1) Give an equation for the line which goes through (1,-5) and has slope m=-3.

Given: the table:

x -3 -2 -1 0 1 2 3

f(x) 8 7 6 5 4 3 2

g(x) -7 -2 0 1 0 -2 -7

Let's solve for the following:

• (a). (f o g)(1)

To solve this function operation, we have:

(f o g)(1) = f(g(1))

Here we are to find the value of f when g(1).

Therefore, we have:

g(1) = 0

f(g(1)) = f(0) = 5

Hence, we have:

(f o g)(1) = 5

• (b). (f o g)(2)

Apply the formula:

(f o g)(x) = f(g(x))

Thus, we have:

(f o g)(2) = f(g(2))

From the table, we have:

g(2) = -2

f(g(2) = f(-2) = 7

Hence, we have:

(f o g)(2) = 7

• (c). (g o f)(2)

We have:

(g o f)(2) = g(f(2))

From the table, we have:

f(2) = 3

g(f(2)) = g(3) = -7

Thus we have:

(f o g)(2) = -7

• (d). (g o f)(3)

Apply the f

1)

Consider P to be at the same vertical distance between the maximum and minimum height the blades can reach. Therefore, at t=0, P has to be at h=0 (the maximum height is 1 and the minimum one is -1).

Then, since the fan blades rotate counterclockwise, after t=0, h has to increase until it reaches a value of 1.

Finally, a revolution is completed after 1 second; therefore, at t=1, the h has to be equal to 0 (the same height as at t=0).

2)

Approximately, every year the Earth reaches its maximum distance from the sun and its minimum distance once a year, and that is a cycle that repeats almost without alteration. Furthermore, since the position of the Earth around the sun is given by an ellipse, the position of the Earth around the Sun can be expressed using trigonometric functions (because of polar coordinates).

Similarly, a rotating wheel will reach its maximum and minimum height eventually; therefore, it can be modeled using trigonometric functions which are periodic.

Finally, as for the area of a sheet of paper. Notice that the more we fold it, the less its area becomes, it does not reach its maximum anymore.

Given x inches, the number of centimeters is 2.54x, this is not a periodic function.

Due to the effects of gravity, the height of a pendulum can be expressed using a periodic function given that no energy is lost.

The trajectory of a tossed ball is given by a parabola, unless one tosses the ball again at the same initial height, option F cannot be modeled using a periodic function.

The quantity of ribbon that Ali started with was 16/21 feet, based on the mathematical operation of addition.

The basic mathematical operations include addition, subtraction, division, and multiplication.

In the addition operation, two or more addends are added to obtain a result called the sum or total using the equation symbol (=) and the addition operand (+).

The quantity of ribbon attached to the rearview mirror = 2/7

The remaining quantity of ribbon after the attachment = 10/21

The quantity of ribbon Ali started with = 16/21 (2/7 + 10/21)

Thus, using the addition operation, we can conclude that Ali started with 16/21 feet of ribbon.

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Yes, there is a difference in the shapes of the displacement-time graphs for uniform acceleration towards the positive direction, uniform acceleration towards the negative direction, uniform deceleration towards the positive direction, and uniform deceleration towards the negative direction.

Uniform acceleration towards the positive direction:

In this case, the object's velocity increases in the positive direction over time. The displacement-time graph will have a concave-upward shape, forming a curve that starts with a small slope and gradually becomes steeper as time progresses.

Uniform acceleration towards the negative direction:

Here, the object's velocity increases in the negative direction, meaning it accelerates in the opposite direction to its positive direction.

The displacement-time graph will have a concave-downward shape, forming a curve that starts with a steep slope and gradually becomes less steep as time progresses.

Uniform deceleration towards the positive direction:

In this scenario, the object's velocity decreases in the positive direction, but it still moves towards the positive direction.

The displacement-time graph will show a curve with a decreasing slope, forming a concave-downward shape, indicating that the object is slowing down.

Uniform deceleration towards the negative direction:

Here, the object's velocity decreases in the negative direction, opposing its initial direction.

The displacement-time graph will have a curve with a decreasing slope, forming a concave-upward shape, indicating that the object is slowing down but still moving in the negative direction.

In summary, the shapes of the displacement-time graphs differ based on the direction and type of acceleration (positive or negative) and whether the object is undergoing uniform acceleration or uniform deceleration. These differences can be observed through the concavity and slope of the graphs.

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Answer:

Every f(x) shall decrease to 5 times the previous value.

Answer:

Slope = -7

Step-by-step explanation:

Take any two points from the table:

   (39 , 36) ⇒ x₁ = 39 & y₁ = 36

    (41 , 22) ⇒ x₂ = 41 & y₂ = 22

Substitute the points in the below formula:

                    \(\boxed{\bf Slope = \dfrac{y_2-y_1}{x_2-x_1}}\)

                                 \(\sf = \dfrac{22-36}{41-39}\\\\\\=\dfrac{-14}{2}\\\\=-7\)

Answer:

\(\large \boxed{\sf \ \ x=1, \ \ x=2+5i, \ \ x=2-5i \ \ }\)

Step-by-step explanation:

Hello,

I assume that we are working in \(\mathbb{C}\), otherwise there is only one zero which is 1. Please consider the following.

First of all, we can notice that 1 is a trivial solution as

   \(p(1) = 1^3-5\cdot 1^2 + 33\cdot 1-29=1-5+33-29=0\)

It means that (x-1) is a factor of p(x) so we can find two real numbers, a and b, so that we can write the following.

\(p(x)=(x-1)(x^2+ax+b)=x^3+ax^2+bx-x^2-ax-b=x^3+(a-1)x^2+(b-a)x-b\)

Let's identify like terms as below.

a-1 = -5 <=> a = -5 + 1 = -4

b-a = 33

-b = -29 <=> b = 29

So

\(\boxed{ \ p(x)=(x-1)(x^2-4x+29) \ }\)

Now, we need to find the zeroes of the second factor, meaning finding x so that:

\(x^2-4x+29=0 \ \text{ complete the square, 29 = 25 + 4} \\ \\ <=> x^2-2\cdot 2 \cdot x+2^2+25=0 \\ \\ <=>(x-2)^2=-25=(5i)^2 \ \text{ take the root } \\ \\<=>x-2=\pm 5i \ \text{ add 2 } \\ \\ <=> x = 2+5i \ \text{ or } \ x = 2-5i\)

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

Domain of 1/x = x<0 or x>0

range of 1/x = f(x) <0 or f(x) >0

Step-by-step explanation:

hello

it is c

hehehehe hope it helps

Answer:

The option c. (x-6)(x-1)

Step-by-step explanation:

x^2 - 7x +6

S=-7

P=6

x^2-1x-6x+6

x(x-1)-6(x-1)

(x-6)(x-1)

Answer:

Step-by-step explanation:

The right statistical procedure is by applying a hypothesis test that uses a single mean. Here, if we are to talk about comparison, it should be between the mean IQ of the students in the class and the national average IQ. The class is not for a comparison between two population means because it is viewed as the sample of the population. That is to say, the required task is to determine if the sample mean is greater than the population mean. We can conclude that this obeys a hypothesis test rather than a confidence interval.

Answer:

Step-by-step explan

Answer:

D

Step-by-step explanation:

why the panic ? you only need to compare the tiles with the actual terms in the equations and add them up.

x²

-x²

-x -x

x x x x (clearly that means 4x)

-1 -1 -1

1 1

so, we see it is D.

9514 1404 393

Answer:

  y = 2x

Step-by-step explanation:

The blank is filled with the ratio y/x. Pick any x and y pair from the table and compute y/x to find that value. (It is generally convenient to choose x=1 for this purpose.)

  y/x = 2/1 = 2

Then ...

  y = 2x

Answer:

y=2x

Step-by-step explanation:

when x is one y would be 2, and so on

The given decimal can be written as a quotient of 513/1000.

