The student council at Hillsdale High School is making T-shirts to sell for a fundraiser, at a price of $
10
10 each. The costs, meanwhile, are $
9
9 per shirt, plus a one-time setup fee of $
79
79 .

​Selling a certain number of shirts will allow the student council to cover their costs.

​What will the costs be? How many shirts must be sold?

Given:

The objective is to prove that each pair of consecutive angles of a parallelogram are supplementary angles.

Explanation:

Consider a parallelogram ABCD with opposite parallel sides.

First consider the parallel sides AB || CD. Then, the sides AD and BC are transversal lines.

By the property of parallel lines, the sum of the angles on same side of a transversal is 180°.

Now, consider the parallel sides as AD || BC. Then, the sides AB and CD are transversal lines.

By the property of parallel lines, the sum of the angles on same side of a transversal is 180°.

Thus, the sum of any two sides of a parallelogram will always be 180°.

Hence, it is proved that in a parallelogram each pair of consecutive angles are supplementary.

Answer:4 x 1,424 = 5,696

Step-by-step explanation:

To multiply 4 by 1,424, we first multiply the ones digit of 1,424 by 4, which gives us 4 x 4 = 16. We write down the 6 and carry the 1.

Next, we multiply the tens digit of 1,424 by 4, which gives us 4 x 2 = 8. We add the carried 1 to get 9, and write down the 9 in the tens place. We carry the remaining 1.

Then, we multiply the hundreds digit of 1,424 by 4, which gives us 4 x 4 = 16. We add the carried 1 to get 17, and write down the 7 in the hundreds place. We carry the remaining 1.

Finally, we multiply the thousands digit of 1,424 by 4, which gives us 4 x 1 = 4. We add the carried 1 to get 5, and write down the 5 in the thousands place.

Putting it all together, we get 5,696 as the product of 4 and 1,424.

Answer: 5696

Step-by-step explanation:

1424 is 1000+400+ 20+4

multiply each by 4

4000+1600+80+16

This equals 5696

With enough practice, you'll be able to do it in your head!

Answer:

After 8 minutes ; altitude = 22,400 feet

Step-by-step explanation:

s1 = 2800t

s2 = -3200t + 48 000

2800t = -3200t + 48 000

28t = -32t + 480

7t = -8t + 120

7t + 8t = 120

15t = 120

15/15 t = 120/15

t = 8 minutes

s = 8 * (2800)  =   22400 feet

The most famous version of the song was recorded by the Nitty Gritty Dirt Band. "Will the Circle Be Unbroken" is a traditional Christian hymn that has been recorded by many artists over the years.

However, the most famous version of the song was recorded by the Nitty Gritty Dirt Band in 1972 as a collaborative project that featured a wide variety of country, bluegrass, and folk musicians, including legends such as Mother Maybelle Carter, Earl Scruggs, and Doc Watson. The three-disc album was a critical and commercial success and helped to popularize traditional country and bluegrass music among a wider audience. The Nitty Gritty Dirt Band's rendition of "Will the Circle Be Unbroken" remains a beloved classic in the history of American music.

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The factor that does NOT control the stability of a slope is the angle of repose for intact bedrock. The angle of repose refers to the steepest angle at which a pile of loose material remains stable without sliding. It is mainly applicable to loose materials like soil and granular substances, not intact bedrock.

Bedrock stability depends on factors such as its strength, fracturing, and geological properties, rather than the angle of repose. Factors that control the stability of a slope include whether the slope is rock or soil. Rock slopes tend to be more stable than soil slopes due to the cohesive nature of intact rock.

The amount of water in the soil also affects slope stability, as excessive water can increase pore pressure and reduce the shear strength of the soil, leading to slope failure. Additionally, the orientation of fractures, cleavage, and bedding in the rock can influence slope stability by creating planes of weakness or strength.

To summarize, while the angle of repose is a significant factor in slope stability, it is not applicable to intact bedrock. The stability of a slope is influenced by the type of material (rock or soil), the presence of water, and the orientation of fractures and bedding.

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Answer:

Combine

1

3

and

4

x

.

f

(

x

)

=

4

x

3

Step-by-step explanation:

Let's assume the cost of one package of chicken is represented by 'C' and the cost of one case of barbecue sauce is represented by 'B'.

