 + 2r ) - 4r = 4

→ Expand

30 + 12r - 4r = 4

→ Simplify and solve

r = - 3.25

→ Substitute into p - 2r = 5

p + 6.5 = 5

→ Minus 6.5 from both sides

p = -1.5

Answer:

[tex]n = 14[/tex]

Step-by-step explanation:

[tex]~~~~~~~2^n+2^n+2^n+2^n = 2^{16}\\\\\implies 4 \cdot 2^n = 2^{16}\\\\\implies 2^2 \cdot 2^n = 2^{16}\\\\\implies 2^{n+2} = 2^{16}~~~~~~~~~~~~~~~~~~~~~~~~~~~~;[a^m \cdot a^n = a^{m+n}]\\\\\implies n+ 2 = 16\\\\\implies n = 16-2 \\\\\implies n = 14[/tex]

The function that models the horizontal displacement as a function of time in seconds is y = 5cos(2π/3 x)

The given parameters are:

Start by calculating the amplitude, A using:

A = h/2

This gives

A = 10/2

A = 5

Next, we calculate the period using:

B = π/t

This gives

B = π/1.5

Evaluate

B = 2π/3

The pendulum is at the middle.

So, it has no vertical displacement

The function is then represented as:

y = Acos(Bx)

This gives

y = 5cos(2π/3 x)

Hence, the function that models the horizontal displacement as a function of time in seconds is y = 5cos(2π/3 x)

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Answer:

B

Step-by-step explanation:

pythagorus theorem

a² + b² = c²

c² - b² = a²

26² - 24² = a²

676 - 576 = a²

a² = 100

a = 10

Answer:

x = 9

y = 61

Step-by-step explanation:

let me know if you want an explanation!

Answer:

#1 (4b + 6a) #2  150y

Step-by-step explanation:

#1 :area of right triangle: ab/2

4x2/2 = 4b

area of rectangle: length x width

2 x 3 = 6a

#2:

5y + 2.5y = 7.5y x 2 = 15y

so the top and bottom are both 15 y

the sides are each 5y so thats 10 y

15x10= 150y

Answer:

⇒   Let marked price be Rs.x.

⇒  Discount = 20% of marked price.

⇒  Discount=  

100

20

​  

×x=  

100

20x

​

⇒  Selling price = Marked price - Discount.

⇒  192=x−  

100

20x

⇒  192=  

100

80x

⇒  x=  

80

19200

=Rs.240

Answer:

S.p = 992

discount = 20%

marked price = S. p + discount

= 992 + 20/100*992

= 992 + 198.4

= 1190.4

Correct answer is option D.

The graph crosses the y-axis at (0, 5), increasing from x = -10 to x = 2 and remaining constant from x = 2 to x = 10.

A function f(x) is said to be increasing on an interval I if for any two numbers x and y in I such that x < y, we have f(x) ≤ f(y).

For this case, the first thing you should observe is that you have a different function in two distinct intervals.

We have then:

For [-10, 2]:

The linear function has a positive slope, therefore it grows and cuts the y-axis at the point (0, 5)

For [2, 10]:

We have a constant function whose equation is:

y = 5

Thus, the correct Answer is:

D. The graph crosses the y-axis at (0, 5), increasing from x = -10 to x = 2 and remaining constant from x = 2 to x = 10.

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Answer:  [tex]\textsf{y = 3/4x - 7.75}[/tex]

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Given:  [tex]\textsf{Passes through (5, -4) with a slope of 3/4}[/tex]

Find:  [tex]\textsf{The equation in slope-intercept form}[/tex]

Solution:  In order to determine the equation we need to first plug the values into the point-slope form, simplify, distribute, and solve for y to get our final result.

Plug in the values

Simplify the expression and distribute

Subtract 4 from both sides

The equation in slope-intercept form that follows the information that was provided is y = 3/4x - 7.75

The equation in slope-intercept form is y = 13/8x -17/8 and the equation in standard form is 13x -8y = 17

A line is the shortest distance between two points. The equation of a line in slope-intercept form is y = mx + b while as a standard notation is Ax+By = C

Given the coordinate points (-3, -7) and (5, 6)

Determine the slope

Slope = 6-(-7)/5-(-3)

Slope = 13/8

For the y-intercept

6 = 13/8(5) + b

6 = 65/8 + b

b = 6 - 65/8

b = -17/8

The equation in slope-intercept form is y = 13/8x -17/8

Write in standard form

Recall y = 13/8x - 17/8

Multiply through by 8

8y = 13x - 17

-13x + 8y = -17

13x -8y = 17

Hence the equation in standard form is 13x -8y = 17

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