Given
f(x) = 4x2 − 1
and
g(x) = −4x + 8,
find the following.
f(2) − g(2)

Answer:

Step-by-step explanationuuh soo I don’t understand this app:

The exponential function is an exponential growth.

The general exponential function is:

f(x) = a*(b)^x

Where a is the initial value and b is the base, if:

b > 1 then it is a growth.

0 < b < 1 then it is a decay.

In this case, b = 1 + r

Where r is the growth rate, in this case is 6%, writting it as a decimal we get:

b = 1 + 6%/100% = 1.06

It is larger than 1, so this is a growth.

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Answer:

46

Step-by-step explanation:

27+4*5+8-7-2=

27+20+8-7-2=

47+8-7-2=

55-7-2=

48-2=

46

Step-by-step explanation:

First, we need to perform the multiplication operation within the parentheses, following the order of operations:

2⅓ × 1¼ = (7/3) × (5/4) = 35/12

Now, we can substitute the values in the expression:

3½ - (2⅓ × 1¼) + ⅗ = 7/2 - 35/12 + 3/5

To add or subtract fractions with different denominators, we need to find a common denominator. The least common multiple of 2, 12, and 5 is 60, so we can rewrite the fractions with this denominator:

7/2 - 35/12 + 3/5 = (210/60) / (2/2) - (175/60) / (12/12) + (36/60) / (5/5)

Simplifying the fractions within the parentheses:

= 210/60 - 175/60 + 36/60

= 71/60

Therefore, 3½ - (2⅓ × 1¼) + ⅗ simplifies to 71/60.

Answer:

Seven dozen eggs would equal a total of 84 eggs

Step-by-step explanation:

Answer:

84 eggs

Step-by-step explanation:

1 dozen of eggs = 12 eggs

Then :

1 dozen -------- 12 eggs

7 dozen -------   x eggs

x = (7 x 12) / 1 = 84 eggs

The proof that proves the two triangles are congruent by the AAS congruence theorem is shown below.

Angle-Angle-Side (AAS) is an abbreviation that refers to a method of determining congruence in triangles. If two triangles have two corresponding angles that are equal, and the non-included side between these angles is also equal, then the triangles are considered congruent.

The proof below shows how to apply the AAS congruence theorem to prove both triangles are congruent.

Statement                           Reason                                  

1. ∠B ≅ ∠D; BC║AD           1. Given

2. AC ≅ CA                         2. Reflexive property

3. ∠BCA ≅ ∠DAC               3. Alternate interior angles theorem

4. △ABC ≅ △CDA              4. AAS congruence theorem

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The graph below shows a parabola, indicating that the possible function for f is a quadratic equation.

Graph is a data structure consisting of nodes (vertices) and edges that connect them. Graphs are used to represent networks of data, such as social or computer networks. Graphs are also used to represent mathematical and logical equations, as well as to store and display data. Graphs are composed of two basic components: nodes (vertices) and edges (arcs). Nodes represent the objects in the network, while edges represent the connections between them. Graphs can be used to model many different types of relationships and can be used to solve a variety of problems in different areas, such as computer science, mathematics, engineering, and social sciences.

A quadratic equation is an equation of the form ax2 + bx + c = 0, where a, b and c are real numbers and a ≠ 0. This type of equation is important in mathematics, as it can represent many physical situations, such as a ball thrown into the air, or a spring that is stretched or compressed. Quadratic equations can be solved using the quadratic formula, which uses the coefficients a, b and c to calculate the two solutions for x. In the graph, the parabola has an equation of the form y = ax2 + bx + c, and so the possible function for f is a quadratic equation.

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Answer: If Colleen selected one egg, cracked it open and found out it was raw, the probability of selecting the hard-boiled egg on her second pick is 1/5, and the probability of Colleen selecting the hard-boiled egg on her first try is 1/6.

To see why, let's consider the possible scenarios:

Colleen selects the hard-boiled egg on her first try. There is only 1 hard-boiled egg out of the 6, so the probability of this happening is 1/6.

Colleen selects a raw egg on her first try. There are 5 raw eggs out of the 6, so the probability of this happening is 5/6. After she cracks open the raw egg, there will be 4 raw eggs and 1 hard-boiled egg left. So the probability of selecting the hard-boiled egg on her second pick is 1/5.

Therefore, the statement "If Colleen selected one egg, cracked it open and found out it was raw, the probability of selecting the hard-boiled egg on her second pick is 1/5, and the probability of Colleen selecting the hard-boiled egg on her first try is 1/6" is true.

Step-by-step explanation:

Answer:

20% of the number is 44.0.

Step-by-step explanation:

Let's say the number is "x".

We can start by setting up two equations based on the given information:

0.55x = 121

0.75x = 165

We can solve for x by dividing both sides of each equation by the coefficient of x:

x = 121/0.55 ≈ 220.0

x = 165/0.75 = 220.0

Now that we know the value of x, we can find 20% of it by multiplying it by 0.20:

0.20 * 220.0 = 44.0

Therefore, 20% of the number is 44.0.

Answer:

Proofs attached to answer

Step-by-step explanation:

Proofs attached to answer

Answer: Lily

Step-by-step explanation:

3/4 is larger than 2/6

Answer: Lily

Step-by-step explanation: 3/4 > 2/6

3/4 = 0.75

2/6= 0.33

compare the two decimal places, 0.75 > 0.33

The probability that a randomly selected driver in the 20-24 age bracket will be in a car crash during the next year is 0.86%.

It is unlikely for a driver in that age bracket to be involved in a car crash during a year

The resulting probability of 0.0086 is relatively low.

The approximate probability can be calculated by dividing the number of drivers who were in a car crash in the last year by the total number of drivers in the 20-24 age bracket:

Probability = Number of drivers in a car crash / Total number of drivers in the age bracket

Probability = 3/350

Probability ≈ 0.0086

Part 2

Since the probability is less than 0.05, it is unlikely for a driver in that age bracket to be involved in a car crash during a year.

Part 3

While any car accident can be a concern, the resulting probability of 0.0086 is relatively low.

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Answer:

it's C

All the graphs except C crosses the x axis at the roots but C doesn't

We can conclude that the set of points {(−9,0),(−4,5),(0,9),(4,5),(9,0)} does not represent a function.

In mathematics, a function is a relation between a set of inputs and a set of possible outputs with the property that each input is related to exactly one output. In other words, a function is a rule that assigns a unique output value to each input value. Functions are commonly denoted using functional notation, where the function name is followed by its input, such as f(x) or g(t).

To determine if the set of points {(−9,0),(−4,5),(0,9),(4,5),(9,0)} represents a function, we need to check if for every x-coordinate there is only one corresponding y-coordinate.

We can start by graphing the set of points:

From the graph, we can see that for x = -4 and x = 4, there are two different y-coordinates, which means that the set of points does not represent a function.

Therefore, we can conclude that the set of points {(−9,0),(−4,5),(0,9),(4,5),(9,0)} does not represent a function.

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The equation of the line that represents the total cost is c = 4d + 8 and the total cost when 1 drink is bought is $ 12.

The slope-intercept form of a line has used to form a linear equation in two variables. It is called the slope-intercept form because it gives us two pieces of information about the line its slope and y-intercept.

The slope-intercept form of a line is given by the equation:

where:

m is the slope of the line

b is the y-intercept of the line

Here we have

The graph shows the total cost c of buying one large bucket of popcorn and d large drinks.  

From the graph, the line passes through points (0, 8) and (1, 12)  

Hence, slope of the line (m) = [(y₂ - y₁) / (x₂ - x₁) ]

= [(12 - 8) / (1 - 0) ] = [4 / 1] = 4

Let y = mx + c be the lines

=> y = 4x + c

Since the line passes through (0, 8)

=> 8 = 4(0) + c

=> c = 8

Hence, the required equation is y = 4x + 8  

From the data,

The y-axis represents the total cost 'c' and the x-axis represents the number of drinks 'd'

=>  Total cost c = 4d + 8

Hence,

The equation of the line that represents the total cost is c = 4d + 8

If we bought 1 large drink

=> c = 4(1) + 8 = 12

Therefore,

The equation of the line that represents the total cost is c = 4d + 8 and the total cost when 1 drink is bought is $ 12.

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Answer:

I speak english so this might be wrong...

Step-by-step explanation:

Build the distribution table

of frequencies and histogram of the height (in cm) of 80 third-secondary students.

(Construir la tabla de distribución

de frecuencias e histograma de la altura (en cm) de 80 estudiantes de tercero medio.)

I think this is what you sayed?

For the following:

a) To determine the range of the heights, find the difference between the highest and lowest values.

Range = Highest value - Lowest value

The highest value is 188 cm, and the lowest value is 162 cm.

Range = 188 - 162 = 26 cm

b) The amplitude is the interval width of each class in the frequency table. To determine the amplitude, Know the number of classes. Assume to create 10 classes for the height data.

Amplitude = Range / Number of classes

Amplitude = 26 cm / 10 = 2.6 cm

c) To build the frequency table, to create the class intervals for the height data. Since the amplitude is 2.6 cm, choose the class intervals accordingly.

Set up the frequency table with 10 classes:

Class Intervals: (160 - 162.6], (162.6 - 165.2], (165.2 - 167.8], ..., (185 - 187.6], (187.6 - 190]

Next, count the number of data points falling into each class interval and calculate the absolute frequency (frequency), cumulative frequency, relative frequency, and percentage relative frequency.

The frequency table for the height data is attached.

In the frequency table, the "Cumulative Frequency" column shows the running total of frequencies, the "Relative Frequency" column shows the proportion of each class frequency to the total number of data points (80), and the "Percentage Relative Frequency" column shows the relative frequency expressed as a percentage.

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Answer:

The given equation is of the form:

((x - h)^2)/a^2 - ((y - k)^2)/b^2 = 1

Comparing it with the given equation:

((x - 3)^2)/10 - ((y + 5)^2)/9 = 4

We can rewrite the equation in the standard form by dividing both sides by 4, then adding (y+5)^2/9 to both sides:

((x - 3)^2)/40 - ((y + 5)^2)/36 = 1

Now, we can see that the equation is in the standard form of a hyperbola. The center of the hyperbola is (3, -5), the distance between the center and each vertex is sqrt(10) in the x-direction and sqrt(9) in the y-direction, and the hyperbola opens to the left and right.

The figure has rotational symmetry of order 2 and to achieve rotational symmetry of order 4, three plates need to added.

Explain about symmetry?

Symmetry is a property of an object that describes how it appears identical after some transformation, such as reflection, rotation, or translation. It is an essential concept in mathematics, science, art, and many other fields.

There are several types of symmetry, including:

Reflectional symmetry (also called bilateral symmetry).
Rotational symmetry.

Translational symmetry.

According to the question:

a. The figure has rotational symmetry of order 2. This means that if we rotate the figure 180 degrees around its center, the figure will look exactly the same as it did before the rotation.

b. To achieve rotational symmetry of order 4, we need to add plates in such a way that the figure looks the same after a rotation of 90 degrees, 180 degrees, and 270 degrees around its center.
To achieve this, we can add three more plates to the figure, one in between each pair of existing plates, After adding these plates, the figure has rotational symmetry of order 4. We can see this by rotating the figure 90 degrees, 180 degrees, and 270 degrees around its center

so the figure has rotational symmetry of order 4. Therefore, we only needed to add three plates to the figure to achieve rotational symmetry of order 4 around its center.

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We can write the equivalent value of the matrix {A - 2B} as -

[9    2]

[2    6]

[3   -10]

In mathematics, a matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object.

Given are the matrices as given in the equation.

We can write the elements for {A - 2B} as -

A{ 1 } = 3 + 6 = 9

A{ 2 } = 4 - 2 = 2

A{ 3 } = 6 - 4 = 2

A{ 4 } = - 2 + 8 = 6

A{ 5 } = 1 + 2 = 3

A{ 6 } = - 10

So, we can write the matrix as -

A - 2B =

[9    2]

[2    6]

[3   -10]

Therefore, we can write the equivalent value of the matrix {A - 2B} as -

[9    2]

[2    6]

[3   -10]

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Answer:

Answer on pic

Step-by-step explanation:

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The number of polygons that can be formed are

Points (0, 1) and (2, 3)

The set of points (0, 1) and (2, 3) cannot form a polygon as they are collinear (i.e., lie on the same straight line) and do not enclose an area.

Points  (4, 5), (6, 7), and (8, 9)

These are three different points.

Because a triangle has three sides, one triangle can be formed by the set of points (4,5), (6,7), and (8,9). i.e. One polygon

Points (3, 5) and the x-axis.

One polygon can be formed by the set of points (3,5) and the x-axis: a triangle with vertices at (3,5), (0,0), and (6,0).

Polygon (4)

This is a rectangle with the dimension:

6 units by 5 units

So, we have

Perimeter = 2 * (6 + 5) = 22 units

Area = 6 * 5 = 30 squared units

Polygon (5)

This is a composite figure with the following dimensions:

Square of 4 units

Rectangle: 6 units by 2 units

So, we have

Perimeter = 4 * 4 + 2 * (6 + 2) = 32 units

Area = 4 * 4 + 6 * 2 = 28 squared units

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The equation for number of miles is 14/7 = x and she ran 2 miles each day.

Simplify the equation to bring all the variable terms to one side and the constant value to the other in order to solve linear equations with a single variable. Find the LCM (least common multiple) if there are any fractional terms, then simplify them so that the variable values are on one line and the steady terms are on the other.

Let us suppose the number of miles she ran each day = x.

Given that, Aroline ran 14 miles in 7 days.

Thus,

Total distance / Number of days = x

14/7 = x

x = 2

Hence, the equation is 14/7 = x and she ran 2 miles each day.

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Out of the fifty people surveyed, thirty prefer vanilla frozen yogurt. The circle graph is a useful visual representation of the survey results.

A circle graph, also known as a pie chart, is a type of graph that displays data in a circular format. It is divided into sections that each represent a proportion of the whole. The sections are labeled and the relative sizes of each section show the proportion of the whole that each part represents.

The circle graph indicates that 30 people prefer vanilla flavor. This is the highest amount out of the five flavors represented. The graph shows that the next most popular flavor is chocolate, preferred by 20 people, followed by strawberry, preferred by 10 people. There are five people who prefer a different flavor, and five people who have no preference. Therefore, out of the fifty people surveyed, thirty prefer vanilla frozen yogurt.

The circle graph is a useful visual representation of the survey results. By looking at the graph, it is clear that vanilla is the most popular flavor, with thirty people preferring it.

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The exact values of the trigonometric functions associated with the geometric system are:

sin α = √161 / 15, cos α = 8 / 15, tan α = √161 / 8, sin θ = 8 / 15, cos θ = √161 / 15, tan θ = 8 / √161

In this problem we find a geometric system formed by two similar right triangles. Two triangles are similar if both have congruent internal angles and sides are not congruent though proportional. Then, we find the following relationships:

∠ B ≅ ∠ E

ED = √(EC² - DC²)

And the exact trigonometric functions are listed below:

sin α = DE / EC

cos α = DC / EC

tan α = DE / DC

sin θ = DC / EC

cos θ = DE / EC

tan θ = DC / DE

If we know that DC = 8 cm and EC = 15 cm, then the exact values of the trigonometric functions are:

DE = √[(15 cm)² - (8 cm)²]

DE = √161

sin α = √161 / 15

cos α = 8 / 15

tan α = √161 / 8

sin θ = 8 / 15

cos θ = √161 / 15

tan θ = 8 / √161

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2k + 5 = 2(8) + 5 = 16 + 5 = 21

k is substituted into the expression

Therefore, if a population of 150 mice triples in size every four months, there will be approximately 2,952,450 mice in the neighbourhood in 3 years.

Mathematicians use the unitary method to answer proportional relationship problems involving two or more quantities. It entails calculating the worth of one unit of one quantity in relation to another. For instance, let's say we are aware that 3 pencils cost $6. The following is how we can calculate the price of a solitary pen using the unitary method: The value of a single entity of the quantity "pen cost" in terms of the quantity "number of pens" was determined in this case. Once we are aware of a unit's worth, we can use that knowledge to determine the value of any other quantity that is related to it.

given

The population triples, or grows three times, in number, after four months. As a result, if we commence with 150 mice, the population will look like this after 4 months:

150 × 3 = 450 mice

The populace will triple once more after another 4 months (or 8 months from the beginning), becoming:

450 × 3 = 1350 mice

The populace will triple once more after another 4 months (or 12 months from the beginning), becoming:

1350 × 3 = 4050 mice

There is a pattern here: every four months, the populace triples. Therefore, we can determine how many times the population triples after three years (or 36 months) have passed:

36 months divided by 4 months per triple equals 9 triples.

the following group will exist after three years:

2,952,450 mice are equal to 150 × 39 (150 x 19,683).

Therefore, if a population of 150 mice triples in size every four months, there will be approximately 2,952,450 mice in the neighbourhood in 3 years.

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The result is a statistic because it describes some characteristic of a sample (the 60 states).

what is statistics?

Statistics is the study of collecting, analyzing, and interpreting numerical data to make inferences and decisions. It involves techniques such as sampling, probability, hypothesis testing, and regression analysis to extract meaningful insights from data and make informed decisions based on them.

Solution:

The result is a statistic because it describes some characteristic of a sample (the 60 states).

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