Do absolute value functions pass the vertical line test?

Answer:

2x^2 + x + 9 + (18/(x+2))

Step-by-step explanation:

To find the result when 2x^3 - 5x^2 - 9x + 18 is divided by x + 2 using the long division method, you can follow these steps:

Divide the first term of the dividend (2x^3) by the first term of the divisor (x). The result is 2x^2.

Multiply the divisor (x + 2) by 2x^2. The result is 2x^3 + 4x^2.

Subtract this result from the dividend (2x^3 - 5x^2 - 9x + 18). The result is -x^2 - 9x + 18

Bring down the next term of the dividend (-5x^2) and add it to the result from step 3. The result is -6x^2 - 9x + 18

Divide -6x^2 by -6x and the result is x.

Multiply the divisor by x. The result is x^2 + 2x

Subtract this result from the result of step 4. The result is -9x + 18

Bring down the next term of the dividend (-9x) and add it to the result from step 7. The result is -18x + 18

Divide -18x by -18 and the result is x

Multiply the divisor by x. The result is x^2 + 2x

Subtract this result from the result of step 8. The result is 18

Therefore, the quotient is 2x^2 + x + 9 and the remainder is 18

So the result when 2x^3 - 5x^2 - 9x + 18 is divided by x + 2 is 2x^2 + x + 9 + (18/(x+2))

The horizontal distance travelled by the ball when it hits ground is 119.67 feet

An equation is an expression composed of variables and numbers linked together by mathematical operations.

Let x represent the horizontal distance traveled by the ball and h represent the height of the ball. Given that:

h = -0.01x² + 1.18x + 2

The ball hits the ground when h = 0, hence:

-0.01x² + 1.18x + 2 = 0

x = 119.67

The horizontal distance is 119.67 feet

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The solution to the system does not exist

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

y = −2x + 1

4x + 2y = −3

Divide the first equation by 1

So, we have

y = −2x + 1

By substitution, the second equation becomes

Substitute y = −2x + 1 in the second equation

4x + 2(-2x + 1) = -3

So, we have

4x - 4x + 2 = -3

Evaluate the like terms

2 = -3

This equation is false

Hence, the system has no solution

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Complete question

What is the solution to the system of equation? (Page 84, #1b)

y = −2x + 1

4x + 2y = −3

The symbol of absolute value is two vertical bars (||).

The absolute value of a number is the distance between that number and zero on a number line. The absolute value of a number is always positive, regardless of the sign of the original number. For example, the absolute value of -5 is 5 and the absolute value of 5 is also 5.

In mathematical notation, the absolute value of a number is represented by placing the number between the vertical bars, like this: |x|. When the absolute value is applied to a variable or an expression, the result is the positive value of that variable or expression. For example, |-5| = 5, and |5| = 5.

The absolute value is used in many branches of mathematics, including algebra, calculus and geometry, and it is used to represent the magnitude of a number, regardless of its sign, and also it is used to define the distance between two points on a number line.

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(8, 3) is the point that is two-thirds segment of the way from point $r$ to point $s$, we can use the following method:

initially to get the difference between the x-coordinates of points $r$ and $s$, and multiply the values  by 2/3. let us consider that value as  $dx$.

and to get the difference between the y-coordinates of points $r$ and $s$, and multiply it by 2/3. let us assume the value as  $dy$. then add $dx$ to the x-coordinate of point $r$ and $dy$ to the y-coordinate of point $r$.on doing certain operations we get as:

hence the  coordinates of the point at two-thirds of the way from $r$ to $s$ is $(x,y)$ can be established as

x = -6 + (15 - (-6))(2/3) = -6 + 21(2/3) = -6 + 14 = 8

y = 19 + (-5 - 19)(2/3) = 19 - 24(2/3) = 19 - 16 = 3

therefore  the point two-thirds of the distance from point $r$ to point $s$ is (8, 3).

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Rates of birth and death within that group dictate the rate at which world's population would double.

200 years

500 million people became 1 billion people around the world in 200 years, or until 1825. The second doubling, from 1 billion to 2 billion in 1930, only took 100 years. The subsequent doubling, from 4 billion to 6 billion by 1975, only took 45 years. The first billion people on earth were present in the year 1830; the second billion were present in the years 1830 to 1930; and the third billion were present in the year 1990, which happened 60 years later.

The world's population increased to 500 million to one billion people in 200 years, starting in 1825.

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Answer:

Step-by-step explanation:

1/13 x 18

of= multiply

18x1=18

13x1=13

18/13

As a PROPER FRACTION, it is 1 5/13

Answer: 18/13

Step-by-step explanation:

You have to multiply the fractions.

From the correlation table , based on the correlation values , then the predictor that would lead to least prediction error in predicting happiness using simple regression is stats class .

What is Predictor Variable ?

The predictor variable is used to predict the future outcome based on some given circumstances. The Other names by which predictor variable is known as "criterion variable" and "explanatory variable" .

the best predictor from the given correlation table is the highest value in the table ; irrespective of the sign .

We have to predict happiness using the simple regression ;

So to find the predictor , we select the row in the happiness row ,

we can see that the biggest value for the happiness row is 0.41 , which is the stats class .

Therefore , The predictor that lead to least prediction error is Stats Class .

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Possible solution for the first system of inequality is (-4,-3) and Possible solution for the second system of inequality is (-2,-2).

A linear inequality is one that would result in a linear equation if we were to substitute the equals relation for the inequality. When solving the inequality, the direction of an inequality is reversed when we multiply or divide both sides by a negative value.The collection of all solutions makes up the solution set for an inequality.

Here,

1. x <-4 and y<-x-7

The graph of this system is attached as a below as Graph 1.

In the graph, red represents x <-4 and green represents y<-x-7.

Possible solution

Putting x=-4 in y=-x-7, we get

y=-(-4)-7

y=-3

So, the solution of the system is (-4,-3).

2. y<-3x-8 and y>5x+8

The graph of this system is attached as a below as Graph 2.

In the graph, red represents y<-3x-8 and green represents y>5x+8.

Possible solution

Putting x=-2 in y=5x+8, we get

y=5(-2)+8

y=-10+8

y=-2

So, the solution of the system is (-2,-2).

Hence, the possible solutions are (-4,-3) and (-2,-2) respectively.

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The dependent variable in this case would be the total number of hot dogs needed for the cookout.

In mathematics, a variable is a symbol, usually a letter, used to represent a quantity in an equation or in a mathematical expression. It can be thought of as a placeholder that can take on different values in a given equation or expression. Variables are essential for mathematics because they allow us to explore different scenarios and solve problems.

This is dependent on the number of guests attending, which is the independent variable. Depending on how many people show up, the individual will need to adjust the amount of hot dogs to accommodate the guests.

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Step-by-step explanation:

one way of simply calculating this is by using basic percentage calculations.

So because 90% of bacteria was left after every hour, one could use the intial number we were given to find out the next bacteria count. You could work it out by :

so in the 1hr the bacteria count was 90.

so you continue working it out for each hr

then work it out until u hve calculated for 5hrs, so the answers for each hr will be 90, 81, 72.9, 65.61, 59.049

then add them up and it will give you 368.559 bacteria count. When rounded off it will be 369.

thats how i would hve tackled it

The bacteria count after 5 hours was found to be 59.

For this case we have a function of the form:

y = A × ([tex]b^{x}[/tex]) <  br/ >

Where,

A - the initial amount of bacteria

b - decrease rate

x - time in hours

Substituting values we have in the above form, we get:

y = 100 × [tex](0.90)^{x}[/tex] <  br/ >

Then after 5 hours we have the equation,

y = 100 × [tex](0.90)^{x}[/tex] <  br/ > <  br/ > y = 59.049 <  br/ >

Rounding to the nearest whole number the equation becomes,

y = 59 <  br/ >

Therefore, the bacterium count after 5 hours was found to be 59.

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Answer:

To solve this problem, we will use the following steps:

Step 1: Convert the amount of roast beef used in each sandwich to a decimal by dividing the numerator by the denominator: 3/8 pound = 0.375 pound

Step 2: Subtract the amount of roast beef that Marisa has left from the amount of roast beef that she started with to find the amount of roast beef used: 5 - 2.75 = 2.25 pounds

Step 3: Divide the amount of roast beef used by the amount of roast beef used in each sandwich: 2.25 pounds / 0.375 pounds = 6

Final Answer: Marisa made 6 deli sandwiches.

Using the Fundamental Counting Theorem, it is found that 6 different possible outcomes are there.

What is the fundamental principle of counting?

The total number of times an event can occur is m n if there are m possible ways for one event to happen and n various ways for another. A rule used to determine the total number of potential outcomes in a circumstance is known as the fundamental counting principle.

                        It states that there are n m times m n times m methods to do both of these activities if there are n ways to perform one action and m ways to perform another action after that.

For the coin, there are two outcomes, hence . n₁ = 2

For the spinner, there are three outcomes, hence n₂ = 3

Then, the number of outcomes is given by:

N = 2 x 3 = 6.

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Answer:

They both type at the same rate.

Step-by-step explanation:

Ms. Leah's unit rate

186/3 = 62  She can type 62 words in 1 minute

Mr. Thomas's unit rate:

310/5 = 62  He can type 62 words in 1 minute.

The algorithm completes in an acceptable amount of time because it will draw n forms in around n2 steps.

A mathematical algorithm is a process that describes a series of steps that can be used to accomplish a mathematical computation. A typical illustration of a mathematical algorithm would be the step-by-step process used in long division. A set of instructions called an algorithm is used to solve a problem or complete a task. An algorithm is a set of instructions that spells out how to carry out a task. An algorithm can be thought of as a series of detailed instructions that result in a predictable pattern in a set of numbers or in lines of code.

given

Which of the following best describes the algorithm for drawing n forms, where n is a very big number  based on the numbers in the table.

Because it will take around n2 steps to draw n forms, the algorithm completes in a fair length of time.

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Answer:

4/7

Step-by-step explanation:

=> The simplest form of

56

:

98

56:98 is

4

:

7.

4:7.

Step-by-step explanation:

Given ratio -

56

:

98

56:98

We have to reduce it to its simplest form,

For that, we have to find the GCD of the numerator as well as the denominator:

So, the GCD for

56

56 and

98

98 is

14.

14.

Now, divide both the numerator and denominator by the GCD:

=

>

56

÷

14

98

÷

14

=>

98÷14

56÷14

=

>

4

7

=>

7

4

Hence, the simplest form is

4

:

7.

4:7.

Answer:
Check Attached Picture

Step-by-step explanation:

x coordinate equals 0

Y coordinate equals 6

plotted on coordinate plane attached

*drew it wrong the first time sorry

Answer:

Step-by-step explanation:

In order to plot the point, you would need to understand how coordinates work. So, the base of a coordinate is (x,y), meaning you would move your point along the x-axis by 6 units, and along the y-axis by 0 units. This would mean that on your grid, your point would be on the x-axis line (because moving 0 units just means you don't move it along that axis) and it would rest at the number 6.

The number of hot cocoas that Mei Mei would be predicted to sell if the day’s high temperature was of 42 ºF is given as follows:

58.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

For which the parameters are given as follows:

The function touches the y-axis at y = 100, meaning that the intercept b is defined as follows:

b = 100.

When x increases to six, y decays to 94, hence the slope m is obtained as follows:

m = (94 - 100)/(6 - 0)

m = -1.

Hence the function that predicts the amount of hot cocoa sold for a high temperature of x ºF is given as follows:

y = -x + 100.

The estimate if the high temperature was of 42 ºF is given as follows:

y = -42 + 100

y = 58.

The graph of the linear function is given by the image presented at the end of the answer.

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The true statement is t = 2 years.

What is simple interest?

Simple interest is calculated based on a loan's principal or the initial deposit into a savings account. Simple interest doesn't compound, therefore a creditor will only charge interest on the principal sum, and a borrower will never be required to pay further interest on the interest that has already accrued.

Here, we have

Given: suppose you deposited $400 in a saving account 2 years ago.

The simple interest rate is 2.5%. The interest you earned in those 2 years is $18.40.

We have to find the true statement.

We concluded that

I = 2.5%

P = $400

t = 2 years

Hence, the true statement is t = 2 years.

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The coach can select the 6 starting players in 20 different ways, as probability are 6 players to choose from and they must consist of 3 boys and 3 girls. There are 7 boys and 6 girls, so each player is eligible to play each position. To calculate this, the formula 6! / (3! * 3!) is used.

1. Calculate 6 factorial (6!) which is 6*5*4*3*2*1 = 720

2. Calculate 3 factorial (3!) which is 3*2*1 = 6

3. Calculate 3 factorial (3!) again which is also 6

4. Divide 6! by (3! * 3!) which is 720 / (6 * 6) = 20

When selecting a starting lineup for an indoor soccer team consisting of 6 players who must be 3 boys and 3 girls, there are 20 possible combinations. To calculate this, the coach must use the formula 6! / (3! * 3!). This formula is used to calculate the number of possible combinations when selecting a certain number of items from a set of items, where all items are unique. 6! is 6 factorial, which is calculated by multiplying the numbers from 6 down to 1 (6*5*4*3*2*1). 3! is 3 factorial, which is calculated by multiplying the numbers from 3 down to 1 (3*2*1). When 6! is divided by the product of 3! multiplied by 3!, the result is 20. This shows that the coach can select the 6 starting players in 20 different ways, as there are 6 players to choose from and they must consist of 3 boys and 3 girls. There are 7 boys and 6 girls, so each player is eligible to play each position.

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Answer:

Step-by-step explanation:

Assuming the interest rate remains constant throughout the 10-year period, Rajesh will have enough money in the account to cover all of the required loan payments. The total amount of money he will withdraw over the 10-year period will be $30,000 (250 x 12 months x 10 years). At the end of the 10-year period, he will have $50,847.90 in the account, which is more than enough to cover the required loan payments.

The given point has been plotted on the graph as (-3.5, 4.75).

Coordinate, is represented as the values on the x-axis and y-axis of the graph. while the coordinate x is called abscissa and the coordinate of the y is called ordinate.

Here,
Given coordinate,
(−3 1/2, 4 3/4}
x = -[3 1/2]
x = -3.5

y = 4 3 /4
y = 4 + 0.75
y = 4.75

So, the coordinates of (x, y) is shown,

Thus, the given point has been plotted on the graph as (-3.5, 4.75).

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Answer:

in the picture below

Step-by-step explanation:

QC ≅ Q'C'  and ∠AQC  is a right angle.

What is the transformation?

A transformation is a general term for four specific ways to manipulate the shape and/or position of a point, a line, or a geometric figure. The original shape of the object is called the Pre-Image and the final shape and position of the object is the Image under the transformation.

Given: A reflection is a transformation that maps point Q in a figure over a line, AB, such that for point C at the intersection of AB and QQ'.

We know that reflection creates an image equidistant from the line of reflection.

Thus,  QC ≅ Q'C'

Also in reflection, a line drawn from the point is perpendicular to the line of reflection.

Therefore,  ∠AQC is a right angle.

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K5 is a non-plannar graph with a minimum number of edges on 5 vertices and K3,3 is a non-plannar graph with a minimum number of edges on 6 vertices.

What is the K3-3 graph or K5?

K5 is a five-vertex graph with one edge between each pair of vertices. One edge connects each pair of vertices from opposing sets in graph K3,3 which has six vertices in two sets of three.

Both K5 and K3,3 are non-planar graphs having a minimal number of edges on their respective sets of 5 and 6 vertices, respectively.

Every appropriate sub-graph of a minimum non-planar graph G is a planar non-planar graph. 4.

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The height is 2 and radius is √2 of the largest right circular cylinder that can be put into a sphere of radius √3.

A cylinder whose bases are circular in shape and parallel to each other is called the right circular cylinder. It is a three-dimensional shape.

Given that the radius of a sphere R = √3

Let the radius of the cylinder is r and the height of the cylinder is h.

than.

r² = R² − h²/4

and Vc = πr²h

⇒ Vc = π(R² − h²/4)h

⇒ Vc = πR²h − πh³/4

dVc/dh = πR² − 3πh²/4  

(dVc/dh)R=√3 = 3π − 3πh²/4

For maximum or minimum volume,

dVc/dh = 0

⇒ 3π − 3πh²/4 = 0

⇒ 3πh²/4 = 3π

⇒ 3πh² = 3π*4

⇒ h² = 4

⇒ h=2

Also,  dVc/dh changes sign from positive to negative in the neighborhood of h=2. Hence, h=2 is a maximum point.

r² = R² − h²/4

⇒ r² = (√3)² - 2²/4

⇒ r² = 3 - 1

⇒ r² = 2

​⇒ r = √2

So, the height is 2 and radius is √2 of the largest right circular cylinder

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The rate of increase of the volume of the cube is 0.8 cubic inches per second.

Let x denote the edge of the cube at any given instant.

The total surface area of the cube

= 6x^2

The given condition is: 6x^2 = 150

=> x^2 = 25

=> x = 5

Now, the rate of increase of the edge of the cube is 0.2 inches/second.

Therefore, the rate of increase of the volume of the cube = rate of increase of the edge * rate of increase of the edge * rate of increase of the edge

=> 0.2 * 0.2 * 0.2

= 0.008 inches^3/second

= 0.8 cubic inches/second

The rate of increase of the volume of the cube is 0.8 cubic inches per second, which is calculated by multiplying the rate of increase of the edge (0.2 inches/second) three times.

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When two players A and B alternately flip a fair coin, the probability  E(T) is 4. (A tosses the coin first, then B tosses the coin, then A, then B and so on).

Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty.

Two players, A and B, turn a fair coin in succession (A tosses the coin first, then B tosses the coin, then A, then B and so on). The order of the heads and tails is noted. If there is a head followed by a tail, the game is done, and the person who throws the tail wins (HT sub-sequence).

We must ascertain the game's estimated duration. Allow T coin tosses for the game to proceed. Find E (T).

[tex]E(T) = first instance of HT in seriesE(T) =0.5×(1+2)+0.5×(1+E(T))\\0.5×E(T)=0.5×4\\E(T) =4[/tex]

As a result, when two players A and B alternately flip a fair coin, The E(T) is 4. (A tosses the coin first, then B tosses the coin, then A, then B and so on).

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Answer:

To find the percent markup, we can use the following formula:

Markup = (selling price - cost price) / cost price * 100

We know that the department store buys 100 shirts at a cost of $1,200 and sells them at a selling price of $20 each.

Markup = ($20 - $12) / $12 * 100

Markup = $8 / $12 * 100

Markup = 2/3 * 100

Markup = 67%

So the percent markup is 67%.

The air pressure at the center of the hurricane when the mean sustained wind velocity is 54.5 meters per second is 1011.5 millibars.

Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.

Given:

In a hurricane,

the mean sustained wind velocity v (in meters per second) can be modeled by v(p) = 6.3/(1013-p)

The mean sustained wind velocity = 54.5 M/s

To find the air pressure at the center of the hurricane when the mean sustained wind velocity is 54.5 meters per second:

That means,

the equation

54.5 = 6.3/(1013-p)

63 = (1013 - p)54.5

63 = 55208.5 - p54.5

p = 55145.5 / 54.5

p = 1011.844

Therefore, the air pressure is 1011.844 millibars.

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Answer:

Step-by-step explanation:

Total Student in a class = 80

No. of students passed = 80*80% = 64

No. of students failed = Total Students in a class - No. of students passed

No. of students failed  = 80-64 =16