(a-8b) if a=-3 and b=1/4​

The length of the shorter leg is 16 units which was found using the given data.

A quadratic equation is a second-degree algebraic equation in x. In its usual form, the quadratic equation is ax² + bx + c = 0.

Given: The larger leg of a right triangle is twice more than three times the shorter leg, and the triangle's area is 400.

We know that,

Area of triangle = 1/2(larger leg)(shorter leg)

                  400=1/2(larger leg)(shorter leg)   Equation(1)

larger leg = 2 + 3(shorter leg)

We need to substitute this in Equation(1)

400 = 1/2[2+3(shorter leg)](shorter leg)

800 = 2(shorter leg) + 3(shorter leg)²

3(shorter leg)² + 2(shorter leg) - 800 = 0

Solving this quadratic equation,

we get, shorter leg = - 16 or +16

Thus, we found that the length of the shorter leg is 16 units as -16 cannot be the length because it is negative.

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Answer:

C. Print Nothing

Step-by-step explanation:

For those who don't wanna read

Answer:

The program is going to print nothing because the script does not tell it to say anything other than when the grade (x) is greater than 90.

Therefore,the correct option is 3, print nothing

(a) Cylindrical coordinates: r² = 5rcos(θ)

(b) Spherical coordinates: ρ²sin²(φ) = 5ρsin(φ)cos(θ)

(a) To convert the equation x² + y² = 5y to cylindrical coordinates, we substitute x = rcos(θ) and y = rsin(θ). After substituting these values, we obtain r²cos²(θ) + r²sin²(θ) = 5rsin(θ), which simplifies to r² = 5rcos(θ).

(b) To convert the equation x² + y² = 5y to spherical coordinates, we first convert the cylindrical coordinates to spherical coordinates: x = ρsin(φ)cos(θ), y = ρsin(φ)sin(θ), and z = ρcos(φ). Substituting these values, we have (ρsin(φ)cos(θ))² + (ρsin(φ)sin(θ))² = 5(ρsin(φ)sin(θ)), which simplifies to ρ²sin²(φ) = 5ρsin(φ)cos(θ).

In cylindrical coordinates, the equation becomes r² = 5rcos(θ), where r represents the distance from the z-axis, and θ represents the angle in the xy-plane.

In spherical coordinates, the equation becomes ρ²sin²(φ) = 5ρsin(φ)cos(θ), where ρ represents the distance from the origin, φ represents the angle between the positive z-axis and the line connecting the point to the origin, and θ represents the angle in the xy-plane.

These conversions allow us to express the equation in alternative coordinate systems, which can be useful in different contexts or when solving specific problems.

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Answer:

x = 0 and y = -2

Step-by-step explanation:

x - 2y = 4 and X - 1y = 2

you mentioned elemination aka substraction

so you when substract x - x =  0  -2y -( -y) = -y and 4 -2 = 2

so - y = 2

or y = 2

now substitute the numbers

x + 4 = 4

x = 0

and try it with one of the equation  or sometimes trying on both of them can be very helpful

Answer:

The given graph only shows one point, which is (-10, 8042). A single point cannot be used to determine whether the graph represents a function or not. We need at least two or more points to determine whether a graph represents a function or not. Therefore, we cannot conclude whether this graph represents a function or not based on the given information.In order to determine whether a graph represents a function or not, we can use the vertical line test. If any vertical line passes through the graph at more than one point, then the graph does not represent a function. Conversely, if every vertical line passes through the graph at most one point, then the graph represents a function.

Answer:

56/6 or 9.33

Step-by-step explanation:

8x5 -4^2/

2x3

40 - 4^2/

2x3

40 + 16/

6

56/6 or 9.33

The answer is 4 because when simplifying the top of the fraction it equals to  24  and the bottom is 6 so when dividing it equals 4.

Maximize Z = -2x1 + x2 - 4x3 + 3x4 subject to the following constraints:

x1 + x2 + x3 + 2x4 + s1 = 4,

-x1 + x3 + x4 - s2 = -1,

2x1 + x2 + s3 = 2,

and x1 + 2x2 + x3 + 2x4 = 2, where x1, x2, x3, x4, s1, s2, s3 ≥ 0.

To reformulate the given problem in the standard form of a linear programming model, we need to convert all the inequalities into equations and express all variables as non-negative.

The standard form of a linear programming problem is as follows:

Maximize (Z) = c1x1 + c2x2 + c3x3 + c4x4

Subject to:

a11x1 + a12x2 + a13x3 + a14x4 = b1

a21x1 + a22x2 + a23x3 + a24x4 = b2

a31x1 + a32x2 + a33x3 + a34x4 = b3

an1x1 + an2x2 + an3x3 + an4x4 = bn

x1, x2, x3, x4 >= 0

Now let's reformulate the given problem:

Maximize (Z) = -2x1 + x2 - 4x3 + 3x4

Subject to:

x1 + x2 + x3 + 2x4 <= 4

-x1 + 0x2 + x3 + x4 >= -1

2x1 + x2 + 0x3 + 0x4 <= 2

x1 + 2x2 + x3 + 2x4 = 2

x1, x2, x3, x4 >= 0

The reformulated linear programming problem in standard form is as follows:

Maximize (Z) = -2x1 + x2 - 4x3 + 3x4

Subject to:

x1 + x2 + x3 + 2x4 + s1 = 4

-x1 + x3 + x4 - s2 = -1

2x1 + x2 + s3 = 2

x1 + 2x2 + x3 + 2x4 = 2

x1, x2, x3, x4, s1, s2, s3 >= 0

Note: The reformulated problem includes slack variables s1, s2, and s3 to convert the inequalities into equations, and all variables are non-negative.

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Answer:

C

Step-by-step explanation:

\(\sqrt{3}\) times \(\sqrt{3}\) = 3 and \(\sqrt{3}\) times x = \(\sqrt{3}\)x

So that means that answer is 3+\(\sqrt{3}\)x which is C

We need to measure volume to check capacity of substance, to see that how much material it can hold inside it.

Answer: yes, they form a proportion

Step-by-step explanation: a proportion is made when the two ratios are equal. If you multiply both sides of the ratio, 8/5, by 3, you will get 24/15.

Given, marginal cost function is: C'(x) = 0.04e^(0.02x)Fixed cost is $9.Now, let's find the cost function from the marginal cost function. To find the cost function, we need to integrate the marginal cost function. So, C(x) = ∫C'(x) dxWe have marginal cost function, C'(x) = 0.04e^(0.02x)Now, integrate it with respect to x.

∫C'(x)dx = ∫0.04e^(0.02x) dxLet ' s integrate it using the formula: ∫e^(ax)dx = (1/a) e^(ax) + CI = (0.04/0.02) e^(0.02x) + CNow , we know that fixed cost is $9 which means, when x = 0, C(x) = 9Using this, let's find the value of C. Substitute x = 0 and C(x) = 9 in the above equation. C(x) = (0.04/0.02) e^(0.02x) + C9 = (0.04/0.02) e^(0.02(0)) + C9 = (0.04/0.02) e^(0) + C9 = (0.04/0.02) (1) + C9 = 2 + CC = 9 - 2C = 7Now, substitute the value of C in the equation we obtained above. C(x) = (0.04/0.02) e^(0.02x) + CC(x) = 2 e^(0.02x) + 7The cost function is C(x) = 2 e^(0.02x) + 7.The answer is 2 e^(0.02x) + 7.

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The cost function C(x) is \(C(x) = 2e^{0.02x} + 7\)

We have,

To find the cost function C(x) given the marginal cost function C'(x) and the fixed cost, we need to integrate the marginal cost function.

The marginal cost function is given as \(C'(x) = 0.04e^{0.02x}.\)

To integrate C'(x) with respect to x, we can use the power rule for integration and the fact that the integral of \(e^u\) du is \(e^u\).

∫ C'(x) dx = ∫ \(0.04e^{0.02x} dx\)

Using the power rule, we can rewrite the integral as:

C(x) = ∫ \(0.04e^{0.02x} dx = 0.04 \times (1/0.02) \times e^{0.02x} + C\)

Simplifying further:

\(C(x) = 2e^{0.02x} + C\)

We know that the fixed cost is $9, which means that when x = 0, the cost is equal to $9.

Substituting this into the equation:

\(C(0) = 2e^{0.02 \times 0} + C = 2e^0 + C = 2 + C\)

Since C(0) is equal to the fixed cost of $9, we have:

2 + C = 9

Solving for C:

C = 9 - 2

C = 7

Therefore,

The cost function C(x) is\(C(x) = 2e^{0.02x} + 7\)

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Answer:

6, 7, 63, 6, 7, 63, 130.9

Jut pit those numbers in the blanks

Answer:

63

Step-by-step explanation:

You have to multiply 10.5 by 6 and you get 63 then add that to 9.7 multipled by 7 and you get 130.9. Then subtract that by 67.9 and you get 63 to check add 63 to 67.9 and you get 130.9 so thereof the answer is 63.

Answer:

To estimate the total weight of the pet food Adam buys, we can use benchmark fractions to compare the weight of the dog food (7/8 pound) and the weight of the cat food (1 3/4 pounds) to a benchmark fraction that we are familiar with.

We know that 1 whole pound is equal to 16 ounces. So, we can use this as a benchmark to estimate the weight of the dog food and cat food.

First, we'll convert 7/8 pound to ounces. 7/8 pound is equal to 7/8 * 16 = 14 ounces

Next, we'll convert 1 3/4 pound to ounces. 1 3/4 pound is equal to 1 * 16 + 3/4 * 16 = 16 + 12 = 28 ounces.

Now we can add the weight of the dog food and the cat food to get the total weight of the pet food Adam buys.

14 ounces + 28 ounces = 42 ounces

So, the total weight of the pet food Adam buys is approximately 42 ounces, which is roughly 2.6 pounds.

The estimate was made with benchmark fractions, which allows us to make a rough estimation of the weight of the pet food, but it's not as precise as the exact weight in pound or ounces.

The inverse of the function f(x) = 2x is y = x/2.

How to calculate inverse of a function ?

To find the inverse of a function, write the function y as a function of x i.e. y = f(x) and then solve for x as a function of y. To find the inverse of any function, first, replace the function variable with the other variable and then solve for the other variable by replacing each other.

F(x)=2x

U should put it in normal standard

Y=2x

Then where u see x sub with y and where u see y sub with x

x=2y

Then divide by 2 both sides to have y as ur subject of the formular

X/2=2y/2

Ur answer will be

y=x/2

Hence , the inverse of the function f(x) = 2x is y = x/2.

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Answer:

17 sq. cm

Step-by-step explanation:

1st you split into 2 smaller shapes

Smaller shape:

A = lw

= 1(2)

= 2

Bigger Shape:

A = lw

= 3(5)

= 15

Add them together

15 + 2 = 17

True. Hexadecimal numbers are written using the base 16 number system, where digits range from 0 to 9 and A to F. They are commonly used in computer systems for concise representation and easy conversion to binary.

In the hexadecimal number system, there are 16 symbols used to represent values, namely 0-9 and A-F. Each digit in a hexadecimal number represents a multiple of a power of 16.

The symbols 0-9 represent the values 0-9, respectively. The symbols A-F represent the values 10-15, respectively, where A represents 10, B represents 11, C represents 12, D represents 13, E represents 14, and F represents 15.

For example, the hexadecimal number "3F" represents the value (3 * 16^1) + (15 * 16^0) = 48 + 15 = 63 in decimal.

Similarly, the hexadecimal number "AB8" represents the value (10 * 16^2) + (11 * 16^1) + (8 * 16^0) = 2560 + 176 + 8 = 2744 in decimal.

Hexadecimal numbers are commonly used in computer systems, as they provide a convenient way to represent large binary numbers concisely. Each hexadecimal digit corresponds to a four-bit binary number, allowing for easy conversion between binary and hexadecimal representations.

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From the given information provided,  the function f(x) is: \(f(x) = (\frac{1}{3})(ln(x))]^3 + 2 - [(\frac{1}{3})(ln(5))]^3\)

Finding a function's integral is a step in the mathematical process of integration. A new function called the integral of a function describes the region of the original function's curve that is under consideration.

Calculus, physics, and statistics are just a few of the mathematics, scientific, and engineering fields where integration is applied. It is used to resolve issues with computing the volume of a solid, determining the average value of a function over a specific range, and determining the area under a curve.

To find the function f(x), we need to integrate the derivative f'(x):

\(f(x) = \int \frac{ln(x)^2}{x} dx\)

Using u-substitution with u = ln(x), we have:

\(\frac{du}{dx} = \frac{1}{x}\)

⇒ \(dx = x du\)

Substituting this value into the integral, we get:

\(f(x) = \int u^2 du\)

\(= (\frac{1}{3})u^3 + C\)

\(= (\frac{1}{3})(ln(x))^3 + C\)

Where C is the constant of integration.

To find C, we use the fact that f(5) = 2:

\(f(5) = (\frac{1}{3})(ln(5))^3 + C = 2\)

Solving for C, we get:

\(C = 2 - (\frac{1}{3})(ln(5))^3\)

Putting the value of C in the integral, we get the required function

\(f(x) = (\frac{1}{3})(ln(x))]^3 + 2 - [(\frac{1}{3})(ln(5))]^3\)

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Answer:

64

Step-by-step explanation:

Marcello sells coupon books to his neighbors

4 neighbors each buy 2 coupon books

Each book have 8 coupons

Therefore the total number of coupons that all neighbors will get can be calculated as follows

Each neighbor will get 16 coupon

Hence the whole neighbors will get

16×4

= 64 coupons

There will be 230 lifeguards stationed on the beach.

To find the number of lifeguards on the beach, we need to divide the total length of the beach by the distance between each lifeguard station.

The total length of the beach is 18.4 kilometers, and the distance between each lifeguard station is 0.08 kilometers.

Therefore, the number of lifeguards can be calculated as:

Number of lifeguards = Total length of the beach / Distance between each lifeguard station

Number of lifeguards = 18.4 km / 0.08 km

Number of lifeguards = 230

So, there will be 230 lifeguards stationed on the beach.

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\(\bf \colorbox{black} {\bf {\textcolor{blue}{topic = }{ \bf { \textcolor{orange}{mathematics = }{ \bf{ \textcolor{cyan}{answer = }}}}}}}\)

M.C.M=

\( \bf \textcolor{red}{ \huge{48}}\)

3-16-2|2

3-8-1 |2

3-4-1 |2

3-2-1 |2

3-1-1 |3

1-1-1

2⁴•3

M.C.M=

2•2=4

2•2=4

4•4=16

16•3=48

\( \bf \textcolor{green}{ \underbrace{48}}\)

Answer:

- 28

Step-by-step explanation:

Answer:

10 times its value

Step-by-step explanation:

In case of 24,513 , 5 is at 100th place which will be 10 times its value

The coefficient of in the expansion of (2x + 3) using the Binomial Theorem is 1 .

The Binomial Theorem provides a way to expand a binomial raised to a positive integer power. In this case, we have the binomial (2x + 3) raised to the first power, which simplifies to (2x + 3). The general form of the Binomial Theorem is given by:

\((x + y)^n = C(n, 0) * x^n * y^0 + C(n, 1) * x^(n-1) * y^1 + C(n, 2) * x^(n-2) * y^2 + ... + C(n, n-1) * x^1 * y^(n-1) + C(n, n) * x^0 * y^n,\)

where C(n, k) represents the binomial coefficient, also known as "n choose k," and is given by the formula:

C(n, k) = n! / (k! * (n - k)!),

where n! represents the factorial of n.

In our case, we need to find the coefficient of the term with x^1. Plugging in the values for n = 1, k = 1, x = 2x, and y = 3 into the formula for the binomial coefficient, we get:

C(1, 1) = 1! / (1! * (1 - 1)!) = 1.

Therefore, the coefficient of in the expansion of (2x + 3) is 1.

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The required equation of tangent is: y = 5 sin (7T + 6) x - 5 cos (7T + 6) + 10. The correct option is d) y = x.

The curve given by the equation л 5п cosx + suny 10 and the equation of the tangent to the curve at the point O (7T + 6) are needed to be found.

The equation of the tangent to the curve at O (7T + 6) is given by the equation

y - y1 = m (x - x1)

where x1 and y1 represent the co-ordinates of the point on the curve and m is the slope of the tangent.

The equation of the curve is given by

y = 10 - 5 cos x

Therefore, at x = 7T + 6,

y = 10 - 5 cos (7T + 6)

⇒ y1 = 10 - 5 cos (7T + 6)

Also, we know that the slope of the tangent to the curve at any point is given by the derivative of the curve at that point.

Therefore, the derivative of y = 10 - 5 cos x is

dy/dx = 5 sin x

Thus, at x = 7T + 6, the slope of the tangent is

dy/dx = 5 sin (7T + 6)

Therefore, the equation of the tangent at O (7T + 6) is given by:

y - y1 = m (x - x1)

⇒ y - [10 - 5 cos (7T + 6)]

= [5 sin (7T + 6)] (x - 7T - 6)

Simplifying the above equation, we get

y - 10 + 5 cos (7T + 6)

= 5 sin (7T + 6) x - 35 sin (7T + 6)

Therefore, the required equation of the tangent is:

y = 5 sin (7T + 6) x - 5 cos (7T + 6) + 10

The options provided are:

y = xy = - xy

= xy = x

Therefore, the correct option is d) y = x.

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The value given is from a continuous data set because there are infinitely many possible values.

In statistics, a discrete data set is a set of data that can only take certain values, typically whole numbers, that can be counted. A continuous data set is a set of data that can take any value within a certain range, and the values can't be counted as they are infinite in number.

In the given scenario, the weight of a car can take any value within a certain range, and there are infinitely many possible values between any two values. For example, between 1628.3 kg and 1628.4 kg, the car's weight could be an infinite number of values. Hence, the weight of the car is a continuous variable, and the given value of 1628.3 kg is part of a continuous data set.

Hence, the correct answer is d.

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Answer:1. B 2. D

Step-by-step explanation:

Answer:

1-b 2-c

Step-by-step explanation:

The union set for the given sets X and Y are: X∪Y = {0,1,2,4,6,8,9}.

The elements shared by all of the sets are contained in the union of two (maybe three, as well as four, or more) sets.

The given sets are;

X={1,2,8,9}

Y={0,1,2,4,6,8,9}

So, union set contains all the values from both set without repeating the values.

Thus,

X∪Y = {0,1,2,4,6,8,9}.

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========================================================

Explanation:

The parabola has its lowest point when either x = -8 or x = 8

Plug either value into the function

f(x) = -x^2 + 4

f(-8) = -(-8)^2 + 4

f(-8) = -60

You should find that f(8) = -60 as well

This is the lowest output possible. Confirmation of such can be done using a graph. Look for the lowest point and only focus on the interval \(-8 \le \text{x} \le 8\)

The highest point is at the vertex (0, 4), so the largest output is y = 4

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

We have the lowest output y = -60 and the highest output y = 4

The possible set of outputs is the interval \(-60 \le \text{y} \le 4\) which turns into the interval notation [-60, 4]

Check out the graph below.

Yes, we need financial accounting theory even if we are only interested in 'doing'.

Financial accounting theory provides a conceptual framework for financial accounting. It is an important tool that helps to understand the concepts and principles that guide financial accounting practice.Even if a person is only interested in doing financial accounting, they still need to have an understanding of the theory underlying the practice to make informed decisions.

Financial accounting theory explains the underlying assumptions and concepts that govern the practice of financial accounting. It provides a framework for understanding the principles of financial accounting, which can then be applied to real-world situations.

For example, if an individual is only interested in doing financial accounting for a small business, they still need to have an understanding of the accounting principles and concepts that guide the practice.

This knowledge will enable them to make informed decisions when recording financial transactions and preparing financial statements. Without an understanding of financial accounting theory, the person may make errors or misinterpretations that could lead to incorrect financial statements.

Financial accounting theory is essential even if one is only interested in 'doing' financial accounting. It provides the underlying principles and concepts that guide the practice of financial accounting, enabling individuals to make informed decisions when recording financial transactions and preparing financial statements.

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