the point p(2 -1) lies on the curve y=1/(1-x)

The two functions of f(x)= -6x2 + 5 and g(x)= 5 result in the y-intercept of function g(x) being 2 as a result (1. 5)

Mathematics deals with numbers and their variants, equations and related structures, shapes and their locations, and locations where they might be found. The term "function" describes the connection between a group of inputs, each of which has a corresponding output. A function is an association between inputs and outputs where each input results in a single, unique output. A domain and a codomain, or scope, are assigned to each function. Functions are typically denoted by the letter f. (x). The input is an x. On functions, one-to-one functions, many-to-one functions, within functions, and on functions are the four main categories of functions that are available.

given

y-intercept for f(x) is f(0)

so f(0) =

=> 0+5

=>5

so the y-intercept of f(x) is 5

now y-intercept of g(x) is g(0)

so g(0) = 7*0 +2

=>0 +2

=>2

The two functions of f(x)= -6x2 + 5 and g(x)= 5 result in the y-intercept of function g(x) being 2 as a result (1. 5) .

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The area of the rectangle is x(14-x).

The area can be defined as the amount of space covered by a flat surface of a particular shape. It is measured in terms of the "number of" square units (square centimeters, square inches, square feet, etc.) The area of a rectangle is the number of unit squares that can fit into a rectangle. Some examples of rectangular shapes are the flat surfaces of laptop monitors, blackboards, painting canvas, etc. You can use the formula of the area of a rectangle to find the space occupied by these objects. For example, let us consider a rectangle of length 4 inches and width 3 inches.

Yes, the expression a(x) = x(14-x) represents the area of a rectangle with width x. The expression is a function that takes the width of the rectangle as input and returns the area of the rectangle as output. The area of a rectangle is given by the formula A = lw, where A is the area, l is the length of the rectangle, and w is the width of the rectangle. In this case, the length of the rectangle is 14 and the width is x, so the area of the rectangle can be expressed as a(x) = x(14-x).

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The perimeter of the rectangle is fixed at P(x) =28

Now, According to the question:

Let's Know:

Area and Perimeter of Rectangle

Areas and perimeters are the most basic parameters involved in shapes, with the former being the space that can be covered by a shape and the latter being the measure of the outline of the shape.

A rectangle has dimensions defined by the length, l, and the width, w, which can be used in determining its area and perimeter. These are obtained using the following formulas.

A = l × w

P = 2l+ 2w

We are given the area of a rectangle as a function of x, which is

a(x) = x(14−x) We are asked to determine the perimeter of the rectangle.

the area of a rectangle is given by:

A = l × w

l is the length and w is the width. We may notice that in this formula, the two dimensions or components are simply multiplied together. Going back to the given function, we can see that the components on the right side of the equation also have this relation. If we look closely, we can see that we have two factors, x  and (14 − x), and that they are multiplied to each other. We can assume that x is the length of the rectangle and (14−x)  is the width of the rectangle. The product of these two expressions gives the area function.

Now, let's apply these to the perimeter of a rectangle. Generally, the perimeter of a rectangle is given by

            P = 2l + 2w

Since, for our case, the length is x and the width is (14− x), substituting these into the formula for the perimeter gives us

P(x) = 2x + 2(14 - x)

P(x) = 2x + 28 - 2x

P(x) = 28

Therefore, the perimeter of the rectangle is fixed at P(x) =28.

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Answer:

60

Step-by-step explanation:

Total angle of triangle= 180

so 4x + 5x + 3x = 180

12x = 180

x = 180/12

x = 15

E = 5x = 5×12 = 60

Answer: -7x+2x+5-4x=-9x+6

The equation -7x+2x+5-4x=-9x+6 is an example of an equation that has no solution. This is because the left side of the equation, -7x+2x+5-4x, is not equal to the right side, -9x+6.

When we simplify the left side of the equation, we get -7x+2x+5-4x = -9x. We can see that the left side and right side of the equation are not equal and thus have no solution.

In general, an equation has no solution when the two sides of the equation are not equal, and there is no value of the variable that can make them equal.

