5. Nicolet is fencing off a rectangular pen for her chickens. She has 80 feet of fencing and will use all of it. The area of the pen, A(x), is a function of its length, x, in feet.

The values of (a + b)(a - b) is a²-b² = (a-b) (a+b) and (x+7)² is x² + 14x+49 =  (x+7)(x+7)

Any equation using the formula ax² + bx + c = 0 is a quadratic equation.

where a, b and c are constants, and x is an unknown variable.

It is called "quadratic" because the variable is squared (in other words, raised to the power of 2).

The most common way to solve a quadratic equation is to factor it into two linear equations, which can then be solved using the methods of linear algebra.

Another way is to use the quadratic formula, which expresses the roots of the equation in terms of the coefficients a, b and c.

It is called a quadratic equation because it can be written in the form

ax² + bx + c = 0

which is the standard form for a quadratic equation.

Examples:

1) x² + 4x – 5 = 0

2) 4x² – 7x + 3 = 0

3) 2x² + 3x – 4 = 0

Therefore , The values of (a + b)(a - b) is a²-b² = (a-b) (a+b) and (x+7)² is x² + 14x+49 =  (x+7)(x+7)

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Answer:

Step-by-step explanation: 1*23= 23 because anything times one is equal to itself

Answer: To determine the order of the temperature of the mixtures from least to greatest, we need to compare the values of the temperatures in their simplified fractional forms.

-33.625℉ = -33 5/8℉

-33 5/6℉ = -33 5/6℉

-33 6/25℉ = -33 24/100℉

We can compare the fractions by comparing the numerators, if they are the same we can compare the denominators.

So, the order from least to greatest temperature of the mixtures is:

-33 6/25℉ < -33 5/6℉ < -33 5/8℉

It's important to notice that these temperatures are negative.

Step-by-step explanation:

Projects that adopt agile methodology are not prone to the typical rapid changes that occur throughout the system development lifecycle, The statement is False.

The methodology is defined as to the overarching strategy and rationale of your research project.

It involves studying the methods used in your field and the theories or principles behind them, in order to develop an approach that matches your objectives.

Agile project management methodology is commonly used for software development projects. It has greater adaptability to frequently changing scopes. Adopt Agile because they want to increase speed to market, meet customer demand, or increase team productivity.

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This is a system of equations problem. We can set up the following equations:

x = number of children admitted

y = number of adults admitted

1.25x + 7.20y = 1060 (the total amount of money collected)

x + y = 253 (the total number of people admitted)

To find the number of children admitted, we can use the second equation to solve for one of the variables in terms of the other.

x + y = 253

x = 253 - y

Now we can substitute this expression into the first equation:

1.25(253 - y) + 7.20y = 1060

Solving for y we get

y = 120

So there were 120 adults admitted.

We can use the second equation to find the number of children admitted:

x + y = 253

x = 253 - y

x = 253 - 120

x = 133

So there were 133 children admitted.

Therefore,

There were 133 children admitted.

There were 120 adults admitted.

Answer:

128 children, 128 adults

Step-by-step explanation:

1.25  per child (c)

7.2 per adult (a)

a+c = 253 so c = 253-a

1.25c+7.2a=1060

2 equations 2 variables, solve

1.25 (253-a) + 7.2*a = 1.25*253 -1.25a + 7.2a =1060

sp 5.95a =1060- 1.25*253

so a =125

c = 253-125 = 128

Answer:

150 students in total

Step-by-step explanation:

30 students is 20%

20% x 5 = 100%

30 x 5 = 150 students

The x-intercepts of this graph from least to greatest are x = -0.73, x = 1, and x = 2.73.

The local minimum of this graph is (0, -2).

The local maximum of this graph is (2, 2).

The intervals on which the function is decreasing are x < -0.73 and x > 1.

The intervals on which the function is increasing are 1 < x < 2.73.

The local minimum of a graph can be defined as the point on the graph of a function where it changes from a decreasing function to an increasing function, which is given by this ordered pair (0, -2).

Conversely, the local maximum of a graph can be defined as the point on the graph of a function where it changes from an increasing function to a decreasing function, which is given by this ordered pair (2, 2).

