If f(3x) = f(3) + f(x) then show that f(1) = f(3) = f(9) = f(27) = f(81)​

Answer:

8)  x = 5, y = -5

10)  x = -2.8, y = 3.4

Step-by-step explanation:

To solve a system of linear equations we can use either the substitution method or the elimination method.

Given system of linear equations:

[tex]\begin{cases}-6x-3y=-15\\6y+6x=0\end{cases}[/tex]

Solve the given system of linear equations using the elimination method.

Add the two equations to eliminate the term in x:

[tex]\begin{array}{crcccl}&-6x & - & 3y & = & -15\\+&(6x & + &6y & = & \;\;\;\;0)\\\cline{2-6}&0&+&3y&=&-15\end{array}[/tex]

Solve the resulting equation for y by dividing both sides by 3:

[tex]\implies 3y \div 3 &=-15 \div 3[/tex]

[tex]\implies y=-5[/tex]

Substitute the found value of y into the second equation and solve for x:

[tex]\implies 6(-5)+6x=0[/tex]

[tex]\implies -30+6x=0[/tex]

[tex]\implies 6x=30[/tex]

[tex]\implies 6x \div 6=30 \div 6[/tex]

[tex]\implies x=5[/tex]

Therefore, the solution to the given system of equations is:

[tex]\begin{cases}-x+3y=13\\-3x-y=5\end{cases}[/tex]

Solve the given system of linear equations using the substitution method.

Rearrange the first equation to isolate x:

[tex]\implies -x+3y=13[/tex]

[tex]\implies 3y=x+13[/tex]

[tex]\implies x=3y-13[/tex]

Substitute the expression for x into the second equation and solve for y:

[tex]\implies -3(3y-13)-y=5[/tex]

[tex]\implies -9y+39-y=5[/tex]

[tex]\implies -10y+39=5[/tex]

[tex]\implies -10y=-34[/tex]

[tex]\implies -10y\div -10=-34 \div -10[/tex]

[tex]\implies y=3.4[/tex]

Substitute the found value of y into the expression for x and solve for x:

[tex]\implies x=3(3.4)-13[/tex]

[tex]\implies x=10.2-13[/tex]

[tex]\implies x=-2.8[/tex]

Therefore, the solution to the given system of equations is:

the probability of the numbers will add to 4 or less will be 25%

What is the percentage?

A percentage that represents a tenth of a quantity. One percent, denoted by the symbol 1%, is equal to one-hundredth of something; hence, 100 percent denotes the full thing, and 200 percent designates twice the amount specified. A portion per hundred is what the percentage denotes. The percentage refers to one in a hundred. The % sign is used to denote it.

The orange spinner is spun and then the aqua spinner is spun.

The probability that the numbers will add to 4 or less will be of 1 out of 4 that will be 1/4*100

= 25%

Hence the probability of the numbers will add to 4 or less will be 25%

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Using trigonometric functions, the width of the volleyball court is approximately 31.13 meters.

What are trigonometric functions?

Trigonometric functions are mathematical functions that relate the angles and sides of a right triangle.

The basic trigonometric functions are:

Sine (sin): the ratio of the length of the side opposite an angle to the length of the hypotenuse of the triangle.

Cosine (cos): the ratio of the length of the side adjacent to an angle to the length of the hypotenuse of the triangle.

Tangent (tan): the ratio of the length of the side opposite an angle to the length of the side adjacent to the angle.

We can use basic trigonometry to solve this problem.

Let's assume that the width of the volleyball court is "x" meters.

From the corner of the court to the opposite player, we have a right triangle with the following sides:

the adjacent side: x meters (since it is parallel to the court's sideline)

the opposite side: 18 meters (since it is perpendicular to the sideline)

the hypotenuse: we don't know it yet, but we can find it using the given angle.

We can use the tangent function to find the hypotenuse:

tan(30) = opposite / adjacent

tan(30) = 18 / x

Multiplying both sides by x:

x * tan(30) = 18

x = 18 / tan(30)

x = 18 / 0.5774

x ≈ 31.13 meters

Therefore, the width of the volleyball court is approximately 31.13 meters.