Step-by-step explanation:

A similarity transformation is a rigid movement followed by scaling, so this type of transformation can change the position and size, but not the shape.

In geometry, a similarity transformation is a rigid movement followed by scaling, so this type of transformation can change the position and size, but preserve the shape and angles.

Thus, two or more shapes are similar if they have the same shape and corresponding angles, but their corresponding sides are proportional in length.

This type of transformation is often also referred to as dilation.

The rule of dilatation:

[tex]D_{k}[/tex] (x,y) = (kx, ky)

with [tex]D_{k}[/tex] is the coordinate point of the new image and k is the scale factor.

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A convex polygon is a polygon which has all its interior angles as less than 180° . The correct option is B

Convex polygon is a closed figure where all its interior angles are less than 180° and the vertices are pointing outwards. convex is used to refer to a shape that has a curve.

Therefore from visual inspection of all four options only option B seems to fulfill the criteria mentioned . A convex shape is a shape where all of its parts point outwards. No part of it points inwards,

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Answer:

18 cubic units

Step-by-step explanation:

The volume of prism is equal to:

base area x height

therefore;

V = 1.33333 x 13.5

   = 17.999955 ≈ 18

Answer:

The volume of a prism is given by the formula:

V = Bh

Where V is the volume, B is the area of the base, and h is the height of the prism.

Given the height of 1.33333 and an area of the base of 13.5, the volume can be calculated as:

V = 13.5 * 1.33333

V = 18.08332

So the volume of the prism is 18.08332 cubic units.

Step-by-step explanation:

Answer:

[tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] + 7 : a₁ = 2

Step-by-step explanation:

An explicit formula has the form

[tex]a_{n}[/tex] = a₁ + d(n - 1)

compare with [tex]a_{n}[/tex] = 2 + 7(n - 1)

then a₁ = 2 and common difference d = 7

the recursive rule allows a term to be found by adding d to the previous term, that is

[tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] + 7 : with a₁ = 2

The values of x when solved;

a. x≥ 3. 44

b. x≥3. 44

c. x ≤ 8. 8

Inequalities are simply described as relations that makes a non-equal comparison between two numbers, variable or other mathematical expressions.

They are used to compare numbers on the number line on the basis of size

From the information given, we have to determine the value of x in the inequality given;

a. 5 1/2≥1.6x

convert to improper fraction

11/2 ≥1.6x

divide both sides by 1. 6

x≥ 3. 44

b. x≥3 7/16

convert to improper fraction

x≥ 55/ 16

x≥3. 44

c. x≤8 4/5

convert to improper fraction

x≤ 44/ 5

x ≤ 8. 8

Hence, the value are  x≥ 3. 44, x≥3. 44 and x ≤ 8. 8

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Answer:

No

Step-by-step explanation:

outliers are numbers in a line that exceed out from the range.

Considering the expression of a line, the equation of the line that passes through the pair of points (-4,1) and (4, -1) is y=-1/4x +2.

A linear equation o line can be expressed in the form y = mx + b

where

Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope m can be calculated using:

m= (y₂ - y₁)÷ (x₂ - x₁)

Substituting the value of the slope m and the value of one of the points in the expression of a line, the value of the ordinate to the origin b can be obtained.

In this case, being (x₁, y₁)=  (-4, 1) and (x₂, y₂)= (4, -1), the slope m can be calculated as:

m= (-1 -1)÷ (4 - (-4))

m= (-1 -1)÷ (4 +4)

m= (-2)÷ 8

m= -1/4

Considering point 1 and the slope m, you obtain:

1= (-1/4)× (-4) + b

1= -1 +b

1 +1= b

2= b

Finally, the equation of the line is y=-1/4x +2.

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It takes 10 hours to reach a population of 200,000 at the growth rate of 7% per hour.

We can use the formula for compound interest to calculate the time it takes for the population of bacteria to reach 200,000.

The formula is:
A = P(1+r)^t

Where:
A = final amount (200,000)
P = initial amount (50,000)
r = growth rate (7% per hour expressed as decimal)
t = time (in hours)

We can rearrange the formula to solve for t:
t = log(A/P) / log(1+r)

By plugging in the given values:
t = log(200000/50000) / log(1+ 0.07)

The answer will be in hours, so we need to use a calculator or a log function in a programming language to get the answer.

Alternatively, you can use the rule of 70, which says that the number of years required to double a population at a given growth rate is approximately 70/growth rate. So in this case it is 70/7 = 10 hrs.

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The value of g(-2) is 0 and the value of g(4) is -4.

The function g is defined as a piecewise function that assigns a specific value to the input x depending on the range of x.

For x between -8 and -2 (not including -2) the function g assigns 6 as the output, for x between -2 and 4 (not including 4) the function g assigns 0 as the output, and for x between 4 and 10 (not including 10) the function g assigns -4 as the output. Therefore, for input x = -2, the function g assigns 0 as the output and for input x = 4, the function g assigns -4 as the output.

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Complete question :

consider a function g.

given

g(x) = 6    if  -8 ≤ x < -2

g(x) = 0     if  -2 ≤ x < 4

g(x) = -4     if  -4 ≤ x < 10

find the value of g(-2) and g(4)

The balance in your account after 5 years, given the annual simple interest rate and the amount deposited, is $ 1, 612. 50

To find the balance on the account after 5 years, you first need to find the simple interest on the account every year ;

= Amount deposited x Simple interest rate

= 1, 500 x 1. 5 %

= $ 22. 50

The interest over 5 years is :

= 22. 50 x 5

= $ 112. 50

The balance is therefore:

= 1, 500 + 112. 50

= $ 1, 612. 50

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Full question is:

A savings account pays an annual simple interest rate of 1.5%. What would be the balance in your account after 5 years, if you deposited $ 1, 500?

If Polygon q is a scaled copy of polygon p the value of x is 6 value of y would be 2/9

Here, the idea of scale factor is used.

A figure's scale factor determines how much larger or smaller it is compared to the other figure. The scale factor refers to the amount by which a figure would indeed be increased or decreased.

In mathematics, a scale factor is the ratio between similar measurements of an object as well as a representation of this same object.

Polygon Q is a scaled copy of Polygon P.

The value of x is 6

Therefore, From the given statement,

4/3 = x/y

When x = 6 then

4/3 = x/ y

4/3 = 6/y

y = 4/3 (1/6)

y = 2/9

here, the scale factor would be:

k = y/x

k = 3/4

so, if Polygon q is a scaled copy of polygon p the value of x is 6 value of y would be 2/9

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It is not possible to answer this question  for polygon without additional information.

In order to answer this question, we need to know the value of y in the original polygon p. Without knowing this value, it is impossible to calculate the corresponding value in polygon q. For example, if polygon p has a side length of 10 units, and polygon q has a side length of 60 units, then the value of y in polygon q would be 6 times the value of y in polygon p. However, without knowing the value of y in polygon p, we cannot calculate the value of y in polygon q.

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The minimum sample size required for the estimate is given as follows:

385.

The bounds of a z-distribution confidence interval, which is used as we have the standard deviation for the population, are given as follows:

[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]

In which the parameters are given as follows:

Hence the equation for the margin of error is given as follows:

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

The variance is known to be 3.61, hence the standard deviation is given as follows:

[tex]\sigma = \sqrt{3.61} = 1.9[/tex]

The critical value for a 95% confidence interval is given as follows:

z = 1.96.

Hence the required sample size for a margin of error of M = 0.19 is calculated as follows:

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]0.19 = 1.96\frac{1.9}{\sqrt{n}}[/tex]

[tex]0.19\sqrt{n} = 1.96 \times 1.9[/tex]

[tex]\sqrt{n} = \frac{1.96 \times 1.9}{0.19}[/tex]

[tex](\sqrt{n})^2 = \left(\frac{1.96 \times 1.9}{0.19}\right)^2[/tex]

n = 385.

