Basically, the question is asking to solve a problem about rectangular prisms. It says the the shape of one box, with (h) height in feet, has a volume defined by the function:V(h) = h (h-5)(h-6)It says to graph the function. What is the maximum volume for the domain 0

Answer:

f(x) = 1(x - 4.5)² - 6.25

Step-by-step explanation:

Hello!

Let's find the Vertex Form of the quadratic by Completing the Square.

The formula for a Perfect Square Trinomial is (a+b)² = a² + 2ab + b².

To find b², we need to divide -9 by 2 and square it.

Add this number to both sides and factor. Remember, the b term here is simply half of the b term in the equation (-4.5).

Convert this back to function form:

The equation is f(x) = 1(x - 4.5)² - 6.25.

Let the price of each ticket be represented by

The price of two tickets will be

The tax on the price of the tickets is 6% which be represented as

The price of the two tickets after tax will be

Therefore,

The price of the tickets after adding an additional booking fee of $20 will be given below as

Since,

We were asked to get the algebraic expression person, we would therefore divide the above expression by 2

Hence,

The algebraic expression to represent the price per person using variable t is

=0.53t + 10

The point of the problem is to remember the cosine relation. It says, in this case, that

Converting the last equation by the inverse function, we get

For the first decimal place (5) equals 5, and by the rounding rule to the nearest degree, we get 63. The answer is A.

As per given by the question,

There are given that function,

Now,

Find the value of f(g(3)).

Then,

There are given that,

And,

According to question, value of x is 3, that means g(3).

So,

Put the value of x in g(x).

Then,

Now,

For find the value f(g(3));

Put the value of g(3) in the above condition,

f(g(3)).

So,

Instead of x in f(x), put the g(3).

Then,

So, the value of f(g(x)) is 7.

Hence, the option first is correct.

The equation for number of books collected by Robert is given as;

n= 14 d + 21

where d is the number of days he spent collecting .

Answer A. represents the number of books per day that are collected

For this problem, we have three circles with different radii. We need to determine which circles are similar and point out the reason for our statement.

Every circle has the same shape, the only thing that sets them apart is the radii. Since we can represent the relationship between the radii as fractions, then all circles are similar. Due to this, the only correct option is the second one. "Circle 1 is similar to both circle 2 and circle 3".

The rates of return for each of the two projects for X Corp are as follows:

The rate of return refers to the percentage gain or loss over the initial cost of the investment.

For this purpose, the rate of return is expressed as the percentage of the expected returns (which is a product based on the probability of different scenarios) over the initial investment cost.

                                                        Project C                     Project D

                                        Amount         Probability     Amount      Probability  

Initial Investment          $135,000                               $145,000    

Annual Rate of Return

Pessimistic   39%                                     .30      25%                        .35

Most Likely   27%                                     .45      15%                         .40

Optimistic    25%                                     .25      30%                         .25

Pessimistic $15,795 ($135,000 x 39% x 30%)

Most likely $16,402.50 ($135,000 x 27% x 45%)

Optimistic    $8,437.50 ($135,000 x 25% x 25%)

Total expected returns = $40,635

Rate of return = 30.1% ($40,635/$135,000 x 100)

Pessimistic   $9,062.50 ($145,000 x 25% x 35%)

Most Likely  $8,700 ($145,000 x 15% x 40%)

Optimistic    $10,875 ($145,000 x 30% x 25%)

Total expected returns = $28,637.50

Rate of return = 19.75% ($28,637.50/$145,000 x 100)

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y varies directly as x, y = 7 when x = 21. Determine x when y = 5.

Step 1

Let

y varies directly as x, it is y depends on x, in math terms

f(x)=y

y = 7 when x = 21

f(21)=7

Determine x when y = 5. f(?)=5

Step 2

there is a proportion, this must be equal, make a rule of three to find the value

so

x y

so , when y=5, x=15

Congruency in this context is a term that describes a pair of angles as being identical.

In our shape, we have a parallelogram and

Multiply both sides by t:

Multiply both sides by 10:

Divide both sides by 12:

She will need 12 flats and there will be 5 leftovers

From the question, we have

The number of flats is calculated as

So, we have the following equation

Number of flats = (Length)/Rate

So, we have

Number of flats = (77)/6

Evaluate

Number of flats = 12

This is calculated as

Leftover = Length - Number of flats * Rate

So, we have

Leftover = 77 - 12 * 6

Evaluate

Leftover = 5

Hence, the left over is 5

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Missing information in the question

[tex]~~~~~~~~~~~~\stackrel{\textit{payments at the beginning of the period}}{\textit{Future Value of an annuity due}} \\\\ A=pmt\left[ \cfrac{\left( 1+\frac{r}{n} \right)^{nt}-1}{\frac{r}{n}} \right]\left(1+\frac{r}{n}\right)[/tex]

[tex]\qquad \begin{cases} A=\textit{accumulated amount}\dotfill&\$400000 \\ pmt=\textit{periodic payments}\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &25 \end{cases}[/tex]

[tex]400000=pmt\left[ \cfrac{\left( 1+\frac{0.04}{12} \right)^{12 \cdot 25}-1}{\frac{0.04}{12}} \right]\left(1+\frac{0.04}{12}\right)[/tex]

[tex]\cfrac{400000}{\left[ \frac{\left( 1+\frac{0.04}{12} \right)^{12 \cdot 25}-1}{\frac{0.04}{12}} \right]\left(1+\frac{0.04}{12}\right)}=pmt\implies \cfrac{400000}{\left[ \frac{\left( \frac{301}{300} \right)^{300}-1}{\frac{1}{300}} \right]\left(\frac{301}{300}\right)}=pmt \\\\\\ \cfrac{400000}{515.84}\approx pmt\implies {\Large \begin{array}{llll} 775.43\approx pmt \end{array}}[/tex]

how much will it be in interest alone?

well, for 25 years every month you'd have been putting down that much, so we can just subtract what you put it from the 400,000 and what's left is the interest earned

[tex]400000~~ - ~~(25)(12)(775.43) ~~ \approx ~~ \text{\LARGE 167317}[/tex]

Given the functions:

We will find: f(x) • g(x)

So, we will find the product of the functions

We will use the distributive property to get the result of the multiplications

So,

so, the answer will be:

a quadratic function has any root when replacing that number the equation is equal to zero

so

now solve the multiplication

Number 4

The meaning of the symbols are

> means greater than

< means less than

For the first statement, 30 is greater than 10. It is true

For the second statement, 30 is less than 10. It is not true

For the third statement, 10 is greater than 30. It is not true

For the fourth statement, 10 is less than 30. It is true

Given the equation:

Let y = distance

Let x = time

- The distance from Denver when she began is given by x = 0, therefore:

Answer 1. 475 miles

- The change for each four hours, this is x = 4, so:

Answer 2. 235 miles

A pair of numbers that have a sum of 50

Let the number is x, so the other number is 50 - x

Let f(x) be the largest product so:

Simplify the expression :

Diffrentiate with respect to x

Now for to check for the f(x) is maximum for x = 25

Calculate the second derivative and put x = 25 is the f(x) is negative then the multiplication f(x) is maximum

Thus, the first number is 25

Second number is : 50 -x = 50-25 = 25

Numbers are 25, 25

Answer : 25 + 25 =50 (sum)

25 * 25 = 625 (maximum possible product)

We are given the following triangle:

We need to determine the area of the triangle. To do that we need to determine sides "a" and "b". We will use the sine law to determine the side "b":

Now, we multiply both sides by "sin107":

Solving the operations:

Now, before determining side "a" we will determine the angle "x" that is opposed to "a". To do that we will use the fact that the sum of the interior angles of a triangle is 180, therefore:

Adding the values:

Now, we subtract 155 from both sides:

Therefore, the angle opposite to "a" is 25 degrees. Now, we apply the sine law:

Now, we multiply both sides by "sin(25)":

Solving the operations:

Now, we determine the area using the following formula:

Where:

Now, we determine the value of "s":

Solving the operation:

Now, we substitute the value in the formula for the area:

Solving the operations:

Now, since the search party can cover 300 ft^2/h we can use a rule of 3 to determine the number of hours it takes them to cover 2611.43 ft^2:

Now, we cross multiply:

Now, we divide both sides by 300ft^2:

Solving the operations:

Therefore, it takes 8.7 hours to cover the area. Therefore, the search party won't be able to conclude before the sun goes down.

A class has 21 children, 10 are girls and 11 are boys. what fraction of the class is made up of boys?​

Let

x -----> number of boys

y -----> total number of children

we have that

x=11 -----> given

y=21 ----> given

therefore

The fraction of the class that is made up of boys is equal to

x/y

substitute

If The Muffin Shop wants a 40% markup on cost and produces 800 muffins, The Muffin Shop should price each muffin at $1.15.

The total expected revenue is divided by the total unspoiled units sold to determine the selling price.

This is illustrated below.

Cost per unit of muffins = $0.70

The spoilage rate = 15%

Expected markup on cost = 40%

The total production units = 800 muffins

The total good units sold = 680 (800 x 1 - 15%)

Total cost for 800 units = $560 (0.70 x 800)

The markup on cost = $224 ($560 x 40%)

The total expected sales revenue = $784 ($560 + $224)

Seling price per unit = $1.15 ($784/680)

Thus, The Muffin Shop should price each muffin at $1.15 to meet its goals.

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By solving the equations, we can conclude that the two numbers are 4 and 6.

So, the two numbers are:

The equation will be:

Now, solve this equation for 'x' as follows:

Now, 4x - 20:

Therefore, by solving the equations, we can conclude that the two numbers are 4 and 6.

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Answer:

A. 83 1/3 miles

B. Less than 9/10 of the way there

Step-by-step explanation:

A.

2/3 of the way. "of" means to multiply, so multiply 2/3 and 125.

[tex]\frac{2}{3}[/tex] × [tex]\frac{125}{1}[/tex] = [tex]\frac{250}{3}[/tex]

Simplify by dividing 250 and 3.

250 ÷ 3

[tex]83 \frac{1}{3}[/tex] miles

B.

Multiply 125 by 9/10 then compare the answer to 110 to see if she is more or less than 110 miles.

[tex]\frac{125}{1}[/tex] × [tex]\frac{9}{10}[/tex] [tex]= \frac{1125}{10}[/tex]

Divide 1125 by 10

1125 ÷ 10 = 112.5

Since 9/10 of the distance is 112.5 miles, 110 miles is less than 9/10 of the way there.

The amount should be charged to each attendee to cover the cost of the event is (300 + 45x) / x

Given,

The cost of a convention center to host an event = $300 + $45 per person attending

Number of attendees = x

We have to find a rational expression that represents how much you would need to charge each attendee in order to cover the cost of hosting the event.

Here,

Total cost for the event = Fixed cost + cost per person attending x number of person

Total cost = 300 + 45 × x

Total cost = 300 + 45x

Now,

The amount should be charged to each attendee to cover the cost of the event = (300 + 45x) / x

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State A have 42 counties and State B have 40 counties.

Define Linear equation

An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation.  The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant

Let,

x = The number of counties of state B

x + 2 = The number of counties of State A

It's given, The sum of counties of state A and state B is 82

so, the equation become is linear.

The linear equation will be,

x + (x + 2) = 82

solve for x,

2x + 2 = 82

2x = 82 - 2

2x = 80

x = 80/2

x = 40  (counties of State B)

put the value in x in x + 2,

40 + 2 = 42 (counties of State A)

Therefore, State A have 42 counties and State B have 40 counties.

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The price of one adult ticket is $9 and the price of child ticket is $8

First day of ticket sales the school sold 4 adult tickets and 9 child tickets for a total of $108

Consider the price of adult ticket as x and child ticket as y

Then the equation will be

4x+9y = 108

Similarly the school took in $114 on the second day by selling 10 adult tickets and 3 child tickets

10x+3y = 114

Here we have to use the elimination method

Multiply the first equation by 10 and second equation by 4

40x+90y = 1080

40x+12y = 456

Subtract the equation 2 from equation 1

90y-12y = 1080-456

78y = 624

y = 624/78

y = $8

Substitute the value of y in any equation

10x+3y =114

10x+3×8 =114

10x +24 =114

10x = 90

x = 90/10

x = $9

Hence, the price of one adult ticket is $9 and the price of child ticket is $8

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Sidney will use 57 cups of soda for 19 cups of ice cream.

The ratio shows how many times one value is contained in another value.

Example:

There are 3 apples and 2 oranges in a basket.

The ratio of apples to oranges is 3:2 or 3/2.

We have,

From the table,

The ratio of cups of ice cream to cups of soda.

3.5 cups ice cream = 10.5 cups of soda

Divide both sides by 3.5.

1 cup of ice cream = 3 cups of soda

Multiply 19 on both sides.

19 cup of ice cream = 57 cups of soda

Thus,

57 cups of soda.

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okay so the answer is 9ft so option B

now we can take a look at how we arrived to that answer

do you know the formula for the volume?

Answer:

2 and 3

Explanation:

Given the equation:

Now, observe the following:

Taking the indices:

Given the polynomial:

Let's factor the polynomial.

To factor, let's use the AC method.

Find a pair of numbers whose product is -18 and whose sum is 7.

We have the pair:

9 and -2

We have the factors:

(w + 9)(w - 2)

Therefore, the factored form of the polynomial is:

ANSWER: