If the function f(x) = 4x^2 - x + 3, evaluate f(-2)

The function y = - 2(x - 1)² + 5 is reflected along the y-axis, shifted horizontally to the right by 1 unit, and then shifted vertically by 5 units.

Suppose we have a function f(x).

f(x) ± d = Vertical upshift/downshift by d units (x, y ±d).

f(x ± c) = Horizontal left/right shift by c units (x - + c, y).

(a)f(x) = Vertical stretch for a > 0, vertical shrink a < 0. (x, ay).

f(bx) = Horizonatal compression b > 0, horizontal stretch for b < 0. (bx , y).

f(-x) = Reflection over y axis, (-x, y).

-f(x) = Reflection over x-axis, (x, -y).

Given, The parent function is y = x² which is quadratic.

Now, y = - 2(x - 1)² + 5,

First is reflected along the y-axis (-) sign,

(x - 1) is shifted by 1 unit to the right horizontally and (+5) is shifted vertically 5 units up.

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The solution for [tex]11^{\frac{1}{4} }[/tex] in radical form is 1.82116028... .

Radical form is pretty straight-forward. It refers to the form of a number or algebraic expression in which the number or algebraic expression is under a radical. However, we can better that by manipulating a number or algebraic expression in radical form to put it in a form called simplest radical form.

Apply the rule [tex]x^{\frac{m}{n} }[/tex]=[tex]\sqrt[n]{x^{m} }[/tex] to rewrite the exponential as a radical .

[tex]\sqrt[4]{11^{1} }[/tex]

Anything raised to 1 is the base itself.

[tex]\sqrt[4]{11}[/tex]

So the result can be shown in multiple forms like

Exact form: [tex]\sqrt[4]{11}[/tex]

Decimal form: 1.82116...

So the result for the expression in radical form is 1.82116...

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The average of age of team is 21.3 .

The age of new player is 30 .

What is average value ?

Generally, an “average” value purports to represent or to summaries the relevant features of a set of values; and in this sense the term would include the median and the mode. In a more limited sense an average compounds all the values of the set, e.g. in the case of the arithmetic or geometric means.

Have given ,

Ages of team  are 19,20,21,22,23

and frequencies are 1,2,2,5,1

Average of team = [tex]\frac{19 * 1 + 20 * 2 + 21 * 2 + 22 * 5 + 23 * 1}{11}[/tex]

Average of team = 21.3

Let x age of new join player ,

[tex]\frac{234 + x}{11} = 22[/tex]

x = 30

The average of age of team is 21.3 the age of new player is 30.

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Given ,

Ages of team  are 19,20,21,22,23

and frequencies are 1,2,2,5,1

Average of team = 21.3

Let x age of new join player ,

x = 30

The average of age of team is 21.3 the age of new player is 30.

Distance of 125 feet covered in 5 seconds, so the speed is 25 feet/second.

Any object's distance traveled in a unit of time is referred to as speed.

In mathematical term, Speed is express as S = D/T,

where S=speed, D=distance, T= time.

Given that,

The distance = 125 feet.

The time taken to cover the distance = 5 seconds.

To find the unit rate.

Apply formula,

speed = distance / time

          = 125 / 5

          = 25 feet / second

The required speed is 25 feet / second.

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Answer:

46 students

Step-by-step explanation:

20 female prefers dogs + 26 female prefer cats + 6 female no preference = 46 female total.

The two variables involved in the graph are: input variable (x - value) and output variable (y- value)

We know that many types of problems require  two variables at the same time. such relation can be described algebraically by a two variable function or equation.

To represent such function graphically we use two perpendicular lines called axes and their point of intersection is called as the origin. This method of representation is known as the Cartesian coordinate system. The numerical value of one variable is measured along the horizontal axis called the x axis. Whereas the numerical value of the other variable is measured along the vertical axis called the y axis.

The four sections formed due to these axex are called quadrants.

Therefore, the two variables involved in the graph are input variable which  measured along x-axis and output variable which  measured along y-axis.

