7,11,2,18,-7
What's the next number in this sequence and how did you arrive at that number

Answers

Answer 1

The last term of the missing pattern is 57.

What is Sequence?

A sequence is a list of items where repetitions are allowed and hierarchy is crucial. The same as a set, it has members. The number of items determines how long the sequence is.

Given:

Sequence: 7,11,2,18,-7

As, the difference between the first two-term is 4,

while in the next two-term is 16(4²),

So, in the next two-term the difference will be equal to 64(4³).

Then, the last term is

x- (-7)= 64

x+ 7= 64

x= 57

Hence, the last term is 54.

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Related Questions

indicate which of the following sentences are statements. (select all that apply.) A. 1,024 is the smallest four-digit number that is a perfect square. B.he is a mathematics major. C.128=26 D.X=26

Answers

D. X=26 is a mathematical statements, since it can be either correct or incorrect.

To comprehend any mathematical statement, we must first understand what mathematics is all about. When we answer a math problem, the solution is either correct or incorrect. There is no midway to the problems! Any mathematical statement is in the same scenario. A mathematical statement is either correct or incorrect.

In this scenario, the statement, 'A. 1,024 is the smallest four-digit number that is a perfect square.', and 'B. He is a mathematics major.' are correct statements. And 'C. 128=26' is a incorrect statement. Therefore, these options are not the mathematical statements because A and B is correct statement and C is a false statement. Meanwhile, D. X=26 is a mathematical statement because it is either correct or incorrect, depending on the given problem. Therefore D. X=26 is the correct answer for a mathematical statement.

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i don’t understand and cant find the formulas to find these things

Answers

Answer:

7.30%; $1452.024.45%; 15.56 years

Step-by-step explanation:

You want the interest rate and account balance after 10 years if the investment of $700 doubles in 9 1/2 years with interest compounded continuously. And, you want the interest rate and doubling time if a $900 investment has a value of $1405 after 10 years with continuous compounding.

Compound interest

These problems are solved by making use of the compound interest formula for continuously compounded interest. In each case, you fill in the values you know, and solve for the one you don't know.

  A = Pe^(rt)

$700

The investment doubles after 9.5 years, so we have ...

  2·700 = 700e^(9.5r)

Dividing by 700 and taking natural logs, we find the rate to be ...

  ln(2) = 9.5r

  r = ln(2)/9.5 ≈ 0.072963 ≈ 7.30%

Using the exact value in the computation of the balance, we get ...

  A = 700e^(10·(ln(2)/9.5)) = 700·2^(10/9.5) = 700·2^(20/19)

  A = 1452.02

The annual rate is 7.30%; the balance in 10 years is $1452.02.

$900

The balance after 10 years is ...

  1405 = 900e^(r·10)

  ln(1405/900) = 10r

  r = ln(1405/900)/10 ≈ 0.0445398 ≈ 4.45%

As we found above, the relation between r and doubling time is ...

  r = ln(2)/t   ⇒   t = ln(2)/r

  t = ln(2)/0.0445398 ≈ 15.56 . . . . years

The annual rate is about 4.45%; the doubling time is about 15.56 years.

__

Additional comment

In the first problem, we could find the account balance after 10 years using the found interest rate. In that case, it would be $1452.56. Instead, we chose the doubling time to be the exact value in the problem.

There is a "rule of 70" or sometimes the "rule of 72" that tells you the approximate doubling time in years (y) for an interest rate of r%. It is ...

  y = 70/r

The amount of error depends on the interest rate and the way interest is compounded.

When the interest is compounded continuously, a slightly different rule gives the exact doubling time:

  y = 100·ln(2)/r ≈ 69.31472/r

This is effectively the rule we used above.

solve each of the given inequalities for z. Which of the inequalities has 5 as a solution

Answers

The inequality  4(2.8z + 1.75) > -26.6  has 5 as a solution and its solution is, z > - 3.

What is Inequality?

A relation by which we can compare two or more mathematical expression is called an inequality.

We have to given that;

The inequalities are,

⇒ 4(2.8z + 1.75) > -26.6

⇒ 2(1.9z + 1.5) ≤ 18.2

Now, We can solve the inequalities as;

1) ⇒ 4(2.8z + 1.75) > -26.6

Divide by 4;

⇒ 2.8z + 1.75 > - 6.65

Subtract 1.75 both side,

⇒ 2.8z > - 6.65 - 1.75

⇒ 2.8z > - 8.4

Divide by 2.8;

⇒ z > - 8.4/2.8

⇒ z > - 3

Clearly, z = 5 is the solution of the above inequality.

2) 2(1.9z + 1.5) ≤ 18.2

Divide by 2;

⇒ 1.9z + 1.5 ≤ 9.1

Subtract 1.5 both side,

⇒ 1.9z ≤ 9.1 - 1.5

⇒ 1.9z ≤ 7.6

Divide by 1.9;

⇒ z ≤ 7.6/1.9

⇒ z ≤ 4

Clearly, z = 5 is not the solution of the above inequality.

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The complete question is this,

Solve each of the given inequalities for z. Which of the inequalities has 5 as a solution?

   Inequality 1                                 Inequality 2

4(2.8z + 1.75) > -26.6                2(1.9z + 1.5) ≤ 18.2

NO LINKS!!

Shown in the figure is a cross-section of a design for a two-story home. The center height h of the second story has not yet been determined. Find h such that the second story will have the same cross-sectional area as the first story.

h = __________ ft

Answers

Answer:

h = 13 ft

Step-by-step explanation:

The cross-sectional area of the first story is the area of a rectangle with width 30 ft and height 8 ft.  The area of a rectangle is the product of its width and height.

[tex]\begin{aligned}\implies \textsf{Cross-sectional area of first story}&=30 \times 8\\&=240\; \sf ft^2\end{aligned}[/tex]

The cross-sectional area of the second story is made up of a rectangle with width 30 ft and height 3 ft, and a triangle with base 30 ft and height (h - 3).  The area of a triangle is half the product of its base and height.

[tex]\begin{aligned}\implies \textsf{Cross-sectional area of second story}&=(30 \times 3)+\dfrac{1}{2} \times 30 \times (h-3)\\&=90+15(h-3)\\&=90+15h-45\\&=(15h+45)\; \sf ft^2\end{aligned}[/tex]

If the second story has the same cross-sectional area as the first story, then:

[tex]\implies 15h+45=240[/tex]

To find h, solve the equation:

[tex]\begin{aligned}\implies 15h+45&=240\\15h&=195\\h&=13\; \sf ft\end{aligned}[/tex]

Therefore, the value of h such that the second story will have the same cross-sectional area as the first story is 13 ft.

A pyramid is composed of six isosceles triangles and a hexagonal base. Each isosceles triangle has a height of 8 inches and a base of 6 inches. The area of the hexagonal base is 93.5 square inches. What is the surface area of the pyramid? Enter your answer in the box. in²

Answers

The surface area of the pyramid is A = 265.23 inches²

What is the surface area of the pyramid?

The total surface area is the summation of the areas of the base and the three other sides. A = B + ( 1/2 ) ( P x h ), where B is the area of the base of the pyramid, P is the perimeter of the base, and h is the slant height of the pyramid

Surface Area of Pyramid = B + ( 1/2 ) ( P x h )

Given data ,

Let the surface area of hexagonal pyramid be represented as A

Surface area of hexagonal pyramid = Area of base + area of lateral surface

Area of the base = 93.5 inches²

Now , the Area of the lateral surface = 3a √ ( h² + ( 3a²/4 ) )

where a = 6 inches

h = 8 inches

Substituting the values in the equation , we get

Area of the lateral surface = ( 3 x 6 ) √ ( 64 + ( 3 x 36 / 4 ) )

On simplifying the equation , we get

Area of the lateral surface = 171.7 inches²

So , Surface area of hexagonal pyramid = Area of base + area of lateral surface

Surface area of hexagonal pyramid A = 93.5 inches² + 171.7 inches²

Surface area of hexagonal pyramid A = 265.23 inches²

Hence , the surface area of hexagonal pyramid is 265.23 inches²

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Please I need help , thanks

Answers

Answer:

y =  -3/4 x + 3                                                                                                            

Step-by-step explanation:

y = mx + b  You need the m value (slope) and the b (y-intercept value) to the write the equations.

Slope:

Look that the two intercepts of x (4,0) and the y intercept of (0,3).  If you start and (4,0) and go up 3 and left 4, you will land back on the line at the point (0,3).  Slope is the rise over the run.  The rise is up and positive 3.  The run is left and negative -4

3/-4 is the same as -3/4

-3/4 is the slope.

y-intercept:

The y intercept is at the point (0,b)  In this case, the point is (0,3).

3 is the y-intercept.

y = mx + b  Substitute -3/4 for m and 3 for b

y = -3/4 x + 3

four more than h is no less than 27.

Answers

Answer:

Below

Step-by-step explanation:

four more than h   is     h+4

no less than 27 means it is greater than or equal to 27

h+4 >= 27

Find the 59th term of the
arithmetic sequence 29, 37, 45, ...

Answers

Answer:

383

Step-by-step explanation:

37 - 29 = 6

59 x 6 = 353

353 + 29

An report describes a survey of 251 adult Americans. Participants in the survey were asked how often they change the sheets on their bed and were asked to respond with one of the following categories: more than once a week, once a week, every other week, every three weeks, or less often than every three weeks. For this group, 11% responded more than once a week, 51% responded once a week, 26% responded every other week, 5% responded every three weeks, and 7% responded less often than every three weeks.
(a) Use the given information to make a relative frequency distribution for the responses to the question. How Often? Relative frequency
More than once a week Once a week Every other week Every three weeks Less often than
every three weeks

Answers

More than once a week: 0.11

Once a week: 0.51

Every other week: 0.26

Every three weeks: 0.05

Less often than every three weeks: 0.07

Relative Frequency Survey Results

To make a relative frequency distribution, follow these steps:

Count the number of occurrences of each category in the data. In this case, 11% of the 251 participants responded "more than once a week", so the number of occurrences for this category is 0.11 * 251 = 27.61 (rounded to 28). Similarly, 51% of the participants responded "once a week", so the number of occurrences for this category is 0.51 * 251 = 127.51 (rounded to 128). And so on for the other categories.

Divide the number of occurrences for each category by the total number of participants. In this case, the total number of participants is 251, so the relative frequency for "more than once a week" is 28 / 251 = 0.11. The relative frequency for "once a week" is 128 / 251 = 0.51. And so on for the other categories.

And that's it! These are the relative frequencies for each category in the data.

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7j+5−8kb; when j = 0.5 and k = 0.25

Answers

The given expression becomes 5.35-2b.

What is an expression?

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.

The given expression is 7j+5-8kb.

Here,  j = 0.5 and k = 0.25

Now, substitute j = 0.5 and k = 0.25 in the given expression, we get

7×0.5+5-8×0.25×b

= 0.35+5-2b

= 5.35-2b

Therefore, the expression is 5.35-2b.

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Answer:

6.5

Step-by-step explanation:

Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s). Triangle ABC is defined by the points A(2,9), B(8,4), and C(-3,-2). Complete the following equation for a line passing through point C and perpendicular AB.​

Answers

The equation of the line passing through point C and perpendicular to line AB is: y = -6/5x - 20/5 + 2

Describe slope using an example.

The slope-intercept form of an equation is used whenever the equation of a line is expressed in the form y = mx + b. M represents the line's slope. B is the b in the location where the y-intercept is located (0, b). For instance, the slope and y-intercept of the equation y = 3x - 7 are 3 and 0, respectively.

