Find the mode of the data set.
9, 4, 2, 7, 4, 8, 12, 11, 7, 13, 1, 4, 8, 6, 9, 7

Answer:

C.  f(x) = (x - 3)² + 4

Step-by-step explanation:

Given parent function:

[tex]f(x)=x^2[/tex]

When a graph is translated "a" units right, subtract "a" from the x-value of the function.

Therefore, the translation of the parent function 3 units right is:

[tex]\implies f(x-3)=(x-3)^2[/tex]

When a graph is translated "a" units up, add "a" to the function.

Therefore, the translation of the function 4 units up is:

[tex]\implies f(x-3)+4=(x-3)^2+4[/tex]

Considering the expression of a line, the equation of the line that passes through the points (-6,1) and (6,7) is y=1/2x +4.

A linear equation o line can be expressed in the form y = mx + b

where

Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope can be calculated using:

m= (y₂ - y₁)÷ (x₂ - x₁)

Substituting the value of the slope and the value of one of the points in y= mx + b, the value of the ordinate to the origin b can be calculated.

In this case, being (x₁, y₁)= (-6, 1) and (x₂, y₂)= (6,7), the slope can be calculated as:

m= (7 -1)÷ (6 -(-6))

m= (7 -1)÷ (6 +6)

m= 6÷ 12

m= 1/2

Considering point 2 and the slope m, you obtain:

7= 1/2×6 + b

7= 3 +b

7 -3= b

4= b

Finally, the equation of the line is y=1/2x +4.

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The measure of the larger angle is obtained as follows:

70º

Two angles are defined as complementary is the sum of their measures is of 90º.

The variables that represent each angle in this problem are given as follows:

x and y.

They are complementary angles, hence:

x + y = 90.

The difference between four times the measure of the smaller angle and the measure of the larger angle is 10, hence:

4y - x = 10.

x = 4y - 10.

Hence the value of y is obtained as follows:

4y - 10 + y = 90

5y = 100

y = 100/5

y = 20º.

Hence the measure of the larger angle is given as follows:

x + 20 = 90

x = 70º.

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Answer:

please see below

Step-by-step explanation:

(2.35-2.1)÷2.1 ×100%

The answer is point C is further from point A than point B

A Cartesian coordinate system in a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates,

Given here: The points A(-5,8) ,  B(1,0) C(-10,16)

length of AB= [tex]\sqrt{(-5-1)^2+(8-1)^2}[/tex]

                   =9.22 units

Similarly length of AC= [tex]\sqrt{(-5+10)^2+(8-16)^2}[/tex]

                                   = 9.433 units

Hence, point C is further from point A than point B

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An inequality is defined as an unfair comparison between two numbers or other mathematical expressions. When comparing the sizes of two numbers on a number line, it is most commonly used. The graph for each inequality or equation is included in the attachment.

A graph is a visual representation of statistical data or a functional relationship between variables. Graphs are useful for forecasting because they can highlight broad trends in the quantitative behaviour of data. However, as mere approximations, they can be inaccurate and occasionally deceptive.

Most graphs have two axes: one for a set of independent variables and one for a set of dependent variables. The most common type of graph is a broken-line graph, with time serving as the independent variable.

16. 2y – 4x < 8

=  2y < 4x + 8

= y < 2x + 4

17. -4y > -x + 12

= y > x/4 + -3

18. | x + 3 |= y

y = | x + 3 |

19.  |2x – 6| + 2 = y

y = |2x – 6| + 2

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Answer:

[tex]\mathrm{Factoring}\:4x^3-15x^2-31x+30:\quad \boxed{\left(x+2\right)\left(4x-3\right)\left(x-5\right)}[/tex]

Step-by-step explanation:

This is a particularly tough question. It involves polynomial division(a real laborious process) and solving using quadratic formula.

I presume your school has provided you the resources for both.