(rounding up, as for a sample size of 384, the margin of error would be slightly above 0.19).

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Answer:

3n³-19n²+20n

Step-by-step explanation:

(g×f)(n)= g(n) × f(n)

= (n²-5n)(3n-4)

=3n³-4n²-15n²+20n

=3n³-19n²+20n

A. The number of red balls he had was 8  at the beginning.

Duke's starting red ball total can be found by setting up a system of equations. First, let x represent the number of red balls and y represent the number of blue balls.

After 5 days, the equation is x-15=y+10. This equation states that after 5 days, the number of red balls (x) minus 15 will equal the number of blue balls (y) plus 10. After 9 days, the equation is x-27=2y+20.

This equation states that after 9 days, the number of red balls (x) minus 27 will equal twice the number of blue balls (y) plus 20. To solve for x, both equations can be set equal to each other and solved. This results in x=8. Therefore, Duke had 8 red balls at the beginning.

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Answer:

[tex]\boxed{22}.[/tex]

Step-by-step explanation:

In June, the camp had 325 campers and 26 counselors, for a ratio of 325/26=<<325/26=12.5>>12.5 campers per counselor.

In July, there are 325-265=<<325-265=60>>60 remaining campers from June, and 215 new campers arrive, for a total of 60+215=<<60+215=275>>275 campers in July.

To maintain the same ratio of campers to counselors as in June, the camp would need 275/12.5=<<275/12.5=22>>22 counselors in July.

Answer:

6 -19i

Step-by-step explanation:

5 - 8i + 1 - 11i

Collect like terms

5 + 1 -11i -8i

6 - 19i

Answer:

Step-by-step explanation:

the squares of consecutive odd numbers are always divisible by 8

The expression 2(m - 4) is equivalent to 2m - 8.

In the expression 2(m - 4), the term inside the parentheses is m - 4. When you multiply this term by 2, you get 2(m - 4) = 2m - 8.

So, the expression 2(m - 4) is equivalent to 2m - 8.

Of the five options given, the only one that is equivalent to 2(m - 4) is 2m - 8. The other options are not equivalent because they do not have the same value as 2(m - 4) when you plug in different values for m.

For example, if you plug in m = 6, the expression 2(m - 4) becomes 2(6 - 4) = 2(2) = 4.

On the other hand, the other options do not give the same result when you plug in the same value for m:

2m - 7: 2(6) - 7 = 12 - 7 = 5

2m - 3: 2(6) - 3 = 12 - 3 = 9

2m: 2(6) = 12

2m + 10: 2(6) + 10 = 12 + 10 = 22

Since none of these options gives the same result as 2(m - 4) when you plug in the same value for m, they are not equivalent to 2(m - 4).

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The equivalent expression of 2(m − 4) + 1 is 2m − 7. So the option a is corect.

In the given question, we have to find which expression is equivalent to 2(m − 4) + 1.

The given expression is 2(m − 4) + 1.

To solve this expression we firstly solve the small bracket. To solve the small bracket we use distributive property. In this property:

a(b+c) = ab + bc

Now solving the expression.

2(m − 4) + 1 = 2m − 2*4 + 1

2(m − 4) + 1 = 2m − 8 + 1

2(m − 4) + 1 = 2m − 7

Hence, the equivalent expression of 2(m − 4) + 1 is 2m − 7. So the option a is corect.

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The complete question is:

Which expression is equivalent to 2(m − 4) + 1?

(1) 2m − 7

(2) 2m − 3

(3) 2m − 9

(4) 2m − 10

Answer:

Step-by-step explanation:

I think it would  it  be a) because (-2 b - 12 c)

i might be wrong but i hope it helps

The rate of change of this linear function is -2.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The formula to find the slope of a line is slope = (y₂-y₁)/(x₂-x₁)

From the given table, (-2, 15), (-4, 23) and (-5, 27).

Substitute, (x₁, y₁)=(-2, 15) and (x₂, y₂)=(-4, 23) in (y₂-y₁)/(x₂-x₁), we get

Rate of change =(23-15)/(-4+2)

= 8/(-2)

= -4

Therefore, the rate of change of this linear function is -2.

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Answer:

A) 3.6 meters

B) 3.24 meters

C) 13 Times

Step-by-step explanation:

:)

Answer: 10

Step-by-step explanation: 1/2 + 3/4= 5/4 or 1 1/4

1 1/4 / 1/8= 10

The range of the ordered pairs  {(4, -2), (3, 2), (-1, 0), (-3, 4)} is {-2, 2, 0, 4}

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

{(4, -2), (3, 2), (-1, 0), (-3, 4)}

This means that

Ordered pairs =  {(4, -2), (3, 2), (-1, 0), (-3, 4)}

Rewrite as

(x, y) =  {(4, -2), (3, 2), (-1, 0), (-3, 4)}

The domain is the set of the x values

So, we have the following representation

x = {4, 3, -1, -3}

Remove repeated entries

x = {4, 3, -1, -3}

So, the domain is x = {4, 3, -1, -3}

On the other hand, the range of the ordered pairs is the set of the y values

So, we have

Range = {-2, 2, 0, 4}

So, the range is {-2, 2, 0, 4}

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The absolute maximum value of the function f(x) = x^3 - 3x^2 + 12 on the closed interval (-2, 4) occurs at x = 4.

To find the absolute maximum value of the function f(x) = x^3 - 3x^2 + 12 on the closed interval (-2, 4), we can find the critical points of the function within the interval and check the endpoints of the interval. A critical point is a value of x where the first derivative of the function is equal to zero or is undefined.

First we will find the first derivative of the function:

f'(x) = 3x^2 - 6x

The critical points occur when the first derivative is equal to zero:

3x^2 - 6x = 0

x(3x - 6) = 0

x = 0, x = 2

We now need to check if these critical points are maximum or minimum points. For this we need to calculate the second derivative of the function:

f''(x) = 6x - 6

If the second derivative at a critical point is positive, the critical point is a local minimum. If the second derivative at a critical point is negative, the critical point is a local maximum.

f''(0) = 60 - 6 = -6

f''(2) = 62 - 6 = 6

We can see that the second derivative at x = 2 is positive and the second derivative at x = 0 is negative, therefore x = 2 is a local minimum and x = 0 is a local maximum.

Now we need to check the endpoints of the interval to see if they are the absolute maximum or minimum

(-2)^3 - 3(-2)^2 + 12 = -2 - 12 + 12 = -2

(4)^3 - 3(4)^2 + 12 = 64 - 48 + 12 = 28

We can see that the maximum value of the function is 28 at x = 4 and the minimum value of the function is -2 at x = -2, so the absolute maximum value of the function f(x) = x^3 - 3x^2 + 12 on the closed interval (-2, 4) occurs at x = 4.

Therefore, The absolute maximum value of the function f(x) = x^3 - 3x^2 + 12 on the closed interval (-2, 4) occurs at x = 4.

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Solutions for the given graph can be be given as function  [tex]$ f(y) \left \{ {{y < -2x - 3} \atop {y < 0.75x + 3}} \right.[/tex]

A relation called a "function" is one in which each input has just one Solution.

In the relationship, y is a function of x because there is only one solution y for each input x (1, 2, 3, or 0). Since y = 3 has multiple solution (x = 1 and x = 2), x is not a function of y.

As we can see, f(x) has two inequalities

in first case x ≤ -1.5

And equation is

[tex]$m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

m = -2

Line equation

y - 0 =  -2(x - (-1.5))

y = −2x − 3

in second case x ≤ -1.5

And equation is

[tex]$m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

m = 0.75

Line equation

y - 0 =  0.75(x - (-4))

y = 0.75x + 3

[tex]$ f(y) \left \{ {{y < -2x - 3} \atop {y < 0.75x + 3}} \right.[/tex]

Thus, Solutions for the given graph can be be given as function  [tex]$ f(y) \left \{ {{y < -2x - 3} \atop {y < 0.75x + 3}} \right.[/tex]

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