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The semicircle's radius is roughly 1.38 cm, and its perimeter is roughly 5.37 cm.

the perimeter of the semicircle is:

P = l + C(semi)

P = r + πr

P = (1 + π)r

P ≈ 5.37 cm

The area encircling a two-dimensional figure is known as its perimeter. Whether it is a triangle, square, rectangle, or circle, it specifies the length of the shape. The two primary characteristics of a 2D shape are area and perimeter.

Each form has a different perimeter depending on its measurements. The perimeter is only ever stated as the circle's diameter when referring to a circle. So we must add all of the sides of each polygon to determine its perimeter, which is the same for all polygons.

from the question:

Let's start with finding the radius of the semicircle.

The formula for the area of a semicircle is:

A = (πr²)/2,

where A is the area and r is the radius.

We are informed that the semicircle's area is 6 [tex]cm^2[/tex]. So, we can enter this value into the formula and find r:

6 = (πr²)/2

Multiplying both sides by 2:

12 = πr²

Dividing both sides by π:

r² = 12/π

Taking the square root of both sides:

r = √(12/π)

Now we can simplify this expression by rationalizing the denominator:

r = √(12/π) * (√π/√π)

r = √(12π)/π

r ≈ 1.38 cm

Thus, the semicircle's radius is roughly 1.38 cm.

We must multiply the circumference of the semicircle by the length of the straight edge to determine the semicircle's perimeter. The formula for calculating a circle's circumference is:

C = 2πr

But for a semicircle, we only need half of the circumference:

C(semi) = πr

So the perimeter of the semicircle is:

P = l + C(semi)

P = r + πr

P = (1 + π)r

P ≈ 5.37 cm

As a result, the semicircle's radius is roughly 1.38 cm, and its perimeter is roughly 5.37 cm.

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Carrying an ax in one's teeth is a dangerous and potentially deadly action.

The weight and sharpness of the ax could easily cause injury or even death if it were to slip or the individual were to lose their balance.

Additionally, carrying an ax in this manner would likely result in the person being unable to communicate effectively, as their mouth would be occupied and their ability to speak clearly would be hindered.

If someone were to attempt to carry an ax in their teeth, they would be risking their safety and potentially the safety of those around them.

It is not a recommended or advisable course of action, and anyone who witnessed such behavior should exercise caution and avoid interacting with the individual until the ax has been safely secured.

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The object will be 6.1 m from the ground after 2 seconds.

The falling object model is used to calculate the height of an object after it has been dropped for a certain period of time. The equation used is h=h0−1/2gt2, where h0 is the initial height, g is the acceleration due to gravity and t is the time elapsed.

For example, if an object is dropped from a height of 15 m and falls for 2 seconds, we can calculate the height it will be at after 2 seconds.

The equation is then h=15−1/2(9.8)22

h=15−4.9•4

h=6.1 m

Therefore, the object will be 6.1 m from the ground after 2 seconds.

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The height of the balcony from which the ball was kicked is 40 feet.

A ball was kicked into the air from the balcony of an apartment building.

The height of the ball, in feet, can be represented by the equation y= -16t^2+24t +40

where t is the time in seconds since the ball was kicked and y is the height of the ball.

The equation to represent the height of the ball is given as:

y = -16t² + 24t + 40Where y represents the height of the ball in feet and t represents the time in seconds since the ball was kicked.

To find the height of the balcony from which the ball was kicked, we need to find the initial height of the ball.

That is when the ball is at the balcony of the apartment building.

This happens when t = 0.

Substituting t = 0 in the equation, we get:

y = -16(0)² + 24(0) + 40y = 40

Therefore, the height of the balcony from which the ball was kicked is 40 feet.

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Answer:

Step-by-ste10p explanation:

The equation of the line is y = (-1/3)x + 2.

This is the equation of the line in slope-intercept form, where the slope is -1/3 and the y-intercept is 2.

What is the equation of the line?

A linear equation is an algebraic equation of the form y=mx+b. where m is the slope and b is the y-intercept.

The place on the x-axis where the line crosses. This is the x-intercept of the linear function.

If the line is horizontal (and not the x-axis), the linear function will have no x-intercept.

Here, the line crosses the x-axis at 6.

The place on the y-axis where the line crosses. This is the y-intercept of the linear function

Here, the line crosses the y-axis at 2.

If a line crosses the x-axis at the point (6,0), it means that the line intersects the x-axis when the y-coordinate is 0 and the x-coordinate is 6. Similarly, if the line crosses the y-axis at the point (0,2), it means that the line intersects the y-axis when the x-coordinate is 0 and the y-coordinate is 2.

We can use these two points to find the equation of the line using the slope-intercept form:

y = mx + b

where m is the slope of the line and b is the y-intercept (the point where the line crosses the y-axis).

To find the slope, we can use the two points (6,0) and (0,2):

m = (y2 - y1) / (x2 - x1)

m = (2 - 0) / (0 - 6)

m = -1/3

To find the y-intercept, we can use the point (0,2):

y = mx + b

2 = (-1/3)(0) + b

b = 2

Therefore, the equation of the line is y = (-1/3)x + 2.

This is the equation of the line in slope-intercept form, where the slope is -1/3 and the y-intercept is 2.

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As per the unitary method, the amount saved by Aaron after one year is  $780

We can use the following formula to find out how much Aaron saves per month:

Amount saved per month = Total amount saved / Number of months

We can use this formula to find out how much Aaron saves per month for each period:

For the first period (3 months):

Amount saved per month = 195 / 3

= 65

For the second period (4 months):

Amount saved per month = 260 / 4

= 65

For the third period (6 months):

Amount saved per month = 390 / 6

= 65

For the fourth period (7 months):

Amount saved per month = 455 / 7

= 65

We can see that Aaron saves $65 per month, regardless of the time period. Therefore, we can use this value to find out how much he will save in one year (12 months):

Amount saved in 1 year = Amount saved per month x Number of months

= 65 x 12

= 780

Therefore, we can predict that Aaron will save $780 after one year.

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The least biased sampling strategy is D) Go through the company’s customer records, selecting every 40th subscriber. Send employees to those homes to interview the people chosen.

Four new sampling strategies have been proposed to help PTV determine whether enough cable subscribers are likely to purchase high-speed Internet Service. For each, indicate what kind of sampling strategy is involved and what (if any) biases might result.A) Run a poll on the local TV news, asking people to dial one of two phone numbers to indicate whether they would be interested. This type of sampling strategy is known as convenience sampling.

This technique is biased since only those who watch the local TV news and are interested in high-speed internet services can participate in the survey. The majority of the consumers who are in need of high-speed internet may not watch the local TV news. Hence the survey is biased and does not represent the entire population.B) Hold a meeting in each of the fifteen towns and tally the opinions expressed by those who attend the meetings. This type of sampling strategy is called a Quota sampling. It is biased since there is no guarantee that everyone will attend the meeting or that they will represent the opinions of the entire population.

This sampling strategy also has a higher risk of selection bias since the people who are likely to attend the meeting are the ones who are interested in the product.C) Randomly select one street in each town and contact each of the households on that street. This type of sampling strategy is called Cluster Sampling. This method is less biased compared to the other two strategies mentioned earlier. Since each street is chosen at random, there is a higher chance of getting opinions from a wider range of customers. However, this strategy can still be biased as the opinions may differ from one street to another.D) Go through the company’s customer records, selecting every 40th subscriber. Send employees to those homes to interview the people chosen. This type of sampling strategy is called Systematic Sampling.

This strategy is the least biased among the four strategies. Since customers are selected randomly, there is a higher chance of obtaining a representative sample. The opinions of customers who have discontinued the services are not included, and the survey can only be conducted with current customers. 

Hence, the least biased sampling strategy is D) Go through the company’s customer records, selecting every 40th subscriber. Send employees to those homes to interview the people chosen.

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Answer:

C. Since the amount added per unit time is constant, the amount of water in the bucket increases by a constant amount for equal time intervals. This is a linear function.

B. The interest paid each year is constant, so the amount earned increases by a constant amount for equal time intervals. This is a linear function.

B. The interest paid each month is a factor of the current balance, so the balance is multiplied by a constant factor for equal time intervals. This is an exponential function.

Step-by-step explanation:

Answer: Your welcome!

Step-by-step explanation:

1. Answer: D. Since the amount added per unit time is constant, the amount of water in the bucket is multiplied by a constant factor for equal time intervals. This is an exponential function. As time increases, the amount of water in the bucket will increase exponentially (each successive unit of time will add a multiple of the original amount).

2. A. The amount earned is described by a linear function. The interest paid each year is constant, so the amount earned increases by a constant amount for equal time intervals. This is a linear function.

3. Answer: B. The interest paid each month is a factor of the current balance, so the balance is multiplied by a constant factor for equal time intervals. This is an exponential function.

An exponential function is one in which the value of a variable increases or decreases by a constant factor for each equal time interval. In this case, the balance of the savings account increases by a fixed amount of interest each month, which is calculated from the current balance. This amount is multiplied by the current balance, resulting in an exponential function.

Answer:

Assuming an ideal pulley system, the force required to lift a 10 Newton box with one pulley would be 10 Newtons. This is because the force required to lift an object using a pulley system is equal to the weight of the object being lifted. In an ideal pulley system, there is no friction or energy loss, so the force required is equal to the weight of the object. Therefore, if the weight of the box is 10 Newtons, a force of 10 Newtons would be required to lift it with one pulley.

Answer:

I would say twv

Step-by-step explanation:

BODMAS rule, helps us to determine the value of expression. The expanded value of expression,

63 - [(- 3){- 2 - 8 - 3}] ÷ [3{5 + (- 2)(- 1)}], is equals to the 61.14.

Mathematical operations such as addition, subtraction, multiplication, and division are included in arithmetic operations. For solving expression according to specific priority, we use the BODMAS rule, which follows as

Now, we have an expression, 63 - [(- 3){- 2 - 8 - 3}] ÷ [3{5 + (- 2)(- 1)}] say x

=> x = 63 - [(- 3){- 2 - 8 - 3}] ÷ [3{5 + (- 2)(- 1)}]

we have to calculate value of x,

Using BODMAS rule,

=> x = 63 - [(- 3){- 13 }] ÷ [3{5 + 2}] (expands inner bracket)

=> x = 63 - [ 39 ] ÷ [3×7]

=> x = 63 - [ 39 ÷ 21]

=> x = 63/1 - 13/7

Taking least common multiple, (1,7) = 7

=> x = ( 63×7 - 13)/7

=> x = (441 - 13)/7 = 428/7

=> x = 61.14

Hence, value of expression is 61.14.

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Answer: (x-y)

Step-by-step explanation:

To find the range you must subtract the largest number from the smallest.  

The directional angles of [tex]\vec u[/tex] are approximately 101.14° with respect to the x-axis, 164.08° with respect to the y-axis, and 82.46° with respect to the z-axis.

To find the directional angles of  [tex]\vec u[/tex] , we can use the following formula:

[tex]cos\theta = u_i / |u|[/tex]

where θ is the angle between the vector and the positive x, y, or z-axis, [tex]u_i[/tex]  is the x, y, or z-component of the vector, and |u| is the magnitude of the vector.

