12) A function f(x) = x² is given. Answer the following question for the function i) What is the algebraic nature of the function? ii) Write the name of the locus of the curve. iii) Write the vertex of the function. iv) Write any one property for sketching the curve. v) Write the domain of the function.​

The distance between Point P and Point Q on the number line is the absolute value of the difference between the coordinates of the two points.

In other words, if Point P has coordinate x and Point Q has coordinate y, then the distance between the two points is |x - y|. For example, if Point P has coordinate 3 and Point Q has coordinate 7, then the distance between the two points is |3 - 7| = |-4| = 4. This is because it is measuring the distance between two points in one dimension, that is on the number line.

The number line is a visual representation of the set of real numbers. It is a straight line with points that correspond to the numbers on the line. Each point on the number line corresponds to a unique real number, and the position of the point on the line indicates its value. The numbers on the left side of the number line are generally considered as negatives and the numbers on the right side as positives. The numbers on the line are evenly spaced, with the distance between any two consecutive numbers being the same, typically represented by 1 unit.

This question should be provided as:

The question is incomplete, thus the answer is general.

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The range would be [75,212] because the lowest Y value is 75 and the greatest one is around 212.5. .5] a domain and a range.

You may recall this by saying "DoLaR RiBiT," where "DoLaR" stands for "domain," "L" and "R" stand for "left to right," "R" stands for "range," and "B" and "T" stand for "bottom to top," and "R" stands for "range." Since the function doesn't approach 250, as can be seen in the graph, 250 is not inside the range.

Between the minimum and greatest value are the numbers that make up the range. The range would be [75,212] because the lowest Y value is 75 and the greatest one is around 212.5. .5] a domain and a range. The collection of values that can be plugged into a function's domain are called its parameters.

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Because the lowest Y value is 75 and the highest one is around 212.5, the range would be [75,212].

You may remind yourself of this by repeating "DoLaR RiBiT," where "DoLaR" stands for "domain," "L" and "R" are "left to right," "R" is "range," "B" and "T" are "bottom to top," and "R" is "range." Since the function doesn't approach 250, as can be seen in the graph, 250 is not inside the range.

1. The numbers that make up the range lie between the lowest and highest value. Because the lowest Y value is 75 and the highest one is around 212.5, the range would be [75,212].

The set of values that can be plugged into the domain of a function is referred to as its parameters.

Thus, the range would be [75,212] because the lowest Y value is 75 and the maximum is somewhere around 212.5.

2. The set of all temperatures that the water can attain is the function's range. The temperature of the water rises quickly at first, then more gradually, and after 30 minutes, it levels off and stops rising altogether, as shown by the graph.

As a result, the range of the function is a range of temperatures, beginning at the water's initial temperature and ending at the water's highest temperature.

3. The time at which the water reaches a temperature of 0 degrees Fahrenheit is represented by the equation W(t) = 0. We can observe from the provided graph that the water temperature rises quickly at first and subsequently more gradually.

The water is therefore unlikely to ever reach a temperature of 0 degrees Fahrenheit. As a result, W(t) = 0 cannot be solved.

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Using Algebraic expressions,  the number of baskets Desiree can assemble in 6 hours is 4.5. It will take her 5.5 days to complete the order.

We are describing an algebraic expression when we explain an expression in words that has a variable (an expression with a variable). For instance, the algebraic expression for "3 more than x" can be written. x + 3 x+ 3 x+3 .

According to the question,

Using Algebraic expressions,

Each basket takes her 3/4 of an hour to put together

5 baskets already assembled that Desirae can use for this order

a) the number of baskets Desiree can assemble in 6 hours = 3/4 × 6

= 4.5 baskets

b) Total baskets to prepare = 25

Days it will take her to complete the order = 25/4.5

= 5.5 days.

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Answer:

To prove that cosA/sinA -sinA/cosA=2cos^2A-1/sinA cosA, we can start by multiplying both sides of the equation by sinA cosA:

cosA/sinA -sinA/cosAsinA cosA = (2cos^2A-1)/sinA cosAsinA cosA

Now we can simplify the left side of the equation by using the identity sin^2A + cos^2A = 1:

cosAcosA -sinAsinA = (2cos^2A-1)cosAsinA

Now we can simplify the right side of the equation by using the identity cos^2A = 1 - sin^2A:

cosAcosA -sinAsinA = (2(1 - sin^2A)-1)cosAsinA

Finally, we can simplify the right side of the equation by using the identity sinAcosA = (sinAcosA)/(sinA*cosA):

cosAcosA -sinAsinA = (2(1 - sin^2A)-1)(sinAcosA)/(sinA*cosA)

Since both sides of the equation are equal, we can conclude that the statement is true.

The value h(x) = f(x)g(x) is h(x) = f(x)g(x) = (2x - 4g(x) + 1)(g(x)) = 2xg(x) - 4g(x)^2 + g(x)

Factorization is the process of finding the factors of a number or expression. In mathematics, factorization or factoring is the breaking apart of a polynomial into a product of other smaller polynomials, or the breaking apart of a number into a product of other smaller numbers. For example, the factorization of the polynomial x^2 + 2x + 1 is (x+1)^2, and the factorization of the number 15 is 3*5.

It can then be concluded that the equation of f(x) = 2x - 4 g(x) + 1 what is h(x) = f(x)g(x) is (2x - 4g(x) + 1)(g(x)) = 2xg(x) - 4g(x)^2 + g(x)

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Answer:

Adding or subtracting (depending on the missing sign) will eliminate the y term and make it easy to solve for x

Step-by-step explanation:

The first equation is missing a + or - sign

Regardless, it is easier to solve using elimination since the y coefficients are the same.

Adding or subtracting (depending on the missing sign) will eliminate the y term and make it easy to solve for x

The correct option is a. At least 5 which indicates the number of pants that can be bought.

To avail discount Nina needs 30 shirts. So, calculating the cost on buying minimum required number of t-shirts.

So, 150 × 30 = php 4,500

Total php available with Nina = 8,000

Now, leftover money for pants = total money - money spent on t-shirts

Leftover money for pants = 8000-4500

Leftover money for pants = 3500

Now, total pants Nina can buy = leftover money divided by php for pants

So, 3500/600=5

Thus Nina should buy atleast 5 pants.

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To work out the value of 3 2/5 × 10, we need to first convert the mixed number 3 2/5 into an improper fraction. To do this, we multiply the whole number (3) by the denominator (5) and add the numerator (2) to get:

3 2/5 = (3 x 5) + 2 / 5 = 15 + 2 / 5 = 17/5

Now that we have the improper fraction, we can multiply it by 10:

17/5 x 10 = (17 x 10) / (5 x 10) = 170 / 50 = 34 / 10

The answer is 34/10, which can be simplified to 17/5. Therefore, the value of 3 2/5 × 10 is 17/5.

(3, 4, 5), (5, 12, 13), (6, 8, 10), (9, 12, 15), and (15, 20, 25) are the five most common Pythagorean triples.

Any three positive integers that completely satisfy the Pythagorean theorem are considered Pythagorean triples. According to the theorem, the hypotenuse's square is equal to the sum of the squares of the other two legs of any right triangle. The Pythagorean triples are made up of the right triangle's three sides. In this article, we will learn how to make a few Pythagorean triples.

A set of three positive numbers known as Pythagorean triples conforms to the Pythagoras theorem's formula, which reads as follows: a2 + b2 = c2, where a, b, and c are positive integers. "c" denotes the "hypotenuse," or longest side, and "a" and "b" denote the remaining two legs of the right-angled triangle. (a,b,c) is how the Pythagorean triples are shown. Three, four, and five are the most well-known Pythagorean triples. We are able to demonstrate that the equations 3, 4, and 5 are correct. Find out how! 32 + 42 = 52 ⇒ 9 + 16 = 25. The Pythagorean triples 3, 4, and 5 are depicted in the right-angled triangle below.

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Answer: 77.05

Step-by-step explanation:

The more rainfall little town will receive 2016 than in 2015 is 7.12

Suppose you've got 3 numbers as a, b, and c.

Then, we have

(a+b) + c = a + (b + c)

This property is called associative property and it is called so because we can associate b with a, or b with c without altering the value of the addition.

Given;

2015 -4.17

2016 +2.95

To find out the more rainfall in 2016;

We will add the two numbers

=4.17 +2.95

=7.12

Therefore, the rainfall after addition will be 7.12

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Answer:

58°

Step-by-step explanation:

A right triangle is a type of triangle with exactly one angle equal to 90°. The other two angles sum up to 90°.

A triangle measures 180°. We plug in the given information from the question above…

90° + 32° = 122°

Applying the Triangle Sum Property…

180° - 122° = 58°

Answer: 1,2,4,7,14 and 28

Step-by-step explanation:  Todos los Factores de 28 = Factors of 28

Answer:

3/4 square points

Step-by-step explanation:

An equilateral triangle is a triangle with all sides of equal length.

To find the area of an equilateral triangle, we can use the formula:

Area = (√3/4) * (side length)^2

In this case, the side length is √3/4 * 1 point. To calculate the area, we need to square the side length first.

(√3/4 * 1)^2 = (√3/4)^2 * 1^2 = (3/4) * 1 = 3/4

So, the area of the equilateral triangle is 3/4 square points.

To read and plot coordinates, first you need to understand what the coordinates are and what they represent. Coordinates are used to indicate the position of a point on a graph or map.

They are typically composed of two or three numbers that represent an x- or y-axis on a graph.

To plot coordinates, start by plotting the x-coordinates on the x-axis and the y-coordinates on the y-axis. When plotting a point, start by drawing a circle at the coordinates. Then, draw a line connecting the point to the origin (the point where the x- and y-axes intersect). Finally, label the point with its coordinates.

When plotting multiple points, start by plotting each point individually and then connecting them with straight lines. This will create a graph with the points connected in a specific order.

When plotting coordinates, it is important to make sure that the data is accurate. Any mistakes in the coordinates can lead to wrong results. Additionally, it is important to use the same scale when plotting coordinates so that the points are accurately represented.

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In a case whereby Rowan spends 20% of his monthly salary on food while spending 30% of the remainder on transport the percentage of the salary does he save for clothes is 50%.

The concept that will be used here is the percentage. A percentage, often known as percent, is a division by 100. Percentage, which meaning "per 100," designates a portion of a total sum. 45 out of 100 is represented by 45%, for instance. Finding the percentage of a whole in terms of 100 is what percentage calculation is.

The percentage of overall value  is always 100%

Given :  monthly salary on food  = 20%

              monthly salary on transport = 30%

The percentage of the salary  save for clothes = 100% - 30%  -  20% = 50%

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An equation of the line through the points (-6, 5) and (-3, -3) is y = -8x/3 - 11.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

Next, we would determine the linear equation representing the line which passes through the points (-6, 5) and (-3, -3) by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - 5 = (-3 - 5)/(-3 + 6)(x + 6)

y - 5 = -8/3(x + 6)

y - 5 = -8x/3 - 16

y = -8x/3 - 16 + 5

y = -8x/3 - 11

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Feynman says Phlogiston Theory was not scientific is because it didn't utilized methods that were related to science.

The phlogiston theory, a debunked scientific hypothesis, suggested that combustible bodies contained a fire-like substance called phlogiston, which was released during combustion. Johann Joachim Becher first put forth the concept in 1667, and Georg Ernst Stahl later formalized it. Phlogiston theory sought to explain oxidation, the modern term for chemical processes like combustion and rusting.

According to the phlogiston theory, when something is burned, it dephlogisticates, releasing stored phlogiston that is then taken in by the air. The phlogiston is then absorbed by developing plants, which is why air does not spontaneously ignite and why plant matter burns so effectively.

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The solution of the given inequality is x < 0  or x > 6. [ And the Graph is given below]

It is quite similar to graphing linear equations to draw inequalities. Two further steps must be taken while concentrating on the inequality sign.