Anyways, here goes a brief explanation

To find the roots(zeros) of a polynomial, [tex]f(x)[/tex] , set [tex]f(x) = 0[/tex]  and solve for values of [tex]x[/tex]

In general, if [tex]a[/tex] is a zero of [tex]f(x)[/tex], then [tex]f(x) \div(x-a)[/tex]  will leave no remainder. In other words, it is a factor of the polynomial. It also means [tex]x - a = 0[/tex]

The given polynomial is  [tex]4 x^{3} - 15 x^{2} - 31 x + 30[/tex]

We are given that [tex]- 2[/tex]  is a zero of [tex]f(x)[/tex]. This simply means that [tex]f(-2) = 0[/tex]

Plugging [tex]-2[/tex] into the function gives

[tex]f(-2) = 4(-2)^3 -15(-2)^2 - 31x + 30\\\\ = 0 =4\left(-8\right)-15\cdot \:4-31\left(-2\right)+30[/tex]

Which indeed is 0

Here [tex]a = -2[/tex] , so [tex]x - (-2)[/tex] which is [tex]x + 2[/tex] is a factor of[tex]f(x)[/tex]. It also means that
[tex]x-(-2) = 0 \;or\; x + 2 = 0[/tex]

Steps to factor the polynomial [tex]4 x^{3} - 15 x^{2} - 31 x + 30[/tex] :

Multiplying both sides of the above by [tex]4[/tex] gives [tex]4x -3 = 0.[/tex] So [tex]4x-3[/tex] is the third factor, replacing [tex]x - \dfrac{3}{4}[/tex]

The factors of [tex]4 x^{3} - 15 x^{2} - 31 x + 30[/tex]
are:

[tex]x+2, x-5 \;and \;4x-3[/tex]

Answer:
[tex]\mathrm{Factor}\:4x^3-15x^2-31x+30:\quad \boxed{\left(x+2\right)\left(4x-3\right)\left(x-5\right)}[/tex]

Use a polynomial division calculator which you can find on the web and a quadratic formula calculator (on the we or on your own calculator)

Answer:

3x+7

Step-by-step explanation:

You need to combine like terms. Add 2x + x. It is 3x add the six and the one to make seven \

Hope this helps

Answer:

3x+7

Step-by-step explanation:

First, you want to group the variables, which in this case, is x. You take the 2x and x and make it 3x.

3x+1+6

Now that you have this done, you want to group the numbers, by making the 1+6 to 7.

3x+7

This is your answer, 3x+7.

The value of the expression 2/5 + 5./5 is 7/5.

A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.

Example: 1/2, 1/3 is a fraction.

We have,

2/5 + 5/5

= 2/5 + 1

= (2 + 5) / 5

= 7/5

Thus,

The value is 7/5.

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[tex]x^2-2px+2p^2 \\ \\ =(x^2-2px+p^2)+p^2 \\ \\ =(x-p)^2+p^2[/tex]

Assuming [tex]p \in \mathbb{R}[/tex], [tex](x-p)^2 \geq 0[/tex] and [tex]p^2 \geq 0[/tex], meaning that [tex](x-p)^2+p^2 =x^2-2px+2p^2 \geq 0 \forall x \in \mathbb{R}[/tex]

Particularly there is no formula for substitution just insert the given values in the equations.

One of the methods to solve a system of linear equations in two data algebraically is the substitution method. In this method, we find the value of any one of the variables by discordant it on one side and taking every other term on the other side of the equation.

This method is a simple way to resolve a system of linear equations algebraically and find the answer to the variables.

As the name suggests, it involves finding the value of the x-variable in terms of the y-variable from the first equation and then substituting or exchanging the value of the x-variable in the second equation.

The substitution method is one of the algebraic methods to solve coincident linear equations. It concludes by substituting the value of any one of the variables from one equation into the other equation.

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The approximate side length of the square game board is 13 inches.

A square is a two-dimensional figure that has four sides and all four sides are equal.

The area of a square is side².

We have,

Area of a square game board = Side².

Area of the square = 162 inches²

Now,

Side² = 162 inches²

Side = √162 inches

Side = 12.73 inches

Side = 13 inches

Thus,

The side length of the square game board is 13 inches.

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Answer: I can't see the question

Step-by-step explanation:

The International System of Units (SI) units, the British Imperial System, and the US Customary System are the three common systems of measurement.

Measurement systems that are metric.

American National Standards Institute:

Different Metric Systems of Measurement:

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Answer:

The French system, British system and the Metric system.

Step-by-step explanation:

C.G.S. system (or French system): In this system, the unit of length is centimeter (cm), unit of mass is gramme (g) and unit of time is second (s).

F.P.S. system (or British system): In this system, the unit of length is foot (ft), unit of mass is pound (lb) and unit of time is second (s).

M.K.S. system (or Metric system): In this system, the unit of length is meter (m), unit of mass is kilogram (kg) and unit of time is second (s).

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The formula for a triangular method is: (x1 + x2 + x3) / 3

1. The triangular method is the average of three different values: x1, x2, and x3.

2. To calculate the average, add the three values together and divide by three.

3. The formula for a triangular method is therefore (x1 + x2 + x3) / 3.

The triangular method is a method used to calculate an average of three different values. This method is most useful when there is not enough information available to calculate a more accurate average. To calculate an average using the triangular method, the three values (x1, x2, and x3) are added together and then divided by three. The formula for a triangular method is (x1 + x2 + x3) / 3. This method is useful for finding an average when a more accurate average cannot be calculated due to a lack of data. It is also used when data points are not necessarily related, as the triangular method is less affected by outliers than other methods of calculating an average. The triangular method is a quick and easy way to find an average when more complex calculations are not possible.

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Therefore , the solution of  given trigonometric equation has been proved.

A trigonometric equation is one that contains one or more ratios of unknown trigonometric angles. The ratios of sine, cosine, tangent, cotangent, secant, and cosecant angles are used to express it. A trigonometric equation is cos2 x + 5 sin x = 0, for instance.

Here,

Given :

Cosec A cosec²A cot A+ cot² A

LHS=(1+cot2A)2- (1 + cot2 A)

=1+2cot2A+cot A-1- cot2 A

= cot2A+ cot1A

= RHS

Hence, Cosec1A- cosec² A = cot ⁴A-cot ²A

Therefore , the solution of  given trigonometric equation  comes out to be it has been proved

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Answer:

Step-by-step explanation:

A and C will both work. 4 goes into 56 evenly and so does 7.

The total of the equation 5 wholes and 2/3 x 3/4 is 4 1/4

The total of the equation is found by multiplication of fractions.

Fractions are system of numbers used to represent a number in forms which has two basic parts

The fraction required are:

5 wholes and 2/3 = 5 2/3

3/4

The multiplication

= 5 2/3 * 3/4

The first step is  done by converting the mixed number to improper fraction = = 5 2/3  = 17/3

= 17/3 * 3/4

= 17/4

17/4 is an improper fraction and 4 1/4 as a mixed number

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Therefore , the solution of the given problem of unitary method comes out to be 3.5.

One can utilize the unit strategy to solve a problem by first multiplying the value of one unit by the quantity of units required. The unit function, to put it simply, is used to separate a single entity amount from just a given many. 400 pence, or the equivalent of one pen, would buy 40 needles. There might be a common approach to determining this. only one country. Anything has a distinguishing feature. Matrix logic, algebra, and its interpellation & inverse are all comparable terms.

Here,

Given : Josh gathered 2 pounds of plastic while cleaning up the park.

Josh received 1 ¾  times as much money from Sherri.

thus ,

To find the total plastic collected by both of them:

=>  1 ¾ * 2 + 2

=> 7/4 * 2

=> 14/4

=> 7/2

=>3.5

Therefore , the solution of the given problem of unitary method comes out to be 3.5.

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Yes, y² = 5y - 10 is a quadratic equation.

In algebra, a quadratic equation is that which can be rearranged in standard form as

ax² + bx + c = 0,

where x is an unknown value, and a, b, and c are known numbers, where a ≠ 0. (If a = 0 and b ≠ 0 then the equation is linear). Quadratic equations are the polynomial equations of degree 2 in one variable of type f(x) = ax² + bx + c = 0 where a, b, c, ∈ R and a ≠ 0.

We have the equation

y² = 5y - 10

y² - 5y + 10 = 0

The highest degree of this equation is 2, therefore it is a quadratic equation.

-- The given question is incorrect, the correct form of equation is

"Is y² = 5y - 10 a quadratic equation justify?" --

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The area occupied by the garden is 185 square feet.

Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a shape on paper is the area that it occupies.

Given:

Base = 10 feet, height = 8 feet

First, Area of Garden without patio

= 15 x 15

= 225 square feet.

Now, The patio is in the shape of a triangle which has a height of 8 feet and a base length of 10 feet.

So, Area of triangular patio

= 0.5 x 8 x 10

= 0.5 x 80

= 40 square feet.

Then, Actual Area of garden

= area of garden without patio - area of patio

= 225 square feet - 40 square feet

= 185 square feet.

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The solution is the set of all points (x,y) that satisfy the inequalities:

y < 2x + 4,  y < x/4 - 3, x + 3 = y, and 2x - 6 + 2 = y.

What is the graph of a function?

The graph of a function is a visual representation of the relationship between the input values (x-coordinates) and the output values (y-coordinates) of the function. In other words, it is a visual representation of the function's rule.

The graph of a function can take many different forms, depending on the function's rule. Linear functions, for example, will produce a straight line on the graph.

i) 2y - 4x < 8 can be solved by adding 4x to both sides and then dividing by 2, giving:

y < 2x + 4.

ii) -4y > -x + 12 can be solved by adding x to both sides and then dividing by -4, giving: y < x/4 - 3.

iii) | x + 3 | = y, you can split this into two cases:

i. x + 3 = y

ii. -(x + 3) = y

iv) |2x – 6| + 2 = y, you can split this into two cases:

i. 2x - 6 + 2 = y

ii. -(2x - 6) + 2 = y

We can use these equations to plot the graph on a coordinate plane.

Hence, the solution is the set of all points (x,y) that satisfy the inequalities:

y < 2x + 4,  y < x/4 - 3, x + 3 = y, and 2x - 6 + 2 = y.

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Answer:

1, 2, 5 and 10

Step-by-step explanation:

Step-by-step explanation:

1x10

2x5

4x5

.................

Answer:

Step-by-step explanation:

The expressions that are equivalent to 4/9 x 7 are 28/9,  3¹/₉ and 3.11

As no options are included, I will include the expression that is equivalent to 4/9 x 7 in both fractions and decimal.

In fractions:

= 4/9 x 7

= 28/9

or,

= 3¹/₉

In decimals:

= 4/9 x 7

= 28/9

= 28 ÷ 9

= 3.11

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Based on the information provided, the area in Nina's garden is 0.26 square meters.

The word area refers to the space occupied by a surface, in this case, the space of the garden. In a rectangle, this area can be calculated with the following formula,  although for other shapes the formula might be different:

area = length x width

To make this process easier, let's convert the fractions into regular numbers

4 1/5 = 4.2 (1/5 = 0.2)

3/10 = 0.3

4.2 x 0.3 = 1.26 square meters

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Answer:

[tex]1386 in^2[/tex]

r: radius

Circumference:  [tex]2\pi r[/tex]

Area: [tex]\pi r^2\\[/tex]

In this case, we are using 22/7 as an estimation for pi.

Plug into the area formula.

22/7 * (21)^2

22/7 * 441

[tex]1386 in^2[/tex]

Answer:

its the second one: -5<x<2

Step-by-step explanation:

I did out the math