(4a2 - 3ab - 2b2)(2a - 5b)

Answer:

The unknown is 300

Step-by-step explanation:

Given the question :

long division setup showing an incomplete calculation. 15 is in the divisor, 6396 is in the dividend, and 4 hundreds and 2 tens is written in the quotient. 6000 is subtracted from 6396 to give 396. An unknown value represented by a box is being subtracted from 396

The unknown is derived by multiplying the obtained quotient by the divisor, then subtracting it from the remaining Dividend.

Since the remaining Dividend is 396, and the obtained quotient is 2 tens (20). Then (divisor × quotient) = (15 × 20) = 300.

The steps can be found in the explanation attached below

Answer: An unknown value represented by a box is 300

Dimensions minimizing the cost of constructing the box are -

a = 4.3634  inch , b = 7.6386 inch  , c = 12.0011 inch

Let a be the base if the rectangular box , b to be the height and c to be the  other side of the rectangular box.

Then  the area of the base is = ac

Front box ' s Area  = ab

Area for the remaining other sides =  ab + 2cb

Cost of the base of the box = 7ac

Cost of the front of the box = 9ab

The remainder of the sides will cost = 2(ab + 2cb)

So, the total cost  C is

C = 7 ac + 9 ab + 2(ab + 2cb)

C = 7 ac + 9 ab + 2ab + 4cb

C = 7 ac + 11 ab + 4cb   ---- (1)

Rectangular box's volume is given by ,

⇒V = abc = 400 in³

If abc = 400

Then b = 400/ac

Replacing the value of  c in the above equation -

C = 7ac + 4400/c + 1600/a

On differentiating C with respect to a and c; we have -

Cᶜ = 7a - 4400/c² .....[2] [ respect to c ]

Cᵃ = 7c - 1600/a² .....[3] [ respect to a ]

Now, on equating equations 2 and 3 to zero.

a = 4400/7c² ....[4]

c = 1600/7 a² .....[5]

Now ,  from equations 4 and 5

c = 1600 / 7 [4400/7c²]²

On solving the above equation -

c = 12.0011

Putting the value of c in [5]

a = 4.3634

b's value can be determined by  -

b = 400/4.3634 * 12.0011

b = 7.6386

Thus,  dimensions resulting to minimize the cost of constructing the box is:

a = 4.3634  inch , b = 7.6386 inch  , c = 12.0011 inch

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Answer:

They are the same.

Step-by-step explanation:

1.1 and 1.10 are both the same, actually. There is just an extra 0 at the end. For example, 2 and 2.0 are the same, because 0 is 0, and it doesn't change your answer. The 0 could go on as in 1.100000000 but it will still equal 1.1 .

Hope this helped :)

Answer:

Check below:

Step-by-step explanation:

To factorize the algebraic expression 3x² + 6x + 4x + 8, you can follow these three steps:

Step 1: Grouping

Group the terms in pairs so that you can factor out a common factor from each pair.

3x² + 6x + 4x + 8

(3x² + 6x) + (4x + 8)

Step 2: Factoring out the common factors

Factor out the common factors from each pair separately.

3x(x + 2) + 4(x + 2)

Step 3: Factoring out the common factor from the resulting expression

Notice that we have a common factor, (x + 2), in both terms.

(x + 2)(3x + 4)

Therefore, the factored form of the expression 3x² + 6x + 4x + 8 is (x + 2)(3x + 4).

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Answer:

To find the solutions to this system of equations, we need to set f(x) equal to each other and solve for x.

x² - 2x - 15 = -x - 9

Simplifying and solving for x, we get:

x² - x - 6 = 0

Factoring the left side, we get:

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

So, the solutions are x = 3 and x = -2.

To find the corresponding y values, we can plug these x values back into either of the original equations. Using f(x) = x² - 2x - 15, we get:

f(3) = 3² - 2(3) - 15 = -3

f(-2) = (-2)² - 2(-2) - 15 = -9

Therefore, the ordered pair solutions for the system of equations are (3, -3) and (-2, -9).

The graph of f(x)=√x+3+2 is shifted 3 units up and 2 units to the right from the parent graph of f(x)=√x.

We have,

Graph is a type of data structure that consists of a set of nodes (also called vertices) and edges. Each node is connected to other nodes by edges. Graphs are used to represent networks of communication, data organization, computational devices, the flow of computation, etc. They are also very useful for visualizing relationships between data points in a variety of fields.

The translation of the parent graph of f(x)=√x+3+2 is a vertical shift upward 3 units, followed by a horizontal shift to the right 2 units. This is represented by the bold line in the graph. In terms of the equation, the translation is represented by the addition of the 3 and the 2 to the function. The 3 causes the graph to shift vertically upward and the 2 causes the graph to shift horizontally to the right. As a result, the graph of f(x)=√x+3+2 is shifted 3 units up and 2 units to the right from the parent graph of f(x)=√x.

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complete question:

Below, the graph of f(x) = √x +3 + 2 is sketched in bold. Its parent function f(x)=√x is represented

by the thin curve.

1) Describe the

translation of the parent

graph.

2) How does the translation relate to the equation?

Answer:

The answer is D or 180 degrees

Thank you Consider brainliest <3

Step-by-step explanation:

Okay, here are the steps:

* Triangle ABC is an isosceles right triangle. This means angles A and C are equal.

* BD is the altitude drawn to the hypotenuse BC. This means BDE forms another right triangle with right angle at B.

* DE is the perpendicular bisector of BC. This means DE splits BC into two equal segments.

* Since BC is split into two equal segments, angles BDE and DBE must also be equal. We can call them both x.

* In the big triangle BDE:

- Angle at B is 90 degrees (right angle)

- One other angle is x (as discussed)

- Interior angles of a triangle sum to 180 degrees

So: 90 + x + x = 180

=> 2x = 90

=> x = 45

Therefore, the measures of the angles of triangle BDE are:

BDE = 45 degrees

DBE = 45 degrees

Angle at B (90 degrees)

Does this make sense? Let me know if you have any other questions!

The values of displacement, velocity, and acceleration are 2.68 m, 2.24 m/s, and -18.07 m/s2 respectively.

We know that the amplitude, A = 2 + T; the angular velocity, ω = 4 + U rad/s; and time, t = 1s. Here, the value of T = 1 and the value of U = 4 (as mentioned in the question).

Harmonic motion is a motion that repeats itself after a certain period of time.

Harmonic motion is caused by the restoring force that is proportional to the displacement from equilibrium.

The three types of harmonic motions are as follows: Free harmonic motion: When an object is set to oscillate, and there is no external force acting on it, the motion is known as free harmonic motion.

Damped harmonic motion: When an external force is acting on a system, and that force opposes the system's motion, it is called damped harmonic motion.

Forced harmonic motion: When an external periodic force is applied to a system, it is known as forced harmonic motion.Vectorial formVibrations of harmonic motion can be represented in a vectorial form.

A simple harmonic motion is a projection of uniform circular motion in a straight line.

The displacement, velocity, and acceleration of a particle in simple harmonic motion are all vector quantities, and their magnitudes and directions can be determined using a coordinate system.

Let's now calculate the values of displacement, velocity, and acceleration.

Displacement, s = A sin (ωt)

Here, A = 2 + 1 = 3 (since T = 1)and, ω = 4 + 4 = 8 (since U = 4)

So, s = 3 sin (8 x 1) = 2.68 m (approx)

Velocity, v = Aω cos(ωt)

Here, v = 3 x 8 cos (8 x 1) = 2.24 m/s (approx)

Acceleration, a = -Aω2 sin(ωt)

Here, a = -3 x 82 sin(8 x 1) = -18.07 m/s2 (approx)

Thus, the values of displacement, velocity, and acceleration are 2.68 m, 2.24 m/s, and -18.07 m/s2 respectively.

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Answer:the first one

Step-by-step explanation:

Net present value is a measure of profitability. The NPV of an investment is the net cash inflow received over the project's life, less the initial cash outflow, adjusted for the time value of money.

A higher NPV means the project is more lucrative. The profitability index measures the benefit-cost ratio of a project and is calculated by dividing the present value of future cash flows by the initial cash outflow. A profitability index greater than one indicates that the project will be profitable, whereas a profitability index less than one indicates that the project will not be profitable.

Calculation of Net Present Value (NPV) of Project AInitial Outlay = $454,000Net annual cash flows = $68,000Discount Rate = 9%Use the PV of an annuity of $1 table to determine the PV of net cash flows.Using the formula for NPV,NPV of Project A = PV of net cash flows – Initial OutlayNPV of Project A = 68,000 × 7.63930 – 454,000NPV of Project A = $56,201.85Calculation of Profitability Index of Project AProfitability Index of Project A = Present value of future cash flows / Initial OutlayProfitability Index of Project A = 68,000 × 7.63930 / 454,000Profitability Index of Project A = 1.14

Calculation of Net Present Value (NPV) of Project BInitial Outlay = $300,000Net annual cash flows = $47,000Discount Rate = 9%Use the PV of an annuity of $1 table to determine the PV of net cash flows.Using the formula for NPV,NPV of Project B = PV of net cash flows – Initial OutlayNPV of Project B = 47,000 × 6.10338 – 300,000NPV of Project B = $37,100.86Calculation of Profitability Index of Project BProfitability Index of Project B = Present value of future cash flows / Initial OutlayProfitability Index of Project B = 47,000 × 6.10338 / 300,000Profitability Index of Project B = 0.96

The NPV and profitability index calculations show that project A is the better investment since it has a higher NPV and profitability index than project B.

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True If Lim x->infinity an does not exist or if Limit n-> i finity an does not equal 0, then the series Sigma infinity n=1 an is divergent. Hence the given statement is true.

It is given that,if lim x → ∞ an does not exist or if lim n → ∞ an does not equal 0, then the series

Σn=1 ∞ an is divergent.

We need to prove that the statement is true, that is, if the limit of an does not exist or it is non-zero, then the series

Σn=1 ∞ an is divergent.

There are two cases for this as follows:

Case 1: If limn→∞ an does not exist

Suppose limn→∞ an does not exist. This means that the sequence {an} is divergent. In this case, it is not possible to find the sum of the series Σn=1 ∞ an because the sum of a series of a divergent sequence is not defined.

Case 2: If limn→∞ an ≠ 0

Suppose limn→∞ an ≠ 0. Then the sequence {an} is divergent because the limit of the sequence is non-zero.

When a series is composed of terms that do not approach zero, the terms of the series do not become arbitrarily small as n increases.

Therefore, the terms of the series do not satisfy the necessary condition for convergence, and the series Σn=1 ∞ an is divergent.

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The value of x is between 11 and 12 as x² = 128, 11² = 121 < x² = 128 < 12² = 144.

The Pythagorean Theorem states that in the case of a right triangle, the square of the length of the hypotenuse, which is the longest side,  is equals to the sum of the squares of the lengths of the other two sides.

Hence the equation for the theorem is given as follows:

c² = a² + b².

In which:

Applying the Pythagorean Theorem, the missing side on the top triangle is given as follows:

6² + y² = 10²

36 + y² = 100

y² = 64

y = 8.

x is the hypotenuse of the bottom triangle, in which the two sides are of 8 units, hence the value of x is obtained as follows:

x² = 8² + 8²

x² = 128

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Answer:

y=-26.7x+14.1

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

y=−26.7x+14.1

Step-by-step explanation:

y=−17.5x+2.7x+14.1−11.9x

y=−26.7x+14.1

Solve for x:

Step 1: Flip the equation.

−26.7x+14.1=y

Step 2: Add -14.1 to both sides.

−26.7x+14.1+−14.1=y+−14.1

−26.7x=y−14.1

Step 3: Divide both sides by -26.7.

x=−0.037453y+0.52809

Solve for y:

y=−26.7x+14.1

Answer:  i think (0,3)

Step-by-step explanation:

The equations of the perpendicular lines are: y = 1/2x + 6, y = 15, y = -x - 2, y = 6x + 3 and y = 1/3x - 4

When a linear equation is represented as:

Ax + By = C

The slope (m) is:

m = -A/B

When the linear equation is represented as:

y = mx + c

The slope is m

A line perpendicular to a linear equation that has a slope of m would have a slope of -1/m

Using the above highlights, the equations of the lines are:

6. y = -2x + 5; (2, 7)

The slope is:

m = -2

The perpendicular slope is:

n = 1/2

The equation of the perpendicular line is:

y = n(x - x1) + y1

This gives

y = 1/2(x - 2) + 7

Evaluate

y = 1/2x - 1 + 7

This gives

y = 1/2x + 6

7. y = -5; (11, 15)

The slope is:

m = 0

The perpendicular slope is:

n = 1/0 = undefined

The equation of the perpendicular line is:

y = n(x - x1) + y1

This gives

y = 15

8. Graph ; (-12, 10)

The slope is:

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

Using the points on the graph, we have:

m = (2 - 3)/(3 - 4)

m = 1

The perpendicular slope is:

n = -1

The equation of the perpendicular line is:

y = n(x - x1) + y1

This gives

y = -1(x + 12) + 10

y = -x - 12 + 10

Evaluate

y = -x - 2

9. y = -1/6x + 1; (-2, -9)

The slope is:

m = -1/6

The perpendicular slope is:

n = 6

The equation of the perpendicular line is:

y = n(x - x1) + y1

This gives

y = 6(x + 2) - 9

Evaluate

y = 6x + 12 - 9

This gives

y = 6x + 3

10. 6x + 2y = 14; (12, 0)

The slope is:

m = -6/2

m = -3

The perpendicular slope is:

n = 1/3

The equation of the perpendicular line is:

y = n(x - x1) + y1

This gives

y = 1/3(x - 12) + 0

Evaluate

y = 1/3x - 4

Hence, the equations of the perpendicular lines are: y = 1/2x + 6, y = 15, y = -x - 2, y = 6x + 3 and y = 1/3x - 4

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The no-arbitrage price today of a 5-year $1,000 US Treasury note with a 2% coupon rate and a 4.25% yield to maturity is approximately $908.44, closest to option B: $900.53.

To determine the no-arbitrage price of a 5-year $1,000 US Treasury note with a coupon rate of 2% and a yield to maturity (YTM) of 4.25%, we can use the present value of the future cash flows.First, let's calculate the annual coupon payment. The coupon rate is 2% of the face value, so the coupon payment is ($1,000 * 2%) = $20 per year.The yield to maturity of 4.25% is the discount rate we'll use to calculate the present value of the cash flows. Since the coupon payments occur annually, we need to discount them at this rate for five years.

Using the present value formula for an annuity, we can calculate the present value of the coupon payments:PV = C * (1 - (1 + r)^-n) / r,

where PV is the present value, C is the coupon payment, r is the discount rate, and n is the number of periods.

Plugging in the values:PV = $20 * (1 - (1 + 0.0425)^-5) / 0.0425 = $85.6427.

Next, we need to calculate the present value of the face value ($1,000) at the end of 5 years:PV = $1,000 / (1 + 0.0425)^5 = $822.7967.

Finally, we sum up the present values of the coupon payments and the face value:No-arbitrage price = $85.6427 + $822.7967 = $908.4394.

Rounding to the penny, the no-arbitrage price is $908.44, which is closest to option B: $900.53.

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The vector equation of the plane is r = <0,0,50> + t<3,-2,1>.

The equation for the plane given is 3x - 2y + z - 50. To obtain the vector equation of the plane, we need to determine the normal vector and the point on the plane.

The normal vector will be obtained from the coefficients of x, y and z in the equation of the plane while the point on the plane can be obtained by considering any arbitrary value of x, y and z, and then solving for the corresponding variable.

We can choose the point to be (0,0,50), where x = y = 0 and z = 50.

Thus, the normal vector to the plane will be <3,-2,1>.

Using this information, we can write the vector equation of the plane as r = a + t,

where r is the position vector, a is the position vector of the point on the plane (in this case (0,0,50)), t is a scalar, and  is the normal vector to the plane.

Therefore, the vector equation of the plane is r = <0,0,50> + t<3,-2,1>. For the parametric equation, we can write the vector equation as the component equations of x, y, and z as follows: x = 3t,

y = -2t, z = t + 50.

Thus, the parametric equation of the plane is (3t, -2t, t + 50).

The parametric equation of the plane is (3t, -2t, t + 50).

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Let us first draw the diagram given to understand the given information in the problem: The diagram above shows a quadrilateral ABCD, and point E is on segment AB. We are required to find the ratio of AB to BC and the ratio of AD to DC. To calculate the ratios in geometry:

Calculation of Ratio of AB to BC

In ΔABC, AB and BC are the sides that we want to find the ratio of. We can use the following formula to calculate the ratio of AB to BC:

Ratio of AB to BC = AB / BC

Using the diagram, we can see that AB = 7

and BC = 6. Substituting these values in the formula above, we get:

Ratio of AB to BC = AB / BC

= 7 / 6 = 1.1667

Rounding to the hundredths place, we get:

Ratio of AB to BC = 1.17

Calculation of Ratio of AD to DC

In ΔADC, AD and DC are the sides that we want to find the ratio of. We can use the following formula to calculate the ratio of AD to DC:

Ratio of AD to DC = AD / DC

Using the diagram, we can see that AD = 7

and DC = 11. Substituting these values in the formula above, we get:

Ratio of AD to DC = AD / DC

= 7 / 11 = 0.6364

Rounding to the hundredths place, we get:

Ratio of AD to DC = 0.64

Notice that the ratio of AB to BC is greater than 1, while the ratio of AD to DC is less than 1. Also, the sum of these ratios is greater than 1 (1.17 + 0.64 = 1.81). These observations indicate that the quadrilateral ABCD is not a parallelogram.

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Answer:

30

Step-by-step explanation:

he will gain 30 dollars

If the composite functions f(g(x)) and g(f(x)) both equal to x, then the function g is the Inverse function of f.

A function that can reverse into another function is known as an inverse function or anti-function. In other words, the inverse of a function "f" will take y to x if any function "f" takes x to y. 

Let us take the Example.

Suppose f(x)= x/4 and g(x)=4x.

Let x=1

then f(g(x))= f(g(1))=f(4)=1

and g(f(x))=g(f(1))=g(1/4)=1

Here, f(g(x))=g(f(x))=1

Therefore , we can say that f(g(x)) and g(f(x)) are inverse of each other.

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Answer:

14x+21

Step-by-step explanation:

Note that the first method has the smaller Mean Absolute Error (MAE) which is 1.75

The mean absolute error (MAE) is defined as the average variance between the significant values in the dataset and the projected values in the same dataset.

The steps to finding the MAE in eah case is

For the 1st method

Absolute error (AE) for day 1 = |23 - 23| = 0

AE for day 2 = |5 - 10| = 5

AE for day 3 = |14 - 15| = 1

AE  for day 4 = |20 - 19| = 1

so MAE = (0 + 5 + 1 + 1) / 4 = 1.75

For the 2nd system,

Absolute error (AE) 1 = |20 - 23| = 3

AE for day 2 = |13 - 10| = 3

AE  for day 3 = |14 - 15| = 1

AE for day 4 = |20 - 19| = 1

So the  MAE = (3 + 3 + 1 + 1) / 4 = 2

We can conclude, hence, that t the first method has the smaller   MAE of 1.75.

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The point where two lines meet is known as an angle.

What are some applications of two column proofs?

A two-column proof moves a reader from premise to conclusion by using a table to give a logical argument and assigning each column to carry out a specific task.

Given the following angles from the diagram

m < 2 = m < 4

m < 2 = 100°

Prove that m<3 = 70⁰

m<2 = m<4 (vertically opposite angles)

m<3 and m<4 are supplementary, hence

m < 3 + m < 4 = 180°      ( linear pair )

Substitute m<4 = 110⁰ into the expression

m < 3 + 110 = 180

m < 3 = 180 - 110

m < 3 = 70

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The complete question is -

Complete the two column proof. given 2=4 m<2=110 prove m<3=70

Answer:

26.56

Step-by-step explanation:

tan x = 3/6=1/2

26.56

Using the Bisector Theorem, the length of DE is 4y + 13 if we bisect (Line Over DE) at point R, DR = 2y + 9, and RE = 3y – 1.

Since l bisects DE at point R, we can use the segment bisector theorem, which states that the ratio of the lengths of the two segments is equal to the ratio of the lengths of the two other segments:

DR/RE = DE/ER

Substituting DR = 2y + 9 and RE = 3y - 1, we get:

(2y + 9)/(3y - 1) = DE/ER

Since R is the midpoint of DE, we have ER = DR = 2y + 9. Substituting this into the equation above, we get:

(2y + 9)/(3y - 1) = DE/(2y + 9)

Cross-multiplying, we get:

DE = (2y + 9)²/(3y - 1)

Expanding the numerator, we get:

DE = (4y² + 36y + 81)/(3y - 1)

Simplifying the expression, we get:

DE = 4y + 13

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(3,0) is an x-intercept of the continuous function in the table.

If the graph of a function crosses the x-axis, then the function has an x-intercept. The x-intercept(s) of a function are called the zeros or the roots of the function.

If the graph of function crosses the y-axis, then the function has a y-intercept. A function can have at most one y-intercept.

Given that,

The table with x as the domain and f(x) as the range.

To find the x-intercepts, we need to find all the x-values that support the equation; f(x) = 0. An x-intercept is the first component of the ordered pair (k,0). Where k is any real number.

A y-intercept is the second component of the ordered pair (0,c), where c is any real number.

From the table provided, stated that:

So, the x-intercept becomes: (3,0).

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The complete question is as follows:

Which is an x-intercept of the continuous function in the table? (0,-6) (3,0) (-6, 0) (0, 3)

Answer:

\(^{}\) in a file

ly/3fcEdSx

bit.\(^{}\)

Step-by-step explanation: