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Given the recursive formula for a geometric sequence find the common ratio, the first five terms, the term named in the problem, and the explicit formula.
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Find f(9)

11) f(n) = f(n - 1) x 4
f(1) = 4

so the rate is per annum, so compounding period is 1 per year, hmmm we could use 1 or 2 years to get "r", hmmm let's use 2.

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \pounds 5903.13\\ P=\textit{original amount deposited}\dotfill &\pounds 5500\\ r=rate\to r\%\to \frac{r}{100}\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{per annum, thus once} \end{array}\dotfill &1\\ t=years\dotfill &2 \end{cases}[/tex]

[tex]5903.13 = 5500\left(1+\frac{\frac{r}{100}}{1}\right)^{1\cdot 2} \implies \cfrac{5903.13}{5500}=\left( 1+\cfrac{r}{100} \right)^2 \\\\\\ \sqrt{\cfrac{5903.13}{5500}}=\cfrac{100+r}{100}\implies 100\sqrt{\cfrac{5903.13}{5500}}=100+r \\\\\\ 100\sqrt{\cfrac{5903.13}{5500}}-100=r\implies \stackrel{ \% ~ ~~ ~ }{\boxed{3.6\approx r}}[/tex]

Answer:

20.5 in.

Step-by-step explanation:

Just divide 82 by 4 to get the answer since  1 inch equals to 4 feet.

Answer:

The quotient of 5984 divided by 32 is 187.5

Step-by-step explanation:

Answer:

The quotient of 5984 divided by 32 is 187.

When ff. is written it refers to the page or line mentioned and two or more pages or lines after it or a set of numbers as a function.

What is set?

A set is a clearly defined group of things in mathematics. Set names and symbols begin with a capital letter.

According to set theory, a set's constituent parts can be anything, including humans, alphabetic letters, numbers, shapes, variables, etc.

The types of set are:

Empty Set or Null set: It has no element present in it.Example: A = {} is a null set.

Finite Set: It has a limited number of elements.Example: A = {1,2,3,4}

Infinite Set: It has an infinite number of elements.Example: A = {x: x is the set of all whole numbers}

Equal Set: Two sets that have the same members.Example: A = {1,2,5} and B={2,5,1}: Set A = Set B

Subsets: A set ‘A’ is said to be a subset of B if each element of A is also an element of B.Example: A={1,2}, B={1,2,3,4}, then A ⊆ B

Universal Set: A set that consists of all elements of other sets present in a Venn diagram.Example: A={1,2}, B={2,3}, The universal set here will be, U = {1, 2,3}

Hence, ff(x) means that you have to replace x with f(x) in f(x).

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Answer:

the answer is A

So basically it's simple just use some scientific calculator and put the number one by one with the bracket because there's a rule of mathematics which we call BODMAS

It appears that Nolan has met the conditions for constructing a confidence interval for the mean birth weight in Somalia. However, he should also check the skewness and presence of outliers in the sample to ensure that the normal approximation is appropriate.

In other words, data with a lower bound are frequently skewed right, and data with an upper bound are typically biased left.

Start-up effects can also cause skewness.

To construct a confidence interval for the mean birth weight in Somalia, we need to ensure that the following conditions are met:

Random Sampling: Nolan used a simple random sample of 100 births, which meets the condition of random sampling.

Independence: Each birth weight in the sample should be independent of the other. This condition is met if the sample size is less than 10% of the total population of births in Somalia.

Sample size: In general, a sample size of at least 30 is recommended to use the normal distribution to approximate the sampling distribution of the sample mean. Since Nolan's sample size is 100, this condition is met.

Skewness and outliers: Nolan mentioned that the sample data was slightly skewed with a few outliers.

Therefore, all the required conditions are given above.

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Answer:

the data is a random sample from the population of interest.

the sampling distribution of x is approximately normal.

individual observations can be considered independent.

Step-by-step explanation:

The area of the sign is 35 square feet. The solution has been obtained by using the area of the trapezoid.

The entire area occupied by the sides of a trapezoid is its area. A trapezoid's area is determined by how many unit squares fit inside of it.

We know that area of the trapezoid is

Area (A) = (a + b ) * h/ 2

Now, here we are given the following:

a = 8

b = 6

h = 5

Now, on substituting these values in the formula, we get

⇒A = (8 + 6 ) * 5 / 2

⇒A = (14 * 5) / 2

⇒A = 70 / 2

⇒A = 35 square feet

Hence, the area of the sign is 35 square feet.

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The solution to the inequality 6x + 9 ≥ −(x − 9) is x ≥ 0, and the solution set in interval notation is [0, ∞).

To solve the inequality 6x + 9 ≥ −(x − 9), we need to first distribute the negative sign on the right side of the inequality. This gives us:

6x + 9 ≥ -x + 9

Next, we need to isolate the variable on one side of the inequality. We can do this by adding x to both sides and subtracting 9 from both sides:

7x ≥ 0

Finally, we can divide both sides by 7 to solve for x:

x ≥ 0

Now, we can write the solution set in interval notation. Since x is greater than or equal to 0, the solution set is [0, ∞).

So, the solution to the inequality 6x + 9 ≥ −(x − 9) is x ≥ 0, and the solution set in interval notation is [0, ∞).

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Answer:6

Step-by-step explanation:If jayden made 5% of his free throws and he shot 120 free throws you have to find 5% of 120.

5% of 120 = 6  

So Jayden shot a total of 6 free throws during the season

Larry will need an annual rate of return of approximately 1.35% (rounded to two decimal places) to reach his goal of $3,500 in 20 years, if interest is compounded continuously.

The formula for continuous compounding is [tex]A = Pe^{rt}[/tex], where A is the amount of money at the end of the investment period, P is the initial principal, e is Euler's number (approximately 2.71828), r is the annual interest rate, and t is the time in years.

In this case, Larry has P = $3,000 and needs A = $3,500 in t = 20 years. We can solve for r by rearranging the formula:

[tex]r = ln(A/P)/(t)[/tex]

Plugging in the values, we get:

[tex]r = ln(3500/3000)/(20) = 0.0135[/tex] or 1.35%

Therefore, Larry will need an annual rate of return of approximately 1.35% (rounded to two decimal places) to reach his goal of $3,500 in 20 years, if interest is compounded continuously.

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The number of ID numbers that can be made out of 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 is 3265920.


To find the number of ID numbers that can be made, we can use the permutation formula:

P(n,r) = n! / (n-r)!

Where n is the total number of digits available and r is the number of digits in the ID number.

In this case, n = 10 (the digits 0-9) and r = 8 (the number of digits in the ID number).

Plugging these values into the formula gives us:

P(10,8) = 10! / (10-8)!

P(10,8) = 10! / 2!

P(10,8) = 3628800 / 2

P(10,8) = 1814400

However, we need to subtract the number of ID numbers that start with 0, since these would not be valid eight-digit numbers. To find this number, we can use the permutation formula again with n = 9 (the digits 1-9) and r = 7 (the remaining digits in the ID number):

P(9,7) = 9! / (9-7)!

P(9,7) = 9! / 2!

P(9,7) = 362880 / 2

P(9,7) = 181440

Subtracting this from the total number of ID numbers gives us:

3265920 - 181440 = 3084480

So the number of ID numbers that can be made out of 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 is 3084480.

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The total number of entities depicted by the given requirements is the sum of the number of students, teachers, and classrooms, which is 100 + 10 + 5 = 115. Hence, the answer is (C) 115.

What is the algebraic operation?

An algebraic expression in mathematics is an expression that is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.). Expressions are made up of terms.

The question asks us to determine the number of entities depicted by the given requirements, which include School XYZ keeping track of its 100 students, 10 teachers, and 5 classrooms.

An entity can be defined as a distinct object or concept that is represented in a system, such as a database or software application.

In this case, the entities can be identified as follows:

Students: There are 100 students in the school, and each student can be considered as a separate entity.

Teachers: There are 10 teachers in the school, and each teacher can be considered as a separate entity.

Classrooms: There are 5 classrooms in the school, and each classroom can be considered separate.

Therefore, the total number of entities depicted by the given requirements is the sum of the number of students, teachers, and classrooms, which is 100 + 10 + 5 = 115. Hence, the answer is (C) 115.

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According to the information, the ratio of taco shells and cups of chicken is 9:4.

To identify the ratio of Taco shells and cups of chicken we must take into account the information in the image. In this case we must count how many units of each element we have. So we have 9 Taco shells and 4 cups of chicken.

According to the above, the ratio would be 9:4, that is to say that for every 9 taco shells that we have, we would have to use 4 cups of chicken. Therefore, if we want to double or triple the recipe we must use the following ingredients:

Double

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The variable in the equation? x + 2 = 8 is 'x'.

An expression is a grouping of terms that have been joined together using mathematical operations such as subtraction, addition, multiplication, and division. In mathematics, the terms involved in an expression are:

We have the Equation: x+ 2 = 8.

as, we know that Equation is the combination of variables, Operation, numbers and Equal Sign,

So, the variable is x

and, Number is 8

and, Operation is +

Thus, the Variable in equation is x.

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o(a) = o(a-1) for any element a ∈ G.</p>,o(a) = o(a-1) for both the finite and infinite order cases

<p>Let G be a group and a ∈ G. To show that o(a) = o(a-1), we need to consider both the finite and infinite order cases.</p>
Finite order</p>
<p>If a has finite order, then there exists a positive integer n such that a^n = 1. We want to show that (a-1)^n = 1 as well. By the binomial theorem, we have:</p>
<p>(a-1)^n = a^n - na^(n-1) + (n(n-1)/2)a^(n-2) - ... + (-1)^n</p>
<p>Since a^n = 1, we can simplify this to:</p>
<p>(a-1)^n = 1 - na^(n-1) + (n(n-1)/2)a^(n-2) - ... + (-1)^n</p>
<p>All of the terms except for the last one are multiples of a, so they will all cancel out when we multiply by a^n. This leaves us with:</p>
<p>(a-1)^n * a^n = (-1)^n * a^n</p>
<p>Since a^n = 1, this simplifies to:</p>
<p>(a-1)^n = (-1)^n</p>
<p>If n is even, then (-1)^n = 1, so (a-1)^n = 1. If n is odd, then (-1)^n = -1, so (a-1)^n = -1. But since a-1 is an element of G, it must have an inverse, so (a-1)^n = 1. Therefore, o(a) = o(a-1) in the finite order case.</p>
Infinite order</p>
<p>If a has infinite order, then there is no positive integer n such that a^n = 1. We want to show that there is also no positive integer n such that (a-1)^n = 1. Suppose there exists such an n. Then we have:</p>
<p>(a-1)^n = 1</p>
<p>Multiplying both sides by a^n gives us:</p>
<p>(a-1)^n * a^n = a^n</p>
<p>But this is equivalent to:</p>
<p>(a^n - 1)^n = a^n</p>
<p>Since a has infinite order, a^n ≠ 1 for any positive integer n. Therefore, there is no positive integer n such that (a-1)^n = 1, so o(a) = o(a-1) in the infinite order case as well.</p>
<p>In conclusion, o(a) = o(a-1) for both the finite and infinite order cases. Therefore, o(a) = o(a-1) for any element a ∈ G.</p>

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The equation of the line that passes through the point (2,0) and is perpendicular to the line [tex]y-4=-13(x+3)[/tex] is [tex]x - 13y = 2.[/tex]

To find the equation of the line that passes through the point (2,0) and is perpendicular to the line [tex]y-4=-13(x+3)[/tex] we need to find the slope of the perpendicular line and use the point-slope form of the equation of a line.

Step 1: Find the slope of the given line.
The equation of the given line is[tex]y-4=-13(x+3)[/tex]. This is in the form [tex]y - y1 = m(x - x1)[/tex], where m is the slope of the line. Therefore, the slope of the given line is -13.

Step 2: Find the slope of the perpendicular line.
The slope of two perpendicular lines are negative reciprocals of each other. So, the slope of the perpendicular line is 1/13.

Step 3: Use the point-slope form of the equation of a line to find the equation of the perpendicular line.
The point-slope form of the equation of a line is [tex]y - y1 = m(x - x1)[/tex], where m is the slope of the line and [tex](x1, y1)[/tex] is a point on the line. Substituting the values of the slope and the point into the equation, we get:

[tex]y - 0 = (1/13)(x - 2)[/tex]
[tex]y = (1/13)x - (2/13)[/tex]

Step 4: Simplify the equation.
Multiplying both sides of the equation by 13, we get:

[tex]13y = x - 2[/tex]

Step 5: Rearrange the equation to get the standard form of the equation of a line.
The standard form of the equation of a line is Ax + By = C, where A, B, and C are constants. Rearranging the equation, we get:

[tex]x - 13y = 2[/tex]

Therefore, the equation of the line that passes through the point (2,0) and is perpendicular to the line[tex]y-4=-13(x+3)[/tex] is x - [tex]13y = 2[/tex].

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The solutions to the equation are x = π/2 and x = 11π/6. We can write these as a list separated by commas:

X = π/2, 11π/6

To solve the equation 2 sin^2 (x) – sin(x) – 1=0 for all solutions 0 < x < 2π, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 2, b = -1, and c = -1. Plugging these values into the quadratic formula gives us:

x = (-(-1) ± √((-1)^2 - 4(2)(-1))) / (2(2))

Simplifying the expression inside the square root gives us:

x = (1 ± √(1 + 8)) / 4

x = (1 ± √9) / 4

x = (1 ± 3) / 4

This gives us two possible values for x:

x = (1 + 3) / 4 = 1

x = (1 - 3) / 4 = -0.5

Now we need to find the values of x that satisfy the original equation and are within the given range of 0 < x < 2π. To do this, we can use the inverse sine function:

x = sin^-1(1) = π/2

x = sin^-1(-0.5) = -π/6

Since we are looking for solutions within the range of 0 < x < 2π, we need to add 2π to the nagetive solution to get a positive value:

x = -π/6 + 2π = 11π/6

Therefore, the solutions to the equation are x = π/2 and x = 11π/6. We can write these as a list separated by commas:

X = π/2, 11π/6

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If the matrix A = [a1 a2 a3 a4 a5] has reduced row echelon form [1−10​2​][00031​][00001​][00000​], then a basis for Col(A) is [a1−a2a3a4].

Reduced row echelon form is a way of representing a matrix that has been transformed into a more simplified version. It is commonly used in linear algebra and has many applications.

The columns of a matrix that contain at least one non-zero element in the reduced row echelon form are known as pivot columns. Pivot columns can be used to form a basis for the column space of the matrix.

The number of pivot columns determines the rank of the matrix. Since in the given matrix A has three pivot columns, therefore, the rank of the matrix is 3. Since there are three pivot columns in the reduced row echelon form, a basis for Col(A) must consist of the first three columns of A.

Hence, the required basis for Col(A) is [a1−a2a3a4].

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The width of the rectangular prism as required to be determined is 12 centimetres.

As evident in the task content; the rectangular prism is 6 centimeters long and 16 centimeters high while Its volume is 1,152 cubic centimeters.

Since for rectangular prisms;

Volume = length × width × height

Where,

Length = 6 centimeters

Width = w

Height = 16 centimeters

So,

Volume = length × width × height

1152 = 6 × w × 16

w = 1152 / 96

w = 12 centimeters

Ultimately the width of the rectangular prism in discuss is;12 centimetres.

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[tex]\left \{ {{2y-x=-9} \atop {y=2x-3}} \right. \iff \left \{ {{2(2x-3)-x=-9} \atop {y=2x-3}} \right. \iff \{ {{4x-6-x=-9} \atop {y=2x-3}} \right. \\[/tex]

[tex]\{ {{3x=-9+6} \atop {y=2x-3}} \right. \iff \{ {{3x=-3} \atop {y=2x-3}} \right. \iff \{ {{x=-1} \atop {y=2x-3}} \right. \\[/tex]

[tex]\{ {{x=-1} \atop {y=2(-1)-3}} \right \iff \{ {{x=-1} \atop {y=-2-3}} \right \implies \bf \{ {{x=-1} \atop {y=-5}}[/tex]

[tex]\implies (x, \ y) = (-1, \ -5)[/tex]

The quadratic equation with roots 1 and 5 and leading coefficient 2 is 2x^2 - 12x + 10 = 0

To write the quadratic equation with roots 1 and 5 and leading coefficient 2, we can use the fact that the general form of a quadratic equation is:

ax^2 + bx + c = 0

where a, b, and c are constants.

Since the roots are 1 and 5, we know that the factors of the quadratic equation are:

(x - 1) and (x - 5)

Multiplying these factors together, we get:

(x - 1)(x - 5) = x^2 - 6x + 5

To satisfy the condition of having a leading coefficient of 2, we can simply multiply the entire equation by 2

2(x^2 - 6x + 5) = 2x^2 - 12x + 10

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The equation expressed with x and y to find the tourist's average speed over the whole distance he walked is (5x + 4y) / (x + y)

Average speed = Total distance traveled / Total time taken

Distance = speed × time

= 5 km/h × x

= 5x km/h

Distance = speed × time

= 4 km/h × y

= 4y km/h

Average speed = Total distance traveled / Total time taken

= (5x + 4y) / (x + y)

Therefore, the tourist's average speed over the whole distance he walked is represented by (5x + 4y) / (x + y)

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the height of the antenna is approximately 24 meters.

A triangle is said to be right-angled if one of its angles is exactly 90 degrees. The total of the other two angles is 90 degrees. Perpendicular and the triangle's base are the sides that make up the right angle. The longest of the three sides, the third side is known as the hypotenuse.

From the diagram, we see that we need to find the distance d and the height h. We can use the tangent function to find these values.

First, let's find d:

tan(θ) = h / (d + 1.51)

Rearranging, we get:

d = (h / tan(θ)) - 1.51

Next, let's find h:

tan(θ') = h / d

Substituting the expression for d that we found above, we get:

tan(θ') = h / ((h / tan(θ)) - 1.51)

Multiplying both sides by (h/tan(θ1)) - 1.51 and simplifying, we get:

h = (29 * tan(θ') * tan(θ)) / (tan(θ') - tan(θ))

Now we can plug in the values for the angles and solve for h:

h = (29 * tan(31°) * tan(17°)) / (tan(31°) - tan(17°))

h ≈ 24

So the height of the antenna is approximately 24 meters.

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Answer:

Step-by-step explanation

First divide 29.6 by 8.  Your answer will be 3.7.

The percentage increase in the new monthly payment is a 35.5% decrease compared to the old monthly payment.

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

Here,
The original monthly payment per thousand dollars of the loan is $10.67. So, for a loan amount of x dollars, the original monthly payment can be written as:

10.67 x (x/1000) = 0.01067x

The term (x/1000) is used to convert the loan amount from dollars to thousands of dollars.

Jim has been paying this monthly payment for 4 years or 48 months. So, the total amount he has paid towards the loan is:

48 x 0.01067x = 0.51216x

At the end of 4 years, Jim owes the bank $70,000. So, we can write:

x - 0.51216x = 70000

0.48784x = 70000

x = 143391.99 (rounded to the nearest cent)

Now, we can use the new interest rate and monthly payment information to find the new monthly payment.

The new monthly payment per thousand dollars of the loan is $11.72. So, for a loan amount of x dollars, the new monthly payment can be written as:

11.72 x (x/1000) = 0.01172x

The new interest rate is 13%, which is applied to the remaining loan amount of $70,000. So, the new loan amount can be written as:

0.13 x 70000 + 70000 = 79100

Therefore, the new monthly payment for the loan amount of $79,100 is:

0.01172 x 79100 = $927.11 (rounded to the nearest cent)

To find the percentage increase in the new monthly payment, we can use the formula:

% increase = (new value - old value) / old value x 100

% increase = (927.11 - 1437.32) / 1437.32 x 100

% increase = -35.5%

Therefore, the percentage increase in the new monthly payment is a 35.5% decrease compared to the old monthly payment.

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Answer:

28 units

Step-by-step explanation:

To find the area of a rectangle, multiply the base by its height.

Area = b · h

Area = 7 · 4

Area = 28 units

The correct option is (b) i.e. there are 38 students age 15 and above who take a car to school.

What is a linear equation?

A linear equation is one in which the maximum power of the variable is one. Mathematically, an equation of the type axe + b = 0 or axe + by + c = 0, where a, b, and c are real integers and x and y are variables of maximum power one.

We know that,

Students under age 15 who prefer walk/bike + Students age 15 and above who prefer walk/bike = total of column

So, Students under age 15 who prefer walk/bike

   = total of column - Students age 15 and above who prefer walk/bike

   = 152 - 65

   = 87.

Now, total of rows = total of columns

       Row 1 + Row 2 = 360

      Row 1 = 360 - Row 2

                 =360-195

                 = 165.

Now, Students under age 15 who prefer bus + Students under age 15 who prefer walk/bike + Students under age 15 who prefer car = Row table

So, Students under age 15 who prefer bus

    = 165 - 60 - 87

    = 18.

Similarly,

Students under age 15 who prefer bus + Students 15 and above who prefer bus  = column total

So, Students 15 and above who prefer bus  = 110 - 18

                                                                         = 92.

Finally, students age 15 and above take a car to school

           = 195 - 92 - 65

           = 38.

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The logarithmic expression can be rewritten as a single logarithm with the same base as [tex]log_{4} (12.8)[/tex].

To rewrite the logarithmic expression as a single logarithm with the same base means that we have to do logarithmic expression simplification.

To do so, we can use the logarithmic properties:

[tex]log_{b} (a)[/tex] + [tex]log_{b} (c)[/tex] = [tex]log_{b} (ac)[/tex]

[tex]log_{b} (a)[/tex] - [tex]log_{b} (c)[/tex] = [tex]log_{b} (a/c)[/tex]

b · [tex]log_{a} (x)[/tex] = [tex]log_{a} (x^{b} )[/tex]

Using these properties, we can rewrite the given expression:

9 · [tex]log_{4} (2)[/tex] - [tex]log_{4} (40)[/tex] = [tex]log_{4} (2^{9} )[/tex] - [tex]log_{4} (40)[/tex]

= [tex]log_{4} (512)[/tex] - [tex]log_{4} (40)[/tex]

= [tex]log_{4} (512/40)[/tex]

= [tex]log_{4} (12.8)[/tex]


So the logarithmic expression can be rewritten as a single logarithm with the same base as [tex]log_{4} (12.8)[/tex]

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As the value of x (time in seconds) increases, the height of the soccer ball decreases until it hits the ground at x=3.

what is domain of the function?

The domain of a function is the set of all possible values of the input variable (independent variable) for which the function is defined. It is the set of all x-values for which the function produces a valid output. In order to determine the domain of a function, one needs to consider any restrictions or limitations that the function may have.

The given problem is related to the motion of a soccer ball kicked by Lin. The height of the soccer ball (in feet) is a function of time (in seconds), and it is represented by a graph.

Domain: The domain of the function is the set of all possible values of the input variable (time in seconds). In this case, the soccer ball was in the air for 3 seconds, so the domain is [0, 3], which means that the height function is defined for all values of time between 0 and 3 seconds, including 0 and 3.

Range: The range of the function is the set of all possible values of the output variable (height of the soccer ball in feet). In this case, the soccer ball reached a height of approximately 30 ft while it was in the air. Therefore, the range of the function is [0, 30], which means that the height of the soccer ball is defined for all values between 0 and 30 feet, including 0 and 30.

Line of symmetry: The line of symmetry is a vertical line that passes through the vertex of the parabola (in this case, the highest point that the soccer ball reaches). The parabolic graph of the soccer ball's height function is symmetric with respect to the vertical line passing through the midpoint of the domain. Since the domain is [0, 3], the midpoint is (3/2, 0), so the line of symmetry is x = 3/2.

As the value of x (time in seconds) increases, the height of the soccer ball decreases until it hits the ground at x=3. As the value of x decreases from 3 to 0, the height of the soccer ball increases from 0 to 30 and then decreases again as it hits the ground. The rate of change of the height of the soccer ball is not constant but rather depends on the shape of the parabolic graph of the height function.

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The graph of g(x) = 3x² + 6 is steeper and shifted upward compared to the graph of f(x) = x².

A graph can be defined as a pictorial representation or a diagram that represents data or values.

The graphs of g(x) = 3x² + 6 and f(x) = x² are both quadratic functions, which means that their graphs are parabolas.

However, they have different coefficients and constant terms, which means that they will have different shapes and positions.

Here, the graph of g(x) = 3x² + 6 is steeper and shifted upward compared to the graph of f(x) = x².

Both graphs have a vertex at the origin, but g(x) has a larger coefficient of x², which makes it steeper, and an added constant term, which shifts it upward.

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