What is quotient?

In maths, the result of dividing a number by any divisor is known as the quotient. It refers to how many times the dividend contains the divisor. The statement of division, which identifies the dividend, quotient, and divisor, is shown in the accompanying figure. The dividend 12 contains the divisor 2 six times. The quotient is always less than the dividend, whether it is larger or smaller than the divisor.

we can write the decimal given 0.513 as a answer of of 513 divided by 1000.

I.e.

\(0.513 = \frac{513}{1000}\)

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The equation of the relationship is f(200) = 0.75 * 200

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

Total number of drinks = 200

Cost of each drink = 0.75

Using the above as a guide, we have the following:

f(x) = Cost of each drink * Total number of drinks

Where

f(x) = Total cost

Substitute the known values in the above equation, so, we have the following representation

f(200) = 0.75 * 200

Hence, the equation is f(200) = 0.75 * 200

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Answer:

infinity

Step-by-step explanation:

Given the function

Limit b⇒0 (Sin b)/b³

First substitute the value of b into the function to have

Limit b⇒0 (Sin b)/b³

= sin 0/0³

= 0/0 (Ind)

Apply lhospital rule

Limit b⇒0 (d./db(Sin b))/(d/db(b³))

=>Limit b⇒0 (cos b)/3b²

Substitute the value of b

Cos 0/3(0)²

= 1/0

= infinity

Hence the answer is infinity

Answer:

  m = 20

Step-by-step explanation:

You want the value of m when (4m +10)° represents an angle of 90°.

The perpendicular bisector XZ intersects segment WY at right angles. The measure of a right angle is 90°, so we have ...

  (4m +10)° = 90°

Dividing by ° and subtracting 10 gives ...

  4m +10 = 90

  4m = 80

  m = 20 . . . . . . divide by 4

The value of m is 20.

<95141404393>

Answer: M is the coefficient

Step-by-step explanation:

Answer:

15-18

Step-by-step explanation:

The IQR is the middle 50% of a set of numbers

There are 8 numbers, so its the middle 4

The middle 4 consists of 15,15,16,18

The range is 15-18

Answer:

11

Step-by-step explanation:

Opposite sides of a trapezoid are parallel. So, by the same-side interior angles theorem,

\(-16x+10x+86=180 \\ \\ 10x+70=180 \\ \\ 10x=110 \\ \\ x=11\)

Answer:

infinite 7v + 6v could be anything theres no context to find out what v represents and how much it could amount to

Step-by-step explanation:

The temperature drops by \(31\°C\) from day to night in this city.

To calculate the temperature drop from day to night in \(\°C\), we subtract the average nightly low temperature from the average daily high temperature.

Given:

Average nightly low temperature: \(-40\°C\)

Average daily high temperature: \(-9\°C\)

The temperature drop can be calculated as:

Temperature drop = Average daily high temperature - Average nightly low temperature

Substituting the given values:

Temperature drop = \(-9\°C - (-40\°C)\)

Simplifying the equation:

Temperature drop = \(-9\°C + 40\°C\)

Temperature drop = \(31\°C\)

The concept of temperature drop refers to the difference in temperature between two specific periods or conditions. In this case, we are looking at the temperature drop from day to night in a city in China known for its cold climate.

Therefore, the temperature drops by \(31\°C\) from day to night in this city.

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\(\boxed{A}\\\\ U=5(2n+22)+2\left( n+\cfrac{3}{2} \right) \\\\\\ U=10n+110+2n+3 \implies U=12n+113 \\\\[-0.35em] ~\dotfill\\\\ \boxed{B}\hspace{5em}\textit{in 2009, that's 9 years after 2000, n = 9}\\\\ U(9)=12(9)+113\implies U(9)=221 ~~ millions\)

Using Pythagorean theorem, the length of the ladder is 10ft

In mathematical terms, if y and z are the lengths of the two shorter sides (also known as the legs) of a right triangle, and x is the length of the hypotenuse, the Pythagorean theorem can be expressed as:

x² = y² + z²

In the questions given, the only one we can use Pythagorean theorem to solve is the one with ladder since it's forms a right-angle triangle.

To calculate the length of the ladder, we can write the formula as;

x² = 8² + 6²

x² = 64 + 36

x² = 100

x = √100

x = 10

The length of the ladder is 10 feet

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The top left graph represents the weight of the radioactive isotope over time.

An exponential function has the definition presented according to the equation as follows:

\(y = ab^x\)

In which the parameters are given as follows:

The parameter values for the function in this problem are given as follows:

a = 96, b = 0.5.

Hence the function is given as follows:

\(y = 96(0.5)^x\)

Two points on the graph of the function are given as follows:

(1,48) and (2, 24).

Hence the top left graph represents the weight of the radioactive isotope over time.

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Answer:

Graph W

Step-by-step explanation:

The given information describes a radioactive decay process, where the weight of the isotope decreases by half at regular intervals. This type of decay is characteristic of exponential decay.

Based on the description, the graph that represents the weight of the radioactive isotope over time would be a decreasing exponential curve, where the y-axis represents the weight of the isotope (in grams), and the x-axis represents time (in hours).

The initial weight of the isotope is 96 grams, and after each subsequent hour, the weight becomes half of what it was in the previous hour. Therefore, the correct graph would start at 96 grams (the initial weight when x = 0) and then decrease by half every hour. It would be a curve that gets closer and closer to zero but never quite reaches it.

Initial weight: 96 grams

After 1 hour: 96 / 2 = 48 grams

After 2 hours: 48 / 2 = 24 grams

After 3 hours: 24 / 2 = 12 grams

After 4 hours: 12 / 2 = 6 grams

After 5 hours: 6 / 2 = 3 grams

So, the points on the graph would be:

Therefore, the graph that represents the weight of the radioactive isotope over time is Graph W.

The value of x for each item is given as follows:

28. x = 5.

29. x = 3.44.

For item 28, we apply the crossing chord theorem, which states that the products of the parts of the chords are equal, hence the value of x is obtained as follows:

16x = 10 x 8

16x = 80

x = 5.

For item 29, we apply the two secant theorem, hence the value of x is obtained as follows:

10(x + 10) = 12(12 + 25)

10x + 100 = 444

10x = 344

x = 3.44.

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According to the equation the given all necessary math work are:

\(A: (x -f)^2 +(y -g)^2 = h^2\)

B:  domain: [-5, 11]; range: [-9, 7]

C:  yes, inside

The hypοtenuse's square is equal tο the sum οf the squares οf the οther twο sides if a triangle has a straight angle (90 degrees), accοrding tο the Pythagοras theοrem. Keep in mind that BC² = AB² + AC² in the triangle ABC signifies this. Base AB, height AC, and hypοtenuse BC are all used in this equatiοn. The lοngest side οf a right-angled triangle is its hypοtenuse, it shοuld be emphasized.

Part A:

Use οf the Pythagοrean theοrem gets yοu tο the equatiοn fοr a circle in essentially οne step:

sum οf squares οf sides = square οf hypοtenuse

\((x -f)^2 +(y -g)^2 = h^2\) . . . . . . circle cantered οn (f, g) with radius h

Part B:

The circle will be defined fοr values οf x in the dοmain f ± h, and fοr values οf y in the range g ± h.

dοmain: 3 ± 8 = [-5, 11]

range: -1 ±8 = [-9, 7]

Part C:

The distance frοm pοint (10, -4) tο (f, g) is ...

\(h^2 = (10 -3)^2 +(-4 -(-1))^2\)

\(h^2 = 7^2 +(-3)^2 = 49 +9 = 58\)

h = √58 < 8 . . . . the distance tο the pοint is less than h=8.

The pοint is inside the circle.

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