First, we can calculate the magnitude of [tex]\vec u[/tex]  as:

[tex]|u| = \sqrt{((-8)^2 + (-40)^2 + 7^2)} = \sqrt{(1749)[/tex]

Next, we can calculate the directional angles as:

[tex]cos\theta x = -8 / \sqrt{(1749)[/tex] ≈ [tex]-0.1939[/tex]

θx ≈ 101.14°

[tex]cos\theta y = -40 / \sqrt{(1749)[/tex] ≈ -0.9679

θy ≈ 164.08°

[tex]cos\theta z = 7 / \sqrt{(1749)[/tex] ≈ 0.1441

θz ≈ 82.46°

Therefore, the directional angles of [tex]\vec u[/tex] are approximately 101.14° with respect to the x-axis, 164.08° with respect to the y-axis, and 82.46° with respect to the z-axis.

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The complete question is :

Let [tex]\vec{u}= -8i -40j + 7k[/tex] be a vector in space. Calculate and give the directional angles of u in degrees.

a.F=kx is the formula that expresses F as a function of x

b. k=F/x=8/0.3=26.67.

c.72.01 lbs

Hooke's law is a principle of physics that describes the elasticity of springs when stretched or compressed. The amount of stretch or compression of the spring is directly proportional to the force applied, according to the law.What is Hooke's Law and how can you express F as a function of x?Hooke's law is a principle of physics that describes the elasticity of springs when stretched or compressed. The amount of stretch or compression of the spring is directly proportional to the force applied, according to the law. F=kx is the formula that expresses F as a function of x using the constant of proportionality k.What is the value of k in part (a)?It is given that F=kx, and that the weight of 8 pounds stretches a spring from its natural length of 10.4 inches to a length of 10.7 inches. We have to find the value of k.8 pounds, according to Hooke's law, stretches the spring 10.7-10.4=0.3 inches from its natural length.Using F=kx, we can say that the force applied is 8 pounds, or F=8. Therefore, we have k=F/x=8/0.3=26.67.What weight will stretch the spring in part (b) to a length of 13.1 inches?We are given that the spring stretches from its natural length of 10.4 inches to a length of 13.1 inches. To find the force required to produce this extension, we need to subtract the natural length from the final length, as we did before.13.1-10.4=2.7 inches is the distance by which the spring will be stretched.The formula for F is still F=kx, and we know the value of k, which is 26.67. Thus, F=26.67*2.7=72.01 lbs.

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A. Using similar triangles, Slope of AB = Slope of AC = 42

B. The y-intercepts = 63; Slope = 42

The slope of a graph refers to the measure of the steepness of a line or a curve on a graph, calculated as the ratio of the vertical change (rise) between two points on the line to the corresponding horizontal change (run). In other words, it represents how much the y-axis changes for a given change in the x-axis.

A. Using similar triangles, we have the following:

Slope of AB = 147 - 105 / 2 -1 = 42/1

= 42

Slope of AC = 147 - 63 / 2 - 0 = 84/2

= 42

B. The line intercepts the y-axis at 63, therefore, the y-intercept is 63.

Slope of the graph is 42.

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Answer:

[tex]\frac{24}{5}[/tex]

The statement required to complete the proof is

            Statement                                        Reason

6 ∠ CDB and ∠ BDE are supplementary    If two angles form a linear pair,

                                                                      then they are supplementary

In geometry, a linear pair is a pair of adjacent angles formed by two intersecting lines. The angles in a linear pair are always supplementary, which means they add up to 180 degrees.

According to the proof,  

line 2 of the proof have it that ∠ BDE = ∠ BED

hence we say that ∠ CDB is congruent to ∠ AEB since they are supplementary to same angle

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[tex]\huge\text{Hey there!}[/tex]

[tex]\mathtt{5x + 2 = 3}[/tex]

[tex]\large\textsf{SUBTRACT 2 to BOTH SIDES}[/tex]

[tex]\mathtt{5x + 2 - 2 = 3 - 2}[/tex]

[tex]\large\textsf{SIMPLIFY it}[/tex]

[tex]\mathtt{5x = 3 - 2}[/tex]

[tex]\mathtt{5x = 1}[/tex]

[tex]\large\textsf{DIVIDE 5 to BOTH SIDES}[/tex]

[tex]\mathtt{\dfrac{5x}{5} = \dfrac{1}{5}}[/tex]

[tex]\large\textsf{SIMPLIFY it}[/tex]

[tex]\mathtt{x = \dfrac{1}{5}}[/tex]

[tex]\huge\text{Therefore your answer should be:}[/tex]

[tex]\huge\boxed{\mathtt{x = \dfrac{1}{5}}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

The length of the rectangle is 10 inches and the rectangle is 10 inches long and 2 inches wide.

The total distance around the outside of the rectangle is termed as Perimeter of a rectangle. It is equal to the sum of the lengths of all four sides of the rectangle.

Let's assume that the width as "w" inches.

As per the problem statement, the length of the rectangle is 5 times its width, which means that the length is 5w inches.

The perimeter of a rectangle is :

P = 2(l + w)

Substituting the values, we get:

24 = 2(5w + w)

Simplifying the above equation, we get:

24 = 12w

Dividing both sides by 12, we get:

w = 2

So, the width of the rectangle is 2 inches.

The length is 5 times of width, that is:-

l = 5w = 5(2) = 10

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80  unit²  is the area of the polygon in square units .

What do you mean by polygon?

A polygon is a closed object in a two-dimensional plane comprised of line segments rather than curves. The word "polygon" is a combination of the words "poly" (which meaning many) and "gon" (means sides). In order to create a closed figure, at least three line segments must be connected end to end.

The area of the polygon is required.

The area of the polygon is D. 80 square units

For triangle BCD

b = Base = 4-2 = 2 units

h = Height = 4 units

Area

    1/2bh

 = 1/2 * 2 * 4

= 4 unit²

For triangle DEF

b = Base = 2-(-1) = 3 units

h = Height = 4 units

Area

   1/2bh

= 1/2 * 3 * 4

=  6 unit²

For trapezoid ABFG

a = 4-(-1) = 5.5 units

b = 4-(-8) = 12 units

h = 8 units

Area

 1/2(a + b)h

= 1/2(5.5 + 12) * 8

 = 70 unit²

Total area is

 4 + 6 + 70  = 80  unit²

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The column headings of a check register and the information that go in that location are:

A check register, also known as a cash disbursements journal, is where you record all of your company's check and cash transactions during an accounting period. A check register is used by businesses to calculate the running balance of their checking account.

A check register will usually show the checking account's running balance. It functions similarly to a real-time record of the bank account. The bookkeeper can ensure that the total bank balance and the check register are in sync.

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The data collected on the daily volumes of water consumed by rabbits in the sample is most likely positively skewed, given the mode of 19, the median of 17, and u = 14.

Positive skewness occurs when there are more data points on the right side of the mean than on the left side, resulting in a “tail” that is skewed to the right side.

In this case, the mode of 19 is greater than the median of 17, which is greater than u of 14, indicating that there are more data points on the right side of the mean than on the left side. This means that the data is likely positively skewed.

It is important to note that the data cannot be negatively skewed, symmetrical, or bimodal based on the information given. Negative skewness occurs when there are more data points on the left side of the mean than on the right side, which is not the case here.

Symmetrical data is when the mean, median, and mode are all the same, which is not the case here.

Bimodal data is when there are two distinct modes, which is not the case here either.

Given the information, the data collected of the daily volumes of water consumed by the rabbits in the sample is most likely positively skewed.

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Solution is in da attachment!! :D

From the diagram, the value of x to the nearest tenth is given as 8cm

We should be aware that Trigonometry ratio is the relationship between the measurement of lengths and angles of a right triangle

The given triangle is a right angle triangle having the following:

Opposite = x

Adjacent = 12 cm and

Angle proportional to x = 35⁰

Using the trigonometrical ratio of Tangent

Tan∅ = opposite/adjacent

Tan35⁰ = x/12

Cross and multiply to have

x= 12*tan35⁰

x= 12*0.7002

The value of x is given by 8.402490459

Therefore the value to the nearest tenth is 8 cm

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