Graphing Quadratic Functions 1. List a, b, and c. 4. What is the y-intercept? 5. Create a table and graph. X f(x) Quadratic Function f(x) = x² - 2x + 6 2. Find the axis of symmetry. F Y 10 9 8 7 6 5 4 3 2 1 -9-8-7-6-5-4-3 -2 -1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 3. Find the vertex. tx 1 2 3 4 5 6 7 8 9 10 X​

The inverse function f-¹(x) as required to be determined from the given function; f(x) = (x-7)³ is; f¯¹(x) = ³√x + 7.

It follows from the task content that the inverse function of the given function; f(x) = (x-7)³ is to be determined.

Therefore, let f(x) = y; so that we have;

y = (x - 7)³

make x the subject so that we have;

³√y = x - 7

x = ³√y + 7

By switching the variables; we have;

y = ³√x + 7

Therefore, the required inverse function; f-¹ as required is; f¯¹(x) = ³√x + 7.

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The coordinates of point C in the given right triangle ABC is (2, 2√3-2)

A triangle is a three-sided polygon, which has three vertices. The three sides are connected with each other end to end at a point, which forms the angles of the triangle. The sum of all three angles of the triangle is equal to 180 degrees.

Given that, triangle ABC is a 30°-60°-90° triangle, where two vertices are A(-4, -2) and B(4, -2).

Now, AB=4-(-4)=8

AC=AB×sin60°= 8×√3/4√3

In right triangle ACD

AD=AC×cos30°

= 4√3×√3/2

= 6

Xc=6-4=2

Yc=AC×sin30°-2

= 4×3×1/2-2

= 2√3-2

The coordinates of point C(2, 2√3-2)

Therefore, coordinates of C(2, 2√3-2).

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Answer:

Step-by-step explanation:

This is a standard quadratic equation in the form ax^2 + bx + c = 0, where a = 1, b = -5 and c = 6. To solve for x, you can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

Where ± represents the positive and negative square root, and the expression under the square root is called the discriminant (b^2 - 4ac).

So, substituting the values for a, b, and c, we have:

x = (-(-5) ± √((-5)^2 - 4 * 1 * 6)) / 2 * 1

x = (5 ± √(25 - 24)) / 2

x = (5 ± √1) / 2

Since the square root of 1 is 1, the two solutions are:

x = (5 + 1) / 2 = 3

x = (5 - 1) / 2 = 2

So, the solutions to the equation x^2 - 5x + 6 = 0 are x = 2 and x = 3.

Answer:

Step-by-step explanation:

The slope of a line is the change in y (the vertical axis) divided by the change in x (the horizontal axis).

Given the two points (6,7) and (16,22), we can calculate the slope as follows:

Change in y = 22 - 7 = 15

Change in x = 16 - 6 = 10

Therefore, the slope of the line passing through the two points is:

slope = change in y / change in x = 15 / 10 = 3/2

So the slope of the line is in its simplest form, 3/2.

Regenerate response

Answer: 71/7

Step-by-step explanation:

I like this problem a lot!

Let the shorter leg length be x:

then the longer leg length is 3x - 9

the hypotenuse length is (3x - 9) + 2 = 3x - 7

Perimeter of Triangle = Sum of all 3 sides of a triangle

24 = x + (3x - 9) + (3x - 7)

24 = 7x - 16

40 = 7x

.: x = 40/7

.: hypotenuse = 3x - 7 = (120/7) - 7 = 71/7

Done!

The coefficients in the expression "9x - 2 + 16x + 8 - x + 10" are the numerical values that multiply the variables. In this expression, the coefficients are 9, -2, 16, 8, -1, and 10.

So, the expression can be written as:

9x + 16x - x + 10 = 24x + 10

where 9, -2, 16, 8, -1, and 10 are the coefficients of the expression.

Answer:

The coefficients in this expression would be 10, -2, 8, -1, 10, 9, 16

Step-by-step explanation:

a numerical or constant quantity placed before and multiplying the variable in an algebraic expression

By using the continuous interest formula, we get 8.54 years that the amount will take to double itself.

The continuous interest formula is used to calculate the future value of a compound interest investment. It is written as follows:

Future Value = Principal × [tex](1 + r)^{n}[/tex]

where Principal is the original investment, r denotes the yearly interest rate, and n denotes the number of compounding periods.

The continuous interest formula is used to compute the future worth of an investment given its current value, yearly interest rate, number of times the interest is compounded each year, and number of years held.

In the given question,

A = A_0[tex]e^{rt}[/tex]

2A_0 = A_0[tex]e^{rt}[/tex]

2 = [tex]e^{rt}[/tex]

ln(2) = rt

t = [tex]\frac{2}{r}[/tex]

t = [tex]\frac{2}{0.08}[/tex]

t = 8.54 years

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Answer:

HI

The scale fact from the smaller to the larger is 3.  The scale factor from the larger to the smaller is 1/3

Step-by-step explanation:

Oliver's number is bigger than that of Chen.

It is a number equal to 10 times 10.

Given is that Oliver and Chen both write down a number. Oliver says, my number has 8 hundreds and Chen's number only has 3 hundreds, my number must be bigger.

Oliver number can be written as follows -

8 x 10 x 10

Chens number can be written as follows -

3 x 10 x 10

It can be concluded that Oliver's number is bigger than that of Chen.

Therefore, Oliver's number is bigger than that of Chen.

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Answer:

Step-by-step explanation:

If you took many random samples of a variable with a BIMODAL distribution, the means of your random samples would follow a normal distribution.

If you took many random samples of a variable with a VERY SKEWED distribution, the means of your random samples would follow a normal distribution. This is due to the Central Limit Theorem, which states that as the sample size increases, the distribution of the sample means approaches a normal distribution, regardless of the shape of the underlying population distribution.

The Central Limit Theorem (CLT) is a fundamental theorem in statistics that states that, as the sample size increases, the distribution of the sample means approaches a normal distribution, regardless of the shape of the underlying population distribution. This means that even if the original population distribution is skewed, bimodal, or any other shape, the distribution of the sample means will tend towards a normal distribution as the sample size increases.

The reason for this is that the sample means are essentially an average of a number of independent random variables, and the normal distribution is the result of the combination of many independent random variables. When the sample size is large, the distribution of the sample means becomes very close to a normal distribution, even if the underlying population is far from normal.

In the case of a bimodal distribution, the sample means will still approach a normal distribution as the sample size increases, but the distribution may have a different mean and standard deviation than the original population.

In the case of a very skewed distribution, the sample means will also approach a normal distribution as the sample size increases, but the distribution may still be skewed, just less so than the original population.

In conclusion, the Central Limit Theorem states that the distribution of the sample means will tend towards a normal distribution as the sample size increases, regardless of the shape of the underlying population distribution.

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Answer:

Below

Step-by-step explanation:

1.4 m = .42     divide both sides of the equation by   1.4 to get

 m = .3     Done.

The transformation used are:

(a)

This is a translation of one unit to the left and one unit up.

(b)

- There is a vertical stretch of 2 units.

- This is a translation of four units down.

It is the movement of the shape in the left, right, up, and down directions.

The translated shape will have the same shape and shape.

There is a positive value when translated to the right and up.

There is a negative value when translated to the left and down.

We have,

The graph from y = h(x) to y = h(-x)  + 1.

This is a translation of one unit to the left and one unit up.

The graph from y = g(x) to y = 2g(x)  - 4.

- There is a vertical stretch of 2 units.

- This is a translation of four units down.

Now,

The graph of y = h(-x)  + 1 is given below.

The graph of y = 2g(x)  - 4 is given below.

Thus,

(a)

This is a translation of one unit to the left and one unit up.

(b)

- There is a vertical stretch of 2 units.

- This is a translation of four units down.

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The approximate arc length is 56.52mm.

What is an arc length?

The distance between two places along a segment of a curve is known as the arc length. Curve rectification is the process of measuring the length of an irregular arc section by simulating it with connected line segments. There are a finite number of segments in the rectification of a rectifiable curve.

Here, we have

Given: A bicycle wheel has a radius of 225 mm and has 25 equally spaced spokes.

To solve this question, we have to use the formula of the length of an arc which is given as

L = θ/360 * 2πr

To find the angle between each spoke, let's divide 360 by 25

θ = 360/25

θ = 14.4

Now that we have the value of the angle, let's substitute it and solve for the length of the arc.

L = 14.4/360 * 2(22/7)(225)

L = 56.52mm

Hence, the approximate arc length is 56.52mm.

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If the drag force due to air resistance is 11 N acting backwards against Shaun. Shaun's acceleration is 4.64 m/s^2 down the slope.

To find Shaun's acceleration, we need to calculate the net force acting on him and his skateboard. The net force is the vector sum of all the forces acting on the object. We can use Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and its acceleration:

Net force = mass × acceleration

Let's break down the forces acting on Shaun and his skateboard:

The force of gravity, which acts vertically downwards with a magnitude of mg, where m is the total mass of Shaun and his skateboard and g is the acceleration due to gravity (9.8 m/s^2).

F₁ = m * g * sin(30°) = 75 kg * 9.8 m/s^2 * sin(30°) = 367.5 N

The force due to rolling friction between the skateboard wheels and the concrete, which acts backward against the skateboard.

F₂ = 9 N (given)

The drag force due to air resistance, which acts backward against Shaun.

F₃ = 11 N (given)

Now, let's add up the forces to get the net force:

Net force = F₁ - F₂ - F₃

= 367.5 N - 9 N - 11 N

= 347.5 N

Using Newton's second law of motion, we can now calculate Shaun's acceleration:

acceleration = Net force / mass

= 347.5 N / 75 kg

= 4.64 m/s^2 (down the slope)

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The simplified value of the expression is [a² + b² - 2ab]/[2a²b² - ab³ - a³b]

From the question, we have the following parameters that can be used in our computation:

1/(b² - ab) - 1/(ab - a²)

Take the LCM of the expression

So, we have the following representation

[ab - a² - b² + ab]/[(b² - ab)(ab - a²)]

Evaluate the like terms

So, we have the following representation

[2ab - a² - b²]/[(b² - ab)(ab - a²)]

Open the bracket

[a² + b² - 2ab]/[2a²b² - ab³ - a³b]

Hence, the solution is [a² + b² - 2ab]/[2a²b² - ab³ - a³b]

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Answer:

f(x)=3x^2+2

Step-by-step explanation:

use pm

The volume of the prism with a trapezoidal base is 312 m³

An equation is an expression that shows how numbers and variables are linked together using mathematical operations such as addition, subtraction, multiplication and division.

The volume of the prism is the product of the base area and the height. It is given by:

Volume = area of base * height

The prism shown in the diagram is a trapezoid prism, hence:

Area of base = (1/2)(5 + 8)(4) = 26 m²

Volume = area of base * height

Volume of prism = 26 m² * 12 m = 312 m³

The volume of the prism is 312 m³

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Since the domain has 4 elements and the range has 2 elements, each element in the domain can be mapped to one of the two elements in the range. Thus, there are a total of [tex]$2^4 = 16$[/tex] functions from the domain to the range.

What is functions ?

In mathematics, a function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the codomain or range) with the property that each input is related to exactly one output. Functions can be represented in many ways, including algebraic expressions, graphs, tables, or verbal descriptions.

Functions are widely used in various fields of mathematics, science, and engineering to model and analyse real-world phenomena, and to make predictions or decisions based on data.

There are 4 elements in the domain and an empty set in the codomain.

Using two-line notation, the functions are:

There is only one possible image for each element in the domain, which means that there is only one function.

Since there is only one function, it is both surjective and injective. Therefore, there is only one bijective function.

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The required graph has been attached below which represents the given linear equation y = (2/5)x - 4.

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

To plot the graph of y = (2/5)x - 4, you can follow these steps:

Choose a range of values for x that you want to plot. For example, you can choose x values from -10 to 10.

Substitute the x values into the equation to find the corresponding y values. For example, if x = -10, then y = (2/5)(-10) - 4 = -8.

Plot the ordered pairs (x, y) on a coordinate plane. For example, if x = -10 and y = -8, plot the point (-10, -8) on the plane.

Repeat this process for several x values to plot additional points.

Connect the points with a straight line to obtain the graph of the equation y = (2/5)x - 4.

Note that the graph should be a straight line with a slope of 2/5 and a y-intercept of -4.

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The question seems incomplete, the correct question would be as:

How to plot the graph of y = (2/5)x — 4?

Answer:

380

Step-by-step explanation:

(34 * 10) + (4 x 10) =

= 10 * (34 + 4) =

= 10 * 38 =

= 380

A pie has 360 degrees, so a pie cut into 5 equal pieces produces 5 slices that each measure 360 / 5 = 72 degrees.

A small slice measures 27 degrees fewer than a large slice, so it measures 72 - 27 = 45 degrees.

To find the number of pieces a pie should be cut into so that each piece is a small slice, we need to determine how many degrees each slice measures. To do this, we divide 360 by the number of pieces:

360 / n = 45

Solving for n, we get:

n = 360 / 45 = 8

So, the Tasty as Pi Bakery should cut a whole pie into 8 equal pieces so that each piece is a small slice.

After solving the system of equations, we found that the number of small chairs is 53 and the number of large chairs is 45.

What is meant by the system of equations?

A set of equations with a finite number of solutions is referred to as a system of equations. A system of equations in algebra consists of two or more equations and looks for common answers to the equations. A group of equations that are all satisfied by the same set of variables are referred to as a system of linear equations.

Given,

  Cost of material for small chair = $10

Cost of material for large chair = $15

The selling price for a small chair = $22

The selling price for a large chair = $51

The total money spent on materials = $305

Designer makes 8 more small chairs than large chairs.

If the number of large chairs = t  and the number of small chairs =  s

Using the given equations, we can write the following system of equations.

10s + 15t = 305

s - t = 8

Now we make the coefficient of s in both equations the same.

Multiply 10 in the second equation.

10s + 15t = 305

10s - 10t = 80

Subtracting,

5t = 225

t = 45

s = 8 + t = 45 + 8 = 53

Therefore after solving the system of equations, we found that the number of small chairs is 53 and the number of large chairs is 45.

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Answer:

14v-2

Step-by-step explanation:

1. distribute

2. combine like terms

see photo for more information

(a) The union set is AUB'={f, k, m, x, y}.

(b) The union set is A'UB'={q,k, x, y}.

The union of two sets is also a set. This set contains all the elements of both two sets.

The universal set is U= {f, k, m, q, x,y} and two subsets are A={f, k, m, y} and B = {f, m,q}.

(a)

B' is the complementary set of B. So, find the elements of B'=U-B.

B'= {f, k, m, q, x,y}-{f, m,q}

={k, x,y}

Now, find the union set AUB'.

AUB' ={f, k, m, y}U{k, x,y}

={f, k, m, x, y}

Therefore, the required answer is AUB'={f, k, m, x, y}.

(b)

Also, A' is the complementary set of A. So, find the elements of A'=A-B.

A'= {f, k, m, q, x,y}-{f, k,m, y}

={q,x}

Now, find the union set A'UB'.

A'UB' ={q,x}U{k, x,y}

={q,k, x, y}

Therefore, the required answer is A'UB'={q,k, x, y}.

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Answer: The future value of an annuity due with a monthly payment of $300 at 6% interest compounded monthly for 10 years can be calculated using the formula:

FV = PMT * ( ( (1 + r)^n - 1) / r) * (1 + r)

where PMT = $300, r = 6%/12 = 0.05, and n = 10 years * 12 months/year = 120 months.

Substituting these values into the formula, we get:

FV = $300 * ( ( (1 + 0.05)^120 - 1) / 0.05) * (1 + 0.05)

FV = $300 * ( ( 1.05^120 - 1) / 0.05) * 1.05

FV = $300 * ( ( 2.704813829421526 - 1) / 0.05) * 1.05

FV = $300 * ( 1.704813829421526 / 0.05) * 1.05

FV = $300 * 34.09627658843153 * 1.05

FV = $52,113.63

Therefore, the future value of the annuity due is $52,113.63.

Step-by-step explanation:

Answer: ~ 7.72 square miles

Step-by-step explanation:

One square kilometer is equal to around 0.386 miles.

To get to 20 square kilometers, multiply 0.386 times 20.

hope this helps

MM

Answer:B

Step-by-step explanation:

Answer: The median is one of several measures of center that can be used to summarize a dataset. The median is the middle value in a set of data when the data is arranged in order from smallest to largest. The median divides a dataset into two equal parts, with half of the data values being smaller than the median and half being larger.

Step-by-step explanation:

The median is one of several measures of center that can be used to summarize a dataset. The median is the middle value in a set of data when the data is arranged in order from smallest to largest. The median divides a dataset into two equal parts, with half of the data values being smaller than the median and half being larger.

The reason why the median can differ relative to the data set is because it is affected by extreme values, or outliers, in the data. For example, if a dataset has a few very large or very small values, the median can be significantly different from the mean (another measure of center), which is affected by all values in the dataset. In these cases, the median provides a better measure of center because it is less sensitive to outliers.

In general, the median is considered the best measure of center when the data is skewed (not symmetrical) or has outliers. In these cases, the median provides a better representation of the "typical" value in the dataset. However, when the data is symmetrical and does not have outliers, the mean can be a good measure of center because it takes into account all values in the dataset.

In conclusion, the best measure of center depends on the shape and distribution of the data. When the data is skewed or has outliers, the median is the best measure of center, while in symmetrical and non-outlier datasets, the mean can provide a good measure of center.

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The slope of the line that passes through (-8,-1) and (12,4) is 1/4.

The equation of the line in slope intercept form is y = x/4 - 31/4.

In Mathematics, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Substituting the given data points into the slope formula, we have the following;

Slope, m = (4 + 1)/(12 + 8)

Slope, m = 5/20

Slope, m = 1/4.

At point (-8, -1), a linear equation of this line can be calculated in slope-intercept form as follows:

y - y₁ = m(x - x₁)

y - (-8) = 1/4(x - (-1))

y + 8 = x/4 + 1/4

y = x/4 - 31/4.

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