For any given function, y = f(x), if the output value is decreasing when the input value is increased, then, the function is referred to as a decreasing function.

In conclusion, we would use an online graphing calculator to plot the given function f(x) = x³ + 3x² - 2 in order to determine its key features.

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Answer:

30 + 4n

Step-by-step explanation:

Company X = 30 + 4n

The length of the ladder used in the question is; 6.974 ft

The 3 main trigonometric ratios are;

sin x = opposite/hypotenuse

cos x = adjacent/hypotenuse

tan x = opposite/adjacent

Now, since the ladder makes an angle of 35 degrees with the wall, it means the ladder will be the hypotenuse of the right angle triangle and the distance from the base of the wall to the base of the ladder will be labelled as h = 4 will be the opposite side of the triangle. Thus;

4/hypotenuse = sin 35

hypotenuse = 4/sin 35

hypotenuse = 4/0.5736

Hypotenuse = 6.974 ft

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The volume of the solid obtained by rotating the region bounded by the given curves about the specified line about x-axis is 3.93740 and y=-1 is 5.0740

We have to find the volume of given curve about x-axis

we have [tex]$\mathrm{y}=\mathrm{e}-\mathrm{x}^2,[/tex] y=0, x=-5, x=5

(a).

The volume of solid of revolution about the x-axis using disk method is evaluated as:

Volume V=[tex]\pi \int_{\mathrm{x}=-5}^{\mathrm{x}=5} \mathrm{y}^2 \mathrm{dx}$[/tex]

[tex]$$\begin{aligned}& \mathrm{V}=\pi \int_{\mathrm{x}=-5}^{x=5}\left(\mathrm{e}^{-\mathrm{x}^2}\right)^2 \mathrm{dx} \\& \mathrm{V}=\pi \int_{\mathrm{x}=-5}^{x=5} \mathrm{e}^{-2 \mathrm{x}^2} \mathrm{dx} \\& \mathrm{V}=\pi \sqrt{\frac{\pi}{2}}=3.93740 .\end{aligned}$$[/tex]

V=3.93740

we use the formula

(b). The volume of solid of revolution about the y= - using washer method is:

[tex]$$\begin{aligned}& \text { volume } \mathrm{V}=\pi \int_{\mathrm{x}=-5}^{\mathrm{x}=5} \mathrm{y}^2-{ }^2 \mathrm{dx} \\& \mathrm{V}=\pi \int_{\mathrm{x}=-5}^{\mathrm{x}=5} \mathrm{y}^2 \quad 2 \mathrm{y}-{ }^2 \mathrm{dx} \\& \mathrm{V}=\pi \int_{\mathrm{x}=-5}^{\mathrm{x}=5} \mathrm{y}^2 2 \mathrm{ydx} \\& \mathrm{V}=\pi \int_{-5}^5 \mathrm{e}^{-2 \mathrm{x}^2} 2 \mathrm{e}^{-\mathrm{x}^2} \mathrm{dx} \\& \mathrm{V}=\pi \sqrt{\frac{\pi}{2}} .77245 \\& \mathrm{~V}=5.0740\end{aligned}$$[/tex]

Therefore, the The volume of solid of revolution about the y= - using washer method is 5.0740

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The value of x that makes the equation true is 12°. The solution has been obtained using angle sum property of triangle.

What is Angle Sum Property?

The Angle Sum Property states that the sum of the measures of the angles of a triangle is 180°. This means that if you add up all three angles of a triangle, the total measure will be 180°. This property is true for all triangles, regardless of the size or shape. It is one of the most important properties in geometry and is used to solve problems involving angles in triangles.

We are given two angles as (2x)° and (5x+18)°

Also, we are given two sides of the triangle are same.

This means that the angles opposite to the sides are also same.

Thus, the angles of the triangle are (2x)°, (5x+18)° and (5x+18)°

Using angle sum property,

⇒ (2x)° + (5x+18)° + (5x+18)° = 180°

⇒ (2x)° + 2 * (5x+18)° = 180°

⇒ (2x)° + (10x+36)° = 180°

⇒ (12x + 36)° = 180°

⇒ (12x)° = 144°

⇒ x = 12°

Hence, the value of x that makes the equation true is 12°.

