What is the graph of y = -3/4x – 2?

a) Domain of f,g,f+g,f-g,fg,ff,gf, : All real numbers, And for fg​ all real numbers except -1.

b) The functions  (f+g)(x) = -3x + 9, (f-g)(x) = 13x + 7, (fg)(x) =  -40x² - 59x + 8, (ff)(x) = 25x + 48, (g/f)(x) = (1-8x) / (5x+8), (f/g)(x) = (5x+8) / (1-8x).

The given functions are,

f(x)=5x+8 and

g(x)=1−8x

a) The domain of f(x) and g(x) is all real numbers.

To find the domain of f + g, we need to find the values of x for which the sum of f(x) and g(x) is defined. The sum is defined for all real numbers, hence the domain of f+g is all real numbers.

Similarly, the domain of f - g is also all real numbers.

To find the domain of fg, we need to find the values of x for which the product of f(x) and g(x) is defined. The product is defined for all real numbers, hence the domain of fg is also all real numbers.

To find the domain of ff, we need to find the values of x for which the composition of f(f(x)) is defined. The composition is defined for all real numbers, hence the domain of ff is also all real numbers.

To find the domain of gf, we need to find the values of x for which the composition of g(f(x)) is defined. The composition is defined for all real numbers, hence the domain of gf is all real numbers.

To find the domain of fg​, we need to find the values of x for which the composition of f(g(x)) is defined. g(x) is defined for all real numbers, but f(x) is not defined for x = -1.

Therefore, the domain of fg​ is all real numbers except -1.

b)

(f+g)(x) = f(x) + g(x) = (5x+8) + (1-8x) = -3x + 9

(f-g)(x) = f(x) - g(x) = (5x+8) - (1-8x) = 13x + 7

(fg)(x) = f(x) g(x) = (5x+8) (1-8x) = -40x² - 59x + 8

(ff)(x) = f(f(x)) = f(5x+8) = 25x + 48

(g/f)(x) = g(x) / f(x) = (1-8x) / (5x+8)

(f/g)(x) = f(x) / g(x) = (5x+8) / (1-8x)

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Answer:

2.4

Step-by-step explanation:

2/3 of 3.6=2.4

3.6÷3=1.2

1.2×2=2.4

Step-by-step explanation:

2x+3y=45

4x+y=55

y=55-4x

2(55-4x)=45

110-8x=45

-8x=-65

x=8.125 adult price

y= 55-4*8.125=22.5 child price

Answer: 81,000

Step-by-step explanation:

We can solve this by using the formula given.

If f(1)=1000x3^1, then 1,000x3=3,000

If f(2)=1000x3^2, then 3^2=9 and 1000x9=9000,

and so on,

Now, f(4) will equal 1000x3^4, and 3^4 is 3x3x3x3, which is 9x9 or 9^2, which would be equal to 81, and 81x1000=81,000

To complete the table of values for the exponential function f(x) = 1000*3^x, we can evaluate the function for x = 0, 1, 2, 3, and 4, since we are interested in the number of bacteria on the phone after 4 hours.

x f(x)

0 1000

1 3000

2 9000

3 27,000

4 81,000

Therefore, after 4 hours, there will be 81,000 bacteria on the surface of the phone, assuming the number of bacteria triples every hour and can be described by the exponential function f(x) = 1000*3^x.

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Answer:

Yes

Step-by-step explanation:

Both equals to 1/2

That's the answer

Answer:

The answer is true.

Step-by-step explanation:

\( \frac{4}{6} = \frac{14}{21} \\ 84 = 84\)

Because the last equation, 84=84, is true, then the ratios are true.

Answer:

\({:}\leadsto \)\(\sf {\dfrac {3}{7}}\)

\({:}\leadsto \)\(\sf {\dfrac {3×3}{7×3}}\)

\({:}\leadsto \)\(\sf {\dfrac {9}{2}}\)

\({:}\leadsto \)\(\sf {\dfrac {1}{3}}\)

\({:}\leadsto \)\(\sf {\dfrac {1×7}{3×7}}\)

\({:}\leadsto \)\(\sf {\dfrac {7}{21}}\)

\({:}\leadsto \)\(\sf {\dfrac {9}{21}}\iff {\dfrac {7}{21}}\)

\({:}\leadsto \)\(\sf {\dfrac{9}{21}} \gt {\dfrac {7}{21}}\)

\(\therefore\)\(\sf {\dfrac {3}{7}} \gt {\dfrac {7}{21}}\)

The sum in summation notation of the expression (a) 1 + 2 + 3 + 4 + X5, where X takes the values 1-4, is ΣX from 1 to 4. In other words, it represents the summation of X over the range 1 to 4.

In summation notation, the expression (a) 1 + 2 + 3 + 4 + X5 can be written as ΣX, where X takes the values from 1 to 4. The capital sigma (Σ) represents the summation operator, and the variable X is summed over the range 1 to 4. This means that we need to substitute X with each value from 1 to 4 and add them together.

When we evaluate the expression, we have:

ΣX = 1 + 2 + 3 + 4 = 10

However, the expression also includes X5, indicating that X takes the value 5 as well. Therefore, we add 5 to the sum:

ΣX = 10 + 5 = 15

So, the sum of 1 + 2 + 3 + 4 + X5, where X takes the values 1-4, is equal to 15.

Moving on to expression (b) y2 + y3 + Y, where Y takes the values y₁ = -1, y₂ = -0.5, y₃ = 0, y₄ = 1.35, we can express it in summation notation as ΣY from 1 to 3. This represents the summation of Y over the range 1 to 3.

Since Y has a different value for each term, we simply substitute Y with each value from 1 to 3 and add them together:

ΣY = y₁ + y₂ + y₃ = -1 + (-0.5) + 0 = -1.5

Hence, the sum of y₂ + y₃ + Y, where Y takes the values y₁ = -1, y₂ = -0.5, y₃ = 0, y₄ = 1.35, is equal to -1.5.

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Answer:

We can write 36 as a product of prime factors: 36 = 2² × 3². The expression 2² × 3² is said to be the prime factorization of 36.

Answer:

2² x 3²

Step-by-step explanation:

The prime factors of 36:

2 x 2 x 3 x 3

= 2² x 3²

Answer:

No, a basis for P2 does not need to contain a polynomial of each degree less than or equal to 2.

Step-by-step explanation:

No, a basis for P2 does not need to contain a polynomial of each degree less than or equal to 2. This is because any set of three linearly independent polynomials of degree 2 or less can form a basis for P2. For example, the set {1, x, x^2} is a basis for P2, but it does not contain a polynomial of degree 1.

To generalize this result to Pn, we can say that any set of n+1 linearly independent polynomials of degree n or less can form a basis for Pn. This is known as the "dimension formula" for Pn.

For example, a basis for P3 would require four linearly independent polynomials of degree 3 or less. One possible basis could be {1, x, x^2, x^3}.

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Step-by-step explanation:

-3x+3x-(b÷2)=-3

0-(b÷2)=-3

-(b÷2)=-3

b=-2×-3=+6

=> b=6

The solution to the given fractional expression (x - 4 3/10=17 2/5) is 217/10 or 21 7/10.

An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.

A fraction can be defined as a numerical quantity which isn't expressed as a whole number. This ultimately implies that, a fraction is simply a part of a whole number.

In Mathematics, a fraction comprises two (2) main parts and these include the following:

Next, we would find a solution to the given fractional expression:

x - 4 3/10 = 17 2/5

Converting the mixed fraction to a proper fraction gives:

x - 43/10 = 87/5

Adding 43/10 to both sides, we have:

x = 87/5 + 43/10

Taking the LCM and adding them together, we have:

x = (174 + 43)/10

x = 217/10

x = 21 7/10.

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Answer:

x=128

Step-by-step explanation:

180-52=128

Answer: x= 128 degrees

Step-by-step explanation:

Angle “x” and angle with measure of 52 degrees are a linear pair.

Linear pairs sum to 180.

52+x=180. Subtract 52 from both sides.

X= 128

*OR you can use angles around a point sum to 360 degrees.

52+38+142+x = 360. Combine like terms.

232+x= 360. Subtract 232 from both sides.

X= 128

It will take Aidan and Bella 5 months to have the same amount in their saving accounts.

Aidan and Bella each plan to open a savings account. Aidan starts with $90 and plans to save $20 every month. Bella starts with $15 and plans to save $35 every month. To find out when Aidan and Bella will have the same amount in their accounts, we can set up an equation and solve for the number of months. Let x represent the number of months.

Aidan's savings: 90 + 20x

Bella's savings: 15 + 35x

Set the two equations equal to each other: 90 + 20x = 15 + 35x

To determine how many months it will take for Aidan and Bella to have the same amount in their accounts, we need to solve the following equation: 90 + 20x = 15 + 35x, where x is the number of months.

We can subtract 15 from both sides to get 90 + 20x - 15 = 35x, and then subtract 20x from both sides to get 75 = 15x. Then, we can divide both sides by 15 to get x = 5. Therefore, it will take Aidan and Bella 5 months to have the same amount in their accounts.

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(a) The probability of ending up with two hits is approximately 0.1406.

(b) The probability of ending up with no hits is approximately 0.4219.

(c) The probability of ending up with exactly three hits is approximately 0.0156.

(d) The probability of ending up with at most one hit is approximately 0.8438.

To solve the given problem, we need to use the concept of binomial probability since each at-bat is independent and has the same probability of a hit. We'll use the batting average of 0.250 to calculate the probabilities.

The probability of a hit is given by the batting average, which is 0.250.

(a) To find the probability that she ends up with two hits:

Using the binomial probability formula, the probability of getting exactly two hits in three at-bats can be calculated as follows:

P(X = 2) = (3 choose 2) * \((0.250)^2 * (1 - 0.250)^(^3^ -^ 2^)\)

Calculating the values:

P(X = 2) = (3 choose 2) * \((0.250)^2 * (0.750)^1\)

P(X = 2) = 3 * 0.0625 * 0.750

P(X = 2) ≈ 0.1406

Therefore, the probability that she ends up with two hits is approximately 0.1406.

(b) To find the probability that she ends up with no hits:

Using the same binomial probability formula, the probability of getting no hits in three at-bats can be calculated as follows:

P(X = 0) = (3 choose 0) *\((0.250)^0 * (1 - 0.250)^(^3^ -^ 0^)\)

Calculating the values:

P(X = 0) = (3 choose 0) *\((0.250)^0 * (0.750)^3\)

P(X = 0) = 1 * 1 * 0.4219

P(X = 0) ≈ 0.4219

Therefore, the probability that she ends up with no hits is approximately 0.4219.

(c) To find the probability that she ends up with exactly three hits:

Using the same binomial probability formula, the probability of getting three hits in three at-bats can be calculated as follows:

P(X = 3) = (3 choose 3) \(* (0.250)^3 * (1 - 0.250)^(^3^ -^ 3^)\)

Calculating the values:

P(X = 3) = (3 choose 3) *\((0.250)^3 * (0.750)^0\)

P(X = 3) = 1 * 0.0156 * 1

P(X = 3) ≈ 0.0156

Therefore, the probability that she ends up with exactly three hits is approximately 0.0156.

(d) To find the probability that she ends up with at most one hit:

We can find this probability by calculating the sum of the probabilities of getting 0 hits and 1 hit.

P(X ≤ 1) = P(X = 0) + P(X = 1)

Substituting the calculated values:

P(X ≤ 1) ≈ 0.4219 + P(X = 1)

To calculate P(X = 1), we can use the binomial probability formula as before:

P(X = 1) = (3 choose 1) * \((0.250)^1 * (0.750)^(^3^-^1^)\)

Calculating the values:

P(X = 1) = (3 choose 1) * \((0.250)^1 * (0.750)^2\)

P(X = 1) = 3 * 0.250 * 0.5625

P(X = 1) ≈ 0.4219

Substituting back into the equation:

P(X ≤ 1)

≈ 0.4219 + 0.4219

P(X ≤ 1) ≈ 0.8438

Therefore, the probability that she ends up with at most one hit is approximately 0.8438.

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Equation for the function g is g(x) = \(a \times \sqrt{(b \times (x - h))} + k\)

A transformation of a function can involve horizontal and/or vertical shifts, reflections, and stretches/shrinks. The general form for transforming the function f(x) is:
g(x) = a × f(b × (x - h)) + k
Here:
- a affects vertical stretching/shrinking and reflections
- b affects horizontal stretching/shrinking and reflections
- h is the horizontal shift
- k is the vertical shift
For f(x) = √x, the transformation equation will look like this:
g(x) = \(a \times \sqrt{(b \times (x - h))} + k\)

Once you have the details about the transformation (shifts, stretches, reflections), plug them into the equation above to find the equation for function g.

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Answer:

45 × 4 = (9 × 5) × (2 × 2) = (9 × 2) × (5 × 2) = 18 × 10 = ?

Step-by-step explanation:

Which equation shows one way to find the value of 45 × 4?

45 × 4

Splitting each number into factors of each other

45 = 9 × 5

4 = 2 × 2

45 × 4 = (9 × 5) × (2 × 2)

45 × 4 = (9 × 2) × (5 × 2)

45 × 4 = 18 × 10

Option A is the correct option

The distance between the two points in simplest radical form. (-1, 3) and (7, 5) is 68

Distance between two points is the length of the line segment that connects the two points in a plane. The formula to find the distance between the two points is usually given by d=√((x2 – x1)² + (y2 – y1)²)

using the formula for distance between two points;

d = \(\sqrt{(x1-x2)^2 + (y1 - y2)^2}\)

Substituting for the values

d = \(\sqrt{(-1-7)^2 + (3 - 5)^2}\)

d = \(\sqrt{(-8)^2 + (-2)^2}\)

d = \(\sqrt{64 + 4}\)

d= \(\sqrt{68}\)

d = 8

Hence, the distance between the two points is 8

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Answer:

( x + 4 ) ( x + 1 )

Step-by-step explanation:

x² + 5x + 4

= x² + 1x + 4x + 4

= x ( x + 1 ) + 4 ( x + 1 )

= ( x + 4 ) ( x + 1 )

Hence, factorised.

To find the absolute maximum and minimum values of f on the given interval, we need to first take the derivative of f and set it equal to zero to find the critical points.

Then, we will check the endpoints of the interval to see if they give us any maximum or minimum values. Taking the derivative of f, we get f'(t) = 5 - (5/2) csc^2(t/2). Setting this equal to zero and solving for t, we get t = π/2, 3π/2. These are the critical points.

Next, we need to check the values of f at the critical points and the endpoints of the interval. At t = π/4, f(π/4) = 5π/4 + 5√2, and at t = 7π/4, f(7π/4) = -3π/4 - 5√2. At the critical points, f(π/2) = 5√2 and f(3π/2) = -5√2.

Therefore, the absolute maximum value of f on the interval [π/4, 7π/4] is 5π/4 + 5√2, and the absolute minimum value of f on the interval is -3π/4 - 5√2.

As there are no critical points in the given interval, the absolute maximum and minimum values must occur at the endpoints. By comparing the function values at these endpoints, we can determine the absolute maximum and minimum values:

Absolute minimum value: min{f(π/4), f(7π/4)}
Absolute maximum value: max{f(π/4), f(7π/4)}

Keep in mind that you'll need to calculate the actual function values at the endpoints to determine the numerical values of the absolute minimum and maximum.

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Answer:

24 pots 2 plates

Step-by-step explanation:

Answer:

24 pots and 2 plates

Step-by-step explanation:

Answer:

Tom weighs 5 times as much as Nicholas

Step-by-step explanation:

To find how many times as much as Nicholas Tom weighs, we will divide Tom's weight by Nicholas' weight. This is done as follows:

Tom's weight = 168.5 pounds

Nicholas' weight = 33.7 pounds

Dividing both weights = 168.5 ÷ 33.7 = 5

∴ Tom weighs 5 times as much as Nicholas

The bball3 dataset appears to take the form of panel data, which is a type of longitudinal data consisting of multiple observations of the same individuals over time

The bball3 dataset appears to take the form of panel data. Panel data is a type of longitudinal data where observations are made on the same individuals over time. This means that the dataset likely consists of multiple observations of a set of individuals, with the observations collected at different points in time. In a panel data set, each individual can be referred to as a ‘panel unit’.

Cross-sectional data, on the other hand, consists of observations that are collected only once, at a single point in time. This means that each observation consists of a snapshot of the population at a given moment, which is different from panel data where each observation may represent different points in time for the same individuals.

Time series data is a type of data that is collected over a period of time. It captures how a certain variable changes over time, and is often used for forecasting purposes. This is different from panel data, which captures information about the same individuals at different points in time.

In conclusion, the bball3 dataset appears to take the form of panel data, which is a type of longitudinal data consisting of multiple observations of the same individuals over time. It is not cross-sectional or time series data.

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Answer:

y=1/2(x-6)-2

Step-by-step explanation:

y=m(x-h)+k

y=1/2(x-6)-2

Answer:

\(y=\frac{1}{2} x-5.\)

Step-by-step explanation:

1) the form of the required line in slope-interception form is:

y=s*x+i, where s [slope] and i [intercept] are numbers;

2) according to the condition s=1/2, it means the required equation can be written as:

y=1/2x+i;

3) in order to calculate the value of 'i', it is needed to substitute (6;-2) into the written required equation:

-2=1/2 *6+i; ⇒ i=-5;

4) finally, if s=1/2 and i=-5, then the required equation is:

y=1/2 *x-5.

P.S. the suggested way is not the shortest one.

The first scenario described is an example of a retrospective cohort study.  The second scenario suggests a retrospective cohort study as well. The third scenario represents a cross-sectional study, where researchers conduct a survey among high school students to assess the prevalence of obesity and diabetes.

1. In the first scenario, a retrospective cohort study is conducted by tracking individuals over a 20-year period. The study begins in 1960 and collects data on cigar smoking practices. After 20 years, the participants are followed up to determine if they developed any cancers. This type of study design allows researchers to examine the long-term effects of smoking Cuban cigars.

2. The second scenario involves a retrospective cohort study as well. The objective is to study the long-term neurological effects of a discontinued anesthetic agent. The researchers identify patients who received the drug before it was discontinued and then assess the occurrence of subsequent neurological disorders. This study design allows for the examination of the relationship between exposure to the anesthetic agent and the development of neurological disorders.

3. The third scenario represents a cross-sectional study. Researchers aim to assess the prevalence of obesity and diabetes among high school students during their junior year. They conduct a survey to gather information on the students' current weight, diabetes status, and other relevant factors. A cross-sectional study provides a snapshot of the population at a specific point in time, allowing researchers to examine the prevalence of certain conditions or characteristics.

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Answer:

Weight of apples = 1.72 kg

Step-by-step explanation:

Given:

Total mass of sale = 8.6 kg

Pears weight = 4/5 of total weight

Find:

Weight of apples

Computation:

Weight of apples = [1 - 4/5]Total mass of sale

Weight of apples = [1/5]8.6

Weight of apples = 1.72 kg

Answer:

(tan-1x)' = 1/(1 + x2)

Step-by-step explanation:

The differentiation of tan inverse x is the process of finding the derivative of tan inverse x with respect to x.

Answer:

B

Step-by-step explanation:

its that how you would look like if you were anime sorry was looking at your pf. have a nice day

Answer:

Yes

Step-by-step explanation:

Yes because if you insert -39 for x and 42 for y then your equation is:

42 = -39 + 81

If you were to solve this equation it would be true.