When you graph linear inequalities, you must perform two more steps i.e Choosing between a solid borderline and a dashed boundary line will be the first stage.

We can identify the boundary line with the inequality symbol.

We use a dotted boundary line if the inequality symbol is greater than or less than. This indicates that the answers are not part of the borderline.

We will use a solid line to denote that the solutions are included on the boundary line if the inequality symbol is greater than or equal to or less than or equal to.

Here we have

3 |x - 3| > 9    

Divide by 3 into both sides

=> [ 3|x - 3| ]/3 > 9/3

=> |x - 3| > 3  

As we know

=> |x - 3| > 3    

=>  (x - 3) < -3  or  (x - 3) > 3  

=>   x < 0         or    x > 6

Therefore,

The solution of the given inequality is x < 0  or x > 6. [ And the Graph is given below]

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The length of the rectangle is L = 29 meters

The perimeter P of a rectangle is given by the formula, P=2 ( L + W) , where L is the length and W is the width of the rectangle.

Perimeter P of rectangle = 2 ( Length + Width )

Given data ,

Let the length of the rectangle be represented as L

Let the width of the rectangle be represented as W

Now , Perimeter P of rectangle = 2 ( Length + Width ) = 74 meters

And , length of a rectangle is three meters less than four times its width

Substituting the values in the equation , we get

L = 4W - 3

And , 74 = 2 ( 4W - 3 + W )

Divide by 2 on both sides of the equation , we get

37 = 5W - 3

Adding 3 on both sides of the equation , we get

5W = 40

Divide by 5 on both sides of the equation , we get

W = 8 meters

Now , the length of the rectangle L = 4 ( 8 ) - 3

Length of the rectangle L = 32 - 3 = 29 meters

Hence , the length of the rectangle is 29 meters

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When 2 percent of cards is 22, then total number of cards that were sold is 1100.

In mathematics, a percentage is a number or ratio that represents a portion of 100. It is just one of a number of ways to represent a dimensionless relationship between two numbers; others include ratios, fractions, and decimals.

Percentages are frequently represented by writing the symbol "%" after a number. Additionally, you can denote them by appending "percent" or "pct" to the end of the number. For instance, the decimal 0.35, the fractions 35/100 and 7/20, and the percentage 35% can all be represented.

Given that 2% of cards is 22 cards, i.e.

2/100 = 22/x

2/100 = 22/x

2x = 100 × 22

2x = 2200

x = 2200/2

x = 1100

Thus, When 2 percent of cards is 22, then total number of cards that were sold is 1100.

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Answer:

When 2% of cards equals 22, the total number of cards sold is 1100.

What exactly is a percentage?

A percentage is a number or ratio that represents a portion of 100 in mathematics. It is one of several ways to represent a dimensionless relationship between two numbers, the others being ratios, fractions, and decimals.

The symbol "%" is commonly used to represent percentages after a number. You can also indicate them by appending "percent" or "pct" to the end of the number. The decimal 0.35, fractions 35/100 and 7/20, and percentage 35%, for example, can all be represented.

So, Given that 2% of cards equals 22. 

Explanation:

2/100 = 22/x

2/100 = 22/x

2x = 100 × 22

2x = 2200

x = 2200/2

x = 1100

Therefore, if 2% of cards equals 22, the total number of cards sold is 1100.

The nth term of an arithmetic sequence is given by aₙ = a + (n – 1).

A series in which the differences between each pair of following terms are the same is known as an arithmetic progression (AP). A formula for the nth term of the AP could be derived from this kind of progression. Because it follows a pattern where each number is acquired by adding 4 to the preceding term, the sequence 2, 6, 10, 14,... is an example of an arithmetic progression (AP). In this series, the nth term equals 4n-2. By changing the nth term to n=1,2,3,..., the sequence's terms can be obtained. i.e.,

First term when n = 1 is 4n-2 = 4. (1)

-2 = 4-2=2

second term = 4n-2 = 4 when n = 2 (2)

-2 = 8-2=6

The third term is 4n-2 = 4 for n = 3. (3)

-2 = 12-2=10

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The product of three fractions is acquired by multiplying the numerators and then multiplying the denominators of the three fractions to get the product fraction.

To find the product of any 3 fractions, multiply the three numerators. After that, multiply the three denominators. After the product of numerators and denominators, write them as fractions. This method will provide the product of 3 fractions in fractional form. To obtain this fraction in decimal form, divide the numerator of the fractional product by its denominator.

For example, consider the fractions 1/5 × 2/5 × 3/5.

In this, first multiply all the numerators: 1×2×3 = 6

Similarly, multiply all the denominators: 5×5×5 = 125

Now, the product of the three fractions is 6/125.

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Answer: True.

A diameter is a line that goes across the whole circle and passes by the center.

A chord is any line segment that connects two points on the circumference.

Since the diameter is a line from one opposite end of the circle to the other, it is connect two points on the circumference, thus it is a chord.

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

becaue o was thinking and i was like oh search it u0 and i got snswer

The following are the zeros for the function h (x) = x2 + 3x - 8: - x= -4 and x=2.

Given a collection of inputs X (domain) and a set of potential outputs Y (codomain), a function is more technically defined as a set of ordered pairings (x,y) where xX and yY with the caveat that there can only be one ordered pair with the same value of x. The function notation f:XY can be used to express that f is a function from X to Y.

The function's zero is a value of x that makes it equal to zero. In other words, the equation f(x) = 0 leads to a zero.

By putting h(x) equal to zero and figuring out x, we may determine the zeroes for the function h(x) = x2 + 3x - 8.

h(x) = x² + 3x - 8 = 0

We may factor the left side of the equation to find x:

x² + 3x - 8 = (x-2)(x+4) = 0

We set each factor to zero and solve for x to discover the zeroes:

x-2 = 0 or x+4 = 0

x = 2 or x = -4

Consequently, the function's zeros are x = 2 and x = -4.

So, A is the right response. x = -4 and x = 2

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The complete question is

What are the zeros of the function h (x) = x² + 3x - 8?

A. x = -4 and x = -2

B. x= -8 and x = 2

C. x = -2 and x = 8

D. x = 2 and x = 8

Answer:

4 km per hour

Step-by-step explanation:

Use the point (15,1)  Since the line is proportional, the slope is y/x or 1/15

1/15 this is in minutes

1/15 x 60/1  To convert  to hours

4 km per hour

Answer:

4 Km per hour

Step-by-step explanation:

average speed (S) is calculated as

S = [tex]\frac{D}{T}[/tex] ( D is distance and T is time, in hours )

the distance ( vertical axis )  from her home to the newspaper shop is 1 Km

time ( horizontal axis )

from 09 00 to 09 30 has 6 divisions

then 1 division = 30 minutes ÷ 6 = 5 minutes

time to walk to the shop is 3 divisions = 3 × 5 = 15 minutes

15 minutes = [tex]\frac{15}{60}[/tex] of an hour = [tex]\frac{1}{4}[/tex] hour

then average speed from home to newspaper shop is

S = [tex]\frac{1}{\frac{1}{4} }[/tex] = 4 Km per hour

All feasible ordered pairs of the elements of the original sets are produced by multiplying two sets.

The Cartesian product in SQL is a brand-new table created from two existing tables. The Cartesian product table will have three and four lines if the two tables have three and four lines, respectively. Every row from the first table so connects every row from the second table.

All feasible ordered pairs of the elements of the original sets are produced by multiplying two sets. The Cartesian product entails numerous computations, many of which are typically redundant. Therefore, we advise utilizing the qualifier operators for huge tables.

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Answer:

see explanation

Step-by-step explanation:

• the diagonals bisect each other

that is the point F is the midpoint of both diagonals GJ and KH

Note that GJ ≠ KH

Then

GF ≅ FJ

KF ≅ FH

your error is in that you have mixed up the appropriate diagonals