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The value of a is 12. Therefore, the equation of the function is f(x) = 12|x|.

In algebra, an objective function function is one where the variables is inside the bars denoting absolute values. The absolute value is also referred to as the modulus function, and its most popular representation is f(x) = |x|, wherein x is a real number.

Finding x values that turn the equation inside the exact amount positive or negative into a constant is how absolute value equations are solved. Plot two for the negative and positive cases that intersect at the expression's 0 to graph exact value functions.

To find the value of a, we can use the point (1, 12) to set up the equation:

a = 12/|1| = 12

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The total profit as the subject of formula is t = 3p

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

p = t/3

Where

Individual Profit = p

total profit = t

Recall that, we have

p = t/3

Multiply both side of the equation by 3

So, we have

3p = t

Rewrite as

t = 3p

Hence, the solution is t = 3p

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Complete question

The equation p=t/3 is used to calculate the individual profit,p, made by each of three brothers operating a lemonade stand with total profit, t

make t the subject

Answer:

3x^2 + 4x + 3

Step-by-step explanation:

we can use this information to find g(x) in terms of f(x).

substitute f(x) = 3x-1 into f(g(x)) = 9x^2 + 12x + 8, we get:

3g(x) - 1 = 9x^2 + 12x + 8

Now, we can solve for g(x) by isolating it on one side of the equation:

3g(x) = 9x^2 + 12x + 9

g(x) = 3x^2 + 4x + 3

therefore g(x) is equal to 3x^2 + 4x + 3

Answer:

D. 45.53 inches

Step-by-step explanation:

Restaurant 1: diameter = 14 inches

Restaurant 2: diameter = 36.83 inches × (1 inch)/(2.54 cm) = 14.5 inches

The larger pizza is from Restaurant 2, and its diameter is 14.5 inches.

circumference = πd = 3.14 × 14.5 inches = 45.53 inches

Answer: D. 45.53 inches

Answer:it is d 45.53

Step-by-step explanation:becuase I did the test

The distance between the Dog from the Home is 360.55 m and the direction of the Dog from Home is North-East.

In the inquiry,

The daring dog begins, let's say, at O.

He walks 300 meters east by 3 blocks.

then,

200 m / 2 blocks north

100 m East of 1 block

Block North = 100 meters.

200 m = 2 blocks west

So,

the separation between the Dog's initial location and ending position.

OE is supplied by,

By using Pythagoras' theorem to triangle OLE,

OE²=OL²+LE²

OE²=200²+300²

OE²=40000+90000

OE=360.55m

Therefore, the distance of the Dog from the Home is 360.55 m and the direction of the Dog from Home is North-East.

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The volume of the solid of revolution is  0

The volume of the solid of revolution obtained by rotating the region bounded by the curves x=0 and y=0 is zero since the area of the region is zero.

To calculate the volume of a solid of revolution, we use the formula V = ∫2dx, where r is the radius of the circle obtained by rotating the curve about the x-axis. Since the region bounded by the curves x=0 and y=0 has an area of 0, the radius r is also 0 and the integral becomes 0. Therefore, the volume of the solid obtained by rotating the region bounded by the curves x=0 and y=0 is 0.

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The set {1,2,3} is not a group under multiplication modulo 4, as it does not contain an identity element. However, the set {1,2,3,4} is a group under multiplication modulo 5.

A group is a set of elements which is closed under an operation and contains an identity element. In order to be a group, the set must satisfy the four group axioms: closure, associativity, identity, and invertibility. The set {1,2,3} does not satisfy the group axioms under multiplication modulo 4, since it does not contain an identity element, and thus is not a group.

On the other hand, the set {1,2,3,4} is a group under multiplication modulo 5, since it contains an identity element (1) and is closed under multiplication. The other group axioms are also satisfied, as the operation is associative, and each element has an inverse (for example, the inverse of 1 is 4). Therefore, {1,2,3,4} is a valid group under multiplication modulo 5.

