If a = 2,
3, find the value of (aº + bª)

\(\textit{area of a trapezoid}\\\\ A=\cfrac{h(a+b)}{2}~~ \begin{cases} h~~=height\\ a,b=\stackrel{parallel~sides}{bases~\hfill }\\[-0.5em] \hrulefill\\ a=2\\ h=1.6\\ A=2.2 \end{cases}\implies 2.2=\cfrac{1.6(2+b)}{2} \\\\\\ 4.4=1.6(2+b)\implies \cfrac{4.4}{1.6}=2+b\implies 2.75=2+b\implies \boxed{0.75=b}\)

Answer:

24 cm square

Step-by-step explanation:

Formula: ab/2. ( a* b = leg * leg)

6*8/2. (formula)

48/2 (simplify)

24 cm square ( answer)

Accuracy not garunteed

Answer:

k = - 8

Step-by-step explanation:

given that (x - a) is a factor of f(x) , then f(a) = 0

given

(x - 1) is a factor of f(x) then f(1) = 0 , that is

3(1)³ + 5(1) + k = 0

3(1) + 5 + k = 0

3 + 5 + k = 0

8 + k = 0 ( subtract 8 from both sides )

k = - 8

y = -6x -25 is equation of slope intercept .

What exactly does slope intercept mean?

 The equation is  y = -6x + 8

     compare with equation y=mx+b

  slope m = -6

Use the point-slope method

y = -6x + 8    

point P(-1,-4)  point given (x1,y1)

y-y1=m(x-x1)  point-slope form

y - ( -1 ) = -6 ( x - (-4))

y + 1 = -6 ( x + 4 )

y + 1 = -6x - 24

y = -6x -25

Learn more about slope-intercept form.

brainly.com/question/9682526

#SPJ13

The correct way to name the image is Southwest Vector BA, indicating the direction of the vector from B to A.

Vector BA : This notation indicates that the vector starts at point B and ends at point A, and it is read as "vector B-A" or "B-A vector". The order of the letters reflects the direction of the arrow, from B to A.

Arrow SW or SW arrow: This notation indicates the direction of the vector, which is towards the southwest, and it is read as "arrow southwest" or "southwest arrow". The order of the letters reflects the direction of the vector, from the northwest to the southeast.

Southwest Vector BA : This notation combines both the direction and the points of the arrow, and it is read as "southwest vector B-A" or "B-A southwest vector". The order of the words reflects the direction of the vector, from the northwest to the southeast, and the order of the letters reflects the starting and ending points of the arrow.

Learn more about vector diagram here: https://brainly.com/question/19802988

#SPJ1

A variable without a clear operational definition can greatly impact the accuracy and reliability of statistics performed on it. To ensure accurate and meaningful results, it is important to have clear, well-defined variables in any research study.

The lack of a clear definition can lead to inconsistencies in data collection, making it difficult to accurately interpret and analyze the results.

Step 1: When a variable has no clear operational definition, researchers may measure or interpret it in different ways, leading to inconsistencies in data collection.

Step 2: These inconsistencies can affect the reliability and validity of the collected data, which in turn impacts the accuracy of the statistical analysis performed.

Step 3: As a result, the findings from such analyses may not accurately represent the true relationships or patterns within the sample or the population, leading to incorrect conclusions.

To learn more about statistical analysis : brainly.com/question/30591800

#SPJ11

Answer:

the answer for this questionis 93(68+7)

Answer:

the probability of rain is 0.3. The probability of no rain is 1–0.3= 0.7

0.7 is the probability that it does not rain.Step-by-step explanation:

Answer:

d. the fourth graph

Step-by-step explanation:

this is correct on edge 2020

Option (D) is correct if the equation of the graph g(x) = = 1.5ˣ⁺¹ + 2 after applying the transformation.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

It is given that:

The equation for the parent function is:

f(x) = 1.5×

F(x) is a parent function.

After applying transformation:

x → x + 1  

f(x)  →  f(x) + 2

After applying the transformation:

The equation for the function g(x) becomes:

g(x) = 1.5ˣ⁺¹ + 2

Graph fourth represents the equation of the function g(x) = 1.5ˣ⁺¹ + 2

Thus, option (D) is correct if the equation of the graph g(x) = = 1.5ˣ⁺¹ + 2 after applying the transformation.

Learn more about the function here:

brainly.com/question/5245372

#SPJ6

The total profit that is earned is 4512.5

100 - q = 0

q = 100

Maximization is where q = 0

MR = mc

100 - q = 5

such that q = 95

Price would be  100 -0.5(95)

= 100 - 47.5

= 52.5

Profit earned would be

= 95*52.5 -5*95

= 4512.5

Read more on profit maximization here: https://brainly.com/question/13464288

#SPJ4

Part A: To find the expression for Pf, we need to integrate F(t) with respect to t over the given time interval.

Given that F(t) = ať + b, where a = -28 N/s^2 and b = 7.0 N, the integral can be calculated as follows:

Pf = po + ∫(F(t) dt)

Pf = po + ∫(ať + b) dt

Pf = po + ∫(ať dt) + ∫(b dt)

Pf = po + (1/2)at^2 + bt + C

Therefore, the correct expression for Pf is:

Pf = po + (1/2)at^2 + bt + C

Part B: The units of momentum can be determined by analyzing the units of the integral. Since F(t) has units of N (newtons) and t has units of s (seconds), the units of the integral will be N * s. Given that 1 N = 1 kg * m/s^2, the units of momentum are kg * m/s.

Therefore, the correct units of momentum are kg * m/s.

Part C: To evaluate the numerical value of the final momentum (Pf), we need to substitute the given values into the expression obtained in Part A. However, the initial momentum (po) and the time interval (t) are not provided in the question. Without these values, it is not possible to calculate the numerical value of Pf.

To know more about interval visit:

brainly.com/question/11051767

#SPJ11

Answer:

a) 33

Step-by-step explanation:

triangle inequality theorem

- the sum of any two sides of a triangle must be greater than the third

Answer:

No

Step-by-step explanation:

We can use the rule [ x^y * x^z = x^y+z ]

h^3 * h^4

h^3+4

h^7

Best of Luck!

Engineers can be held most morally blameworthy for foreseeable harms resulting from technological innovations, engineers have a responsibility to anticipate the potential consequences of their work,

and to take steps to mitigate those consequences. If they fail to do so, and their work results in harm, they can be held morally blameworthy. When engineers develop new technologies, they have a responsibility to consider the potential consequences of their work.

They need to think about how their technology could be used, and whether it could be used to harm people or the environment.

They also need to consider how their technology could be misused, and what steps they can take to prevent misuse.

If engineers fail to consider the potential consequences of their work, and their work results in harm, they can be held morally blameworthy. This is because they have a duty to protect the public from harm, and they have failed to fulfill that duty.

For example, engineers who develop new weapons systems have a responsibility to consider the potential consequences of their work. They need to think about how their weapons could be used,

and whether they could be used to kill or injure innocent people. They also need to consider how their weapons could be misused, and what steps they can take to prevent misuse.

If engineers fail to consider the potential consequences of their work, and their weapons are used to kill or injure innocent people, they can be held morally blameworthy. This is because they have a duty to protect the public from harm, and they have failed to fulfill that duty.

It is important to note that engineers cannot be held morally blameworthy for unforeseeable harms. This is because they did not have the opportunity to anticipate the harm, and they could not have taken steps to prevent it.

For example, engineers who develop new medical treatments cannot be held morally blameworthy if the treatments have unforeseen side effects. This is because the engineers did not have the opportunity to anticipate the side effects, and they could not have taken steps to prevent them.

In conclusion, engineers can be held morally blameworthy for foreseeable harms resulting from technological innovations.

This is because they have a responsibility to anticipate the potential consequences of their work, and to take steps to mitigate those consequences.

To know more about  Engineers click here

brainly.com/question/30592664

#SPJ11

Answer:  \(\frac{8x^3}{27y^6}\)

This is the fraction 8x^3 all over 27y^6

On a keyboard, we can write it as (8x^3)/(27y^6)

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

Explanation:

The exponent tells you how many copies of the base to multiply with itself.

We'll have three copies of \(\left(\frac{2x}{3y^2}\right)\) multiplied with itself due to the cube exponent on the outside.

So,

\(\left(\frac{2x}{3y^2}\right)^3 = \left(\frac{2x}{3y^2}\right)*\left(\frac{2x}{3y^2}\right)*\left(\frac{2x}{3y^2}\right)\\\\\left(\frac{2x}{3y^2}\right)^3 = \frac{2x*2x*2x}{(3y^2)*(3y^2)*(3y^2)}\\\\\left(\frac{2x}{3y^2}\right)^3 = \frac{(2*2*2)*(x*x*x)}{(3*3*3)*(y^2*y^2*y^2)}\\\\\left(\frac{2x}{3y^2}\right)^3 = \frac{8x^3}{9y^6}\\\\\)

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

Or another approach you could take is to cube each component of the fraction. The rule I'm referring to is \(\left(\frac{a}{b}\right)^c = \frac{a^c}{b^c}\)

Applying that rule will lead to:

\(\left(\frac{2x}{3y^2}\right)^3 = \frac{(2x)^3}{(3y^2)^3}\\\\\left(\frac{2x}{3y^2}\right)^3 = \frac{2^3*x^3}{3^3*(y^2)^3}\\\\\left(\frac{2x}{3y^2}\right)^3 = \frac{8x^3}{27y^{2*3}}\\\\\left(\frac{2x}{3y^2}\right)^3 = \frac{8x^3}{27y^6}\\\\\)

Either way you should get 8x^3 all over 27y^6 as one fraction.

Answer:

6/12 of a mile

Step-by-step explanation:

7/12-1/12=16/12

Answer:

I believe the answer is C

Step-by-step explanation:

knowledge

Answer:

Is C

Step-by-step explanation:

(a) A^3 = [1 1]

[−4 −1]

(b) BCT = [−21]

[13]

[0 15]

(c) EC + I3 = [−27 3 0]

[−4 7 0]

[0 24 1]

To perform the indicated computations, we'll multiply and add the matrices according to the given operations.

Given matrices:

A = [−3 1]

[2 −1]

B = [0 3]

[−2 7]

C = [7 0]

[−1 3]

[3 3]

E = [1 3 −7]

[−2 1 −3]

[0 2 6]

I3 = identity matrix of size 3x3

(a) A^3:

To calculate A^3, we need to multiply matrix A by itself three times:

A^2 = A * A

A^3 = A^2 * A

A^2 = [-3 1] [−3 1] [-11 2]

[2 −1] * [2 −1] = [−2 1]

A^3 = [-11 2] [−3 1] [1 1]

[−2 1] * [2 −1] = [−4 −1]

The result is:

A^3 = [1 1]

[−4 −1]

(b) BCT:

To calculate BCT, we need to multiply matrix B by matrix C and then transpose the result:

BCT = (B * C)^T

B * C = [0 3] [7 0] [−21 0]

[−2 7] * [−1 3] = [13 15]

Transposing the result:

(B * C)^T = [−21 0]^T [−21]

[13 15]^T = [13]

[0 15]

The result is:

BCT = [−21]

[13]

[0 15]

(c) EC + I3:

To calculate EC + I3, we need to multiply matrix E by matrix C and then add the identity matrix I3:

EC = E * C

E * C = [1 3 −7] [7 0] [−28 3]

[−2 1 −3] * [−1 3] = [−4 6]

[0 2 6] [3 3] [0 24]

Adding the identity matrix:

EC + I3 = [−28 3] [1 0 0] [−27 3 0]

[−4 6] + [0 1 0] = [−4 7 0]

[0 24] [0 0 1] [0 24 1]

The result is:

EC + I3 = [−27 3 0]

[−4 7 0]

[0 24 1]

Know more about matrix here:

https://brainly.com/question/29132693

#SPJ11

The  possible functions u(x, y) are the harmonic functions, which satisfy the Laplace equation.

To determine the possible functions u(x, y) such that the function f(x + iy) = u(x, y) + iu(x, y) is analytic or complex differentiable, we need to consider the Cauchy-Riemann equations. The Cauchy-Riemann equations are necessary conditions for a function to be complex differentiable. They state that if a function f(z) = u(x, y) + iv(x, y) is differentiable, then the partial derivatives of u and v must satisfy the following equations:

∂u/∂x = ∂v/∂y

∂u/∂y = -∂v/∂x

From these equations, we can see that the partial derivatives of u and v must be related in a specific way. In particular, if we focus on the real part u(x, y), we can determine the possible functions u(x, y) by solving the Cauchy-Riemann equations.

The solutions to the Cauchy-Riemann equations are known as harmonic functions. These functions satisfy the Laplace equation, which states that the sum of the second partial derivatives of u with respect to x and y is equal to zero:

∂²u/∂x² + ∂²u/∂y² = 0

Therefore, the possible functions u(x, y) that make the function f(x + iy) = u(x, y) + iu(x, y) analytic or complex differentiable are the harmonic functions. These functions have continuous partial derivatives and satisfy the Laplace equation.

Learn more about  Cauchy-Riemann equations here:

brainly.com/question/30385079

#SPJ11

The 99% confidence interval for the true population mean income is approximately $40,420 to $42,038.

What is the Z-score corresponding to a 99% confidence level?

The Z-score corresponding to a 99% confidence level is approximately 2.576.

To find the 99% confidence interval for the true population mean income for households in Charleston County, we can use the formula:

Confidence Interval = Sample Mean ± (Z * (Standard Deviation / √n))

Where:

Sample Mean = $41,229

Standard Deviation = $2,793

n = 79 (sample size)

Z = Z-score corresponding to the desired confidence level (99% confidence level)

First, we need to find the Z-score for a 99% confidence level. Since the confidence level is 99%, we will have an alpha (α) value of 0.01 for a two-tailed test. Looking up the Z-score corresponding to an alpha value of 0.01 gives us approximately 2.576.

Confidence Interval = $41,229 ± (2.576 * ($2,793 / √79))

Now we can calculate the confidence interval:

Confidence Interval = $41,229 ± (2.576 * $313.68)

Confidence Interval = $41,229 ± $808.07

Confidence Interval = ($40,420, $42,038)

Therefore, the 99% confidence interval for the true population mean income for households in Charleston County is approximately $40,420 to $42,038 (rounded to the nearest dollar).  

To learn more about the Z-score from the given link

brainly.com/question/15222372

#SPJ4

The position of a particle moving along a curve in the xy-plane can be described using parametric equations, where x and y are both functions of a third variable, usually time (t).


1. Parametric equations are equations that express the coordinates of a point (x, y) in the xy-plane in terms of a single variable, often time (t). In this case, x = f(t) and y = g(t), where f(t) and g(t) are functions of time.

2. To find the position of the particle at any given time, plug the value of time (t) into both functions, f(t) and g(t), to find the corresponding x and y coordinates. The position of the particle at time t is given by (x(t), y(t)).

3. To visualize the path of the particle, you can plot the curve described by the parametric equations x = f(t) and y = g(t) on the xy-plane. The particle moves along this curve as time progresses.

4. If you need to find the particle's velocity or acceleration, you can calculate the first and second derivatives of the position functions with respect to time.

In summary, the position of a particle moving along a curve in the xy-plane can be described by parametric equations, which relate the x and y coordinates to a third variable, usually time (t). The position of the particle at any given time can be found by plugging in the value of time into the parametric equations.

To know more about Parametric equations  visit:

brainly.com/question/29187193

#SPJ11

The graph of the equation x^2/49 + (y + 1)^2/4 = 1 is added as an attachment

The expression that represents the function in words is given as

StartFraction x squared Over 49 EndFraction + StartFraction (y + 1) squared Over 4 EndFraction = 1

Express the equation properly

So, we have

x^2/49 + (y + 1)^2/4 = 1

The above equation is an ellipse

Next, we plot the graph on a coordinate plane using a graphing tool

See attachment for the graph of the equation

Read more about ellipse at

https://brainly.com/question/29187465

#SPJ1

The table can be filled as A:1, B:1/16, C:1/256, D:1, E:4/9 and F:16/81. A mathematical value can generally be any specific mathematical object.

A mathematical value can generally be any specific mathematical object. This is most frequently a number in elementary mathematics, such as a real number like or an integer like 42. Every integer and other mathematical object set to a variable or constant is that object's value.

A mathematical expression's value is the outcome of the computation it describes when its variables and constants are given values. The amount that the function assumes for these input values is the value of such a function, assuming the value(s) given to its argument(s). The table can be filled as A:1, B:1/16, C:1/256, D:1, E:4/9 and F:16/81.

Therefore, the table can be filled as A:1, B:1/16, C:1/256, D:1, E:4/9 and F:16/81.

To know more about mathematical values, here:

https://brainly.com/question/30402650

#SPJ7

Answer:

5,789

Step-by-step explanation:

I got 5,789 because there are 9 one digit numbers. 1-9 -> 9x1=9. There are 90 two digit numbers. (10-99)-> 90x2=180. There are 900 three digit numbers. (100-999)-> 900x3=2700. There are 725 four digit numbers. (1000-1724)-> 724x4= 2900. Then, I added 9+180+2700+2900=5789.

In conclusion, the total number of digits required in numbering a book that has 1724 pages is 5789.

There are 5,789 digits in total required to number the pages of a book with 1,724 pages.

A numbering is the assignment of natural numbers to a set of objects in some formal language, such as functions, rational numbers, graphs, or words, in computability theory.

Given the total number of pages is 1,724

Let's break down the pages now to find the total digits.9

one-digit numbers (1-9) = 9 x 1 = 9 digits make up the number 1,724.90 numbers with two digits (10-99) = 90 x 2 = 180 digits900 three-digit numbers (from 100 to 999) = 900 times three = 2700 digits725 numbers with four digits (1000-1724) = 725 x 4 = 2900 digits

Let's add the digits now.9 + 180 + 2700 + 2900 = 5,789

As a result, the total number of digits required to number the pages of a 1,724-page book is 5,789.

Learn more about numbering here: https://brainly.com/question/251701

#SPJ2

Answer:

38 m

Step-by-step explanation:

Set up as proportion and cross multiply to solve:

x/57 = 18.9/28

x = 38.475

Rounded this would be 38 m.

Answer: 1) 10x+y=7

2) 3x-y=3

x-y=1

Answer:

n-3=12+3n-11

n-3=3n+1

-3-1=3n-n

-4=2n

n=-2

The width of the river is 2AC = \(125\sqrt{5ivec2 + 3} = 125(2.717)\) is approximately 339.63 m.

Let P be the point on the bank of the river that is 50 m from A along the perpendicular bisector of AB.

From point P, let the angle APD = α, and the angle APC = β.

Now, by the Law of Cosines, we have:

cosβ=\(\frac{AP^{2} + AC^{2} - PD^{2}}{2AP.AC}\)

cosα=\(\frac{AP^{2} + AD^{2} - PD^{2}}{2AP.AD}\)

Also, AP = 25 m, AD = 50 m and PC = (AC - AD)

Substituting these values in the above equations of cosβ and cosα, and solving for AC, we find:

AC = √(50² + 25²- 50²cosβcosα)

from which, the width of the river (i.e. 2AC) is equal to

2AC = 2√(50² + 25² - 50²cosβcosα)

Now, from the given bearings of C and B, we have

cosβ = cos320° = -3/2 and cosα = cos230° = (3ivec)/2

Substituting these values in the expression for AC, we have

2AC = \(2\sqrt{50^2 + 25^2 +(3^3)/4}\)

2AC = \(125\sqrt{2 + \frac{3}{2} } = 125\sqrt{5ivec2 + 3}\)

Hence, the width of the river is 2AC = \(125\sqrt{5ivec2 + 3} = 125(2.717)\) is approximately 339.63 m.

Learn more about the trigonometric ratios here:

brainly.com/question/25122825.

#SPJ4

Answer:

D

Step-by-step explanation:

Answer: A

Step-by-step explanation: i just got it correct