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The function f has the property that as x gets closer and closer to 3, the values of f(x) get closer and closer to 5.

The function f has the property that as x gets closer and closer to 3, the values of f(x) get closer and closer to 5.

A) f(3) = 5

C) lim f(x) = 5

x-->3

The function f has the property that as x gets closer and closer to 3, the values of f(x) get closer and closer to 5. This means that the limit of f(x) as x approaches 3 is 5, so C) lim f(x) = 5 x-->3 must be true. Additionally, since the values of f(x) approach 5 as x approaches 3, it follows that f(3) must also equal 5, so A) f(3) = 5 must be true as well. D) lim f(x) = 3 x-->5 is not true since the limit of f(x) as x approaches 5 is not 3. Similarly, B) f(5) = 3 is not true since f(5) does not necessarily equal 3.

The statements A) f(3) = 5 and C) lim f(x) = 5 x-->3 must be true for the given function.

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Answer:

900 kg

Step-by-step explanation:

Let's assume the cost price (C.P.) of sugar is Rs. x per kg.

The total quantity of sugar is 1500 kg.

Let the quantity of sugar sold at 8% profit be represented by y kg.

The quantity of sugar sold at 18% profit would then be (1500 - y) kg.

Using the rule of alligation, we can set up the following proportion:

(8% profit) y kg

-------------- = ------

(18% profit) (1500 - y) kg

Simplifying the proportions, we find that the difference in percentages is 4% (18% - 14% = 4%) and 6% (14% - 8% = 6%).

The ratio of these differences is 2:3.

This means that for every 2 kg of sugar sold at 8% profit, 3 kg of sugar is sold at 18% profit.

Since y represents the quantity sold at 8% profit (2 kg), we can calculate the quantity sold at 18% profit (3 kg) as follows:

(2 kg) * (3/2) = 3 kg

Therefore, the quantity sold at 18% profit is 900 kg.

Step-by-step explanation:

\((9\pi \frac{2}{2} )\div 3\pi \\ \)

\( \frac{9\pi}{3\pi} \\ \)

\(3\pi\)

3π is the answer

Answer:

3 1/2 gallons or 56 cups

Step-by-step explanation:

1. Analyze the questions.

We have 3 gallons, and we add another 1/2 gallon. This means that our equation must be 3 + 1/2.

2. Solve.

3 + 1/2 = 3 1/2 gallons

3. Convert.

1 gallon = 16 cups

1 * 3 1/2 gallons = 16 * 3 1/2 cups

3 1/2 gallons = 56 cups

Answer: 3 1/2

                           Hope this helped! :D

The requried number of days that bruce's worm will take to climb up the well is 7.4 days.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here
As mentioned in the quesiton,

The well is 37 feet deep. Each day, the worm climbs up 7 feet, but each night, it slides back down 2 feet.

Net height, that bruce's worm climbs every day,
= 7 - 2

= 5 feet

Now,
The ratio of the total depth of the well to the net height gives the number of days for the worm to climb up the well,
So,

= 37 / 5
= 7.4 days

Thus, the requried number of days that bruce's worm will take to climb up the well is 7.4 days.

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Answer:

B. 11 MPH

Step-by-step explanation:

60/4=15

15-11=4

Answer:

m = - 1 , m = 0 , m = \(\frac{7}{2}\)

Step-by-step explanation:

2m³ - 5m² - 7m = 0 ← factor out common factor m from each term

m(2m² - 5m - 7) = 0

factorise the quadratic 2m² - 5m - 7

consider the factors of the product of the coefficient of the m² term and the constant term which sum to give the coefficient of the m- term

product = 2 × - 7 = - 14 and sum = - 5

the factors are + 2 and - 7

use these factors to split the m- term

2m² + 2m - 7m - 7 ( factor the first/second and third/fourth terms )

2m(m + 1) - 7(m + 1) ← factor out (m + 1) from each term

(m + 1)(2m - 7)

then

2m³ - 5m² - 7m = 0

m(m + 1)(2m - 7) = 0 ← in factored form

equate each factor to zero and solve for m

m = 0

m + 1 = 0 ( subtract 1 from both sides )

m = - 1

2m - 7 = 0 ( add 7 to both sides )

2m = 7 ( divide both sides by 2 )

m = \(\frac{7}{2}\)

solutions are m = - 1 , m = 0 , m = \(\frac{7}{2}\)

Answer:

T = 2*PI* sq root (L / g)

Squaring both sides

T^2 = 4PI^2 * L/g

g = 4PI^2 * L / T^2

g = 4PI^2 * 1 / (3.27)^2

g = 39.4784176044  * 1 / 10.6929

g = 3.6920215848

(Wikipedia says 3.72076, so I'd say the calculation is correct).

Step-by-step explanation:

Answer:

(8,-43)

(4,-22)

Step-by-step explanation:

In order for the ordered pair to be a solution of the inequality, you must be able to plug in the y-value of the ordered pair and it must be less than or equal to 0.

For example:

(4,-22)

x=4 ; y=-22

Plug y into the inequality

y≤0

-22≤0

Since the statement is true, I know that (4,-22) must be a solution to the inequality.

Another way to solve this problem is by graphing. If an ordered pair is in the shaded region, it is a solution to the inequality. Attached is a graph of both the inequality and ordered pairs plotted.

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Have a GREAT day!!!

Answer:

Step-by-step explanation:

To determine whether each ordered pair is a solution to the inequality y ≤ 0, we need to check if the y-coordinate of each pair is less than or equal to zero.

Let's check each ordered pair:

(8, -43):

The y-coordinate is -43. Since -43 is less than zero, this ordered pair is a solution to the inequality y ≤ 0.

(4, -22):

The y-coordinate is -22. Since -22 is less than zero, this ordered pair is a solution to the inequality y ≤ 0.

(-3, 25):

The y-coordinate is 25. Since 25 is greater than zero, this ordered pair is not a solution to the inequality y ≤ 0.

(-7, 45):

The y-coordinate is 45. Since 45 is greater than zero, this ordered pair is not a solution to the inequality y ≤ 0.

So, the solutions to the inequality y ≤ 0 are:

(8, -43) and (4, -22).

Answer: x = 5

The step-by-step explanation is below.

Combine like terms

8x-6x = 2x

4+5=9

2x+9=19

Subtract 9

2x=10

Divide by 2

x = 5

Hope this helps!

The probability both will be peanut butter sandwiches will be 1/6.

Probability is an area of mathematics that deals with numerical representations of how probable an event is to occur or how likely a statement is to be true.

here, we have,

The probability of an occurrence is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.

The probability that John picks a peanut butter sandwich from the first bag is 6/12 = 1/2.

The probability that John picks a peanut butter sandwich from the second bag is 4/12 = 1/3.

The probability that John picks a peanut butter sandwich from both bags is (1/2) * (1/3) = 1/6.

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9514 1404 393

Answer:

  5∛(x²)

Step-by-step explanation:

The denominator of a rational power is the index of the radical when the expression is written in radical form.

  \(5\times x^{\frac{2}{3}}=\boxed{5\sqrt[3]{x^2}}\)

Answer:

-60

It is -60 because if it takes away 6 points for each cone you hit and you hit 10, then it would be -60 times 10, which equals -60.

Answer:

y = -3x + 9

Step-by-step explanation:

6x + 2y = 18

move 6x to the right of the equation by subtracting on both sides

2y = -6x + 18

then to single out the 'y' divide by 2 on both sides

y = -3x = 9

 Hope this helps <3

Let's make a diagram of the problem

Based on the given information, we can deduct that angle AFC is formed by angles AFB and BFC.

Angle AFC measures 105°.

Now, we use the supplementary angles theorem to find angle AFE.

Hence, angle AFE measures 75°.

As you can observe in the diagram, angles EFD and BFC are vertical angles, so they are equal.

Hence, angle EFD measures 44°.

Answer:

4

Step-by-step explanation:

Set the height of the missing bar to 4 as there are 4 quantities between 21-25.

Answer:

14.6 minutes

Step-by-step explanation:

Since there is a 1 ms increase per day and there are 365 days a year, the time increase per year is 1 ms/day × 365 days/year = 365 ms/year.

So, in 24 centuries, there are 24 × 1 century = 24 × 100 years = 2400 years (since  1 century = 100 years)

So, the total of the daily increase in time in 24 centuries is time increase per year × 24 centuries

= 365 ms/year × 2400 years

= 876000 ms

= 876 s

= 876 s/60s

= 14.6 minutes

Answer:

Step-by-step explanation:

The angle of depression is the downward angle the air traffic controller

looks down from in the tower.  It also equals the angle of elevation which is the angle formed by the runway and the line of sight.

With this information you can find the remaining angle:

180 - (90 + 18)

180 - 108 = 72

Let Angle B = 72°

Angle A = 18°

Angle C =90°

We have one side - 140 feet - this is side a - it is across from angle A.

There is a right triangle formed by the runway (side b) the tower, side a, and the line of sight (side c)

Using the law of sines:

sin A/a = sinB/b

sin 18°/a = sin72°/b

.3090/140 = .9510/x

cross multiply and then divide

140 × .9510/.3090

133.14/.3090

430.873 ft

round to a tenth = 430.9 ft

The only valid option for Adam is to use different dimensions that form a right triangle. The dimensions 40 in., 44 in., 58 in. are the closest valid set of dimensions.

What is a valid triangle?

A valid triangle is a three-sided polygon that satisfies the following conditions:

The sum of the lengths of any two sides of the triangle is greater than the length of the third side.

The lengths of all three sides of the triangle are greater than zero.

Adam should use the dimensions 40 in., 44 in., 58 in. for a triangular frame to form a right triangle.

To determine if a right triangle can be formed, we need to check if the Pythagorean theorem is satisfied, which states that the sum of the squares of the two shorter sides of a right triangle is equal to the square of the length of the longest side (the hypotenuse).

Let's check each set of dimensions:

For 25 in., 60 in., 65 in.:

25^2 + 60^2 = 625 + 3600 = 4225

65^2 = 4225

The Pythagorean theorem is satisfied, so a right triangle can be formed. However, this triangle is not a valid option for Adam because the lengths are too short for building walls.

For 40 in., 44 in., 58 in.:

40^2 + 44^2 = 1600 + 1936 = 3536

58^2 = 3364

The Pythagorean theorem is not satisfied, so a right triangle cannot be formed using these dimensions.

For 50 in., 110 in., 130 in.:

50^2 + 110^2 = 2500 + 12100 = 14600

130^2 = 16900

The Pythagorean theorem is satisfied, so a right triangle can be formed.

For 130 in., 50 in., 60 in.:

50^2 + 60^2 = 2500 + 3600 = 6100

130^2 = 16900

The Pythagorean theorem is satisfied, so a right triangle can be formed.

Out of the options given, only the dimensions 50 in., 110 in., 130 in. and 130 in., 50 in., 60 in. satisfy the Pythagorean theorem, but both are too large for building walls.

Therefore, the only valid option for Adam is to use different dimensions that form a right triangle. The dimensions 40 in., 44 in., 58 in. are the closest valid set of dimensions.

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Answer:

It slopes downward from left to right. You can see the downward slope of that gender, which starts at the left and moves to the right.

Step-by-step explanation:

Hello!

x² - 5x + 6

= (x² - 2x) + (-3x + 6)

= x(x - 2) - 3(x - 2)

= (x - 2)(x - 3)

Answer:

the answer is a

Step-by-step explanation:

radius is the diameter divided by 2

Answer:

31.2

Step-by-step explanation:

Answer: 2 aka B

Step-by-step explanation: the answers B :)

Answer:

Center ( -8, 1 )

Radius ( 13 )

Answer:

y < -14/3

Step-by-step explanation:

y/4 - y - 1/2 > 3

          +1/2     +1/2

---------------------------

y/4 - y > 7/2

*4           *4

---------------------------

y - 4y > 14

-3y > 14

/-3     /-3

---------------------------

y < -14/3

Answer:

y < -14/3 --> final solution

The most appropriate name for the function that takes the length of a race and returns the time needed to complete it would be "time(length)".

When choosing a name for a function, it is important to consider clarity and readability. The name should accurately describe the purpose of the function and provide a clear indication of what it does.

In this case, the function is expected to take the length of a race as input and return the time needed to complete it as output. Among the given options, "time(length)" is the most suitable choice.

a. length(time): This name suggests that the function takes time as input and returns the length. However, in this scenario, we are interested in finding the time needed to complete the race based on its length, so this option is not the best fit.

b. Time(race): This name implies that the function takes a race as input and returns the time. While it conveys the idea of finding the time, it doesn't explicitly mention that the input is the length of the race, making it less clear.

c. time(length): This option accurately describes the purpose of the function, indicating that it takes the length of the race as input and returns the corresponding time. It is concise, clear, and aligns with the conventional naming conventions for functions.

d. cost(time): This name suggests that the function calculates the cost based on time, which is not relevant to the scenario of finding the time needed to complete a race.

Therefore, "time(length)" is the most suitable and appropriate name for the function.

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Answer:

What is a linear function? A linear function is a function whose graph is a straight line. The rate of change of a linear function is constant. The function shown in the graph below, y = x + 2, is an example of a linear function.

Graph of linear function

Graph of linear function

A linear function has a constant rate of change. The rate of change is the slope of the linear function. In the linear function shown above, the rate of change is 1. For every increase of one in the independent variable, x, there is a corresponding increase of one in the dependent variable, y. This gives a slope of 1/1 = 1.

A linear function is typically given in the form y = mx + b, where m is equal to the slope, or constant rate of change.

Examples of linear functions include:

If a person drives at a constant speed, the relationship between the time spent driving (independent variable) and the distance traveled (dependent variable) will remain constant.

Assuming no change in price, the relationship between the number of pounds of bananas a person buys (independent variable) and the total cost of the bananas (dependent variable) will remain constant.

If a person earns an hourly wage at their job, the relationship between the time spent working (independent variable) and the amount earned (dependent variable) will remain constant.

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Exponential Functions

What is an exponential function? An exponential function is a function that involves exponents and whose graph is a smooth curve. The rate of change in an exponential function is not constant. The functions shown in the graph below, y = 0.5x and y = 2x, are examples of exponential functions.

Graphs of exponential functions

Graphs of exponential functions

An exponential function does not have a constant rate of change. The rate of change in an exponential function is the value of the independent variable, x. As the value of x increases or decreases, the rate of change increases or decreases as well. Rather than a constant change, as in the linear function, there is a percent change.

An exponential function is typically given in the form y = (1 + r)x, where r represents the percent change.

Examples of exponential functions include:

Step-by-step explanation:

Answer:    If the algae in Lake Skinner doubles every day, then on the 15th day (halfway between the 1st and 30th) the lake will be covered halfway.

   If the algae doubles every day, then on January 26 it would have only doubled six times, meaning it would only cover 1/64 of the lake's surface. This is why your friend may be skeptical that the lake will be completely covered soon.

   The cleanup crew's efforts on January 29 were able to remove most of the algae, but by February 1 only 1% of the lake's surface was still covered. This means that while the problem has been greatly reduced, it is not completely solved and there may still be some risks to the fish in the lake. Continued monitoring and efforts to prevent future algae blooms may be necessary to fully protect Lake Skinner.

Step-by-step explanation: