write a quadratic function with zeroes 5 and 9

Answer:

24, 36, 48.

Step-by-step explanation:

Represent the three even numbers as 2x, 2y, 2z, where x,y,z are integers.

2x+2y+2z = 108

x+y+z = 54

Let x≤y≤z

x = z/2

y = ¾z

z/2 + 3z/4 + z = 54

2z/4 + 3z/4 + 4z/4 = 54

2z + 3z + 4z = 216

9z = 216

z = 24

x = z/2 = 12

y  = ¾z = 18

Therefore, The numbers are 24, 36, 48.

Joe will catch Jason in 6 hours running at 7mph while Jason is running at 5.5 mph .

Given,

Jason is 9 miles ahead of Joe running at 5.5 miles per hour and Joe is running at the speed of 7 miles per hour.

Now,

Joe speed is more than Jason.

So,

Differences in speed:

(7 - 5.5) = 1.5 miles per hour.

Now,

Jason is ahead of joe by 9 miles.

To cover 9 miles of distance by joe to catch jason,

Distance = Speed * Time

9 miles = 1.5mph* Time

Time = 6hours.

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There are number of thesis that are given for mathematics by various professors and scientists at various levels that are being implemented from time to time.

A theory is nothing but a set of statements which may be based on certain principles that might have been derived by performing some experiments and attaining a proper conclusion. For example, if we say 'the sky is blue'. It means this truth can never be changed irrespective of the situations. This will remain mortal.

Similarly, there are plenty of terms in mathematics such as decimals, percentage, geometry, algebra and more fundamentals. These are existing since ages and have been challenged also. But the theory remains the same. There operas-memoranda remains the same. So various scholars, have given various theories of mathematics.

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Answer: We can solve this system of equations by substituting the expression for y in terms of x from the second equation into the first equation, and then solving for x.

First, we substitute y = 2 + x from the second equation into the first equation, giving:

2x - 3(2 + x) = -5

Simplifying this expression by distributing the -3, we get:

2x - 6 - 3x = -5

Combining like terms, we get:

-x - 6 = -5

Adding 6 to both sides, we get:

-x = 1

Multiplying both sides by -1, we get:

x = -1

Therefore, the value of x in the system of equations is -1.

Step-by-step explanation:

Answer:

7x^2 - 7x + 17

Step-by-step explanation:

we can subtract what they already have from what they total cost for the microphones:

8x^2 - 4x + 9 - (x^2) - (x - 14) - (2x + 6)

simplify this:

8^2 - 4x + 9 - x^2 - x + 14 - 2x - 6 =

7x^2 - 7x + 17

Answer:

[tex]\large\boxed{\tt x^{\frac{5}{6}} + 2x^{\frac{7}{3}}}[/tex]

Step-by-step explanation:

[tex]\textsf{We are asked to simplify the given expression.}[/tex]

[tex]\textsf{We should use the \underline{Distributive Property, and Rule of Multiplying Exponents.}}[/tex]

[tex]\boxed{\begin{minipage}{25 em} \underline{\textsf{\large Distributive Property;}} \\ \\ \textsf{Distributive Property is a property that allows us to multiply the term to the left of the parentheses with the terms inside the parentheses.} \\ \\ \underline{\textsf{\large Example;}} \\ \tt a(b+c) = \boxed{\tt ab+ac} \end{minipage}}[/tex]

[tex]\boxed{\begin{minipage}{25 em} \underline{\textsf{\large Rule of Multiplying Exponents;}} \\ \\ \textsf{Whenever we have to multiply 2 terms with exponents, it's important to know the Rule of Multiplying Exponents. This rule states that whenever 2 exponential terms multiply together, their exponents add together. }\\ \\ \underline{\textsf{\large Example;}} \\ \tt x^{3} \times \tt x^{4} = x^{3+4} = \boxed{\tt x^{7}} \end{minipage}}[/tex]

[tex]\large\underline{\textsf{Solving;}}[/tex]