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The solution of the equation is ( x - 5 )² +23 = 0.

Completing the square entails writing a quadratic in the form of a squared bracket and, if necessary, adding a constant.

Mathematical symbols can represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping, as well as the order of operations and other features of logical syntax.

Given that the equation is x²-10x = 3. The equation will be solved by completing the square method as below,

x²-10x = 3

x² - 10x - 3 = 0

( x - 5 )² - 3 + 5² = 0

( x - 5 )² - 3 + 25 = 0

( x - 5 )² + 23 = 0

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Triangle congruence: If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create an identical appearance. They are in alignment with one another when moved. "≅" is the congruence symbol.

There are a few rules that check congruency of 2 distinct triangles  are:

1.Side-Angle-Side (SAS) Rule

 The triangles are congruent if the two sides and included angle of one     triangle equal the two sides and included angle of another triangle.

2. Angle-Side-Angle (ASA) Rule

  The triangles are congruent if two angles and the included side of one triangle equal two angles and the included side of another triangle.

and some other but these are the conditions that prove congruency of any traingle

Two triangles are similar if :

There are a few rules that check similarity of 2 distinct triangles  are:

1.Side-Angle-Side (SAS) Rule

  Two triangles are similar if they have two pairs of sides that are in the same ratio and if the included angles are likewise equal.

2. Side - Side -Side (SSS) Rule

    Two triangles are similar if they have three pairs of sides that are in the same ratio.

 and some other but these are the conditions that prove similarity of any traingle

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Answer:

The number of unit cubes are 6, its volume is 6 cu cm.

Step-by-step explanation:

The formula for the volume of a prism is V=Bh , where B is the base area and h is the height.

The area is the region defined by an object's form. The area of a form is the space covered by a figure or any two-dimensional geometric shape in a plane. The quantity area indicates the extent of a region on a planar or curved surface. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas area of a plane region or plane area refers to the area of a form or planar lamina.

Here,

V=b*h

b=base area of prism

h=height of prism

The volume of a prism is calculated as V=Bh, where B is the base area and h is the height.

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The probability that all symbols are different is  0.45 and the probability that all all symbols are different and the first number is the largest among the numbers is 0.11.

There are three places for alphabets, which can be filled by any one of the 26 letters. So the total possible ways of selecting 3 letters is 26³.

There are four places for alphabets, which can be filled by any one of the 10 digits. So the total possible ways of selecting 4 numbers is [tex]10^{4}[/tex].

So, the total possible ways of selecting 3 alphabets and 4 numbers for license plates is 26³ × [tex]10^{4}[/tex] = 175760000.

(a) The probability that all symbols are different.

The three letters can be selected in 26! ways = 26 × 25 × 24 = 15600

Similarly, the four numbers can be selected in 10! ways = 10 × 9 × 8 × 7 = 5040

Therefore, the probability that all symbols are different is

= 15600 × 5040 / 175760000

= 0.45 approximately

(b) The probability that all symbols are different and the first number is the largest among the numbers.

The probability that first number is largest among the numbers is = 3!/4! = 1/4

The probability that all symbols are different is  0.45 approximately

Therefore, the required probability is

= 1/4 of 0.45

= 0.11 approximately.

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 Two shapes are congruent if they have the same shape and size. We can also say if two shapes are congruent, then the mirror image of one shape is the same as the other.

  Geometric figures that are congruent share the same size and shape. In other words, figures are congruent if they can be transformed into one another through a series of transformations, rotations, and/or reflections. When the sides and angles of two triangles match, the triangles are said to be congruent. 

Triangles that have comparable sides and equal angles are said to be congruent. Indicating congruence is the sign “≅”.

identical in size and shape.  

Congruent refers to objects that are exactly the same size and shape. Even if we flip, turn, or revolve the shapes, the shape and size must remain the same.

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Answer:

look the photo

The ordered pair of D is(2,6) by the given graph co-ordinates.

What is ordered pair?

By the given graph Point D has x-axis as 2 and y axis as 6.

Hence, the ordered pair is (2,6) by the given graph co-ordinates.

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Answer:

£29

Step-by-step explanation:

20% = 0.2

Take 145 times 0.2 = £29

So, he saves £29

A discrete random variable may take on only a countable number of distinct values such as 0,1,2,3,4,...

Definition of discrete random variable-Discrete random variables are usually (but not necessarily) counts. If a random variable can take only a finite number of distinct values, then it must be discrete. Examples of discrete random variables include the number of children in a family, the Friday night attendance at a cinema, the number of patients in a doctor's surgery, and the number of defective light bulbs in a box of ten.

Explanation-The probability distribution of a discrete random variable is a list of probabilities associated with each of its possible values. It is also sometimes called the probability function or the probability mass function.

Example:-

The cumulative distribution function for the above probability distribution is calculated as follows:

The probability that  is less than or equal to is 0.1,

the probability that  is less than or equal to 2 is 0.1+0.3 = 0.4,

the probability that  is less than or equal to 3 is 0.1+0.3+0.4 = 0.8, and

the probability that  is less than or equal to 4 is 0.1+0.3+0.4+0.2 = 1.

So, finally we can conclude that discrete random variables can only take  a finite number of values.

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To translate a triangle with coordinates, you need to add the same value to each of the x and y coordinates of each vertex of the triangle. This will shift the triangle in the desired direction.

To translate a triangle with coordinates, you need to add the same value to each of the x and y coordinates of each vertex of the triangle. For example, if you wanted to translate the triangle with coordinates (1,2), (3,4), and (5,6) by two units to the right and two units up, you would add two to each x-coordinate and two to each y-coordinate. The new triangle would have coordinates (3,4), (5,6), and (7, 8).

1. Identify the coordinates for the triangle: (1,2), (3,4), and (5,6).

2. Decide how much you want to translate the triangle: two units to the right and two units up.

3. Add two to each x-coordinate and two to each y-coordinate: (3,4), (5,6), and (7,8).

4. The triangle is now translated two units to the right and two units up.

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Based on the Hypotenuse-Length Theorem of Congruence (HL), the values of x and y that will make both right triangles congruent are:

x = 8

y = 4

Two right triangles are congruent to each other by the Hypotenuse-Length Congruence Theorem (HL) if the hypotenuse length and one leg of a right triangle is congruent to the hypotenuse length and leg of the other right triangle.

Thus, for both right triangles to be congruent, it means that their hypotenuse and one of their corresponding legs must be equal to each other.

Use this to create two equations and solve to get the value of x and y.

Equal Hypotenuse:

(eqn. 1)

Equal legs:

(eqn. 2).

Find the value of y, by substituting x = (y + 4) into eqn. 1.

(eqn. 1)

Substitute

Find the value of x, by substituting y = 4 into eqn. 2.

X=y+4

X=4+4

X=8

Therefore, based on the Hypotenuse-Length Theorem of Congruence (HL), the values of x and y that will make both right triangles congruent are:

x = 8

y = 4

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The slope of an angle 30 which in the positive x direction is tanФ = tan30= 1/√3

Slope:

Slope describes the steepness of a line and it also remains constant with the line it also gives us information about the direction. If the slop is negative then the line will be in the negative x-axis if the slop is positive the line will be in the positive x-direction.

A slope of a line is the change in the y coordinate w.r.t the change in the x coordinate.

m = Δy/Δx

m=tan θ = Δy/Δx

m=tan 30 = 1/[tex]\sqrt{3}[/tex]

Therefore the slope of a line that makes an angle of 30 with the positive x direction will be 1/√3

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Z-score of the manufacturer's claim is 0.25.

It is a statistical expression that refers the difference between observed value and standard deviation.

we calculate the Z-score from the following equation.

Z-score= X-μ/σ

           (Observed value- mean value)/standard deviation

as per the question= (manufacturer's claim - sample mean)/standard deviation

                               (1500-1480)/80=0.25

hence, Z-score is 0.25

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Z-score of the manufacturer's claim is 0.25.

It refers to the difference between the observed value and standard deviation and is a statistical statement.

The standard score, also known as a z-score, is a highly helpful statistic since it lets us compare scores from different normal distributions and assess the likelihood that a given score will fall within our normal distribution.

The 90th percentile's z-score is 1.2816, as calculated by the Percentile to Z-Score Calculator. Therefore, a student's z-score would be deemed "excellent" if it was greater than or equal to 1.2816.

we calculate the Z-score from the following equation.

Z-score= X-μ/σ

(Observed value- mean value)/standard deviation

as per the question= (manufacturer's claim - sample mean)/standard deviation

 (1500-1480)/80=0.25

hence, Z-score is 0.25

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Answer:

The answer is False.

Step-by-step explanation:

Check the explanation below

Answer: 470,000

My last answer for the day :)

Explanation: When rounding to the nearest ten thousand, look at the number right after it (the thousand value).

Since the number is 8, round the 6 up by one, so 7.

The slope of the line perpendicular to the given line is equal to -4/1.

The equation is in the form y=mx+b

so, y=(1/4)x -10

First, find the slope of the line which is the value being multiplied by x. Therefore m=1/4

To find the slope perpendicular to the line you must find the negative reciprocal of 1/4. (Which just means change the sign then flip the fraction)

Multiplying 1/4 by -1 which is -1/4

Then flip the fraction and keep the sign with the numerator to find the reciprocal. So now it’s -4/1

Thus, the slope of the line perpendicular to the given line is equal to -4/1.

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The equation is in the form y=mx+b

so, y=(1/4)x -10

First, find the slope of the line which is the value being multiplied by x. Therefore m=1/4

Multiplying 1/4 by -1 which is -1/4

Then flip the fraction and keep the sign with the numerator to find the reciprocal. So now it’s -4/1

Answer:

Slope: - 1/9

Equation: [tex]y=-\frac{1}{9}x +8\frac{1}{9}[/tex]

Step-by-step explanation:

[tex]\frac{y_{2}- y_{1} }{x_{2}- x_{1} }[/tex]

[tex]\frac{8-7}{1-10}[/tex]

[tex]\frac{1}{-9}[/tex]

[tex]y=-\frac{1}{9}x +b[/tex]

[tex]8=-\frac{1}{9}(1) +b[/tex]

[tex]8=-\frac{1}{9}+b[/tex]

[tex]b=8\frac{1}{9}[/tex]

[tex]y=-\frac{1}{9}x +8\frac{1}{9}[/tex]

The area of rectangular deck with length 8 feet and width 2 feet is 16 ft².

Area can be defined as the amount of space covered by a plane of a particular shape. It is measured in "number" of square units (cm², inch², ft² etc.). In other words, the space occupied around this shape is called the area of the rectangle.

We have, a rectangular deck with

length is 4 times its width and perimeter is 20ft.

Let us assume that "l" and "w" be length and width of a rectangular deck.

so, l = 4 w --(1)

Now, perimeter of rectangular deck = 2 ( l+w)

=> 2(l+w) = 20 --(2)

we have to calculate the area of rectangular deck and for this we have to calculate measure of length and width.

plug the value of "l" in equation (2) from (1)

2(l+w) = 20

=> 2(4w + w) = 20

=> 2× 5w = 20

=> w = 20/10 = 2 feet

from equation (1) , l = 4 × 2 = 8 feet

Area of rectangular deck, A = l× w

=> A = 8× 2 = 16 square feet

So, the required area is 16 square feet.

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The four Inverse operations are :

Inverse operations, such as addition and subtraction, multiplication and division, are pairs of mathematical operations where one operation reverses the effect of the other. In most cases, a number's inverse refers to its reciprocal, as in x /1 Equals 1 / x. One results from multiplying a number by its reciprocal, or inverse.

