Lorene plans to make several open-topped boxes in which to carry plants. She makes the boxes from rectangular sheets of cardboard from which she cuts out -12 inch squares from each corner. The length of the original piece of cardboard is 24 inch more than the width. If the volume of the box is 1740 inch , determine the dimensions of the original piece of cardboard.

The value of the equation in terms of x is x = \(\sqrt{\frac{y^2-270}{135}}\).

Given is an equation, y = 3√(x²+2)15, we need to convert it in terms of x,

So,

y = 3√(x²+2) 15​

Squaring both sides,

y² = 9 [(x²+2)15]

y² = 9 [15x²+30]

y² = 135x²+270

y²-270 = 135x²

y²-270 / 135 = x²

x = \(\sqrt{\frac{y^2-270}{135}}\)

Hence, the value of the equation in terms of x is x = \(\sqrt{\frac{y^2-270}{135}}\).

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Answer:

Its C.

Step-by-step explanation:

I had this and its C. trust me

Answer:

the answer is c

Step-by-step explanation:

Please give me brainleist

Answer: p = 12.20h

30.5 hours

Step-by-step explanation:

Answer:

Brianna subtracted $12.50, even though you are not supposed to do that to find the price. You have to subtract $6.50, not $12.50.

The final answer is $7.04 because you subtract two initial prices.

Hope this helps you!

Answer:

The sample answer is :Brianna took both 25% discounts off the original amount. The second discount should have been calculated on the first reduced price of $9.38. The final sale price should have been $7.03.

Step-by-step explanation:

hope this helps :)

The amplitude is 3

for a sine graph, the amplitude is the distance up or down from the midway point. The equation to find the amplitude is (max-min) / 2.

(3 - (-3)) / 2 = 3

The number 459 in the citation 319 N.W. 2d 459 represents the page number where the case or legal opinion can be found in the North Western Reporter, Second Series. The North Western Reporter is a series of case reporters that includes court decisions from various states in the northwestern region of the United States.

In legal citations, the number before the "N.W." indicates the volume number of the reporter. So in this case, "319" refers to the specific volume where the case is located. The abbreviation "N.W." stands for North Western Reporter, which is the name of the reporter series. The number "2d" after "N.W." indicates that this is the second series of the North Western Reporter.

To locate the case within the volume, the number "459" refers to the page number where the case begins. This allows readers, such as lawyers, judges, or researchers, to easily find and reference the specific case within the reporter.

In summary, the number "459" in the citation 319 N.W. 2d 459 represents the page number where the case can be found in the North Western Reporter, Second Series.

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(i) Best Line Fit: a = -1.5, b = 0 (ii) Best Parabola Fit: a = -1, b = -0.5, c = 1. Therefore, the best line fit is given by y = -1.5t, and the best parabola fit is given by y = -t^2 - 0.5t + 1.

To find the best line and parabola fits to the given measurements, we can use the method of least squares. Here are the steps for each case:

(i) Best Line Fit:

The equation of a line is y = at + b, where a is the slope and b is the y-intercept.

We need to find the values of a and b that minimize the sum of the squared residuals (the vertical distance between the measured points and the line).

Set up a system of equations using the given measurements:

(-1, 2): 2 = -a + b

(0, 0): 0 = b

(1, -3): -3 = a + b

(2, -5): -5 = 2a + b

Solve the system of equations to find the values of a and b.

(ii) Best Parabola Fit:

The equation of a parabola is y = at^2 + bt + c, where a, b, and c are the coefficients.

We need to find the values of a, b, and c that minimize the sum of the squared residuals.

Set up a system of equations using the given measurements:

(-1, 2): 2 = a - b + c

(0, 0): 0 = c

(1, -3): -3 = a + b + c

(2, -5): -5 = 4a + 2b + c

Solve the system of equations to find the values of a, b, and c.

By solving the respective systems of equations, we obtain the following results:

(i) Best Line Fit:

a = -1.5

b = 0

(ii) Best Parabola Fit:

a = -1

b = -0.5

c = 1

Therefore, the best line fit is given by y = -1.5t, and the best parabola fit is given by y = -t^2 - 0.5t + 1. These equations represent the lines and parabolas that best fit the given measurements.

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Answer:

60

Step-by-step explanation:

The probability that the person participates in at least one school-sponsored activity given that the student works part-time is 0.58.

The possibility of an event or outcome occurring based on the existence of a prior event or outcome is known as conditional probability.

Assume that events A and B are two independent occurrences with probabilities P(A) and P(B), respectively, such that the probability that event B will occur given that event A is given by: P(B|A) = P(A∩B)/P (A)

Given:

Percentage of the students who have part-time jobs, P(A) = 73%

Percentage of the students who participate in at least one school-sponsored activity, P(B)= 65%

Percentage of the students who work part-time and participate in at least one school-sponsored activity, P(A∩B) = 42%

The probability that the person participates in at least one school-sponsored activity given that the student works part-time is:

P(B|A) = P(A∩B)/P(A)

          = 42/73

          = 0.58

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Answer:

0.575

Step-by-step explanation:

nice job

The extreme points (x, y) along the curve are (-1, -1) and (0, 0).

The given function f(I, y) = e² x² + xy + y² = 1 represents a quadratic equation in two variables, x and y. To find the extreme points, we need to determine the values of x and y that satisfy the equation and minimize or maximize the function.

a) The function defined by f(x, y) = e² x² + xy + \(y^2\) - 1 takes on a minimum and a maximum value along the curve.

To find the extreme points, we need to find the critical points of the function where the gradient is zero.

Step 1: Calculate the partial derivatives of f with respect to x and y:

∂f/∂x = 2\(e^2^x\) + y

∂f/∂y = x + 2y

Step 2: Set the partial derivatives equal to zero and solve for x and y:

2\(e^2^x\) + y = 0

x + 2y = 0

Step 3: Solve the system of equations to find the values of x and y:

Using the second equation, we can solve for x: x = -2y

Substitute x = -2y into the first equation: 2(-2y) + y = 0

Simplify the equation: -4e² y + y = 0

Factor out y: y(-4e^2 + 1) = 0

From this, we have two possibilities:

1) y = 0

2) -4e²  + 1 = 0

Case 1: If y = 0, substitute y = 0 into x + 2y = 0:

x + 2(0) = 0

x = 0

Therefore, one extreme point is (x, y) = (0, 0).

Case 2: If -4e^2 + 1 = 0, solve for e:

-4e²  = -1

e²  = 1/4

e = ±1/2

Substitute e = 1/2 into x + 2y = 0:

x + 2y = 0

x + 2(-1/2)x = 0

x - x = 0

0 = 0

Substitute e = -1/2 into x + 2y = 0:

x + 2y = 0

x + 2(-1/2)x = 0

x - x = 0

0 = 0

Therefore, the second extreme point is (x, y) = (0, 0) when e = ±1/2.

b) The equation (1+x)e = (1+y)e* is satisfied along the line y = x.

To find a critical point on this line where the equation is neither locally uniquely solvable for x nor y, we need to find a point where the equation has multiple solutions.

Substitute y = x into the equation:

(1+x)e = (1+x)e*

Here, we see that for any value of x, the equation is satisfied as long as e = e*.

Therefore, the equation is not locally uniquely solvable for x or y along the line y = x.

c) Taylor expansion up to degree 2:

To understand the solution set of the equation in the vicinity of the critical point, we can use Taylor expansion up to degree 2.

2. Expand the function f(x, y) = e²x²  + xy + \(y^2\) - 1 using Taylor expansion up to degree 2:

f(x, y) = f(a, b) + ∂f/∂x(a, b)(x-a) + ∂f/∂y(a, b)(y-b) + 1/2(∂²f/∂x²(a, b)(x-a)^2 + 2∂²f/∂x∂y(a, b)(x-a)(y-b) + ∂²f/∂y²(a, b)(y-b)^2)

The critical point we found earlier was (a, b) = (0, 0).

Substitute the values into the Taylor expansion equation and simplify the terms:

f(x, y) = 0 + (2e²x + y)(x-0) + (x + 2y)(y-0) + 1/2(2e²x² + 2(x-0)(y-0) + 2(\(y^2\))

Simplify the equation:

f(x, y) = (2e² x² + xy) + ( x² + 2xy + 2\(y^2\)) + e² x² + xy + \(y^2\)

Combine like terms:

f(x, y) = (3e² + 1)x² + (3x + 4y + 1)xy + (3 x² + 4xy + 3 \(y^2\))

In the vicinity of the critical point (0, 0), the solution set of the equation, given by f(x, y) = 0, looks like a second-degree polynomial with terms involving  x² , xy, and  \(y^2\).

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Answer:

m of angle A is 60 degrees, m of angle B is 80 degrees, and m of angle C is 40 degrees

Step-by-step explanation:

Given: BD=DC, this means the triangle BDC is isoceles because of the two equal sides.

Using the base angles Thereom we can tell that m of angle C is equal to m of angle 2.

Given that m of angle BDC is 100 degrees, using sum of angles in triangle we develop the equation

m of angle C= 180-100-angle 2

since angle 2 is equal to angle C we see that they are bothe equal to 40 degrees.

Now for B, we can easily tell it is 80 degrees since we found that angle 2 is 40 degrees and angle 1 is equal to angle 2 40+40=80 degrees

Lastly, for A we can tell it is 60 degrees, the reason is we found angle 1 is 40 degrees and we know that BDA=80 using supplemantary angles to BDC.

Develop the equation A=180-(80+40)=60 degrees

The value of measure of ∠A is, 60° , ∠B is 80° and ∠C is 40°.

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

We have to given that;

In Triangle ABC,

D belongs to AC,

BD = DC,

Measure of angle 1 = measure of angle 2,

Measure of angle BDC = 100 degrees.

Here, we have;

⇒ BD = DC

Hence, We get;

⇒ ∠DBC = ∠BCD

(By opposite angle of equal side are equal.)

Now, In ΔBDC;

⇒ ∠BDC + ∠DBC + ∠BCD = 180°

⇒ 100° + 2∠DBC= 180°

⇒ 2 ∠DBC = 180° - 100°

⇒ 2 ∠DBC = 80°

⇒ ∠DBC = 40°

⇒ ∠DBC = ∠BCD = ∠2 = 40°

Hence, ∠ C = 40°

Here, We have to given that;

⇒ ∠1 = ∠2

Hence, ∠1 = ∠2 = 40°

Now, We have by linear pair angle;

⇒ ∠BDC + ∠BDA = 180°

⇒ 100° + ∠BDA = 180°

⇒ ∠BDA = 80°

In ΔABD;

⇒ ∠ABD + ∠BDA + ∠BAD = 180°

⇒ 40° + 80° + ∠BAD = 180°

⇒ ∠BAD = 180° - 120°

⇒ ∠BAD = 60°

⇒ ∠A = 60°

So, ∠ B = ∠1 + ∠2

           = 40° + 40°

           = 80°

Thus, We get;

The value of measure of ∠A is, 60° , ∠B is 80° and ∠C is 40°.

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Answer:C

Step-by-step explanation:

The function graph for each of the cases with the description of the graph is plotted.

a. The ratio of the height of such a baseball thrown across outfield to home plate to the distance from centerfield.

This, will a parabolic graph as shown.

b. The volume of people who visit the mall per hour during regular business hours on such a particular day.

Thus, this graph will be step wise function as the value of people visiting the mall varies with the time.

c. A cup of coffee's temperature x minutes after it has been poured.

This, will be decreasing graph as the temperature of the coffee will keep on decreasing.

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Answer:

48 and 32

Step-by-step explanation:

both numbers get rounded by 8 going up and down rounding it to 40

he required solution is \(y=c_1e^{2x}+c_2e^{-2x}+c_3\sqrt2\cos(\sqrt2x)+c_4\sqrt2\sin(\sqrt2x)\)

where \(c_1,c_2,c_3\) and \(c_4\) are constants.

Let’s assume the general solution of the given differential equation is,

y=e^{mx}

By taking the derivative of this equation, we get

\(\frac{dy}{dx} = me^{mx}\\\frac{d^2y}{dx^2} = m^2e^{mx}\\\frac{d^3y}{dx^3} = m^3e^{mx}\\\frac{d^4y}{dx^4} = m^4e^{mx}\\\)

Now substitute these values in the given differential equation.

\(\frac{d^4y}{dx^4}-2\frac{d^2y}{dx^2}-8y\\=0m^4e^{mx}-2m^2e^{mx}-8e^{mx}\\=0e^{mx}(m^4-2m^2-8)=0\)

Therefore, \(m^4-2m^2-8=0\)

\((m^2-4)(m^2+2)=0\)

Therefore, the roots are, \(m = ±\sqrt{2} and m=±2\)

By applying the formula for the general solution of a differential equation, we get

General solution is, \(y=c_1e^{2x}+c_2e^{-2x}+c_3\sqrt2\cos(\sqrt2x)+c_4\sqrt2\sin(\sqrt2x)\)

Hence, the required solution is \(y=c_1e^{2x}+c_2e^{-2x}+c_3\sqrt2\cos(\sqrt2x)+c_4\sqrt2\sin(\sqrt2x)\)

where \(c_1,c_2,c_3\) and \(c_4\) are constants.

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Answer:

The given differential equation is:

12y" - 12y' + 30y = 0

To find the general solution, we first need to find the auxiliary equation. We assume a solution of the form:

y(t) = e^(rt)

where r is a constant. Differentiating this equation twice with respect to t, we get:

y'(t) = re^(rt)

y''(t) = r^2 e^(rt)

Substituting these into the differential equation, we get:

12r^2 e^(rt) - 12re^(rt) + 30e^(rt) = 0

Dividing both sides by e^(rt), we get:

12r^2 - 12r + 30 = 0

Simplifying this equation by dividing both sides by 6, we get:

2r^2 - 2r + 5 = 0

This is a quadratic equation with complex roots, which are given by the formula:

r = (2 ± sqrt(-4))/4 = (1 ± i√6)/2

Therefore, the general solution to the differential equation is:

y(t) = c1 e^((1+i√6)/2)t + c2 e^((1-i√6)/2)t

where c1 and c2 are constants determined by the initial conditions or boundary conditions of the problem.

Therefore , the solution of the given problem of equation comes out to be c1*e((1/2)*t)*cos((3/2)t) + c2e((1/2)*t)*sin((3/2)*t) = y(t).

The equation y=mx+b serves as the basis for a linear regression model. B is the slope, and m is the y-intercept. The above line is commonly referred to as the "mathematical problems with two variables," even though y and y are distinct components. Bivariate linear equations only contain two variables. The application areas of linear functions do not have clear-cut solutions.

Here,

For the specified differential equation, the auxiliary equation is:

=> 12r² - 12r + 30 = 0

When we multiply both parts by 6, we get:

=> 2r² - 2r + 5 = 0

Given that the discriminant is negative, the solutions of this quadratic equation are complicated:

=> b² - 4ac = (-2) ² - 4(2)(5) = -36

The following are the roots:

=> r = (2 ± √(-36))/(4) = (1 ± 3i)/2

The differential equation has the following general solution:

=> Y(t) = C1E + C2E (R1T) (r2t)

where c1 and c2 are arbitrary values and r1 and r2 are the auxiliary equation's roots.

When we replace the stems, we obtain:

=>  c1*e((1/2)*t)*cos((3/2)t) + c2e((1/2)*t)*sin((3/2)*t) = y(t).

As a result, the differential equation has the following general solution:

=> c1*e((1/2)*t)*cos((3/2)t) + c2e((1/2)*t)*sin((3/2)*t) = y(t).

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Answer:

3/7

Step-by-step explanation:

Answer:

The expression x⁴ + 8x³ + 34x² + 72x + 81 cannot be factored further using simple integer coefficients. It does not have any rational roots or easy factorizations. Therefore, it remains as an irreducible polynomial.

Answer:

585 is the answer of your question.

Step-by-step explanation:

because formula is

Mp _ d% of mp

The required all three situation are explained to the detector.

a. The equation for the distance-time graph of the student's motion is:

distance = rate × time + initial distance

where rate is the speed at which the student is walking (2 feet per second), time is the elapsed time in seconds, and initial distance is the distance between the student and the motion detector at the start (15 feet). This can be written in slope-intercept form as:

distance = 2t + 15

where the slope is 2 (the rate of change of distance with respect to time) and the y-intercept is 15 (the initial distance from the motion detector).

b. In this situation, the slope of the equation (2) represents the speed at which the student is walking towards the motion detector. It tells us that for every one second that passes, the student moves 2 feet closer to the motion detector. In other words, the slope represents the rate of change of distance with respect to time.

c. The y-intercept of the equation (15) represents the initial distance between the student and the motion detector. It tells us that at the start of the motion detector recording, the student was 15 feet away from the detector. When time is 0 (at the start), the distance traveled is just the initial distance, which is the y-intercept.

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A datagram with the destination IP address 158.30.142.30 would be routed to port 10011110 00011110 10001110 00011110.

What is an IP address explain?

Can I change my IP address?

What is IP address in WIFI?

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Answer:

0 pars

Step-by-step explanation:

3-3=0

Answer:

x=7

Step-by-step explanation:You can plug in the value for x and solve to see if true.

Answer: (0,-9)

Step-by-step explanation:

I put it in math-way hope this helps

Answer:

0.67

Step-by-step explanation:

correct

Answer:

a) $30

b) 30

Step-by-step explanation:

a) Her starting pay is $60. After an hour it goes up to $90. 90-60=30.

b) Every hour, the pay goes up 30.  Slope is calculated as the change in y divided by the change in x. That means 30/1, or just 30 is the slope.

Answer:

Step-by-step explanation:

tru i took the test

The maximum rate of change of function f at the given point occurs in the direction of the gradient vector.

To find the maximum rate of change of a function f at a given point, we need to compute the gradient of the function and evaluate it at that point. The gradient represents the direction of steepest ascent, and its magnitude indicates the maximum rate of change.

By finding the partial derivatives of f with respect to each variable and evaluating them at the given point, we obtain the components of the gradient vector. The maximum rate of change occurs in the direction of this gradient vector. Without the specific function and point, it is not possible to determine the exact maximum rate of change or its direction.

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If P' is another point on line l and N' is any unit normal to l, then for all points X, the normal vector N will be equal to N'. This is because the definition of the omega l function of reflection about line l depends on the line and the normal vector, rather than the specific points P and N.

The omega l function of reflection about line l depends on the line and the normal vector, rather than the specific points P and N. When we have another point P' on line l and any unit normal N', the reflection of any point X about line l will have the same normal vector N as N'.

This is because the reflection operation preserves the orientation of the normal vector, and the unit normal vector to line l remains the same regardless of the specific points P and P'. If we have another point P' on line l and any unit normal N', when we reflect any point X about line l, the resulting reflection will have the same normal vector N as N'.

This is because the reflection operation preserves the orientation of the normal vector, and the unit normal vector to line l remains the same regardless of the specific points P and P'. In other words, for all points X, the normal vector N will be equal to N'.

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