Mateo describes g(x) = 3 * (x + 7) ^ 2 - 6 as the graph of the parent function stretched vertically and translated 7 units left and 6 units down. Complete each statement to justify Mateo's solution.

The graph is stretched vertically because ____(k,h,a) ____ (<,>) 1.
The graph is translated left because ____ (a,h,k)____(<,>)0.
The graph is translated down because ___ (K,h,a) ___(<,>)0.

Answer:

please see below

Step-by-step explanation:

(2.35-2.1)÷2.1 ×100%

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)

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 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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The value of the expression [tex]7^{-8} . 7^6[/tex] is 1/7

The value of the expression [tex]3. 3^7[/tex] is [tex]3^8[/tex].

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

A)

[tex]7^{-8} . 7^6[/tex]

= [tex]7^{-8 + 6}[/tex]

= [tex]7^{-2}[/tex]

= 1/7

B)

3. [tex]3^7[/tex]
= [tex]3^1.3^7[/tex]

= [tex]3^{1 + 7}[/tex]

= [tex]3^8[/tex]

Thus,

The value of the expression is 1/7 and [tex]3^8.[/tex]

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As shown below, the equations are written in slope - intercept form.

formula for the equation            slope - intercept

y + x = 3                                         y = -x + 3

2x + y = x + 4                                 y = -x + 4

x + y = -3                                        y = -x - 3

Those functions with exponents of 1 are known as linear functions.

The slope intercept form of the relation is presented below.

y = mx + b

the meaning of a variable

output variable = y

slope = m

input variable = x

b = intercept of y

The formula for the equation is as follows: y = mx + b.

y + x = 3

placing y at the left side of the equation

y = -x + 3

2x + y = x + 4

placing y at the left side of the equation

y = -2x + x + 4

y = -x + 4

x + y = -3

placing y at the left side of the equation

y = -x - 3

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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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The correct statement for the number of negative zeros and of positive zeros is given as follows:

The number of positive zeros is of 4, while the number of negative roots is of zero.

The number of possible positive and negative roots is obtained using Descartes' Rule.

The Descartes' Rule states that the number of positive roots is at most the number of sign changes in the sequence of polynomial's coefficients (disconsidering the zero coefficients), while the difference between these two numbers is always even.

The number of changes for this problem is given as follows:

4 changes.

The changes are given as follows:

As there are 4 changes, the number of positive roots is of 4, while the number of negative roots is of zero, as the polynomial is of the fourth degree.

The answer was given in general terms, as the statements are not presented.

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The effective interest rate of the loan would be

In this case, we are given 4 options:

The formula of compounded interest rate is:

[tex]A = P (1+\frac{r}{n})^{nt}[/tex]

Where:

A = amount, P = principal amount, r = interest rate, n = number of times interest rate compounded, t = time

Let’s assume the principal amount is $100 for 1 year

Loan L =

[tex]A = 100 (1+\frac{0.08254}{356})^{356x1}[/tex]

A = $108.603

Loan M =

[tex]A = 100 (1+\frac{0.08474}{52})^{52x1}[/tex]

A = $108.834

Loan N =

[tex]A = 100 (1+\frac{0.08533}{12})^{12x1}[/tex]

A = $108.875

Loan O =

[tex]A = 100 (1+\frac{0.08604}{1})^{1x1}[/tex]

A = $108.604

Therefore, the best effective interest rate for Craig is Loan L with nominal rate of 8.254% compounded daily.

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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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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 height that Plant A has grown taller, as regards Plant B, is D. 1 / 2 inch

The height of Plant A is 5 / 6 inches while the height of plant B is 1 / 3 inches. To find how much taller Plant A is than Plant B, you need to subtract the height of Plant B from the height of Plant A.

As these fractions have different denominators, you need to find a common denominator of the bases. This common denominator would be the least common multiple of the denominators of 3 and 6.

This least common multiple is 6. Then divide the common denominator by the denominator of the height and multiply it by the numerator to give ;

= ( 5 - 2 ) / 6

= 3 / 6 inches difference

In the simplest form, this is:

= 3 / 6

= 1 / 2 inches

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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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Answer: I can't see the question

Step-by-step explanation:

Answer:

1, 2, 5 and 10

Step-by-step explanation:

Step-by-step explanation:

1x10

2x5

4x5

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

$1.40 for each wings.

You have to divide $26.60 by 19

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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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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A- The scale factor from Polygon A to Polygon B is 2.

B- The missing length of each side marked with ? in Polygon B is 3, 5

C- The measure of each angle marked with ? in Polygon A is 53°, 82°

Given that,

A- scale factor = side A/ side B = 5 / 2.5 = 2

B- Length of each missing sides= 1.5*2 = 3 and 2.5* 2 = 5

C- Since the scale factor does not change the measure of the angles, the missing angles remain the same that is 53° and 82°

Thus,

The scale factor from Polygon A to Polygon B is 2.

The missing length of each side marked with ? in Polygon B is 3, 5

The measure of each angle marked with ? in Polygon A is 53°, 82°

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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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As per the given displacement value, the value of GG1 is 0.055

The term displacement is defined as the length of shortest distance from initial position to final position of the object.

Here we have given that  a hip of 15,000 Ton displacement when a weight of 55 ton mass i removed from the starboard side through a distance of 15 meter.

Here we know that the following values are given in it.

They are listed as follows:

Total displacement = 15,000 ton

Mass = 55 ton

Distance = 15 meter.

Then the value of GG1 is calculated as,

=> (15 x 55)/15,000

=> 0.055

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The difference in population of 20-24 year old between California and Montana is 148 thousand        

What  major reason for the population difference ?

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Answer:

The answer is attached to this response below.

So, the correct answer is (d) 150 mi.

To find out how far Greg drove, you need to multiply the speed of his car (50 mph) by the amount of time he spent driving (212 hours).

Speed = Distance/Time

Distance = Speed * Time

Distance = 50 * 212

Distance = 10600 miles

So, Greg drove 10600 miles.

It's important to note that the question is asking for the answer in miles and not kilometers.

To convert meters to miles, you can use the conversion factor 1 mile = 1609.344 meters.

To convert a measurement in meters to miles, you can multiply the number of meters by the conversion factor.

For example, if you want to convert 1000 meters to miles, you would multiply 1000 by the conversion factor of 1/1609.344 which is approximately 0.000621371.

1000 meters = 0.000621371 miles

So, the correct answer is (d) 150 mi.

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Answer:

1713

Step-by-step explanation:

Just use order of operations :)

No, the equation is not a good fit because the sum of the residuals is far from zero.

Two or more expressions with an Equal sign is called as Equation.

An equation was created for the line of best fit from the actual enrollment data. which was used to predict the dance studio enrollment values shown in the table.

We need to check whether the equation that produced the predicted values represents a good line of best fit.

No, the equation is not a good fit because the sum of the residuals is far from zero.

A line of best fit is meant to compensate for positive and negative deviation in a matter that balances them. A large residual values' sum shows that they are not balanced.

Hence, No, the equation is not a good fit because the sum of the residuals is far from zero.

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The line of best fit is No, the equation is not a good fit because the sum of the residuals is far from zero.

The difference between an observed value of the response variable and the value of the response variable predicted from the regression line.

Given:

According to the given data,

A line of best fit is designed to balance positive and negative deviation by making up for it.

The residual values are not balanced when their sum is significant.

Although B is near to this answer, A is simply the better appropriate one because the residuals must be somewhat close to zero to fit with the graph and validate the result, making it not a good fit.

Hence, the equation is not a good fit because the residuals are all far from zero.

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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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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]