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Answer:

  -12,731

Step-by-step explanation:

You want to know what integer would be used to represent the value 12,731 feet below sea level.

Usually we measure elevation up from sea level. So, distances below sea level are usually represented with negative numbers. The integer corresponding to 12,731 feet below sea level would be ...

  -12,731 . . . . feet

The resulting matrix by applying the given row operations −2R2+3R1 →R1 is given by [tex]\left[\begin{array}{ccc}-25&5&-6\\8&5&6\end{array}\right][/tex] .

Matrix A is equal to :

A = [tex]\left[\begin{array}{ccc}-3&5&2\\8&5&6\end{array}\right][/tex]

Now replace the row R1 by applying the row operations -2R2 + 3R1 on the given matrix we get ,

First element of row 1 is replaced by :

-2(8) + 3(-3)

= -16 -9

= -25

Second element of row 1 is replaced by :

-2(5) + 3(5)

= -10 + 15

= 5

Third element of row1 is replaced by :

-2(6) + 3(2)

= -12 + 6

= 6

Therefore, the resulting matrix after applying the row operation is given by : [tex]\left[\begin{array}{ccc}-25&5&-6\\8&5&6\end{array}\right][/tex] .

The above question is incomplete , the complete question is :

Consider matrix A.

What matrix results  apply the given row operation(s) R1 to the matrix in order, and give the resulting matrix represented by −2R2+3R1?

A = [tex]\left[\begin{array}{ccc}-3&5&2\\8&5&6\end{array}\right][/tex]

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The function in terms of x and y for the line that contains the points (2, 4) and (6, 16) would be; y=3x-2

The slope is the ratio of the vertical changes to the horizontal changes between two points of the line.

The slope of the line is calculated as follows:

m = Δy/Δx

Given that the line that passes through the points  (2, 4) and (6, 16)

To find the function of the line that passes through points  (2, 4) and (6, 16)

Therefore, the slope of the line is;

m = Δy/Δx

m = 3

The equation is;

y = mx + c

y = 3x - 2

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The first mistake Robbie made was, take improper lengths. AB is the diameter; its length is longer than the sides AX and XB. So, the triangle formed will not be an equilateral triangle.

An equilateral triangle in geometry is a triangle with equally long sides. The three angles opposing the three equal sides are equal in size because the three sides are equal.

The first mistake Robbie made was, take improper lengths. AB is the diameter; its length is longer than the sides AX and XB. So, the triangle formed will not be an equilateral triangle.

He should have, after drawing the diameter AB, construct a circle with point A as the center and AO as the radius. Mark the point of intersection as X. Then, AO, AX and OX would form an equilateral triangle.

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Answer:

1. constructing the perpendicular bisector of AB

2.

Step-by-step explanation:

The 1x8 vector resulting from multiplying each entry of x by 4.x4 = [4*x1, 4*x2, 4*x3, 4*x4, 4*x5, 4*x6, 4*x7, 4*x8]

For example, if x = [1, 2, 3, 4, 5, 6, 7, 8], x4 would be [4, 8, 12, 16, 20, 24, 28, 32]. This can be represented mathematically as x4 = [4x1, 4x2, 4x3, 4x4, 4x5, 4x6, 4x7, 4x8] which is the same as 4*x = [4x1, 4x2, 4x3, 4x4, 4x5, 4x6, 4x7, 4x8]. By multiplying each entry of x by 4, we can create a new vector x4 with every entry multiplied by 4.Multiplying each entry of a 1x8 vector x by 4 can be expressed as multiplying the vector by the scalar 4, resulting in a 1x8 vector x4. For example, if x = [1, 2, 3, 4, 5, 6, 7, 8], then x4 = [4, 8, 12, 16, 20, 24, 28, 32].

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Answer: To graph y = f(x) and y = 1/f(x) on the same axes, you can follow these steps:

First, graph y = f(x) by plotting a few points, such as (-5, -19), (-3, -1), (0, 1) and (5, 19), and then connecting them with a smooth curve.

Then, graph y = 1/f(x) by finding the inverse function of f(x) which will be

1/f(x) = -1/(x+4)²+1

Next, plot a few points on this new function, such as (-5, -1/19), (-3, -1), (0, 1) and (5, 1/19), and then connecting them with a smooth curve.