To produce a result equal to 0, add the original number and the additive inverse by simply reversing the sign of the integer. On the basis of negation of the original number, the characteristics of additive inverse are listed below. For instance, if x is the starting number, then -x is x's additive inverse.

A multiplicative inverse or reciprocal for a number x is a number that, when multiplied by x, produces the multiplicative identity, or 1. It is represented by 1/x or x/1. A fraction a/b has a multiplicative inverse of b/a. Divide 1 by the real number to obtain the multiplicative inverse of the number.

Squares are the numbers that are produced when a value is multiplied by itself. In contrast, a number's square root is a value that, when multiplied by itself, returns the original value.

The definition of a cube is the process of multiplying a number by itself three times, while a cube root is the opposite of a cube. Alternately, we may state that a number's cube root gives us a number that, when cubed, gives us the same number and is referred to as a perfect cube.

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The production possibilities using at least two data points.

In order to illustrate the proper allocation of resources, a minimum of two data points are required. The first data point represents the production of both goods at the same level, while the second data point shows the production of one good at its maximum level while the other good is at its minimum level. The two data points represent the two different production possibilities available to the economy, and they demonstrate the trade-off between the two goods.

For example, if we have an economy that can produce two goods, A and B, the PPC can be used to illustrate the different combinations of these two goods that can be produced with a given level of resources. If we assume that the economy can produce 10 units of A and 8 units of B, the first data point would be (10,8). This represents the combination of A and B that can be produced using the same level of resources. The second data point would be (10,0), which represents the maximum production of A and the minimum production of B. This data point demonstrates the trade-off between the two goods, as more of A can be produced if fewer of B are produced.

Overall, the production possibility curve is a useful tool for understanding the trade-offs that an economy has to make in order to maximize its production of goods and services. By illustrating the production possibilities using at least two data points, the proper allocation of resources can be better understood

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Answer: The answer is three. 3.

Step-by-step explanation:

Got it right on edge.

By referring to the table that summarizes service times of dinners at a fast food restaurant, we can see that there are 49 individuals who are included in the summary.

We may calculate the total number of people by simply adding the frequencies:

9 + 20 + 13 + 4 + 3 = 49 people

A measure of an event's frequency is how often it occurs within a specific time frame. For clarity, it is sometimes referred to as temporal frequency and is distinct from angular frequency. The class interval is the distance between the top and lower class bounds of a frequency distribution table. Data are discrete pieces of factual information that are logged and used for analysis. Raw data is the foundation from which statistics are derived. Statistics are the results of data analysis, including its interpretation and presentation. The outcomes of data analysis, including its interpretation and presentation, are statistics. It includes techniques for data collection, evaluation, analysis, and interpretation, is the study and manipulation of data.

Note that the full question is:

Refer to the table summarizing service times (seconds) of dinners at a fast food restaurant. How many individuals are included in the summary? Is it possible to identify the exact values of all of the original service times?

Time (sec) Frequency

60 to 119 9

120 to 179 20

180 to 239 13

240 to 299 3

300 to 359 4

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Answer:

5

Step-by-step explanation:

-5*-1 = 5

Answer: n= -1

Step-by-step explanation:

6n+8=1-n

6n+n=1-8

7n=-7

n=-1

The graph G represents the solution set for 8x + 5y ≤ 100.

What is Solution set ?

A solution set in mathematics is the collection of values that satisfy a particular set of equations or inequalities. The set of solutions to a constrained optimization problem represents the viable zone.

We have, 8x + 5y ≤ 100

Let's assume it as 8x + 5y = 100,

when x = 0,

   5y = 100

    y = 20

when y = 0,

   8x = 100

    x = 12.5

So, The line touches x-axis and y-axis at 12.5 and 20.

Now, Putting (0, 0) in  8x + 5y ≤ 100,

We get, 0 ≤ 100 which is true.

Hence, The region below the line should be the solution set for 8x + 5y ≤ 100.

So, Graph G represents the solution set for 8x + 5y ≤ 100.

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