[tex]\textsf{We should first use the Distributive Property, then use the Rule of Multiplying}[/tex]

[tex]\textsf{Exponents.}[/tex]

[tex]\tt x^{\frac{1}{3}} (x^{\frac{1}{2}} + 2x^{2})[/tex]

[tex]\underline{\textsf{Use the Distributive Property;}}[/tex]

[tex]\tt x^{\frac{1}{3}} (x^{\frac{1}{2}} + 2x^{2}) = (x^{\frac{1}{3}} \times x^{\frac{1}{2}}) + (x^{\frac{1}{3}} \times 2x^{2})[/tex]

[tex]\underline{\textsf{Use the Rule of Multiplying Exponents;}}[/tex]

[tex]\tt (x^{\frac{1}{3}} \times x^{\frac{1}{2}}) + (x^{\frac{1}{3}} \times 2x^{2}) = x^{\frac{1}{3} + \frac{1}{2}} + 2x^{\frac{1}{3} + \frac{2}{1} }[/tex]

[tex]\underline{\textsf{Find Common Denominators per fractions;}}[/tex]

[tex]\tt x^{\frac{1}{3} + \frac{1}{2}} + 2x^{\frac{1}{3} + \frac{2}{1}} = x^{\frac{2}{6} + \frac{3}{6}} + 2x^{\frac{2}{6} + \frac{12}{6}}[/tex]

[tex]\underline{\textsf{Add;}}[/tex]

[tex]\tt x^{\frac{2}{6} + \frac{3}{6}} + 2x^{\frac{2}{6} + \frac{12}{6}} = x^{\frac{5}{6}} + 2x^{\frac{14}{6}[/tex]

[tex]\underline{\textsf{Simplify Fractions;}}[/tex]

[tex]\large\boxed{\tt x^{\frac{5}{6}} + 2x^{\frac{7}{3}}}[/tex]

A×A is the set {16, 20, 24, 28, 20, 25, 30, 35, 24, 30, 36, 42, 28, 35, 42, 49}

To find A×A, we need to first understand what A represents.

In mathematics, a set is a well-defined collection of distinct objects, called elements or members of the set. These objects can be anything, such as numbers, letters, or even other sets. The elements of a set are typically enclosed in curly braces { } and are separated by commas.

A is a set defined as the set of all whole numbers, x, where 4 ≤ x ≤ 7. In other words, A contains the elements 4, 5, 6, and 7.

To find A×A, we need to take each element in A and multiply it by every other element in A. This means that we need to find the product of (4, 4), (4, 5), (4, 6), (4, 7), (5, 4), (5, 5), (5, 6), (5, 7), (6, 4), (6, 5), (6, 6), (6, 7), (7, 4), (7, 5), (7, 6), and (7, 7).

When we do the multiplication, we get the set {16, 20, 24, 28, 20, 25, 30, 35, 24, 30, 36, 42, 28, 35, 42, 49}.

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Answer:

the answer is 0

Step-by-step explanation:

There are 4 cups of birdseed in the bag.

Algebra is a branch of mathematics that deals with symbols and the rules for manipulating these symbols to solve equations and understand mathematical relationships. It involves the use of letters and symbols to represent variables and numbers, and the manipulation of these variables and numbers using rules and operations such as addition, subtraction, multiplication, and division. The main goal of algebra is to solve equations, which involves finding the value of an unknown variable that satisfies the given equation.

In algebra, equations are often represented graphically as lines or curves on a coordinate plane, which allows for a visual representation of mathematical relationships. Algebraic equations are used in a variety of fields, including physics, engineering, finance, and computer science.

The study of algebra starts with basic arithmetic concepts and progresses to more complex topics such as linear equations, quadratic equations, and functions. The ability to understand and manipulate algebraic expressions is an essential skill in many areas of life, from solving practical problems to understanding complex mathematical theories.

If each of the 16 Cougar Scouts gets 1/4 of a cup of birdseed, then the total amount of birdseed in the bag can be found by multiplying the amount given to each scout by the number of scouts:

Total birdseed = (1/4) x 16 = 4 cups

Therefore, there are 4 cups of birdseed in the bag.

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The complete question is:

Answer:

≈ 11,88

Step-by-step explanation:

Use trigonometry:

cos (62∘) = 8 / x

x = 8 / cos (62∘) ≈ 11,88

According to the given data in question below given are the separate journal entries for each transaction on the books of Metlock, Inc.

"Entries" typically refers to the individual values in a matrix or table. A matrix is a rectangular array of numbers, symbols, or expressions arranged in rows and columns, while a table is an arrangement of data in rows and columns with each intersection representing a single piece of data.

1.On June 10, Metlock, Inc. made an account-based purchase from the Monty Company for $7,400 in goods, FOB shipping point, 3/10, n/30.

Inventory (asset) $7,400

Accounts payable (liability) $7,400

2. On June 11, Metlock, Inc. pays the freight costs of $560:

Freight expense (expense) $560

Cash (asset) $560

3. On June 12, goods totaling $600 are returned to Monty for credit:

Accounts payable (liability) $600

Inventory (asset) $600

4. On June 19, Metlock, Inc pay Monty Company in full, less the purchase discount:

Accounts payable (liability) $7,400

Purchase discounts (contra expense) $222 [($7,400 x 3%) = $222]

Cash (asset) $7,178

Note that the purchase discount is calculated as $7,400 x 3%, or $222.

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The information in issue below is taken from Metlock, Inc.'s books, which include separate journal entries for each transaction.

Purchase discounts (contra expense) $222 [($7,400 x 3%) = $222]

Cash (asset) $7,178

1.On June 10, Metlock, Inc. made an account-based purchase from the Monty Company for $7,400 in goods, FOB shipping point, 3/10, n/30.

Inventory (asset) $7,400

Accounts payable (liability) $7,400

2. On June 11, Metlock, Inc. pays the freight costs of $560:

Freight expense (expense) $560

Cash (asset) $560

3. On June 12, goods totaling $600 are returned to Monty for credit:

Accounts payable (liability) $600

Inventory (asset) $600

4. On June 19, Metlock, Inc pay Monty Company in full, less the purchase discount:

Accounts payable (liability) $7,400

Purchase discounts (contra expense) $222 [($7,400 x 3%) = $222]

Cash (asset) $7,178

Note that the purchase discount is calculated as $7,400 x 3%, or $222.

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Answer:

Step-by-step explanation:

The solution of the given problem of percentage comes out to be  $19,000 in 12 years, they should deposit $170.89 at the conclusion of each quarter.

The abbreviation "a%" is used to indicate a value or number in statistics that is expressed as a percentage of 100. Versions with "pct," "pct," or "pc" as the initials are also rare. However, the most popular method to do this is to use the percentage symbol ("%"). Additionally, both hints nor a constant ratio of every element to the overall amount exist. Since numbers commonly add up to 100, they are essentially integers.

Here,

=>  [tex]FV = PMT * [(1 + r/n)^(n*t) - 1] / (r/n)[/tex].

By entering these numbers, we obtain:

[tex]= > 19000 = PMT * [(1 + 0.07/4)^(4*12) - 1] / (0.07/4)[/tex]

Upon solving for PMT, we obtain:

[tex]= > PMT = 19000 * (0.07/4) / [(1 + 0.07/4)^(4*12) - 1][/tex]

=> PMT = $174.58 (rounded to the nearest cent)

In order to have $19,000 in 12 years, the investor needs to deposit $174.58 at the conclusion of each quarter at a rate of 7% compounded quarterly.

(b) Using the same procedures as in (a), but with an interest rate of 7.2%, we arrive at:

[tex]= > 19000 = PMT * [(1 + 0.072/4)^(4*12) - 1] / (0.072/4)[/tex]

Upon solving for PMT, we obtain:

[tex]= > PMT = 19000 * (0.072/4) / [(1 + 0.072/4)^(4*12) - 1][/tex]

=>  PMT = $170.89 (rounded to the nearest cent)

In order to have $19,000 in 12 years, they should deposit $170.89 at the conclusion of each quarter.

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Yolanda will spend a total of 3 hours / 9 tables,

or **1/3 hour per table**, if she spends an equal amount of time at each table.

Yolana can serve a total of 36 people if she has to serve 9 tables, each of which can hold 4 guests, and she must serve a total of 4 guests per table.

How long does each visitor spend on average?

We need to know the entire length of time Yolana will spend serving all 36 guests in order to calculate the average time spent per guest.

If the entire time is divided by the number of guests,we get:

36 people in 3 hours equals 5 minutes each person.

Thus, each visitor spends 5 minutes on average.

What is the average time?

A measurement of a set of time values' central tendency is the average time. It is determined by multiplying the total number of values in the set by the sum of all the time values.

As an illustration, if you have a series of times of 5, 10, and 15, you would add them all up to reach 30 minutes, divide that number by 3, and get an average time of 10 minutes.

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After answering the presented question, we can conclude that Yet, we equation cannot make final decisions based just on the median.

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x Plus 3" equals the value "9." The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. In the equation "x2 + 2x - 3 = 0," for example, the variable x is raised to the second power. Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.

Whether data is sorted in ascending or descending order, the median is the midway value. In this situation, the median sales amount for Company A is $7,000, which suggests that half of the sales are greater than $7,000 and half are less. The median sales amount for Business B is $6,000, which means that half of the sales are greater than $6,000 and half are less.

The median can be a useful approach to summaries a data set's core tendency. For example, we can see that Company A has a greater median sales amount than Company B, implying that Company A generates more money each sale on average. Yet, we cannot make final decisions based just on the median.

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Answer:

200

Step-by-step explanation:

199+1

I think it could represent the 100-yard dash. The graph represents distance versus time, which is a common way to graphically display motion.

A graph is a visual representation of data that displays the relationship between two or more variables. Graphs can be used to illustrate numerical information in a clear and concise way, making it easier to understand and analyze complex sets of data. Graphs can be created using various types of software or by hand, and there are many different types of graphs, including line graphs, bar graphs, scatter plots, pie charts, and more.

Here,

The vertical axis represents the distance, and the horizontal axis represents time. The line on the graph shows how the distance traveled changes with respect to time.

The graph also shows that the runner covers a certain distance in a specific amount of time, which is a fundamental concept in physics. In the case of the 100-yard dash, the graph shows how the runner covers 100 yards in a certain amount of time.

Overall, the graph displays the key characteristics of motion and can be used to analyze and compare the performance of athletes in various sports.

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Answer:

Step-by-step explanation:

Answer:

In this problem, we have to use the formula

[tex]P= \frac{A}{(1+\frac{r}{n})^{nt} }[/tex]

A = $600,000.00

n = 1  (annually)

t = 25 years

First, convert R as a percent to r as a decimal

r = R/100

r = 8/100

r = 0.08 per year,

Then, solve the equation for P

[tex]P= \frac{A}{(1+\frac{r}{n})^{nt} }[/tex]

[tex]P= \frac{6000000}{(1+\frac{0.8}{1})^{1*25} }[/tex]

P = $87,610.74

The principal investment required to get a total amount of $600,000.00 from compound interest at a rate of 8% per year compounded annually over 25 years is $87,610.74.

Step-by-step explanation:

gradient= 12-10/10-9

= 2

y=mx+c

c= -8

y= 2x-8

when x= -1,

y= 2(-1)-8

= -2-8

= -10

when x= 5,

y= 2(5)-8

= 10-8

= 2

Answer:

D

Step-by-step explanation:

8×16=128

2×4=8

128+8=136m^2

answer: D

To find the mean of the points scored by the teams, we need to add up all the points and divide by the number of teams:

Mean = (30 + 35 + 20 + 30 + 15) / 5

Mean = 130 / 5

Mean = 26

Therefore, the mean of the points scored by the teams is 26.

Answer:

answer is 26

Step-by-step explanation:

add the five numbers and divide them by the number you add them(that means by 5) and it comes

[tex] \frac{30 + 35 + 20 + 30 + 15 \\}{5} = \frac{130}{5} = 26[/tex]

To rank the libraries from 1 having the greatest total number of comic books to 5 having the least total number of comic books, we need to first calculate the total number of books in each library.

Let's start by using the information given to find the total number of books in each library:

For Library A, we know that 30 comic books are 2% of its total books. So, we can set up the following equation:

 30 = 0.02x

where x is the total number of books in Library A. Solving for x, we get:

 x = 1500

Therefore, Library A has a total of 1500 books.

For Library B, we know that 45 comic books are 5% of its total books. So, we can set up the following equation:

 45 = 0.05x

where x is the total number of books in Library B. Solving for x, we get:

 x = 900

Therefore, Library B has a total of 900 books.

For Library C, we know that 65 comic books are 2% of its total books. So, we can set up the following equation:

 65 = 0.02x

where x is the total number of books in Library C. Solving for x, we get:

 x = 3250

Therefore, Library C has a total of 3250 books.

For Library D, we know that 75 comic books are 10% of its total books. So, we can set up the following equation:

 75 = 0.1x

where x is the total number of books in Library D. Solving for x, we get:

 x = 750

Therefore, Library D has a total of 750 books.

For Library E, we know that 90 comic books are 3% of its total books. So, we can set up the following equation:

 90 = 0.03x

where x is the total number of books in Library E. Solving for x, we get:

 x = 3000

Therefore, Library E has a total of 3000 books.

Now that we have the total number of books in each library, we can rank them based on the number of comic books they have:

Library C: 65 comic books

Library E: 90 comic books

Library B: 45 comic books

Library A: 30 comic books

Library D: 75 comic books

Therefore, the libraries ranked from 1 having the greatest total number of comic books to 5 having the least total number of comic books are: C, E, B, A, D.

Answer:

Step-by-step explanation:

ear

.....Answer:

..........Step-by-step explanation:

The statements that are true with regards to the graph of the functions and the sprinter that wins and lead the race are;

The true statements are; A, B, and C

The graph of a function visually represents the rule of the function showing how the output values of the function changes as the input value varies.

The distance the two sprinter's will run = 80 meters

The speed of sprinter A = 9 meters per second

The speed of sprinter B = 9 meters per second

The head start of sprinter B = 14 meter

The analysis of the statements are as follows

A. The graph of the functions representing the speeds of the sprinters have the same slope of 9 which is the rate of change of distance with time, therefore, the graphs are parallel and will never intersect.

The statement is therefore; True

B. Sprinter B will win the race. - True

Sprinter B has a head start of 14 meters and both sprinters have the same speed, therefore, sprinter B will reach the finish line first and win the race.

C. Sprinter B is leading the race at the 4 seconds mark;- True

Sprinter A will cover a distance of 9 m/s × 4 s = 36 m at the 4 seconds mark, while sprinter B will cover a distance in the 80 m race of 9 m/s × 4 s + 14 m = 50 m at the 4 second mark, therefore, sprinter B will be leading at the 4 second mark

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Answer:

[tex]\cos^2x+\cos x-1+\sin^2x[/tex] can be simplified to [tex]\cos x[/tex]

Step-by-step explanation:

Given

[tex]\cos^2x+\cos x-1+\sin^2x[/tex]

We need to use the Pythagorean trig identity in this example.

[tex]\sin^2x+\cos^2x=1[/tex]

Lets simplify.

We can use the Commutative and Associative Properties of Addition to reorder the equation.

[tex]\sin^2x+\cos^2x+\cos x-1[/tex]

Apply the Pythagorean trig identity to [tex]\sin^2x+\cos^2x[/tex].

[tex]1+\cos x-1[/tex]

Group like terms.

[tex]\cos \left(x\right)+\left(1-1\right)[/tex]

1 minus 1 is zero.

That leaves us with

[tex]\cos x[/tex]

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