Finally, make sure that the same x and y scales are used for both graphs, and label the axes and the functions clearly.

It is important to note that as f(x) = -(x+4)²+1, the domain of f(x) is all real numbers but the range is (1, infinity) so the reciprocal will be defined only for the range of f(x) and the domain of 1/f(x) will be (1, infinity)

Also, the graph of y = f(x) will be a parabola opening upwards and y = 1/f(x) will be a parabola opening downwards, both with vertex (-4,1)

The graph of y = -(x+4)²+1 will be a parabola opening upwards and the graph of y = -1/(x+4)²+1 will be a parabola opening downwards.

Step-by-step explanation:

Answer:

We can start solving the problem by using algebraic equations. Let x be the total number of stickers in the box at first.

According to the problem, Wenxuan took 8 more than of the total number of stickers, so he took x + 8 stickers.

The remaining stickers after Wenxuan took his share is x - (x+8) = x - x - 8 = -8 stickers.

Charlene took 7 more than of the remaining stickers, which is -8 + 7 = -1 stickers.

So, Charlene took x - (x+8) + 7 = -1 stickers.

Siti took the last 23 stickers, so the total number of stickers remaining is -1 - 23 = -24.

Now we can use this information to set up the equation:

x + (x+8) + (x-x-8+7) + (-1-23) = x

Solving for x we get x = 32

Therefore, there were 32 stickers in the box at first.

The least common multiple(LCM) of two coprime numbers is their product, ab.

Let a and b be two positive integers, and let LCM(a,b) be the least common multiple of a and b.

By definition, LCM(a,b) is the smallest positive number which is divisible by both a and b.

Now, suppose that a and b are coprime, meaning that there are no positive integers other than 1 that divide both a and b.

Since 1 divides both a and b, and 1 is the smallest positive integer, we know that 1 is the only positive integer that divides both a and b.

Therefore, LCM(a,b) must be divisible by both a and b, and 1 is the only positive integer that divides both a and b.

Thus, LCM(a,b) = ab.

This proves that the least common multiple of a and b is ab precisely when a and b are coprime.

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Answer: c) 130

Step-by-step explanation:

x+8+42=180

x=180-50

x=130

The number of sequential coalitions is 13!

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

System = [13: 14, 6, 4, 2]

This means that

n = 13

The number of sequential coalitiions is calculated as

Coalition = n!

substitute the known values in the above equation, so, we have the following representation

Coalition = 13!

Hence, the coalition is 13!

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Complete question

Consider the weighted voting system [13: 14, 6, 4, 2]

How many sequential coalitions are there?

The correct statement for the given diagram are-

Two angles are said to be supplementary if their sums total 180 degrees.

case A: m∠5+m∠3=m∠4  ...eq A

From the definition of supplementary angles

m∠3+m∠4=180°

m∠4=180°-m∠3   ....eq B

Put eq B in eq A

m∠5+m∠3=180°-m∠3

m∠5+m∠3+m∠3=180°

The result is true for m∠2=m∠3

Thus,

The case is not always true.

case B: m∠3+m∠4+m∠5=180°  ...eq A

From the definition of supplementary angles

m∠3+m∠4=180°

m∠4=180°-m∠3    ....eq B

Put eq B in eq A

m∠3+(180°-m∠3)+m∠5=180°

m∠5=0°

The case is not  true.

case C: m∠5+m∠6=180°

From the definition of supplementary angles

m∠5 and +m∠6 = 180

The case is always true.

case D: m∠2+m∠3=m∠6  ...eq A

From the definition of supplementary angles

m∠5+m∠6 = 180°

m∠6=180°-m∠5    ....eq B

Put eq B in eq A

m∠2+m∠3=180°-m∠5

m∠2+m∠3+m∠5=180°

Sum of interior angles of triangle equals 180 degrees

Thus,

This option will always be true.

case E:

m∠2+m∠3+m∠5=180°

Sum of interior angles of triangle equals 180 degrees

Thus,

This option will always be true.

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The correct question is attached.