the length of a ractangle is 1 meter less than its width. the area of the rectangle is 42 square meters. Find the dimensions of the rectangle (using the x method)

The gradient of the line is 2

\(Distance AB = \sqrt{[(5-(-3))^2 + (2-4)^2]}= \sqrt{68} \\Distance AC = \sqrt{[(-3-0)^2 + (4-(-3))^2]} = \sqrt{58} \\Distance BC = \sqrt{[(5-0)^2 + (2-(-3))^2]}= \sqrt{50}\)

mAB = (2 - 4) / (5 - (-3)) = -1/2

This is the slope of AB

-1 / (-1/2) = 2

we have to find the point that is perpendicular to AB

(-3 + 5) / 2 = 1

(4 + 2) / 2 = 3

1 , 3 are  perpendicular to AB

y - 3 = 2(x - 1)

y - 3 = 2x - 2

y = 2x + 1

There fore the gradient of the line is 2

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Answer: 3.14159265358979.....

Step-by-step explanation:

Answer:

3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510 58209 74944 59230 78164 06286 20899 86280 34825 34211 7067.

Answer:

The answer is the equation for the function describing the movement of the buoy:

f(x) = 5 * sin(2 * pi * x / 16) + 8

Step-by-step explanation:

To graph the function, we need to find an equation that describes the buoy's movement. Since the buoy bobs up and down 5 meters from the ocean's depth, we can use the sine function. The amplitude of the function is 5, since the buoy moves 5 meters from the normal ocean depth. The period of the function is 16 seconds, since it takes 16 seconds for the buoy to go from its highest point to its lowest point.

Using this information, we can write the equation for the function as:

f(x) = 5 * sin(2 * pi * x / 16) + 8

where x is the time in seconds.

The first point on the graph would be (0, 8), since at x = 0 the buoy is at normal ocean depth. The second point would be either a maximum or minimum value on the graph closest to x = 0, which can be found by finding the derivative of the function and setting it equal to zero.

The graph of the function would look like a wave that oscillates up and down, with a maximum value of 5 meters above the normal ocean depth and a minimum value of 3 meters below the normal ocean depth.

isiaiisjjajsihajaihaiahshushsu a habja uahabja ha ha a ha ha Janna j Jabjaban an aka. na a ha ha ha ha a ja aja naja ha. ha aub ah ah ah ha ahahaha a ahba ahbahabhaba babav aha ha ha answer a

Answer:

4.35

Step-by-step explanation:

Answer:

4.35 kilo

Step-by-step explanation:

The above question is related to probability and has seven possible choices. The question requires finding the probabilities of selecting the correct and incorrect choices in different scenarios, such as selecting a choice randomly or after eliminating two of the options. To solve the question, we need to use basic probability concepts and formulas, such as the formula for probability, which is the number of favorable outcomes divided by the total number of possible outcomes.

(a) The probability of selecting the correct choice is 1/7 or approximately 0.143.

(b) The probability of selecting an incorrect choice is 6/7 or approximately 0.857.

(c) If two choices are eliminated, there will be five remaining choices, and the probability of selecting the correct choice will be 1/5 or approximately 0.2.

(d) If two choices are eliminated, there will be five remaining choices, and the probability of selecting an incorrect choice will be 4/5 or approximately 0.8.

It's crucial to remember that while deleting options might enhance the likelihood of picking the correct option, it can also raise the likelihood of selecting an erroneous option if the deleted options were more likely to be inaccurate. In each instance, the overall chance of making a correct or bad decision is always 1.

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1) An equation that gives the total cost in dollars, d, of attending the event if you order z ounces of fro-yo is d = $5 + $0.40z

2) 2. If your cup weighs 14 ounces, you would pay $10.6 in total for the evening.

A mathematical equation is a statement that two amounts or values are equal, such as 6 x 4 = 12 x 2. 2. A noun that counts.

Given,

The school jazz band is playing at Sweet Yo's, a frozen yogurt shop. It costs $5 to get in the door for the event and if you'd like to eat fro-yo to eat while listening to their tunes you can fill your cup with yogurt and toppings for $0.40 per ounce.

1) Total cost = d

Total ounces = z

Equation

d = $5 + $0.40z

2) If cup weighs 14 ounces

d = $5 + 0.40(14)

d = $5 + $5.6

Total cost:

d = $10.6

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Answer:

Step-by-step explanation:

1.5 (x+4)-3=4.5(x-2)=

1.5x+6-3=4.5x-9=

1.5x+3=4.5x-9=

1.5x-4.5x=-3-9=

-3x=-12

x=4

Answer:

x=4

Step-by-step explanation:

1.5(x+4)-3=4.5(x-2)

-Use distributiive prop. to simplify

1.5x+6-3=4.5x-9

-Simplify 6-3

1.5x+3=4.5x-9

-Subtract 1.5x from both sides

3=3x-9

-Isolate the x's by subtracting 9 from both sides

12=3x

-divide by 3

4=x

:) ur welcome

Answer:

x=15

Step-by-step explanation:

5x+17+36=128

5x+53=128

5x=75

x=15

(a) The variable educ might be endogenous

(b) The variable brthord is birth order (one for the first-born child, two for a second-born child and so on) could be used as an instrument for educ in equation

a) The variable instruction might be endogenous because as compensation increases the income expansions which additionally make able to an individual more educating himself. So there is an opportunity for the instruction might be an endogenous variable.

The indigeneity may involve the 32 the coefficient of knowledge as well different variables like married, black, south, urban, etc.

b) There is a substantial high relationship exists between birth order and the status of teaching. it is more possible to have higher schooling with less the order of child-born and the birth order is autonomous of the error term as well with wage. So the variable "birth order" is a good variable to use as an agency for the endogenous variable instruction.

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An inscribed angle is formed by two chords of a circle that intersect at a vertex located on the circle.

The angle itself is formed by the two sides of the angle, which are the line segments connecting the vertex to the endpoints of the chords. The property that makes inscribed angles interesting is that the measure of an inscribed angle is half the measure of the intercepted arc on the circle.

This relationship holds true for any inscribed angle in a circle, making it a useful concept in geometry for solving problems involving angles, arcs, and circles.

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Answer:

the first step would be to distribute the 9 to inside the parenthesis so it would look like 9x+18=90

Step-by-step explanation:

Hope this helps. If it does, click on the red heart as of to say "thanks"

Answer:

it is correct they weigh the same

Step-by-step explanation:

The set of natural numbers {1,2,3,4,...} and the set of positive even numbers {2, 4, 6, 8, . . .} are different because natural numbers include all positive integers, while even numbers only include those that are divisible by 2 with no remainder.

Two important sets of numbers are natural numbers and even numbers. The set of natural numbers consists of numbers that are not negative, beginning with 1 and continuing indefinitely with 2, 3, 4, and so on.

The set of even numbers, on the other hand, consists of numbers that are divisible by 2, beginning with 2, 4, 6, and so on.

Positive integers refer to natural numbers. Any integer greater than zero is a positive integer.

Zero is not a positive integer. Hence, the set of natural numbers consists of {1,2,3,4,…}

On the other hand, the set of even numbers consists of {2, 4, 6, 8, . . .}.

Therefore, {1,2,3,4,…} and {2, 4, 6, 8, . . .} are two different sets of numbers where one set is composed of positive integers (natural numbers) and the other is composed of positive even numbers.

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To determine if the given points are part of the (200) plane, we need to check if their coordinates satisfy the equation of the plane.

The equation of a plane in three-dimensional space is typically written in the form Ax + By + Cz + D = 0, where A, B, C, and D are constants. For the (200) plane, the equation would be 2x + 0y + 0z + 0 = 0, which simplifies to 2x = 0. Let's check the given points: a) (1/2, 0, 0): When we substitute x = 1/2 into the equation 2x = 0, we get 2(1/2) = 0, which is true. Therefore, point a) lies on the (200) plane. b) (-1/3, 0, 0): Substituting x = -1/3 into the equation 2x = 0 gives us 2(-1/3) = 0, which is also true. So, point b) is part of the (200) plane. c) (0, 1, 0):When we substitute x = 0 into the equation 2x = 0, we get 2(0) = 0, which is true. Thus, point c) lies on the (200) plane. All three given points (a), b), and c)) are part of the (200) plane.

In conclusion, all three given points (a), b), and c)) are part of the (200) plane.

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Given:

The angle 140 degree.

The co-terminal angles is defined as an angle, where two angle are drawn in the standard position.

It is determine by adding or subtraction 360 degree to each angle.

Answer: Positive co-terminal angle of 140 degree is 500 degree.

Option A is correct.

The exponential function is f(x) = 12000(1/10)^x.

We have the exponential function: f(x) = ab^x

From the first point (0,12000) we get:

f(0) = ab^0 = a = 12000

From the second point (2,120) we get:

f(2) = ab^2 = 120

Substituting a = 12000 we get:

12000b^2 = 120

b^2 = 1/1000

b = 1/10 or -1/10

However, since b is the base of an exponential function, it must be positive. Therefore, we take b = 1/10.

Thus, a = 12000 and b = 1/10.

Therefore, the exponential function is f(x) = 12000(1/10)^x.

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Answer:

800,000,000

Step-by-step explanation:

The main answer to the question "How long will it take for your money to double?" is C) 9 years.

Compounded interest refers to the process of earning interest on both the initial amount of money deposited and any previously earned interest. In this case, the money in the account earns a 6% interest rate, compounded monthly. To determine how long it will take for the money to double, we can use the concept of the rule of 72.

The rule of 72 is a simplified formula used to estimate the time it takes for an investment to double at a given interest rate. By dividing 72 by the interest rate, you can approximate the number of years it will take for the initial amount to double.

In this scenario, the interest rate is 6%. By dividing 72 by 6, we get 12. This means that the money will double approximately every 12 years. However, since the question asks for the answer to the nearest year, we need to consider that compounding occurs monthly.

Since interest is compounded monthly, we need to adjust the result by dividing by 12 (the number of months in a year). By doing so, we find that the money will double approximately every 1 year. Therefore, it will take approximately 9 years for the money to double.

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Answer:

No Solution

Step-by-step explanation:

26 + y = 8

-26

y = -18

proof 26 + (-18) = 8

83 - y = 2

+83

-y = 85

*-1

y = -85

-18 does not = -85 and I don't see an X in your system of equations

Answer:

Exact Form:

(41036433850368 ^6  x  2419 ^54 )− 328

Decimal Form:

2.48516121  x  10 ^264

Answer:

Heyyy T-T

Step-by-step explanation:

A linear combination of unbiased estimator is also an unbiased estimator.

Given that at1 (1 − a)t2 is an unbiased estimator, then it follows that at1 (1 − a)t2 is also an unbiased estimator.

Linear combination means adding the estimator values.

An estimator is a numerical value calculated from a sample of data.

Thus, if there are two unbiased estimators, say X1 and X2, the linear combination of X1 and X2, denoted as c1X1 + c2X2, is an unbiased estimator.

An unbiased estimator is an estimator with a zero bias. An estimator is said to be unbiased if its expected value is equal to the true value of the parameter. In other words, an estimator is unbiased if it doesn't systematically overestimate or underestimate the true value of the parameter. The expected value of an estimator is denoted as E(θ).

The proof that at1 (1 − a)t2 is also an unbiased estimator for θ is as follows:

First, we need to know the expected value of at1 (1 − a)t2.

This is because the expected value of an estimator is equal to the true value of the parameter.

Hence, E(at1 (1 − a)t2) = θ.Next, we need to show that the estimator is unbiased.

That is, E(at1 (1 − a)t2) = θ.

Using the distributive property of multiplication, we have

at1 (1 − a)t2 = at1t2 − a2t12.

Then,

E(at1 (1 − a)t2) = E(at1t2 − a2t12) = E(at1t2) − E(a2t12)

Since at1t2 and a2t12 are independent random variables, we can use the linearity of the expected value to get

E(at1t2) − E(a2t12) = aE(t12) − a2E(t12) = (a − a2)E(t12).

Since a ∈ [0, 1], then a − a2 is also non-negative.

Therefore, E(at1 (1 − a)t2) = (a − a2)E(t12) ≥ 0.

Therefore, at1 (1 − a)t2 is an unbiased estimator for θ.

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The sum of the series is 15 square units.

The formula for the nth partial sum of a series is given by Sn = a1 + a2 + a3 + ... + an, where a1, a2, a3, ... are the individual terms of the series.

In this case, we are given the nth partial sum sn = 7 − 5(0.8)n.

We can use this expression to find the individual terms of the series as follows:

s1 = 7 - 5\((0.8)^{1}\) = 3

s2 = 7 - 5\((0.8)^{2}\) = 4.6

s3 = 7 - 5\((0.8)^{3}\) = 5.48

s4 = 7 - 5\((0.8)^{4}\)= 5.984

We can see that the series is a decreasing geometric series with first term a1 = 3 and common ratio r = 0.8.

The sum of an infinite geometric series with first term a1 and common ratio r, where |r| < 1, is given by S = a1 / (1 - r).

Using this formula, we can find the sum of our series as:

S = a1 / (1 - r) = 3 / (1 - 0.8) = 15

Therefore, the sum of the series is 15 square units.

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The function f is increasing on the interval (6, ∞).

The function f will be increasing in the intervals where f'(x) > 0.

To find these intervals, we can examine the sign of each factor of f'(x), which is (x + 1)²(x - 3)⁵(x - 6)⁴.

We can analyze the sign of f(x) by considering the factors individually:

(x+1)²: This factor is always positive since it is the square of a real number.

(x - 3)⁵: This factor is positive when x>3 and negative when x< 3.

(x - 6)⁴: This factor is positive when x>6 and  negative when x< 6.

We need to consider the overlapping regions of positivity for each factor.

When x>6, all three factors are positive, so  f ′ (x) is positive.

When 3<x<6: In this interval, the factor  (x+1)² is positive, but both (x−3)⁵ and (x−6)⁴ are negative.

Thus, f ′ (x) is negative.

When x<−1: In this interval,  (x+1)² is negative, while (x−3)⁵ and (x−6)⁴ are positive.

Hence, f ′ (x) is negative.

Therefore,  the function f(x) is increasing on the interval x>6.

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tan x is undefined for x = nπ + π/2, where n is an integer.

To make a table of values using multiples of /4 for x and use the entries in the table to graph the function y = tan x, first we need to substitute the multiples of /4 for x and evaluate y = tan x.  

We have the given function:y = tan x

The table of values using multiples of /4 for x is as follows:  

x    |    y0    |    0म/4    |    0म/2म/4    |    UNDEFINED1म/4    |    12म/4    |    03म/4    |    -14म/4    |    0-3म/4    |    

1By using the table of values, we can now plot these points on a graph. For the values of x where tan x is undefined, we can represent this on the graph with a vertical asymptote.

Here's the graph:From the graph, we can see that the graph of the function y = tan x repeats itself every π units (or 180°).

The conclusion is that the function y = tan x is periodic with a period of π.

Also, we need to note that tan x is undefined for x = nπ + π/2, where n is an integer.

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Answer:

17.50

Step-by-step explanation:

1: 3.50 dollars

multiply by 5 on eahc side

5 : 17.50

The complete table to make a proportional relationship between weight and price is 17.50.

You start with an equation: 1 * 3.50 dollars

You want to multiply both sides of the equation by 5.

So, you have:

1 * 3.50 dollars = 5 * 3.50 dollars

On the left side, when you multiply 1 by 3.50 dollars, you get 3.50 dollars.

On the right side, when you multiply 5 by 3.50 dollars, you get 17.50 dollars.

So, the result of multiplying both sides by 5 is:

3.50 dollars = 17.50 dollars

This shows that if you have 1 item costing 3.50 dollars and you want to buy 5 of those items, the total cost would be 17.50 dollars.

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Downsizing refers to the process of reducing the size and workforce of a company to cut costs, increase efficiency, or adapt to changing market conditions. It involves eliminating positions, reducing staff numbers, or even closing down certain business units or branches.

Downsizing can occur for various reasons, such as financial difficulties, mergers and acquisitions, technological advancements, or strategic reorganization. Companies often assess their operational costs and decide to downsize to improve their financial performance.

During the downsizing process, companies may calculate the potential cost savings by considering factors such as salaries, benefits, severance packages, and operational expenses. For example, if a company decides to eliminate 100 positions with an average salary of $50,000 per year, it could result in annual savings of $5 million.

While downsizing can help companies achieve short-term cost reductions, it often has significant implications for the affected employees, including layoffs, reduced morale, and increased workload for remaining staff. It is crucial for organizations to handle the downsizing process with sensitivity and transparency, providing support to affected employees and communicating the rationale behind the decisions.

It is important to note that downsizing should not be seen as a long-term solution, but rather as a strategic measure to address specific challenges. Companies should also explore alternatives to downsizing, such as retraining and redeploying employees, implementing productivity improvements, or seeking new business opportunities, to ensure sustainable growth and success in the long run.

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Answer:

Step-by-step explanation:

sin = opposite leg / hypotenuse

cos = adjacent leg / hypotenuse

Ratios are same

When using the elimination method to find a general solution for the given linear system, the differentiation is with respect to t, at a.  \(C . 1 e^{-2} t + C^{2}  e^6t\)

The given linear system is x' = 2x-yy' = 2y-16x

To solve this problem by the elimination method, we eliminate x and solve the remaining differential equation for y.x' = 2x-yy' = 2y-16x

Differentiate the first equation with respect to t is 2x'-y' = 2x''

Differentiate the second equation with respect to t is 2y'-16x' = 2y''

Substitute the value of x' from the first equation to the second equation is 2y'-16(2x-y) = 2y''y''-4y'+8x = 0

This is a homogeneous linear differential equation with constant coefficients. The characteristic equation is \(r^2\)-4r+8 = 0

Using the quadratic formula r = -b ± √(\(b^2\) - 4ac)/2a= 2 ± √(-12)/2= 2 ± 2i

We can now write the general solution y(t) = \(C . 1 e^{-2}  t cos 2t + C . 2 e^{-2}t\) sin 2t = \(C . 1 e^{-2} t + C^{2}  e^6t\)

Therefore, option a is the correct answer.

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The number of puppies per kids is 20 puppies.

Given that, there are 180 puppies in the shelter with 9 kids.

Number of puppies per kids = Total number of puppies/Number of kids

= 180/9

= 20 puppies

Therefore, the number of puppies per kids is 20 puppies.

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Answer:

2sqrt(10)

Step-by-step explanation:

Use the Pythagorean theorem.

x^2 + 3^2 = 7^2

x^2 + 9 = 49

x^2 = 40

x = sqrt(40)

x = 2sqrt(10)