Graphing piecewise functions

The rational inequality is not provided, so it is not possible to determine the next smallest critical value, b. To determine the critical values, or the values of x that make the denominator of the rational inequality equal to zero, you would need to set the denominator equal to zero and solve for x.

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The equation of the trend line, can be found to be y = - 25 + 250

To find the equation of the trend line, you first need to find the slope. To do this, pick two points on the trend line. ( 4, 150) and ( 8, 50 ).

The slope is:

= ( Y2 - Y1 )/ ( X 2 - X 1 )

= ( 50 - 150 ) / ( 8 - 4 )

= - 100 / 4

= - 25

The equation of the trend line takes the form:

y = mx + b

m = slope

b = y - intercept

The slope allows you to find the y - intercept :

y = mx + b

50 = - 25 ( 8 ) + b

b = 250

The equation is:

y = - 25 + 250

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The steps for adding and subtracting fractions with whole numbers:

- Write the whole number in the form of a fraction.

- Convert the fractions to like fractions.

- Add/Subtract the numerators while the denominator remains the same.

We know that the fraction is used to represent the portion or part of the whole thing.

The fraction has two parts: numerator and denominator.

The top part of fraction is numerator and the bottom part of fraction is denominator.

consider a fraction 1/8.

Here, numerator is 1, denominator is 8

When certain thing is divided into 8 equal parts then each part of is represented by fraction1/8

In case of adding and subtracting fractions with whole numbers:

Let us assume that 'a' represents the whole number and [tex]\frac{x}{y}[/tex] be fraction

First we write the whole number in the form of a fraction.

So, a = [tex]a = \frac{a}{1}[/tex]

Now we find the LCM of the denominators of fractions [tex]\frac{a}{1} ,\frac{x}{y}[/tex] and then convert the given fractions to like fractions.

Let m be the LCM of the denominators of fractions [tex]\frac{a}{1} ,\frac{x}{y}[/tex]

So, the fractions becomes  [tex]\frac{a}{m} ,\frac{x}{m}[/tex]

Last we Add/Subtract the numerators while the denominator remains the same.

i.e., [tex]\frac{a\pm x}{m}[/tex]

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The complete question is:

How to add /subtract fractions with whole numbers?

Answer:

29/4 or as a mixed fraction 7 1/4

Step-by-step explanation:

The equation for Tomas and Emilio birthday party's celebration is 200 = 45.99 + 17p

In math the term called equation is defined as a mathematical statement that shows that two mathematical expressions are equal.

Here we have know that seven friends accept the invitation to the twins' birthday party.

Where the possible equation that can be set up will have the total budget equal to total expenses.

So it can be written as the Total Cost of party is 200,

Then the amount can be divided as

=> Cost of Party Room + Cost of Movie Tickets + Cost of popcorns

Let us consider that if p people attend the party, then the cost of movie tickets will be $12.50p and cost of popcorns will be $4.50p, assuming that each person get a small popcorn bag.

Hence the equation will be written as

=> 200 = 45.99 + 12.50p + 4.50p

=> 200 = 45.99 + 17p

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Answer:

C

Step-by-step explanation:

not D because B is better than D. not A, still expencive. C is the most reasonable for getting $200 off. unless total is over $600.

Answer:A Store A: Buy 3 tires and get the 4th tire free

Step-by-step explanation:its A

The average number of gallons of fruit juice consumed per person in the country in 2006 is 3.56  gallons per person

The average value in a set of numbers is the middle value calculated by dividing the total of all the values by the number of values.

Given:

Total consumption of fruit = 1.78 billion gallons

= 1,780,000,000

Total population = 500 million

= 500,000,000

Average number of gallons of fruit juice consumed per person = 1,780,000,000 ÷ 500,000,000

= 3.56 gallons per person

About how many gallons would your class consume?

Assume, there are 7 students in your class

Average number of gallons of fruit juice consumed per person = 3.56 gallons / 7

= 0.50 gallons per student

Therefore, the average number of gallons of fruit juice consumed per person in the country in 2006 is 3.56  gallons per person

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The original length is 250 meters and the scale drawing width is 0.67 cm

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

Scale length = 0.5 meters

So, we have

Original length = 0.5/(1/500)

Evaluate

Original length = 250

This means that the original length is 250 meters

Here, we have

Scale drawing width = 335 cm * 1/500

Scale drawing width = 0.67 cm

Hence, the scale drawing width is 0.67 cm

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F(m(v)) = 3,600 v composite function can be used to find the force of the object based on its volume. So the option d is correct.

We have to determine which composite function can be used to find the force of the object based on its volume.

The density of titanium is 4. 5 g/cm^3.

A titanium object is accelerating at a rate of 800 cm/s^2.

The mass of the object can be modeled by the function m(v) = 4.5v, where v is the volume in cubic centimeters.

The force of the object can be found using the function F(m) = 800m.

F(m(v)) = 800 × 4.5 v

F(m(v)) = 3600 v

As a result, the function that can be utilized to simulate the force depending on volume is 3600 v.

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The solution of (n⁴ - 14n³ + 51n² - 19n - 30) / (n - 8) using synthetic division is n³ - 6n² + 3n + 5 + 10/n - 8.

The solution of (n⁴ - 14n³ + 51n² - 19n - 30) / (n - 8) using synthetic division is given below:

(n⁴ - 14n³ + 51n² - 19n - 30) / (n - 8)

The divisor is 8

The coefficients are:

 1   -14   51   -19   -30

Using synthetic division:

the first coefficient is 1

the second coefficient = 1 * (8) + (-14)

the second coefficient = -6

the third coefficient = -6 * (8) + (51)

the third coefficient = 3

the fourth coefficient = 3 * (8) + (-19)

the third coefficient = 5

the remainder = 5 * (8) + (-30)

the remainder = 10

Therefore, the solution =  1(n⁴/n) -6(n³/n) + 3(n²/n) + 5(n/n) + 10/n - 8

The solution = n³ - 6n² + 3n + 5 + 10/n - 8

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     A variable whose value is decided by a random process or experiment is known as a random variable.

    Depending on how the experiment or random process turns out, it may have a range of distinct numerical values. Random variables come in two varieties: discrete and continuous. A continuous random variable can take on any value within a specific range, such as real numbers, but a discrete random variable can only take on a countable number of values, such as integers.

This random variable has the following distribution and is discrete in nature:

P(X=0) = probability of red or white = P(red) + P(white)

P(X=1) = probability of green or blue = P(green) + P(blue)

P(X=2) = probability of yellow or violet = P(yellow) + P(violet)

P(X=x) must have a sum of all possible values of 1, which indicates that

   P(red) + P(white) + P(green) + P(blue) + P(yellow) + P(violet) = 1

    Therefore ,with a probability  of 1/3 for each value, this random variable has a discontinuous uniform distribution over the set of values 0, 1, and 2.

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Answer: False because 20 doesn't equal to 9. Have a nice day ;)

Answer: the answer is false

Step-by-step explanation:

The responses to the survey question are quantitative, as the respondents were asked to provide a numerical answer.

Out of the 79,659 respondents, 79,659 said that they expect driverless cars to be common in the next years.

Out of the 79,659 respondents, 15,030 answered in the range of years. This means that 15,030 respondents provided a numerical answer that was within the range of years.

It is important to note that the survey question was quantitative, so the responses provided by the respondents were numerical. This means that the responses were not categorical, as categorical responses would have been in the form of words or phrases.

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The reflected function is the one below:

g(x) = -√x

This function is represented by the last table.

For a general function y = f(x), we define a reflection over the x-axis as:

g(x) = -f(x)

In this case f(x)=  √x, then the reflected function will be:

g(x) = -f(x) = -√x

Now we can evaluate this function to get some pairs of values.

Then when x = 1

g(1) = -√1 = -1

g(2) = -√2 = -1.41

And so on.

Then the correct option is the last table.

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The proof that shows that triangles ABC and EDC are similar is explained in the table below.

A proof is a logical argument that demonstrates the truth of a statement. So, each step must be justified and flow logically from the previous step.

The proof that shows that the triangles are similar is explained as shown below.

Statement Reason

1. AB || DE 1. Given

2. <A ≅ <E 2. Alternate interior <s theorem

3. <B ≅ <D 3. Alternate interior <s theorem

4. ∆ABC ~ ∆EDC 4. AA Similarity theorem

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The relation as a set of ordered pairs is expressed below.

The domain of the relation is {0, 1, 2, 3, 4, 5}.

The range of the relation is {8, 11, 12, 23, 28}.

In Mathematics, an ordered pair can be defined as a pair of two (2) elements that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate (abscissa) and the y-coordinate (ordinate) on the coordinate plane of any graph such as the following:

Mathematically, the set of ordered pairs which represents the relation include the following:

Based on the mapping diagram (see attachment), the domain and range of the relation is given by:

Domain = {0, 1, 2, 3, 4, 5}.

Range = {8, 11, 12, 23, 28}.

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The particle is at the point (-1.112,3.909) after traveling for 20 microseconds.

We have been given a circle,

(x-3)²+(y-4)²=25

whose center is (3,4)

and with a radius of 5 units.

The particle starts at (3,-1) which is the 6 o'clock position in the circle, and ends at (8,4) after 7 microseconds which are at the 3 o'clock position in the circle.

So, the particle traveled 1/4 of the circumference of the circle in 7 microseconds

therefore according to the unitary method it will travel 5/7 of the circumference of the given circle.

so it will subtend 2π×5/7 of the circle from (3,-1)

from the polar form of the circle and the shifting of center of the circle we can conclude

that it's location will be

(5 × cos (10π/7) - 3 , 5 × sin (10π/7) - 4)

= (-1.112,3.909)

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Answer:

18 years old

Step-by-step explanation:

H=17- A/

H=8hours

8=17- A/

-9=- A/

A=18years

The amounts of each solution are given as follows:

The amounts are obtained solving a system of equations, for which the variables are given as follows:

Joel needs to make 200 milliliters, hence:

x + y = 200.

x = 200 - y.

The rate is of 35%, hence:

0.15x + 0.55y = 0.35 x 200

0.15x + 0.55y = 70.

The solution for y is given as follows:

0.15(200 - y) + 0.55y = 70

0.4y = 40

y = 40/0.4

y = 100.

The solution for x is given as follows:

x = 200 - y

x = 100.

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25 percent of $120 is $30 and yes, he has enough money to buy the music player.

A) Find 25% of $120:

To find 25% of $120, we divide $120 by 100 and then multiply by 25:

$120 / 100 * 25 = $30

So, 25% of $120 is $30.

B) Does Wyatt have enough:

To find the sale price of the music player, we need to apply the 24% discount:

$120 - $120 * 24% = $120 - $120 * 0.24 = $120 - $28.80 = $91.20

So, the music player will be sold for $91.20.

Wyatt has $95, so he has enough money to buy the music player.

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The best interpretation of 14.2 as shown in the equation above is the constant acceleration of the airplane.

A particle's acceleration is the rate at which its velocity changes over time. The term "constant acceleration" refers to the rate at which a particle's velocity changes. When acceleration is constant, the rate of change in velocity is also constant. In the absence of any acceleration, velocity remains constant.

When acceleration is positive, velocity becomes more significant. Acceleration causes a decrease in velocity. The value 14.2 in the equation above represents the constant acceleration of the airplane in meters per second squared (m/s^2). It is the rate at which the velocity of the airplane is changing with respect to time.

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Answer:

125,664 mm³/s

Step-by-step explanation:

V = (4/3)πr³

dV/dt = (4π/3) × 3r² × dr/dt

dV/dt = 4πr² × dr/dt

dr/dt = 4 mm/s

d = 100 mm; r = 50 mm

dV/dt = 4π(50 mm)² × 4 mm/s

dV/dt = 125,664 mm³/s

Two variables are primarily linked when there is a proportionate relationship, which means that as 1 variable rises or falls, the other rises or falls at the same rate.

The ratios between both the two variables should be considered in order to determine whether a relationship is proportional. The relation is proportional if the ratio remains constant. The relationship is indeed not proportional if the ratio shifts.

When two or more items are directly proportionate or change in size according to equivalent ratios, the relationship is said to be proportional. This proportional relationship can be expressed using the formula y = kx.

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Answer:

Two variables are primarily linked when there is a proportionate relationship, which means that as 1 variable rises or falls, the other rises or falls at the same rate.

What factors determine if one relationship is proportional?

The ratios between both the two variables should be considered in order to determine whether a relationship is proportional. The relation is proportional if the ratio remains constant. The relationship is indeed not proportional if the ratio shifts.

What are the two proportional relationships principles?

When two or more items are directly proportionate or change in size according to equivalent ratios, the relationship is said to be proportional. This proportional relationship can be expressed using the formula y = kx.

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Step-by-step explanation:

For x = 0, the sides of parallelogram are equal.

A parallelogram is a straightforward quadrilateral with two sets of parallel sides in Euclidean geometry. A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of similar size.

There are six crucial parallelogram characteristics to be aware of:

Congruent sides are those when AB = DC.

Congruent opposite angels are D = B.

(A + D = 180°) Consecutive angles are supplementary.

All angles are correct if just one of them is.

A parallelogram's diagonals cut each other in half.

A parallelogram is a four-sided, two-dimensional form in geometry. This particular quadrilateral example has equal and parallel opposite sides.

As the sides of parallelogram are parallel and equal,

2x + 15 = x + 15

2x = x

x = 0

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Each person buys a number of cakes

The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.

Given, Andy buys x cakes, Betty buys 4 times as many cakes as andy, and colin buys 3 more cakes than andy

So,

Andy has = x Cakes

Betty have = 4x Cakes

Clin has = x +3 Cakes

Since each cake costs 65p and the total cost of the cakes is £52.65

thus,

0.65( x + 4x + x +3) = 52.62

x + 4x + x +3 = 81

6x = 78

x = 13

Therefore,

Andy has = 13 cakes

Betty has = 4x = 4*13 = 52 cakes

Colin has = x + 3 = 16 cakes

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The coordinates of B, C, and D are (3,-5), (3,5), and (-7,5) respectively.

Given point A (-2,-5) and the lengths of the sides AB = 5 and BC = 10, we can use this information to determine the coordinates of B, C, and D.

Using the information provided, we know that B is 5 units away from A in the positive x-direction. Therefore, the x-coordinate of B is (-2) + 5 = 3 and the y-coordinate of B is the same as that of A, which is -5. So point B is (3,-5).

Next, we know that C is 10 units away from B in the positive y-direction. Therefore, the x-coordinate of C is the same as that of B, which is 3, and the y-coordinate of C is (-5) + 10 = 5. So point C is (3,5).

Finally, we know that D is 10 units away from C in the negative x-direction. Therefore, the x-coordinate of D is 3 - 10 = -7 and the y-coordinate of D is the same as that of C, which is 5. So point D is (-7,5).

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The question is -

Find the coordinates of B, C, and D given that AB = 5 and BC = 10 where A = (-2,-5).

Marvin should put at least $45 more cash in his wallet in order to have at least $60.

Let x be the amount of cash that Marvin needs to put in his wallet. We know that he wants to have at least $60, and he currently has $15, so we can write the inequality as:

x + 15 ≥ 60

To solve for x, we need to subtract 15 from both sides of the inequality:

x ≥ 60 - 15

x ≥ 45

Marvin should put at least $45 more cash in his wallet in order to have at least $60.

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The minimum amount of framing Lorraine needs for the square painting is 31 inches.

We can use the Pythagorean theorem to calculate the length of the side of the square given the length of its diagonal. The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

We know that the diagonal of the square painting is 44 inches, and since the diagonal of a square bisects its angles, the square can be divided into two congruent right-angled triangles. Therefore, the length of one side of the square can be calculated using the Pythagorean theorem:

44 inches^2 = x^2 + x^2

x^2 = 11*11

x = 11 inches

Since the square painting has a side length of 11 inches, and the framing material is sold by the inch, Lorraine will need a minimum of 11 inches of framing on each side, for a total of 44 inches.

A  correct solution for the following system of Inequalities is; (-2, 6)

From the graph, it represents two inequalities and we can say that the solution of the two inequalities is the coordinate of the point where both lines of the inequalities intersect each other.

In the given graph, the coordinate of the point where both lines intersect each other is expressed as;

(-0.5, 4.2)

Now, that coordinate is not among the options but then the solution to the inequality graph will be the region shaded purple which in this case the only correct one is the coordinate (-2, 6)

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