The function — is used to model the height of an object projected in the air, where h(t) is the height in meters and t is the time in seconds. What are the domain and range of the function h(t)? Round values to the nearest hundredth.

Answer:

Below in bold.

Step-by-step explanation:

Part A

At the x-intercepts  f(x) = 0, therefore:

2x^2 - 3x - 5 = 0

(2x - 5)(x + 1) = 0

x = 5/2, -1)

So the x intercepts are (-1, 0) and (5/2, 0).

Part B

The Coefficient  of x^2 is positive ( it is 2) So the graph opens upwards and the vertex will be a minimum.

Convert f(x) to vertex form, by completing the square:

f(x) = 2x^2 - 3x - 5

= 2(x^2 - 3/2x) - 5

= 2[(x - 3/4)^2 - 9/16] - 5

= 2(x - 3/4)^2 -18/16 - 80/16

= 2(x - 3/4)^2 - 49/8

So the coordinates of the vertex are

(3/4, -49/8)  or

(0.75, -6.125) in decimal form.

Part C

To graph f(x) you would first mark the points on the x axis which we found in Part 1 and the vertex found in Part 2. This vertex will be the bottom of the 'U'.

The graph is a parabola shaped roughly like a U, and will be symmetrical about the line x = 0.75 (which passes through the vertex).

You would also plot 2 more points above the x axis so as to get an accurate graph. 1 would be to the left of the line of symmetry and 1 to its right.

Suggest   x = - 2  and calculate f(-2) = 2(-2)^2 - 3(-2) - 5 =  11.

- that is the point (-2,11) and the other would be  x = 4,  f(x) = 15. (4, 15)

Once you have plotted these points draw a smooth u shaped curve through them.

From the graph, the equation of f(x) + g(x) is f(x) + g(x) = 2x + 3

The functions are given as:

f(x) = x + 3

g(x) = x

From the above functions, we can see that the function g(x) is the parent function of a linear function.

When the parent function of a linear function is added to another function to form a composite function, the new function would pass through the following points

(x, y)= (0, b) and (-b, -b)

Where b is the y-intercept of the other function

i.e b = 3 from f(x) = x + 3

So, we have the following points

(0, 3) and (-3, -3)

Next, we draw the points and we connect the points

When the equation of f(x) + g(x) is calculated, we have

f(x) + g(x) = 2x + 3

See attachment for the graph of the functions

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Step-by-step explanation:

f(a):

   So for this you simply plug in "a" as x, and this doesn't really do anything beside replace all values with x, so you just have the equation:

  [tex]f(a) = 5a+4[/tex]

2 f(a):

   So for this one, you want to represent f(a) using the equation it's equal to (5a + 4), and substitute it in for f(a). In doing so, you get the expression:

   2*f(a) -> 2(5a + 4) -> 10a + 8

f(2a):

   So this is very similar to the first question, although you will have to do some multiplication. So just plug in 2a as "x" to get the equation:

   [tex]f(2a) = 5(2a) + 4 = 10a+4[/tex]

f(a+2):

   Basically the same process, you plug in (a+2) as "x" and simplify:

   [tex]f(a+2) = 5(a+2) + 4\\f(a+2) = 10a+10+4\\f(a+2) = 10a+14[/tex]

f(a) + f(2):

  This is similar to the second question, and you simply want to replace the f(a) with the equation that represents it (5a + 4) and same thing for f(2) = 5(2) + 4

   [tex]f(a) + f(2) = (5a+4)+(5(2)+4) \\f(a) + f(2) = (5a+4)+(10+4)\\f(a)+f(2) = (5a+4) + (14)\\f(a) + f(2) = 5a+18[/tex]

The arrow hits the top of a 3 meters tall wigwam at 0.054 seconds

The complete question is added as an attachment

The function is given as:

[tex]h(t) = -9.8t^2 + 28t + 1.5[/tex]

Set the height to 3

[tex]-9.8t^2 + 28t + 1.5 = 3[/tex]

Subtract 3 from both sides

[tex]-9.8t^2 + 28t - 1.5 = 0[/tex]

Apply the following quadratic formula

[tex]t = \frac{-b \pm \sqrt{b^2- 4ac}}{2a}[/tex]

So, we have:

[tex]t = \frac{-28 \pm \sqrt{28^2- 4*-9.8*-1.5}}{2*-9.8}[/tex]

This gives

[tex]t = \frac{-28 \pm \sqrt{725.2}}{-19.6}[/tex]

This gives

[tex]t = \frac{-28 \pm 26.93}{-19.6}[/tex]

Expand

[tex]t = \frac{-28 + 26.93}{-19.6}[/tex] and [tex]t = \frac{-28 - 26.93}{-19.6}[/tex]

This gives

t = 0.054 and t = 2.80

0.054 is less than 2.80

This means that the arrow hits the top of a 3 meter tall wigwam at 0.054 seconds

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Step-by-step explanation:

i)I=PRT/100

I=1800*12*1/100

I=$216

ii) amount to be paid =1800+216

=$2016

iii) monthly installments=2016/12

=$168

b)I=PRT/100

I=

If a trader took a loan of 1,800.00 at an interest of 12 percent per annum

a.  Interest on the loan is $216.

Amount to be paid at the end of the year is $2016

Monthly Installment is $168

b. She took  $2184 to the nearest dollar.

a) i) Interest on the loan:

Interest = Principal × Rate × Time

Interest = $1800 × 0.12 × 1

Interest = $216

ii) Amount to be paid at the end of the year:

Amount = Principal + Interest

Amount = $1800 + $216

Amount = $2016

iii) Monthly installment:

Number of monthly installments = 12

Monthly Installment = Total Amount / Number of Installments

Monthly Installment = $2016 / 12

Monthly Installment ≈ $168

b) Let's X represent the amount she took

Total Payment = Monthly Installment × Number of Months

Total Payment = $200 × 12

Total Payment = $2400

So

Total Payment = X + $216

$2400 = X + $216

Subtract $216 from both sides:

$2400 - $216 = X

$2184 = X

Therefore she took approximately $2184 to the nearest dollar.

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The equation that represents the graph of the ellipse is x² / 4 + y² / 100 = 1. (Correct choice: D)

Herein we have a representation of an ellipse in the image attached aside, ellipses are characterized by the following standard formula:

(x - h)² / a² + (y - k)² / b² = 1     (1)

Where:

Please notice that ellipse will be vertical if b > a, otherwise it will be horizontal. The graph exhibits a vertical ellipse centered at the origin and therefore we conclude that (h, k) = (0, 0) and b > a (b = 10, a = 2). Finally, the equation that represents the graph of the ellipse is x² / 4 + y² / 100 = 1. (Correct choice: D)

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Answer:

4368 ways

Step-by-step explanation:

Use nCk for this. 16C5. This is [tex]\frac{n!}{(n-k)!(k!)}[/tex]. This becomes[tex]\frac{16!}{(11!)(5!)}[/tex]. This is [tex]\frac{16*15*14*13*12}{5*4*3*2*1}[/tex] due to 16! and 5! canceling out. This becomes 4368.

Answer:

x1 = 5-3squareroot 5/2 x2= -5+3 squareroot 5 / 2

Step-by-step explanation:

For the levels of qualitative, the variable called dummy variables is used in the multiple regression method.

According to the statement

we have given that the by which method we use the different levels of a qualitative independent variable and we have to explain about it.

So, For his purpose, we know that the

A dummy variable is a variable that takes values of 0 and 1, where the values indicate the presence or absence of something.

And in the multiple regression method there are a lot of different variables which are used for a qualitative and for this a variable is used which is called the dummy variables.

By this variables we show the analysis between the given data. it gives the output in the 0 and 1 numbers.

So, For the levels of qualitative, the variable called dummy variables is used in the multiple regression method.

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The piecewise function graphed below is given as follows:

A piecewise function is a function that has different definitions, depending on the input.

For x between -4 and -2, inclusive, the function is constant at 3, hence the definition is:

[tex]f(x) = 3, -4 \leq x \leq -2[/tex]

For x greater than -2 until 3, the function is a line with slope 1 and y-intercept 2, hence the definiton is:

[tex]f(x) = x + 2, -2 < x \leq 3[/tex]

For x greater than 3 until 5, the function is constant at -1, hence the definition is:

[tex]f(x) = -1, 3 < x \leq 5[/tex]

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Answer: b. the two triangles are similar by SAS

Step-by-step explanation:

       These two triangles (ABC and ADE) both share angle A. This means that one angle is congruent.

       Next, we will look at the sides. Triangle ADE has side lengths of 6, 9, and x. Triangle ABC has side lengths of 8+6, 12+9, y. Let us see how these side lengths compare.

[tex]\frac{8+6}{12+9} =\frac{14}{21} =0.6666[/tex]

[tex]\frac{6}{9} = 0.6666[/tex]

       THey are similar. This means the triangles can be prooven similar with SAS.

The probability of event A and event B IS  15/91.

What is the probability?

Probability determines the odds that a random event would occur. The odds lie between 0 and 1.

The probability of event A  = number of brown marbles / total number of marbles

= 6/14

The probability of event B = number of orange marbles / total number of marbles -1

= 5/13

P(A and B) =6/14 x 5/13

                 = 30/182

                 = 15/91

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Answer:

B.) 5/13

Step-by-step explanation:

15/3=5

91/7=13

5/13

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Answer:

Step-by-step explanation:

Comment

Begin by removing the brackets.

6+3(n-4)-8+2n

6 + 3n - 12 - 8 + 2n                 Collect like terms

3n + 2n + 6 - 12 - 8                 Combine

5n - 14

Answer

5n - 14

Answer:  25 pounds

Step-by-step explanation: 100% - 20% = 80%

20 divided by 80% = 25

The correct option is D.

An equation to determine the area, a, of the patio that will be painted :

a = (x + 25)(x + 15) - 30

Geometric shapes are the mathematical figures that show how ordinary objects in our world are shaped. Shapes in geometry are the configurations of things with boundary lines, angles, and surfaces.

Length of the rectangular patio is (x+25).

Width of the rectangular patio is (x+15).

Length of bench is 5.

Width of the bench is 1.

Area of a rectangle is:

A = Length x Width

Area of rectangular patio is:

A[tex]_1[/tex] = (x + 25)(x + 15)

Area of bench is:

A[tex]_2[/tex] = 10 x 3

   = 30

The painting area is:

A = A[tex]_1[/tex] - A[tex]_2[/tex]

A = (x + 25)(x + 15) - 30

Therefore, the correct option is D.

An equation to determine the area, a, of the patio that will be painted :

a = (x + 25)(x + 15) - 30

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The surface area of the rectangular prism is 2(lw + wh + lh). A rectangular prism has six rectangular faces.

The area of a rectangle with length and width is

Area = length × width

I.e., A = l × w sq. units

A rectangular prism has six rectangular faces and the length 'l', width 'w', and height 'h'.

So, the areas of each face are as follows:

A(R1) = l × w

A(R2) = l × h

A(R3) = w × h

A(R4) = l × w

A(R5) = l × h

A(R6) = w × h

Thus, the area of the prism = sum of areas of all the faces

⇒ Area of the prism = lw + lh + wh + lw + lh + wh

⇒ A = 2lw + 2lh + 2wh

⇒ A = 2(lw + lh + wh)

Therefore, the area of the rectangular prism is A = 2(lw + lh + wh).

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Using concepts of probability, it exists found that there exists a 4.7% probability that it arrives at American airlines (aa).

A probability exists given by the number of expected outcomes divided by the number of total outcomes.

Over a large number of trials, a percentage can also define the probability of a single event.

In this question, analyzing the problem on the internet, we have that over a considerable number of flights, of those which came on time, 4.7% of them were in  American airlines.

There exists a 4.7% probability that it arrives on American airlines(aa).

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Answer: 2316/16924 = 0.137 = 13.7%

Step-by-step explanation:

Answer: x = 4

Step-by-step explanation:

Given equation

4x - 20 = -x

Add x on both sides

4x - 20 + x = -x + x

5x - 20 = 0

Add 20 on both sides

5x - 20 + 20 = 0 + 20

5x = 20

Divide 5 on both sides

5x / 5 = 20 / 5

[tex]\Large\boxed{x=4}[/tex]

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Rejected masses x are those that weigh less than 9.02 oz or more than 9.48 oz.

To find the rejected masses:

Therefore, rejected masses x are those that weigh less than 9.02 oz or more than 9.48 oz.

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The correct question is given below:

A company did a quality check on all the packs of trail mix it manufactured. each pack of trail mix is targeted to weigh 9.25 oz. a pack must weigh within 0.23 oz of the target weight to be accepted. what is the range of rejected masses, ×, for the manufactured trail mixes?

35miles Rick have to run to burn one pound of adipose tissue.

According to the given question.

Rick runs 5miles to burn 500 calories.

⇒ 1 mile burns the amount of calories = 500/5 = 100 calories.

As we know that

1 pound = 3,500 calories.

So the number of miles Rick needed to run to burn 1 pound of adipose tissue = 3500/100 = 35miles

Hence, 35miles Rick have to run to burn one pound of adipose tissue.

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The attached graph represents the graph of the linear equation y = 1000x - 5000 on a scale of 1 to 1000 units on both axes

Linear equations are equations that have constant average rates of change, slope or gradient

The equation of the linear function is given as:

y = 1000x - 5000

The x values are given as:

x = -3 to 8

This means that the domain of the function is [-3, 8] or -3 <= x <= 8

So, we set x = -3 and x = 8, and we calculate the y values.

So, we have:

y = 1000 * -3 - 5000 = -8000

y = 1000 * 8 - 5000 = 3000

So, we draw two points at (-3, -8000) and (8, 3000) and connect the dots

See attachment for the graph of the function

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The values of the function if the function f(x) is reflected over y-axis is  g(x) = 10/21x

Reflection is a transformation technique that changes the position of an object on an xy-plane.

If the function f(x) is reflected over y-axis, the resulting function is y = f(-x). Given the following function;

f(x) = -2/7(5/3)x

This can also be written as;

f(x) = -10/21 x

Replace x as -x

f(-x) = -10/21(-x)

f(-x) = g(x) = 10/21x

Hence the values of the function if the function f(x) is reflected over y-axis is  g(x) = 10/21x

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First you have to figure out the side length of the triangle.

sin(60)= X/8

Let's call x the side length.

8 sin(60)=X

X=6.93

The multiply it by 4

The area is 27.72

Answer:

120.

Step-by-step explanation:

That would be factorial 5, written 5!.

That  is 5*4*3*2*1

= 120.

Answer:

120

Step-by-step explanation:

We have 5 digits that can be used to create different 5 digit numbers. We are also not allowed to repeat any numbers. Let's say we have 5 boxes to put the 5 numbers in.

Box 1

Box 2

Box 3

Box 4

Box 5

In the first box, we have 5 different choices. Since we aren't allowed to repeat any digits, the second box only has 4 different choices. And so on...

Box 1 --> 5 choices

Box 2 --> 4 choices

Box 3 --> 3 choices

Box 4 --> 2 choices

Box 5 --> 1 choice

Therefore the amount of 5 digit numbers that can be created is:

[tex]5\times4\times3\times2\times1[/tex] or 5 factorial (a factorial is all the product of all the positive integers equal to and less than the number), which is equivalent to:

120 5-digit numbers

Answer:

1. BD bisects <CBE, AE || BD (Given)

2. <EBD ~= <CBD (Definition of < Bisectors)

3. <AEB ~= <EBD (Alternate Interior Angles Theorem)

4. <CAE ~= <CBD (Corresponding Angles Postulate)

5. <CAE ~= <AEB (Transitive Property of Congruence)

6. AB ~= BE (Converse of Isosceles Triangles Theorem)

Answer:

Multiply both sides of the first equation by 2.

Multiply both sides of the second equation by 3.

Step-by-step explanation:

The y terms are

-3y

2y

The LCM of 2 and 3 is 6.

We need the y terms to add to zero.

Multiply both sides of the first equation by 2 to get -6y.

Multiply both sides of the second equation by 3 to get 6y.

Then -6y + 6y = 0 eliminating the y terms after adding the equations.

Answer: [tex]\Large\boxed{Midpoint=(5,~-2 )}[/tex]

Step-by-step explanation:

Given information

[tex](x_1,~y_1)=(6,~-7)[/tex]

[tex](x_2,~y_2)=(4,~3)[/tex]

Given the midpoint formula

[tex]Midpoint=(\dfrac{x_1+x_2}{2} ,~\dfrac{y_1+y_2}{2} )[/tex]

Substitute values into the given formula

[tex]Midpoint=(\dfrac{(6)+(4)}{2} ,~\dfrac{(-7)+(3)}{2} )[/tex]

Simplify values on the numerator

[tex]Midpoint=(\dfrac{10}{2} ,~\dfrac{-4}{2} )[/tex]

Simplify the fractions

[tex]\Large\boxed{Midpoint=(5,~-2 )}[/tex]

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