From the given information, we can form the following equations:

Equation 1: 3C + 4B = 40 (Three packages of chicken and four cases of barbecue sauce cost $40)

Equation 2: 5C + 2B = 34 (Five packages of chicken and two cases of barbecue sauce cost $34)

To solve this system of equations, we can use the method of substitution or elimination.

Let's solve it using the elimination method. Multiply Equation 1 by 5 and Equation 2 by 3 to make the coefficients of 'C' in both equations equal:

5 * (3C + 4B) = 5 * 40

3 * (5C + 2B) = 3 * 34

This gives us:

15C + 20B = 200

15C + 6B = 102

Now, subtract the second equation from the first equation:

(15C + 20B) - (15C + 6B) = 200 - 102

15C - 15C + 20B - 6B = 98

14B = 98

B = 98 / 14

B = 7

Substituting the value of B back into Equation 1:

3C + 4(7) = 40

3C + 28 = 40

3C = 40 - 28

3C = 12

C = 12 / 3

C = 4

Therefore, the cost of one package of chicken is $4, and the cost of one case of barbecue sauce is $7.

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a) au/ax=2xy⁴ and au/ay=4x²y³ ; b) We can differentiate the expression a²u=2ax + c(y) with respect to y to obtain a³u/ax²=0 ; c) f(x,y) has a local maximum at (0,0).

a) To compute the mathematical expressions for al Ək we will have to differentiate the function Q=f(l,k)=(1+1¯ªk¯ß) w.r.t k. Hence, al Ək=0+(-ß)(1+1¯ªk¯ß)-1

=(-ß)/(1+1¯ªk¯ß)

To compute the mathematical expressions for U(x,y) we need to differentiate the function U(x,y)=x²y⁴ w.r.t. x and y. Hence, au/ax=2xy⁴ and au/ay=4x²y³.

b) Let us first differentiate the expression au/ax=x²-a² with respect to x, which gives a². Differentiating the obtained expression with respect to x again gives 2ax,

hence a²u=2ax + c(y), where c(y) is the arbitrary constant of integration that depends on y.

To find c(y), we differentiate the expression au/ax=x²-a² with respect to y, which gives c'(y)=0. Hence, c(y) is a constant, which is determined by the initial condition.

Similarly, we can differentiate the expression au/ay=xy²-b² to obtain a²u=2by + c(x), where c(x) is the arbitrary constant of integration that depends on x.

Hence, c(x) is a constant, which is determined by the initial condition.

Finally, we can differentiate the expression a²u=2ax + c(y) with respect to y to obtain a³u/ax²=0, which means that the second order condition for maximization is satisfied.

c) To find the maxima of the following functions we will have to differentiate each of these functions with respect to x and y and equate them to zero.

f(x)=-x²-x⁴ :

f'(x)=-2x-4x³

=0

=>x=0,

x=±1/√2

f''(x)=-2-12x²

f''(0)=-2<0,

f''(1/√2)=-2+3√2>0,

f''(-1/√2)=-2-3√2<0

=>f(x) has a local maximum at x=-1/√2, a local minimum at x=0, and a local maximum at x=1/√2. Since f(x) is a continuous function, the global maximum and minimum of f(x) must occur at the endpoints of the interval [-1,1], which are x=-1 and x=1.

Hence, f(-1)=f(1)

=-2.

f(x)=-x²+x:

f'(x)=-2x+1

=0

=>x=1/2f''(x)

=-2f''(1/2)

=-2<0

=>f(x) has a local maximum at x=1/2.

Since f(x) is a continuous function, the global maximum and minimum of f(x) must occur at the endpoints of the interval [-1,1], which are x=-1 and x=1.

Hence, f(-1)=0 and f(1)=-2.f

(x,y)=-x²-y²+3:

f'x=-2x

=0

=>x=0,

f'y=-2y

=0

=>y=0

f''xx=-2,

f''xy=0,

f''yy=-2

=>D=(-2)(-2)-0

=4

=>f(x,y) has a local maximum at (0,0).

Since f(x,y) is a continuous function, there is no global maximum or minimum of f(x,y).

f(x,y)=xy-x²-y²+3+9y:

f'x=y-2x

=0

=>y=2x,

f'y=x-2y+9

=0

=>x=2y-9

f''xx=-2,

f''xy=1,

f''yy=-2

=>D=(-2)(-2)-(1)(1)

=3

=>f(x,y) has a saddle point at (2,11/2).

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The limit of (2x-1)(3-x)/(x-1)(x+3) as x approaches infinity is 0.

To find the limit of the function (2x-1)(3-x)/(x-1)(x+3) as x approaches infinity, we will divide both the numerator and denominator through the highest power of x. In this case, the highest power of x is x², so we can divide both the numerator & the denominator through x²:

\([(2x-1)/(x^2)] * [(3-x)/((x-1)/(x^2)(x+3))]\)

Now, as x approaches infinity, every of the fractions within the expression procedures zero except for (2x-1)/(x²). This fraction techniques 0 as x procedures infinity because the denominator grows quicker than the numerator. therefore, the limit of the expression as x strategies infinity is:

0 * 0 = 0

Consequently, When x gets closer to infinity, the limit of (2x-1)(3-x)/(x-1)(x+3) is 0.

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Answer:

300 raisins

Step-by-step explanation:

there are 30 of everything in a box. if there 30,00 that means there are 100 boxes and so just multiply the number of boxes by the number of raisins in a box.

The development of type 1 diabetes appears to be heavily influenced by genetic factors, suggesting that genetics is a major contributor to the condition compared to environmental factors.

This data suggests that there is a strong genetic contribution to the onset of type 1 diabetes, as the concordance rate between monozygotic twins is much higher than that of dizygotic twins.

This indicates that genetic factors play an important role in the development of type 1 diabetes, as the genetic makeup of monozygotic twins is nearly identical, while the genetic makeup of dizygotic twins is much more variable.

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Answer:

15.

If we look at angle BOD, that would form a right angle (90°), given that one part of that whole angle is 30°, the other would be;

30° + x = 90°

-30        -30

x = 60°, therefore ∠BOC = 60°.

If we take a look at angle EOC, we can see that that angle is a straight angle (180°), we can also see that a right angle (90°) is a part of that angle alongside the angle we just previously found (60°). So all of those angles plus the unknown angle (AOE) which we will consider 'x' summed up would result in 180 degrees.

Now we set up the equation;

90° + 60° + x = 180°

150 + x = 180

-150       -150

x = 30°, therefore ∠AOE = 30°.

16.

The sum of the interior angles in a triangle will always equal 180°. (We can also confirm this using the formula (n - 2) x 180.)

Given two of the angles, we must add them and the unknown angle(D) which we will consider 'x' to make it result in 180°.

Now we set up the equation;

55° + 18° + x = 180°

73 + x = 180

-73         -73

x = 107°, therefore ∠EDF = 107°.

17.

To find angle P, we must first find the supplement of 34° because 34° and the angle beside forms a straight angle (180°).

Set up an equation;

34 + x = 180

-34         -34

x = 146°, now that we've found the supplement, we add this supplement with the other given angle (23°) because all three angles (unknown angle which we will consider x + 23 + 146) will equal 180°(sum of interior angles of triangle).

146° + 23° + x = 180°

169 + x = 180

-169        -169

x = 11°, therefore ∠QPR = 11°.

18.

Seeing that the bigger triangle has a 90° angle (indicated with a square), and two other equal angles(indicated with the two lines on both legs of the big triangle), we solve for those two missing equal angles in the bigger triangle which we will then use to solve for the smaller triangle's angle.

2x + 90° = 180°

-90            -90

2x = 90

/2     /2

x = 45°, so now we know the two angles in the bigger triangle excluding the right angle.

One of those equal angles is vertical to the smaller triangle, and vertical angles are congruent.

Hence, the angle vertical to the bigger triangle in the smaller triangle will be 45°.

Now we solve for ∠CDE.

Add the two angles and the missing angle to equal 180°.

Set up the equation;

86° + 45° + x = 180°

131 + x = 180

-131        -131

x = 49°, so ∠CDE = 49°.

Based on the calculation, it appears that Matti had approximately 94 bottles of 0.5 litres and 11 bottles of 0.7 litres in the last patch of moonshine that he sold.

To solve the problem using the determinant method (Cramer's rule), we need to set up a system of equations based on the given information and then solve for the unknowns, which represent the number of 0.5 litre bottles and 0.7 litre bottles.

Let's denote the number of 0.5 litre bottles as x and the number of 0.7 litre bottles as y.

From the given information, we can set up the following equations:

Equation 1: 0.5x + 0.7y = 16.5 (total volume of moonshine)

Equation 2: 8x + 10y = 246 (total earnings from selling moonshine)

We now have a system of linear equations. To solve it using Cramer's rule, we'll find the determinants of various matrices.

Let's calculate the determinants:

D = determinant of the coefficient matrix

Dx = determinant of the matrix obtained by replacing the x column with the constants

Dy = determinant of the matrix obtained by replacing the y column with the constants

Using Cramer's rule, we can find the values of x and y:

x = Dx / D

y = Dy / D

Now, let's calculate the determinants:

D = (0.5)(10) - (0.7)(8) = -1.6

Dx = (16.5)(10) - (0.7)(246) = 150

Dy = (0.5)(246) - (16.5)(8) = -18

Finally, we can calculate the values of x and y:

x = Dx / D = 150 / (-1.6) = -93.75

y = Dy / D = -18 / (-1.6) = 11.25

However, it doesn't make sense to have negative quantities of bottles. So, we can round the values of x and y to the nearest whole number:

x ≈ -94 (rounded to -94)

y ≈ 11 (rounded to 11)

Therefore, based on the calculation, it appears that Matti had approximately 94 bottles of 0.5 litres and 11 bottles of 0.7 litres in the last patch of moonshine that he sold.

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Question

Matti is making moonshine in the woods behind his house. He’s selling the moonshine in two different sized bottles: 0.5 litres and 0.7 litres. The price he asks for a 0.5 litre bottle is 8€, for a 0.7 litre bottle 10€. The last patch of moonshine was 16.5 litres, all of which Matti sold. By doing that, he earned 246 euros. How many 0.5 litre bottles and how many 0.7 litre bottles were there? Solve the problem by using the determinant method (a.k.a. Cramer’s rule).

\(n^{th}\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} a_n=n^{th}\ term\\ n=\stackrel{\textit{term position}}{14}\\ a_1=\stackrel{\textit{first term}}{10}\\ d=\stackrel{\textit{common difference}}{-9} \end{cases} \\\\\\ a_{14}=10+(14-1)(-9)\implies a_{14}=10+(13)(-9)\implies a_{14}=-107\)

Answer:

The 14th term of arithmetic sequence is -107.

Step-by-step explanation:

Here's the required formula to find the arithmetic sequence :

\(\longrightarrow{\pmb{\sf{a_n = a_1 + (n - 1)d}}}\)

Substituting all the given values in the formula to find the 14th term of arithmetic sequence :

\(\begin{gathered} \qquad{\twoheadrightarrow{\sf{a_n = a_1 + (n - 1)d}}}\\\\\qquad{\twoheadrightarrow{\sf{a_{14} = 10 + (14 - 1) - 9}}}\\\\\qquad{\twoheadrightarrow{\sf{a_{14} = 10 + (13) - 9}}}\\\\\qquad{\twoheadrightarrow{\sf{a_{14} = 10 + 13 \times - 9}}}\\\\\qquad{\twoheadrightarrow{\sf{a_{14} = 10 - 117}}}\\\\\qquad{\twoheadrightarrow{\sf{a_{14} = - 107}}}\\\\\qquad{\star{\underline{\boxed{\sf{\pink{a_{14} = - 107}}}}}} \end{gathered}\)

Hence, the 14th term of arithmetic sequence is -107.

\(\rule{300}{2.5}\)

The following is the expected value of a number of books a student buys at the next book fair is 2.404 books.

The random variable b's expected value is then calculated as follows:

E(X) = 1 x 0.285 + 2 x 0.333 + 3 x 0.168 + 4 x 0.136 + 5 x 0.063 + 6 x 0.015 E(X)  = 2.404 books.

Thus, the expected value of discrete probability distribution is 2.404 books.

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The graph for the question is attached.

The real numbers are numbers that can be represented on the number line. Among the given options, the real numbers are: A. -2.22, C. -6, E. 8, and G. 1.

The number -2.22 is a real number because it can be located on the number line. -6 is also a real number since it can be represented as a point on the number line. Similarly, 8 and 1 are real numbers as they can be plotted on the number line.

