What is the correct factorization of
x2 - 11x + 18?

The quadratic equation whose roots are 2√3 and 2-√3 can be written in the form ax² + bx + c = 0.

To solve this equation, we can use the formula x = (-b  ±  √(b²-4ac))/2a.

Substituting the values of 2√3 and 2-√3 for x, we get:

2√3 = (-b + √(b²-4ac))/2a

2-√3 = (-b - √(b²-4ac))/2a

Subtracting the two equations, we get:

0 = √(b²-4ac)

Taking the square of both sides, we get:

b² - 4ac = 0

Rearranging the equation, we get:

ax² + bx + c = 0, where

a = 1

b = 0

c = -4ac

Therefore, the quadratic equation whose roots are 2√3 and 2-√3

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Your answer is False

Answer:

f(f(3))=101

Step-by-step explanation:

To solve this problem, first solve for f(3):

[tex]f(3)=(3)^2+1\\f(3)=9+1\\f(3)=10[/tex]

Then, insert f(3) into f(2) by substituting f(3) in place of x:

[tex]f(f(3))=f(10)\\f(10)=(10)^2+1\\f(10)=101[/tex]

Answer:

90 miles.

Step-by-step explanation:

65 - 50 = 15

In each hour they have a difference of 15 miles.

In six hours:

6 * 15 = 90 miles

Thousands, hundreds and tens are three types of values and there are many more.

Value in mathematics is a number that represents the outcome of a computation or function. In the aforementioned example, you may inform your teacher that 5 + 6 Equals 30 or that x + y = 9 if x = 6 and y = 3. A variable or constant can also be referred to as a value.

The number 4 is in this case in the tens column. As a result, the place value of the number four is tens or tens.

Thousands, hundreds and tens are three types of values and there are many more like ones etc. Moreover after solving any problem for unknown variable the resulting numerical solution can also be termed as value.

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Answer:

AC is longest

BC is middle

AB is shortest

Answer:

Gordon types 280 words per minute

Step-by-step explanation:

2240word/8min

280/min is the same as 4.6/second (280/60)

To find the area of the base of the rectangular prism, we need to find the expression for the area of a rectangle with dimensions equal to the dimensions of the base of the prism.

The volume of a rectangular prism is given by the formula:

Volume = length * width * height

Substituting the given expressions for the volume and the height into this formula, we get:

6x3 + 19x2 + 2x - 3 = (length * width) * (x + 3)

Expanding the right-hand side of the equation, we get:

6x3 + 19x2 + 2x - 3 = length * width * x + length * width * 3

Matching the terms on the left-hand side of the equation with the corresponding terms on the right-hand side, we can see that the expression for the area of the base of the rectangular prism is:

length * width = 6x3 + 19x2 + 2x - 3 - length * width * 3

Simplifying this expression, we get:

length * width = -3x3 - 17x2 - 2x + 3

Therefore, the area of the base of the rectangular prism is given by the expression -3x3 - 17x2 - 2x + 3.

The width of a rectangle is the smaller side length that situated vertically. Width of rectangular area = Area of rectangle/ length of rectangle

or width of rectangular area = (perimeter of rectangle /2) - length of rectangle

The perimeter is the line that goes continuously  along the boundary of a geometrical shape.

the width of rectangle can be found from the area of rectangle formula or area of perimeter formula when the value of length, area and perimeter is known to us.

area = length × width

perimeter = 2(length × width)

hence, the width of a rectangle is the smaller side length along the vertical axis.

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The statement that describes the slope in this equation is that the score of each question is 5

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

Equation: s = 100 - 5m

Also from the question, we have:

s = The total score

m = the number of questions a student missed

Recall that

s = 100 - 5m

A linear equation is represented as

y = mx + c

Where m = slope

By comparing the equations, we have

m = -5

This means that the slope is -5

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Answer:

Step-by-step explanation:

1. The function f(t) represents the concentration of medication in the bloodstream over time. The function has a parabolic shape, with the maximum value at t = 8 hours.

To find the maximum concentration of the medication, we can set the derivative of the function equal to 0 and solve for t. The derivative of f(t) is:

f'(t) = -30t + 120

Setting this equal to 0 and solving for t, we get:

-30t + 120 = 0

-30t = -120

t = 4

Therefore, the maximum concentration of the medication occurs at t = 4 hours. At this time, the concentration of the medication is:

f(4) = -15(4)^2 + 120(4) = 120 mg

It's important to note that this function represents the concentration of the medication in the bloodstream, not the total amount of medication that has been taken. The total amount of medication taken over a given time period can be found by integrating the function over that time period.

2. To determine the maximum amount of medication in the bloodstream, we need to find the maximum concentration of the medication and then multiply that concentration by the volume of the bloodstream.

We have already determined that the maximum concentration of the medication is 120 mg/L. The volume of the bloodstream in an adult is approximately 5 liters. Therefore, the maximum amount of medication in the bloodstream is:

120 mg/L * 5 L = 600 mg

This is the maximum amount of medication that can be present in the bloodstream at any given time. It's important to note that this amount may be affected by various factors, including the rate at which the medication is metabolized and eliminated from the body.

3. To determine the concentration of medication in the bloodstream after 2 hours, we can substitute 2 for t in the function f(t) and solve for the concentration. The function for the concentration of medication in the bloodstream is:

f(t) = -15t^2 + 120t

Substituting 2 for t, we get:

f(2) = -15(2)^2 + 120(2) = 60 mg/L

Therefore, the concentration of the medication in the bloodstream after 2 hours is 60 mg/L. It's important to note that this represents the concentration of the medication at a specific point in time, not the total amount of medication that has been taken. The total amount of medication taken over a given time period can be found by integrating the function over that time period.

Mean mode formula  - Mean = {Sum of Observation} ÷ {Total numbers of Observations}

What does the mode mean?

By summing all the numbers in a data collection and dividing by the total number of values in the set, the mean (average) of the data set can be determined.

              A data collection is ordered from least to largest, and the median is the midpoint number. A data set's mode is the number that appears the most frequently.

What are the mean, median, and example?

The most frequent number, or the one that happens the most frequently, is known as the mode. Example: Since the number 2 appears three times, more than any other number, it is the mode of the numbers 4, 2, 4, 3, and 2.

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3xy has two terms, 3 and xy. The term 3 is a constant and the term xy is a product of two variables.

3xy is a multiplication of three individual components. It consists of three distinct parts, namely 3, x, and y. Each of these components is considered a distinct term, so 3xy has three terms in total. The 3 represents a numerical value, while the x and y are variables that can be assigned any numerical value. When multiplied together, the three terms form a single expression, 3xy, which can then be evaluated for a resulting value.

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The smallest number that is divisible by 3 is 3 itself. Every integer that is divisible by 3 is called a multiple of 3.

For example, some of the multiples of 3 are 6, 9, 12, 15, 18, 21, etc. All of these numbers can be obtained by multiplying 3 by an integer.

If a number evenly divides (leaves no residue) into another number, it can be divided. For instance, 34 may be divided by 2 equally, making it a divisible number. However, because doing so would result in a leftover, 34 cannot be divided by 3.

According to the law of three's divisibility, a number is completely divisible by three if the sum of its digits is also divisible by three. Take 308 as an example. To determine whether or not 308 is divisible by 3, add the digits together and find the sum (3+0+8=11).

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The number of solutions that a system of 2 linear equations in 2 variables can have is explained below.

In the question ,

it is given that ,

the system of 2 linear equations in 2 variables .

we know that the linear equations represent a line .

(i) the two linear equations will have No Solution / Zero Solution if the two lines are parallel .

(ii) the two linear equations will have One Solution/Unique Solution if the two line intersect at a point .

(iii) the two linear equations will have infinitely many solution if the lines overlap on each other .

Therefore , the number of solutions of linear equation is explained above .

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The money received by Marcia =  £ 6

According to the given information

The money is shared between Marcia and Becky in the ratio = 1 : 4

Let the money got by Becky  = £ x

Marcia got £ 18 less than Beck = x - 18

So

Taking the ratio

[tex]\frac{1}{4}=\frac{x-18}{x}[/tex]

Cross multiply both the fractions

x = 4(x - 18)

x = 4x - 72

-3x = -72

x = 24

Money got by Beck = £ 24

Money received by Marcia = 24 - 18

                                             = £ 6

Hence

The money received by Marcia =  £ 6

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Answer:

option b is the answer of the above

The follow up on SSS loan sickness benefit application are as follows :

                - Driver’s License

                - Passport

                - Voter’s ID Card

                - National Bureau of Investigation (NBI) Clearance

                - Postal Identity Card

                - Any other government-issued (secondary) ID      cards/documents

                - Laboratory, X-ray, ECG, and other diagnostic results

                - Operating room/clinical record that will support the diagnosis

For illnesses or injuries that occurred abroad, the issuing nation's official documentation must include an English translation and be properly authenticated by the Philippine Embassy or Consulate Office or properly certified by a notary public of the receiving nation.

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The first five terms of the expression are -7,-3,1,5, and 9.

The sequence in which every next number is the addition of the constant quantity in the series is termed the arithmetic progression

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that , F(1) = -3 and F(n) = F(n-1) + 4. Calculate the first term of the sequence,

F(1) = F(1-1) + 4

-3 = F(0) + 4

F(0) = -7

The common difference is calculated as,

d = -3 - 7

d = 4

The third term will be, -3 + 4 = 1

The fourth term will be, 1 + 4 = 5

The fifth term will be, 5 + 4 = 9

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The number of roots of the given equation x³ -3x² + 4 = 0 is equal to 3 which are -1, 2, 2.

As given in the question,

Given equation is written as:

x³ -3x² + 4 = 0

Number of roots of the given equation are as follow ;

Let f(x) = x³ -3x² + 4

For x = 1

f(1) = 1³ - 3(1)² + 4

    = 2 ≠ 0

x = 1 is not the roots.

Now, x = -1 ,

f(-1) = (-1)³ - 3(-1)² + 4

      = -1 -3 + 4

      = 0

x = -1 is the roots of the given equation x³ -3x² + 4 = 0

x³ -3x² + 4 = 0

⇒x³ + x² -4x² -4x + 4x + 4 =0

⇒x² ( x + 1) - 4x( x + 1) + 4(x+1) =0

⇒(x+1) ( x² -4x +4 ) = 0

⇒(x+1)( x - 2 )² = 0

⇒ x = -1, 2, 2

Therefore, the number of roots of the given equation x³ -3x² + 4 = 0 are 3 and given by x = -1 , 2, 2.

The above question is incomplete , the complete question is :

How many roots does the equation x³ -3x² + 4 = 0 have ?

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Answer:

He pays:

$368.94

Step-by-step explanation:

20 miles ⇒ 1 gallon

2365 miles ⇒ A gallons

A = 2365 miles * 1 gallon / 20 miles

A = 118,25 gallons

Then:

$3.12 ⇒ 1 gallon

$B ⇒ 118.25 gallons

B = 118.25 gallons * $3.12 / 1 gallon

B = $368,94

A statistic is a numerical summary of a sample.

A sample statistic is explained as any number computed from a sample of data.

Examples include the sample average, median, sample standard deviation, and percentiles. A statistic is a random variable because it is based on data obtained by sampling technique in which each sample has an equal probability of being chosen.

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Answer:

Given that a circle has a center (0,4) and the radius 5. 5. So the standard equation of the given circle is x2+(y−4)2=25.

Step-by-step explanation:

In Angle abc and angle pqr ab:pq=4:5 and a(angle pqr)=125cm² then the measure of angle ABC is 100 cm².

Generally, To find the measure of angle ABC in the triangle ABC, we can use the fact that the ratios of the measures of the angles in a triangle sum to 180 degrees.

We are given that the ratio of the measures of angles ABC to PQR is 4:5. This means that if we let x represent the measure of angle ABC, then the measure of angle PQR is 5x/4.

The measure of angle PQR is also given to be 125 cm². We can use this to set up the equation:

5x/4 = 125

Solving for x, we find that the measure of angle ABC is:

x = 100

Therefore, the measure of angle ABC is 100 cm².

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Step-by-step explanation:

So this below is a solution I devised myself when I was around 11 yrs old doing math competitions with my friend so… (I don’t have a name for this solution, and can’t give any reference material)

alright so notice that when you subtract the remainder from the divisor in this question, all of their the values equate to 4:

6–2 = 4

9–5 = 4

11–7 = 4

I am going to use this property to devise a method from the problem.

The property above means

(n+ 4) % 6 = 0

(n+ 4) % 9 = 0

(n+ 4) % 11 = 0

where n is the dividend

notice that for n to be in accordance with the restriction of the question, n+4 must be a multiple of 6, 9 and 11 simultaneously (common multiple)

Since the question asks for the number of “n”s that are three-digit positives…

100 <= n <= 999 (which means)

104<= n+4 <= 1003

ok, so now we have to find the common multiples of 6,9,11 within the range 104~ 1003

the least common multiple of 6,9,11 is 198.

the smallest multiple of 198 that is larger than or equal to 104 is 198, which is 1*198… the largest multiple of 198 smaller than 1003 is 990, which is 5*198

so that means we have all the way from the first multiple of 198 to the fifth multiple of 198, inclusive, which is (5–1) + 1 = 5

and there we have it!!!

the answer is 5

P.S. we could also just count the multiples, but the (5–1)+1 is there because it may not always be countable, and the +1 is there to account for the first number that was subtracted

The solution is 80 servings

The number of servings that can be made from 1 gallon is 80 servings

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number of servings from 1 gallon be = A

Now , the equation will be

The number of cups of milk = 5 cups

The number of servings from 5 cups of milk = 25 servings

So ,

The number of servings from 1 cup of milk = number of servings from 5 cups of milk / 5 cups

Substituting the values in the equation , we get

The number of servings from 1 cup of milk = 25 / 5

The number of servings from 1 cup of milk = 5 servings

Now , 1 gallon = 4 quarts

1 quarts = 2 pints

1 pint = 2 cups

So , 1 gallon = 16 cups

And , number of servings from 1 gallon = number of servings from 16 cups

So ,

The number of servings from 16 cups = number of servings from 1 cup of milk x 16

Substituting the values in the equation , we get

Number of servings from 1 gallon = 5 x 16

Number of servings from 1 gallon = 80 servings

Therefore , the value of A is 80 servings

Hence ,

The number of servings is 80 servings

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A vector that points in the same direction as the vector (i^+j^) and whose magnitude is 9 is (9i^/ √2 + 9j^/ √2).

Therefore the answer is 9i^/ √2 + 9j^/ √2.

The vector direction is same as i^ + j^. We can obtain a unit vector in that direction by dividing the vector with magnitude of i^ + j^, which is √(1² + 1²) = √2.

Unit vector is (i^ + j^)/ √2.

Given that the required vector is of magnitude 9. We can determine the required vector thus by multiplying the magnitude with the unit vector in the direction, that is

9×(i^ + j^)/ √2

= 9i^/ √2 + 9j^/ √2

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