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.
Answers
The graph is stretched vertically because a > 1, translated left because h > 0, and translated down because k < 0.
The graph is stretched vertically because a in the function equation
g(x) = [tex]3 * (x + 7) ^ 2 - 6[/tex]is greater than 1. In the parent function f(x) = x^2, the coefficient of 1 indicates no vertical stretch or compression. However, in g(x), the coefficient of 3 indicates that the graph is stretched vertically by a factor of 3. This means that the y-values of g(x) are three times greater than the corresponding y-values of the parent function.
The graph is translated left because h in the function equation
g(x) =[tex]3 * (x + 7) ^ 2 - 6[/tex] is greater than 0. The term (x + 7) in g(x) indicates a horizontal shift of the graph. By substituting x = -7, we can see that the vertex of the parabola is now located at x = -7 instead of the origin (0,0). This leftward shift of 7 units corresponds to the translation of the graph.
The graph is translated down because k in the function equation
g(x) = [tex]3 * (x + 7) ^ 2 - 6[/tex]is less than 0. The term -6 in g(x) indicates a vertical shift of the graph. The negative value of 6 means that the graph is shifted downward by 6 units compared to the parent function.
In summary, Mateo's description of the graph g(x) =[tex]3 * (x + 7) ^ 2 - 6[/tex]as the parent function stretched vertically by a factor of 3, translated 7 units left, and 6 units down is justified based on the analysis of the function equation.
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Related Questions
HELPPPP PLEAAAASE I HAVE NO IDEA WHAT IM SUPPOSED TO DOOOOO
Answers
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] :
Divide [tex]4 x^{3} - 15 x^{2} - 31 x + 30[/tex] by [tex]x+2[/tex][tex]\dfrac{4 x^{3} - 15 x^{2} - 31 x + 30}{x + 2} = 4x^2-23x\:+\:15[/tex]The quotient is a quadratic equation which can be solved using the quadratic formula available in most scientific calculators
The roots of this quadratic equation are
[tex]x=5,\:x=\dfrac{3}{4}[/tex]
This means [tex]x - 5[/tex] is one factor and
[tex]x - \dfrac{3}{4}[/tex]
is another factor
Since [tex]\dfrac{3}{4}[/tex] is a zero, [tex]x - \dfrac{3}{4} = 0[/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)
I need some help on this question please
Answers
Answer:
The answer is attached to this response below.
Help me please need asap
Answers
The difference in population of 20-24 year old between California and Montana is 148 thousand
What major reason for the population difference ?
The discovery of gold brought many prospectors into the area in the 1860s, and Montana became a territory in 1864. The rapid influx of people led to boomtowns that grew rapidly and declined just as quickly when the gold ran out.It is the fourth-largest state by area, the eighth-least populous state, and the third-least densely populated state. Its state capital is Helena, while the largest city is BillingsThe state rightfully earned its motto, "oro y plata," spanish for "gold and silver." The Treasure State is known for its abundant natural and mineral resources, including coal, copper, gold, manganese, sapphire, silver, lead, oil and zinche airport's direct flights to San Francisco, Los Angeles, and Long Beach contributed to the ease of California residents moving to the greater Bozeman area. It's no surprise why so many people want to live in Montana. “It's the access to recreation,” Bozeman real estate Broker Christy Delger said to the Chronicle.To learn more about population refers to:
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Greg drives at 50 mph for 212 hours. how far did he drive? responsesa. 20 mi b. 75 mi c. 125 mi d. 150 mi
Answers
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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What are the factors of 10m?
Answers
Answer:
1, 2, 5 and 10
Step-by-step explanation:
Step-by-step explanation:
1x10
2x5
4x5
.................
Craig is considering four loans. loan l has a nominal rate of 8.254%, compounded daily. loan m has a nominal rate of 8.474%, compounded weekly. loan n has a nominal rate of 8.533%, compounded monthly. loan o has a nominal rate of 8.604%, compounded yearly. which of these loans will offer craig the best effective interest rate? a. loan l b. loan m c. loan n d. loan o please select the best answer from the choices provided a b c d
Answers
The effective interest rate of the loan would be
In this case, we are given 4 options:
Loan L has a nominal rate of 8.254% compounded dailyLoan M has a nominal rate of 8.474% compounded weeklyLoan N has a nominal rate of 8.533% compounded monthlyLoan O has a nominal rate of 8.604% compounded yearlyThe 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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I need help with this problem number 6
Answers
Answer: I can't see the question
Step-by-step explanation:
What is substitution method formula?
Answers
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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1. Find the GG1 of a hip of 15,000 Tonne diplacement when a weight of 55 tonne ma i removed from the tarboard ide through a ditance of 15 meter
Answers
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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Consider the polynomial function
f(x)=x^4-2x^3+11x^2-5x+6
Which statement correctly describes the number of possible positive zeros and the number of possible negative zeros?
Answers
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.
How to obtain the number of positive and negative roots?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:
x^4 to x^3.x^3 to x^2.x^2 to x.x to constant.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.
Missing InformationThe answer was given in general terms, as the statements are not presented.
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Question content area top
Part 1
Find the approximate side length of a square game board with an area of 162 in2.
Answers
The approximate side length of the square game board is 13 inches.
What is a square?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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An equation was created for the line of best fit from the actual enrollment data. It was used to predict the dance studio enrollment values shown in the table below:
Analyze the data. Determine 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 residuals are all far from zero.
No, the equation is not a good fit because the sum of the residuals is a large number.
Yes, the equation is a good fit because the residuals are not all far from zero.
Yes, the equation is a good fit because the sum of the residuals is a small number.
Answers
No, the equation is not a good fit because the sum of the residuals is far from zero.
What is Equation?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.
What is Residual?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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i forgot how to it can i please get some help2x+1 + x+6=
Answers
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.
Simplify the following expressions. Type out and label your answers for A and B.
Answers
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].
What is an expression?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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I’m The coordinate plane point A has coordinates of A(-5,8). Which is further from A, point B or point C given that they have the coordinates of B(1,0) and C(-10,16)
Answers
The answer is point C is further from point A than point B
what is the Cartesian co-ordinate system?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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A garden in the shape of a square measures 15 feet on each side. A triangular paved patio is in the center.
Answers
The area occupied by the garden is 185 square feet.
What is Area?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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PLSSS HELP IF YOU TURLY KNOW THISS
Answers
A, B, C, or D
please don't lie
picture attached
Answers
The height that Plant A has grown taller, as regards Plant B, is D. 1 / 2 inch
How to find the height difference ?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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Subtract: (1282 - 95 + 15) - (- 482 - 35 + 6)
Answers
Answer:
1713
Step-by-step explanation:
Just use order of operations :)
Record each of the equations in slope intercept form ( y=Mx+b)
Answers
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
What is linear equation?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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Chase bought 19 chicken wings fir $26.60. What was the cost of wings, in dollars per wing?
Answers
$1.40 for each wings.
You have to divide $26.60 by 19
What is an equation that passes through the points (-6,1) and (6,7)
Answers
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.
What is a linear equationA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin.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.
Equation in this caseIn 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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Pleae anwer quick! im being timed!!!!!!! Polygon B i a caled copy of Polygon A. What i the cale factor from Polygon A to Polygon B? Explain your reaoning. Find the miing length of each ide marked with ? in Polygon B. Determine the meaure of each angle marked with ? in Polygon A
Answers
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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2\5+5\5 = 8\5 9\5 7\5 help
Answers
The value of the expression 2/5 + 5./5 is 7/5.
What is a fraction?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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Find the area of a circle with a radius of 21 inches. Use
area: about
in.
22/7
for π.
Answers
Answer:
[tex]1386 in^2[/tex]
Circle Formulasr: 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.
Q)Plug into the area formula.
22/7 * (21)^2
22/7 * 441
[tex]1386 in^2[/tex]
What is the total of the equation : 5 wholes and 2/3 x 3/4?
Answers
The total of the equation 5 wholes and 2/3 x 3/4 is 4 1/4
How to find the total of the equationThe 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 numerator The denominatorThe 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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The price of a cup of coffee was $2.10 yesterday. Today, the price rose to $2.35. Find the percentage increase. Round your answer
to the nearest tenth of a percent.
Answers
Answer:
please see below
Step-by-step explanation:
(2.35-2.1)÷2.1 ×100%
A box contains lemon and banana, if there are 13 bananas in the box and the probability of selecting 2 bananas from the box is 1/10, then find the number of lemons in the box?
Answers
1560=x^2 +25x + 156
Solutions are x=27 and x=-52
You can’t have negative lemons so
The answer is 27 lemons
What are the 3 unit systems?
Answers
The International System of Units (SI) units, the British Imperial System, and the US Customary System are the three common systems of measurement.
Define 3 unit systems of measurements?Associating numbers with physical quantities and phenomena is referred to as a system of measurement. Measurement systems are groups of units of measurement and the rules that link them.Measurement systems that are metric.
The metric system uses three primary units: meters to measure length, kilograms to measure mass, and seconds to measure time.The unit of measurement for length is the meter. The letter (m) serves as the unit's designation. View the graph below. By successively multiplying by 10, we add "Deca," "Hecto," and "Kilo" to the base unit of "m" to measure large units.American National Standards Institute:
The US uses the imperial system of units, also known as the U, just like the metrics system. standard units of S. Things are measured in this place in feet, inches, pounds, ounces, and so on. In the sections that follow, let's examine them in more detail.Different Metric Systems of Measurement:
Although we are aware of the fundamentally defined metric systems for length, mass, and volume, there are many other physical quantities for which we need to define the base unit. Using the fundamental 7 quantities of the metric system of measurement as a starting point, units for quantities like force, power, area, and magnetic intensity were developed.To know more about the unit systems, here
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Answer:
The French system, British system and the Metric system.
Step-by-step explanation:
Three systems of unit and their fundamental units: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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What is the formula of a triangular method?
Answers
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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