On the other hand, the options B. -√-5, D. -√4, and F. √-4 are not real numbers. The expression -√-5 involves the square root of a negative number, which is not defined in the set of real numbers. Similarly, √-4 involves the square root of a negative number and is also not a real number. Option H is not a valid number as it is written as "OH" rather than a numerical value. Therefore, the real numbers among the given options are A. -2.22, C. -6, E. 8, and G. 1.

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Answer:

x = 8.33

Explanation:

y varies directly with x if y can be calculated as a constant k times x. So:

y = k*x

If y is equal to 75 and x is equal to 25, we can calculate the value of k as:

Therefore, y = 3*x

So, to find x when y = 25, we need to replace y by 25 and solve for x as follows:

Therefore, x is equal to 8.33

The width of the waiting area is 95 feet if the length of the area is 120 feet. Thus, option A is correct.

The area of the roller-coaster = 11,400 square feet

Length of area = 120 feet

The shape of Smiler roller coaster is rectangular-shaped. The area of the roller coaster can be calculated by using the product of length and width. The width of the roller coaster is calculated by dividing the total area by length.

Mathematically, the formula is:

width = area/length

width = 11,400 / 120

width = 95 feets

Therefore, we can conclude that the width of the waiting area is 95 feet.

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Answer:

58

Step-by-step explanation:

Total area = 7 × 10 - 6 × 2 = 70 - 12 = 58 units²

Answer:

-22.65x

Step-by-step explanation:

(-0.75x-4)-(9.5x+8.4)=-4.75x-(17.9x)=-22.65

The combined perimeter of

2b (14y - 12)

2c (18y + 4)

2d (14y - 16), is

Add the like terms

The combined perimeter is (46y - 24)

The combined area of

1b (10y^2 - 27y +5)

1c (20y^2 + 11y - 3)

1d (12y^2 -24y), is

Add the like terms

The combined area is (42y^2 - 40y + 2)

The half-life of the substance is approximately 17.78 days.

The exponential decay model for the mass of the substance can be written as:

\(m(t) = m0 \times e^{(-rt)},\)

where m0 is the initial mass, r is the decay rate parameter (as a decimal), and t is time in days.

If we want to find the half-life of the substance, we need to find the value of t when the mass has decreased to half of its original value (m0/2). In other words, we need to solve the equation:

m(t) = m0/2

\(m0 \times e^{(-rt)} = m0/2\)

\(e^{(-rt) }= 1/2\)

Taking the natural logarithm of both sides, we get:

-ln(2) = -rt

t = (-ln(2)) / r

Substituting the value of r (0.039), we get:

t = (-ln(2)) / 0.039

t ≈ 17.78 days

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The graph of the system has been attached below. The solution has been obtained by using linear inequality.

What is linear inequality?

If the equals relation were used in its place, a linear inequality would produce a linear equation.

We are given two inequalities as x+y < 1 and 5x + y > 4

For plotting the points, we need to find x and y

1. x+y < 1

So, let y be 0, then

⇒x < 1

This gives us the point as (1,0).

Now, let x=0, then

⇒y < 1

This gives us the point as (0,1).

From these two points, the graph for the inequality is drawn and represented by red line.

2. 5x + y > 4

So, let y be -1, then

⇒5x > 5

⇒x > 1

This gives us the point as (1,-1).

Now, let x=0, then

⇒y > 4

This gives us the point as (0,4).

From these two points, the graph for the inequality is drawn and represented by green line.

Hence, the graph of the system of linear inequalities is obtained.

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Answer:

ddsdvffgdf gddccd fddf

The derivative of the given expression using the chain rule is -e^(-t/τ) cos(ωt)/τ.

To find the derivative of the given expression using the chain rule, we need to apply the chain rule formula, which states that if y = f(u) and u = g(x), then:

dy/dx = dy/du * du/dx

In this case, we have:

y = e^(-t/τ) * sin(ωt)

u = -t/τ

f(u) = e^u

g(x) = -t/τ

Using the chain rule formula, we can find:

dy/dx = dy/du * du/dx

dy/du = d/dx(e^u) = e^u * du/dx

du/dx = -1/τ

Substituting these values, we get:

dy/dx = e^(-t/τ) * cos(ωt) * (-1/τ)

dy/dx = -e^(-t/τ) * cos(ωt)/τ

Therefore, the value obtained is -e^(-t/τ) * cos(ωt)/τ.

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The value of x is 41

When three line segments cross each other at three non-collinear points, a triangle is formed. A triangle is a three-sided polygon with three sides and three angles.

Using the Angle Bisector Theorem and assuming ED is an angle bisector

⇒ EG/EH = DG/HD

⇒ 49 / 58.8 = 35 / (x + 1)

⇒ 49 (x+1) = 58.8×35 ⇒ 2058

⇒ x + 1 = 2058 /49

⇒ x + 1 = 42

⇒ x = 41

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Complete question-

Assuming ED is an angle bisector and applying the Angle Bisector Theorem.

The value of x is 41

A polygon with three sides and three vertices is called a triangle. It belongs to the basic geometric shapes. A triangle with the parts A, B, and C is referred to as triangle ABC. Any three points that are not collinear in Euclidean geometry result in a separate triangle and a distinct plane. When three line lengths cross each other at three non-collinear points, a triangle is formed. A triangle is a three-sided polygon because it has three sides and three angles.

Assuming ED is an angle bisector and applying the Angle Bisector Theorem

\(\frac{EG}{EH} =\frac{DG}{HD} \\\\\frac{49}{58.8} =\frac{35}{(x+1)}\)

49 (x+1) = 58.8×35 ⇒ 2058

x + 1 = 2058 /49

x + 1 = 42

x = 41

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The complete question is,

1)

Domain is 0 < x < 12.52

Vertex is at x = 6.25

The zeroes of the function are at x = 0 and x = 12.5.

2)

The domain is all real numbers

Vertex is at n = 0

The are no zeroes of the function

3)

The domain is all nonnegative real numbers.

Vertex is at t = 0

The zeroes of the function are at t = 0 and t = √(s/16),

4)

The domain is all nonnegative real numbers.

Vertex is at t = 0

The zeroes of the function are at t = 0 and t =√(567/16).

A function has an input and an output.

A function can be one-to-one or onto one.

It simply indicated the relationships between the input and the output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

1)

Domain = 0 < x < 12.5

Since the perimeter of a rectangle is twice the sum of its sides.

We have 2 sides of length x and 2 sides of length.

i.e

(25-2x)/2 = 12.5 - x.

The input x must be less than half the perimeter (12.5) to produce a valid rectangle, and greater than zero to have a positive area.

Vertex:

It occurs at x = 6.25 and represents the maximum area of the rectangle.

Zeroes of the function.

It occurs at x = 0 and x = 12.5.

It represents the sides of a degenerate rectangle.

2)

Domain.

All real numbers since we can square any real number.

Vertex.

It occurs at n = 0 and represents the lowest possible value of f(n),

which is 4.

Zeroes of the function.

The function has no real zeros since the sum of a square and a positive constant is always positive.

3)

Domain.

All non-negative real numbers since distance cannot be negative.

Vertex:

It occurs at t = 0 and represents the initial position of the object.

Zeroes of the function.

It has a zero at t=0, which represents the time when the object was dropped.

It has a zero at t = √(s/16), where s is the distance that fell.

4)

Domain.

All non-negative real numbers since the height cannot be negative.

Vertex.

The vertex of the function occurs at t = 0 and represents the initial height of the object.

Zeroes of the function.

The function has a zero at t =√(567/16), which represents the time when the object hits the ground.

The function also has a maximum height of 567 feet, which occurs when

t = 0.

Thus,

The domain, vertex, and zeroes for each situation are given above.

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The integral ˆ«(1 to [infinity]) xe^-x2 dx, is  E) divergent, that is, an indefinite integral with an upper limit of infinity.

Let's use the following steps to evaluate indefinite integral:

ˆ«(1 to [infinity]) xe^-x2 dx

We can start by making a substitution to simplify the integral.

We substitute u = -x^2, du = -2x dx. When x approaches infinity, u approaches negative infinity, and when x is 1, u is -1.

Now we can rewrite the integral with the substitution:

ˆ«(-1 to -infinity) e^(u/2) du

Next, we can use the limit property of integrals to evaluate the integral as u approaches negative infinity:

lim[u->-infinity] ˆ«(-1 to u) e^(u/2) du

As u approaches negative infinity, e^(u/2) approaches zero, so the integral becomes zero or the integral converges to zero.

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