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

Where (x1, y1) and (x2, y2) are the coordinates of two points on the line. Using the coordinates of points A and B, we have:

m = (4 - 9) / (8 - 2) = -5 / 6

The slope of a line perpendicular to this line would be the negative reciprocal of this slope, so:

m= -1 / m = -6 / 5

Next, we can use the point-slope form of a line to find the equation of the line, which is:

y - y1 = m * (x - x1)

Substituting the values for m, x1, and y1 (where x1 and y1 are the coordinates of point C), we have:

y - (-2) = -6/5 * (x + 3)

Simplifying and solving for y, we get:

y = -6/5 * x - 20/5 + 2

So, the equation of the line passing through point C and perpendicular to line AB is: y = -6/5x - 20/5 + 2

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Based on the graph above, estimate to one decimal place the average rate of change from

Answers

The average rate of change from x=1 to x=5 is -1.325.

What is Slope of Line?

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

at x=1 the value of y is 8.5

x=5 the value of y is 3.2

slope=3.2-8.5/5-1

=-5.3/4

m=-1.325

Hence,  the average rate of change from x=1 to x=5 is -1.325.

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3(x+4).


susushsjsssjsjsjsjskskkddjd

Answers

Answer:

3x+12 because of the bracket it makes the 3 multiply the x and

at Smalltown University, is reading applications submitted by prospective students. The president of Smalltown University is weary about admitting too many domestic students and not enough international students. However, the applications are blinded so Jenny cannot see if an applicant is a domestic student or international student. Jenny is instructed by the president to admit exactly 14 applicants to the Department of Mathematics in a given year. Suppose that 55 domestic students and 45 international students applied to the Department of Mathematics at Smalltown University this year, and suppose that there is no difference in the qualifications of domestic and international students applying to Smalltown University. Let X represent the number of domestic applicants that Jenny selects this year. Calculate the mean, M. and standard deviation, o, of X. Please give the exact value for the mean and round your standard deviation to the nearest three decimal places. (X) = o(X) =

Answers

The mean of X can be calculated using the expected value formula, E(X) = sum of all possible values of X * probability of each value.

Since Jenny has to admit exactly 14 applicants, the possible values of X can be 0 to 14.

The probability of each value can be calculated using the binomial distribution formula, P(X=k) = (n choose k) * p^k * (1-p)^(n-k)

where n = 14 (number of applicants Jenny has to admit), k = number of domestic applicants, and p = probability of a domestic applicant (55/100).

So, the expected value of X can be calculated as:

E(X) = sum of P(X=k) * k, for k = 0 to 14

= (0 choose 0) * (55/100)^0 * (45/100)^(14-0) * 0 + (14 choose 1) * (55/100)^1 * (45/100)^(14-1) * 1 + ... + (14 choose 14) * (55/100)^14 * (45/100)^(14-14) * 14

= 7

So, the mean of X, M = E(X) = 7

The standard deviation of X can be calculated using the formula, o(X) = sqrt(E((X-M)^2))

= sqrt(E(X^2) - M^2)

= sqrt((sum of P(X=k) * k^2) - M^2)

= sqrt((0 choose 0) * (55/100)^0 * (45/100)^(14-0) * 0^2 + (14 choose 1) * (55/100)^1 * (45/100)^(14-1) * 1^2 + ... + (14 choose 14) * (55/100)^14 * (45/100)^(14-14) * 14^2 - M^2)

= sqrt(3.65)

So, the standard deviation of X, o(X) = 1.91 (rounded to nearest three decimal places).

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Write an exponential function for the graph. Write the function in the form y = a(b)*. W AYA O X please l need help ​

Answers

The exponential function for the graph at the end of the answer is defined as follows:

y = -1.5(2)^x.

How to model the exponential function?

The definition of an exponential function is given as follows:

y = ab^x

In which the parameters are defined as follows:

a is the value of y when x = 0.b is the rate of change, that is, by how much y is multiplied when x is increased by one.

When x = 0, y = -1.5, hence the parameter a is given as follows:

a = -1.5.

When x = 2, y = -6, hence the parameter b is obtained as follows:

-1.5b² = -6

b² = 4.

b = 2.

Then the function is defined as follows:

y = -1.5(2)^x.

Missing Information

The function is given by the image presented at the end of the answer.

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Please help me out, thanks

Answers

Answer:

d

Step-by-step explanation: using logic of dimension analysis , since y represent distance and x represent hours of traveling in train means time then 60 must be speed for equality i.e distance traveled by train per hour , for correcting dimensionaly

How do I combine 4x and 1/2x in the problem 4x-3+1/2x ?
Not getting how 4x and 1/2x turns to 9/2x

Answers

Answer:

Step-by-step explanation:

[tex]4x+\frac{1}{2}x = (4+\frac{1}{2} )x[/tex]

             [tex]=(\frac{8}{2} +\frac{1}{2} )x[/tex]

            [tex]=\frac{9}{2}x[/tex]

Height in P
0
-1
0.5
1
Time in Seconds (t)
function:
2
h(t) = -16t² + 12t
Move the blue lines to indicate where the basketball
player is going UP in the air.
Complete these sentences (reminder: you can click on
the graph to locate certain values).
The player starts going up at
2.25
The player stops going up at
1.76
NC
seconds.
In mathematical terms, when would the player be
rising?
(0,0.375)
seconds.
WELL
TITT
US
Jan 29s

Answers

The quadratic function for the height of the player, h(t) = -16·t² + 12·t indicates the following

The player starts going up at 0 seconds

The player stops going up at 0.375 seconds

The player would be rising in the interval [0, 0.375)

What is a quadratic function?

A quadratic function is a function that can be expressed as; f(x) = a·x² + b·x + c, with the values of a, (a ≠ 0) b, and c representing numbers.

The function for the height is; h(t) = -16·t² + 12·t

The time the player starts going up can be found as follows;

The minimum height = -1

When h(t) = -1, we get; -1 = -16·t² + 12·t

-16·t² + 12·t + 1 = 0

Therefore, t = (3 ± √13)/8

t ≈ 0.826 and t ≈ -0.076

However, the value of the time is a natural number, therefore;

The player starts going up at t = 0 seconds.

The player stops going up at the maximum height, which can be obtained from the value of the maximum point of a quadratic function, which is; t = -12/(2 × (-16)) = 3/8 = 0.375

The player stops going up at 0.375 seconds

In mathematical terms the player will be rising between the interval, 0 ≤ t < 0.375, which can be expressed as; [0, 0.375)

The interval during which the player is rising is; [0, 0.375)

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d (x) = -(x+7)^(2) +9

domain =
function =

Answers

The domain of d(x) = -(x+7)^2 + 9 are the set of all real numbers and the function is d(x) = -(x+7)^2 + 9

How to determine the domain and the function?

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

d(x) = -(x+7)^2 + 9

This means that the function is d(x) = -(x+7)^2 + 9

There is no restriction on the input values, x

So, the domain of d(x) = -(x+7)^2 + 9 is all real numbers, since there is no restriction on the input (x).

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The coordinates of the endpoints of AB are A(–4,8) and B(8,2). Its midpoint is C.
What are the coordinates of C?

Answers

The required coordinate of the midpoint C is given as (2, 5), as per the given conditions.

What is the midpoint?

Midpoint is that point on the line whose distance from both ends of the line is equal.

Here,
The coordinates of the endpoints of AB are A(–4,8) and B(8,2).

Let the coordinate of point C be (x, y)

Now,
x = x₁ + x₂ / 2    ; y = y₁ + y₂/2

Substitute value in the above expression,
x = -4 + 8 / 2    ; y = 8 + 2 / 2
x = 2                 , y = 5

Thus, the required coordinate of the midpoint C is given as (2, 5), as per the given conditions.

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In a year when the maximum income for Social Security was $118,500, Bart worked at two jobs. In one job he earned $99,112. In his second job, he earned $56,222.
Both of his employers took out Social Security tax. As a result, Bart had paid excess Social Security tax, and the government must return some of it to him. How
much does the government owe him for excess Social Security paid?

Answers

Answer:

The government owes Bart the excess Social Security tax that he paid, which is the amount of tax he paid on his income above the maximum income for Social Security. In this case, that would be $118,500 (the maximum income for Social Security) minus $99,112 (what he earned at his first job) minus $56,222 (what he earned at his second job) = $13,166. So the government owes Bart $13,166 for the excess Social Security tax he paid.

Answer:

Step-by-step explanation:

He earned a total of 155,334.

99112 plus 56222.

subtract the max income from the income total

155,334 - 118500 = 36834

He is owed the social security tax he paid on 36834.

The problem does not give the social security rate.

Trisha has a job walking 13 dogs for her neighbors. She can walk one, two, or three dogs on each trip to the park. What is the fewest number of trips Trisha takes to walk all 13 dogs?

Answers

The fewest number of trips Trisha takes to walk all 13 dogs is of

Five trips.

How to obtain the fewest number of trips?

The fewest number of trips is obtained applying the proportions in the context of this problem.

To minimize the number of trips, we must maximize the number of trips with three dogs, hence:

13/3 = 4 with a remainder of 1.

Hence she needs five trips, divided as follows:

Four trips with three dogs.The last trip with the remaining dog. (remainder of the division of 13 by 3).

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The first 4 terms in a sequence are 8,5,2,-1 What is the recursive equation?

Answers

Answer: The recursive equation for this sequence is t(n+1)=t(n) - 3.

Step-by-step explanation:

The recursive equation for the given sequence is t(n+1) = t(n) - 3. This means that to find the next term in the sequence, we take the previous term and subtract 3 from it.

For example:

t(1) = 8 (first term in the sequence)

t(2) = t(1) - 3 = 8 - 3 = 5 (second term in the sequence)

t(3) = t(2) - 3 = 5 - 3 = 2 (third term in the sequence)

t(4) = t(3) - 3 = 2 - 3 = -1 (fourth term in the sequence)

In general, the recursive equation t(n+1) = t(n) - 3 will give the nth term of the sequence.

It should be noted that the initial condition provided in the question t(0)=-3, t(n+1)=t(n) +11 is incorrect and will not give the same sequence.

a medical researcher wants to determine whether exercising can lower blood pressure. she recruits 100 people with high blood pressure to participate in the study. she assigns a random sample of 50 of them to pursue an exercise program that includes daily swimming and jogging. she assigns the other 50 to refrain from vigorous activity. she measures the blood pressure of each of the 100 individuals both before ad after the study. press space or enter to grab observational study a medical researcher wants to determine whether exercising can lower blood pressure. at a health fair he measures the blood pressure of 100 individuals and interviews them about their exercise habits. he divides the individuals into two categories: those whose typical level of exercise is low and those whose level of exercise is high. press space or enter to grab randomized experiment to determine the effectiveness of a new pain reliever a randomly chosen group of pain sufferers is assigned to take the new drug and another randomly chosen group is assigned to take a placebo. press space or enter to grab randomized experiment to assess the effectiveness of a new method for teaching arithmetic to elementary school children a simple random sample of 30 first graders was taught with the new method and another simple random sample of 30 first graders was taught with the currently use method. at the end of eight weeks the children were given a test to assess their knowledge. the press space or enter to grab observational study researchers examine the association between the fluoridation of water and the prevention of tooth decay by comparing the prevalence of tooth decay in countries that have fluoridated water with the prevalence in countries that do not.

Answers

The study described is a randomized experiment.

A randomized experiment is a typical experimental study design. It is a study design in which the researcher or investigator is in complete control of the research environment. For example, an investigator may wish to assess the effects of certain treatments on some experimental units.

The investigator decides the type of treatment, the type of experimental unit to use, and the allocation and assessment procedures of the treatments and effects, respectively, while in an observational study, the researcher or investigator is usually a passive observer as he only observes and analyses facts and events as they occur naturally.

In experimental studies, the researcher is in complete control of the exposure, and the result should therefore provide stronger evidence of an association or lack of association between exposure and a health problem than would an observational study.  

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"Determine whether the study described below is a randomized experiment or an observational study.

A medical researcher wants to determine whether exercise can lower blood pressure. She recruits 100 people with high blood pressure to participate in the study. She assigns a random sample of 50 of them to pursue an exercise program that includes daily swimming and jogging. She assigns the other 50 to refrain from vigorous activity. She measures the blood pressure of each of the 100 individuals both before and after the study."--

Please help if you can, this is due in two days.

Answers

Answer:

8.8

Step-by-step explanation:

Property of similar triangles

The table represents a linear relationship.


x −1 0 1 2
y 2 0 −2 −4


Which of the following graphs shows this relationship?

Answers

W

Answer:

Where is the graph

Step-by-step explanation:

I need it

The weight of a sphere is proportional to its radius cubed. If a sphere of diameter 1 cm has a mass of 10 grams, what diameter sphere has a mass of 640grams?

Answers

Answer:

if 1cm-10grams

what Abt 640 grams=64cm

A farmer wants to make a rectangular field with a total area of 2500 square meters. it is surrounded by a fence. it is divided into 3 equal areas by fences as shown. Express the total length L of all the fence required in terms of the length x of one of the fences which divide the field.

Answers

The fence's shortest overall length is 808 meters.

Describe the rectangle.

A quadrilateral having all four interior angles at 90 degrees is a rectangle.

Given that the square field has an area of 800 m2.

Let the rectangle's length and breadth be x and y.

The rectangle's area is then:

A= xy

Or, xy = 800

x = 800/y (1) (1)

The triangle's perimeter is:

2x +2y

The total length of the fence is equal to the perimeter of the triangle plus twice the length or width of the triangle since the fence divides the triangle into three equal portions.

Consequently, the fence's overall length is:

L = 2x + 2y + 2x

L = 4x +2y

the equation above with x = 800/y as a replacement:

L = 4(800/y) + 2y

L = 3200/y +2y         (2)

Differentiate the equation with respect to y:

L' = -3200/y² +2

Substitute L'= 0 into the above equation:

0 = -3200/y² + 2

y² = 3200/2

y² = 1600

y = 400

Substitute y = 400 into equation (2):

L = 3200/400 + 2(400)

L = 8 + 800

L = 808

Hence, The fence's shortest overall length is 808 meters

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Which city has a population under 500,000?

Answers

Answer:

give a list and then I can help

Answer:

Bangalore

Step-by-step explanation:

new York..

make me brainleast

Can someone solve this please? Ty

Answers

The number of months during which the company is not making a profit 18.

What is a function?

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

C(x) = 17 - 8x - 2x²

R(x) = 5 - 3x

If there is no profit it means,

R(x) - C(x) = 0

Now,

5 - 3x - ( 17 - 8x - 2x²) = 0

5 - 3x - 17 + 8x + 2x² = 0

2x² + 5x - 12 = 0

Solve for x.

2x² + 5x - 12 = 0

2x² + (8 - 3)x - 12 = 0

2x² + 8x - 3x - 12 = 0

2x(x + 4) - 3(x + 4) = 0

(x + 4)(2x - 3) = 0

x = -4 (rejected) and x = 3/2

Now,

x = 3/2 = 1.5

This means,

1.5 years = 18 months

Thus,

The number of months is 18.

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