Multiply.
(3x + 2)(3x - 2)
A. 9x2 + 12x - 4
B. 9x2 - 4
C. 9x2 - 12x - 4
D. 9x2 + 4

The slope of line p is 3, and the slope of line q is -3

From the question, we have the points that can be used in our computation:

Line p

From the line p, we have the following ordered pairs

(2, 2) and (0, -4)

Line q

From the line p, we have the following ordered pairs

(0, 2) and (2, -4)

Rewrite the above points properly

So, we have the following ordered pairs

Line p, (x, y) = (2, 2) and (0, -4)

Line q, (x, y) = (0, 2) and (2, -4)

The slopes of the lines are then calculated using the following slope equation

slope = (y₂ - y₁)/(x₂ - x₁)

Substitute the known values in the above equation

So, we have the following equation

Slope of line p = (-4 - 2)/(0 - 2)

Evaluate

Slope of line p = 3

Slope of line q = (-4 - 2)/(2 - 0)

Evaluate

Slope of line q = -3

Hence, the slopes are 3 and -3, respectively

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The solution to the differential equation D²y(t) + 12 Dy(t) + 36y(t) = 2 \(e^{(-5t)}\), with initial conditions y(0) = 1 and Dy(0) = 0, is \(y(t) = (1 + 6t) e^{(-6t)}\).

To solve the given differential equation using the classical method, we can assume a solution of the form \(y(t) = e^{(rt)}\) and find the values of r that satisfy the equation. We then use these values of r to construct the general solution.

Using the classical method:

Substitute the assumed solution \(y(t) = e^{(rt)}\) into the differential equation:

D²y(t) + 12 Dy(t) + 36y(t) = \(2 e^{(-5t)}\)

This gives the characteristic equation r² + 12r + 36 = 0.

Solve the characteristic equation for r by factoring or using the quadratic formula:

r² + 12r + 36 = (r + 6)(r + 6)

= 0

The repeated root is r = -6.

Since we have a repeated root, the general solution is y(t) = (c₁ + c₂t) \(e^{(-6t)}\)

Taking the first derivative, we get Dy(t) = c₂ \(e^{(-6t)}\)- 6(c₁ + c₂t) e^(-6t).\(e^{(-6t)}\)

Using the initial conditions y(0) = 1 and Dy(0) = 0, we can solve for c₁ and c₂:

y(0) = c₁ = 1

Dy(0) = c₂ - 6c₁ = 0

c₂ - 6(1) = 0

c₂ = 6

The particular solution is y(t) = (1 + 6t) e^(-6t).

Using the Laplace transform method:

Take the Laplace transform of both sides of the differential equation:

L{D²y(t)} + 12L{Dy(t)} + 36L{y(t)} = 2L{e^(-5t)}

s²Y(s) - sy(0) - Dy(0) + 12sY(s) - y(0) + 36Y(s) = 2/(s + 5)

Substitute the initial conditions y(0) = 1 and Dy(0) = 0:

s²Y(s) - s - 0 + 12sY(s) - 1 + 36Y(s) = 2/(s + 5)

Rearrange the equation and solve for Y(s):

(s² + 12s + 36)Y(s) = s + 1 + 2/(s + 5)

Y(s) = (s + 1 + 2/(s + 5))/(s² + 12s + 36)

Perform partial fraction decomposition on Y(s) and find the inverse Laplace transform to obtain y(t):

\(y(t) = L^{(-1)}{Y(s)}\)

Simplifying further, the solution is:

\(y(t) = (1 + 6t) e^{(-6t)\)

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The mean (average) weight of trucks traveling on the interstate system is approximately 15,100 pounds, and the standard deviation (measure of variability) is approximately 6,200 pounds.

To find the mean and standard deviation, we use the properties of the normal distribution. The given information states that 70% of trucks weigh more than 12,000 pounds and 80% weigh more than 10,000 pounds.

Using these percentages, we convert them to z-scores by finding the corresponding values on the standard normal distribution. The z-scores for 70% and 80% are approximately 0.5244 and 0.8416, respectively.

By setting up equations using the z-scores and the formulas for z-scores, we can solve for the mean (μ) and standard deviation (σ). Solving these equations yields the values of μ ≈ 15,148.08 and σ ≈ 6,170.61.

Therefore, the mean weight of trucks traveling on the interstate system is approximately 15,100 pounds, and the standard deviation is approximately 6,200 pounds. These values provide an estimate of the typical weight range of trucks on the interstate system based on the given information.

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The magnitude of vector u (||u||) is approximately 11.704, the magnitude of vector v (||v||) is 5, and the dot product of vectors u and v (u⋅v) is 54.

To compute the requested values, we'll use the definitions of vector norms and the dot product.

Magnitude of vector u (||u||):

||u|| = √\(((-6)^2 + (-10)^2 + 1^2)\)

= √(36 + 100 + 1)

= √(137)

≈ 11.704

Magnitude of vector v (||v||):

||v|| = √\(((-4)^2 + (-3)^2 + 0^2)\)

= √(16 + 9 + 0)

= √(25)

= 5

Dot product of vectors u and v (u⋅v):

u⋅v = (-6)(-4) + (-10)(-3) + (1)(0)

= 24 + 30 + 0

= 54

Therefore, the computed values are:

||u|| ≈ 11.704

||v|| = 5

u⋅v = 54

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True. Two samples probably will have different means even if they are both the same size and they are both selected from the same population.

What is a sample?                                                                                                                                                                                                               A sample is a subset of a population that represents the whole population in a study. There are numerous techniques for sampling. Sampling may be random, stratified, or purposive, among other methods.

Random sampling is when each member of the population has an equal chance of being included in the sample.

Stratified sampling is when the population is divided into subgroups based on certain characteristics, and then a random sample is taken from each subgroup.

Purposive sampling is when participants are selected based on specific criteria, such as having a specific characteristic or being a part of a particular group.

The mean is a statistical measure that represents the average value of a set of data. A population mean is the average of all the values in a population, whereas a sample mean is the average of all the values in a sample. Two samples with the same size selected from the same population may have different means because of random variation, which is the difference in data points between samples that occurs due to chance.

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Answer: 98

Step-by-step explanation: 180 - 82 = 98

180 - 80 = 100, and 100 - 2 is 98.

Answer:

1.30

Step-by-step explanation:

The formula for EP cost is given as:

EP cost = AP cost / yield

From the Question,

AP unit cost = 1.10 per pound

The yield percent = 85%

EP cost = 1.10/85%

EP cost = 1.2941176471

Approximately

The EP unit cost of bell pepper = 1.30

The system will be consistent and will have unique solution.

Given,

Coefficient matrix of 5 equation in 5 variables.

Here,

Let A be a 5x5 coefficient matrix such that its each column has a pivot element, then

Rank A = 5, rank of augmented matrix [A|b] = 5 and number of unknowns = 5

Rank A = rank of augmented matrix [A|b] = number of unknowns = 5

Hence , System is consistent

There is a unique intersection point of all three lines, so values of variables is unique.

Hence, solution of system if unique.

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To find the area under the curve, you can evaluate the anti-derivative of the function and then apply the definite integral over the interval [2, 10].

To compute the area under the curve of the function f(x) = (x - 4)/(2x - 6x^2) cos(x) over the interval [2, 10], three different anti-derivatives were used by Mr. Sosa, Mrs. Perepelitsa, and Mr. Dougmay.

Since the specific anti-derivatives used by each person are not provided, it is not possible to determine the exact values they obtained for the area under the curve. However, if the anti-derivatives were calculated correctly, their results should be equal due to the Fundamental Theorem of Calculus.

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The income plainness of demand for eatery reflections is Income plainness = 200/ 20 = 10

Chance is a way of expressing a volume as a bit of 100. It's frequently denoted using the percent symbol(), which represents" per hundred". For illustration, 25 is original to25/100 or0.25 as a numeric.

By question-

The income plainness of demand measures the responsiveness of the volume demanded of a good or service to a change in income, all other effects being equal .However, it means that the good is a normal good, and the volume demanded increases as income increases, If the income plainness is positive. However, it means that the good is an inferior good, and the volume demanded diminishments as income increases, If the income plainness is negative.

In this case, John's pay increased by 20 percent, and the average number of eatery reflections he consumed increased from one a week to three a week. We can calculate the income plainness of demand for eatery reflections as follows

Income plainness = chance change in volume demanded/ chance change in income

The chance change in volume demanded is

( 3 reflections per week- 1 mess per week)/ 1 mess per week) x 100 = 200

The chance change in income is 20

thus, the income plainness of demand for eatery reflections is

Income plainness = 200/ 20 = 10

Since the income plainness is positive and lesser than 1, we can conclude that eatery reflections are a luxury good for John. Option( b) is the correct answer.

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The multiplicative rule states that when two outcomes are independent, the probability that these outcomes occur together is the product of their probabilities.

Therefore, the multiplicative rule states that when two outcomes are independent, the probability that these outcomes occur together is the product of their probabilities.

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Answer:

The function rule can be written as: f(x) = 2x-3

So, when  we input 3, we replace all of the x's for  3's and have: f(3) = 2(3)-3.

This simplifies to be: f(3) = 3, meaning that 3 is the output.

Hope this helps!

Answer:3

Step-by-step explanation:

The output value is y so set an equation at y=2x-3. Now x is the input value so plug in 3 for x. Two times three is 6 and then you have to subtract three from that. So the output value for an input of 3 is 3.

Answer:

\(d=18.92\ g/cm^3\)

Step-by-step explanation:

Given that,

The mass of a brick, m = 17.3 kg

Volume of the brick, V = 914 cm³

We need to find the density of the brick.

17.3 kg = 17300 g

Density is equal to mass per unit volume. So,

\(d=\dfrac{m}{V}\\\\d=\dfrac{17300\ g}{914\ cm^3}\\\\d=18.92\ g/cm^3\)

So, the density of the brick is \(18.92\ g/cm^3\).

Answer:

x=6

Step-by-step explanation:

5*x+6=36

so 5*6=30

+6=36

Answer:

36

Step-by-step explanation:

Answer:

U' (5, 1 )

Step-by-step explanation:

under a reflection in the x- axis

a point (x, y ) → (x, - y ) , then

U (5, - 1 ) → U' (5, - (- 1) ) → U' (5, 1 )

In summary, the Fourier coefficients for the periodic function y(t) = -3 on the interval -5 ≤ t ≤ 5 are:

c₀ = -3 (DC component)

cₙ = 0 for n ≠ 0 (other coefficients)

To find the Fourier coefficients of the periodic function y(t) = -3 on the interval -5 ≤ t ≤ 5, we can use the formula for Fourier series coefficients:

cn = (1/T) ∫[t₀-T/2, t₀+T/2] y(t) \(e^{(-i2\pi nt/T)}\) dt

where T is the period of the function and n is an integer.

In this case, the function y(t) is constant, y(t) = -3, and the period is T = 10 (since the interval -5 ≤ t ≤ 5 spans 10 units).

To find the Fourier coefficient c₀ (corresponding to the DC component or the average value of the function), we use the formula:

c₀ = (1/T) ∫[-T/2, T/2] y(t) dt

Substituting the given values:

c₀ = (1/10) ∫[-5, 5] (-3) dt

  = (-3/10) \([t]_{-5}^{5}\)

  = (-3/10) [5 - (-5)]

  = (-3/10) [10]

  = -3

Therefore, the DC component (c₀) of the Fourier series of y(t) is -3.

For the other coefficients (cₙ where n ≠ 0), we can calculate them using the formula:

cₙ = (1/T) ∫[-T/2, T/2] y(t)\(e^{(-i2\pi nt/T) }\)dt

Since y(t) is constant, the integral becomes:

cₙ = (1/T) ∫[-T/2, T/2] (-3) \(e^{(-i2\pi nt/T)}\) dt

  = (-3/T) ∫[-T/2, T/2] \(e^{(-i2\pi nt/T)}\) dt

The integral of e^(-i2πnt/T) over the interval [-T/2, T/2] evaluates to 0 when n ≠ 0. This is because the exponential function oscillates and integrates to zero over a symmetric interval.

all the coefficients cₙ for n ≠ 0 are zero.

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Answer:

nope

+8 is greater than -8

Answer:

C

Step-by-step explanation:

Given

V = πr²h

Isolate h by dividing both sides by πr²

\(\frac{V}{\pi r^2}\) = h → C

D has repetitive domain (x = 19). There are (19,11) and (19,10). A single x value only gives a single y-value. If a single x value gives more than one y-value then it's not Function.

So D isn't function

The complementary angles are 89 degree and 1 degree.

Let the complementary θ₁ =  degree

According to the question,

θ₂ = x - 88

Now since we know that,

The total of the two angles' measurements determines their complement and supplement. If the total of the two angles equals the measurement of a right angle, the angles are said to be complimentary.

Now since these angles are complementary,

Therefore,

⇒ θ₁ + θ₂ = 90

Now put the value of θ₁ and θ₂

⇒ x + x - 88 = 90

⇒   2 x - 88 = 90

Add 88 both sides we get

⇒        2 x  = 90 + 88

⇒        2 x  = 178

⇒        2 x  = 178

Divide by 2 both sides we get,

⇒            x  = 89

Hence,

⇒      θ₁ =  89 degree

Then other angle is,

⇒ θ₂ = 89 - 88 = 1 degree

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Answer:

120

Step-by-step explanation:

31x-4 = 29x+4

2x=8

x=4

31(4)-4 = 120

Answer:

l=\(24\*x^{6}\)

w=\(y^{15}\)

Step-by-step explanation:

We know that the area of rectangle can be determined by the multiply the length to the width i.e

A = l • w..................Eq(1)

Here A represented the area .

l=  Length of rectangle

w= Width of rectangle

Here A= \(24x^{6} y^{15}\)...

It can be written as \(A= 24x^{6} \ *y^{15}\)..............Eq(2)

Comparing the Eq(2) to the Eq(1)

\(l=24x^{6}\\ w=y^{15}\)

Answer:

the right answer A. 2x^5y^8 and 12xy^7

Step-by-step explanation:

Based on the information in the graph, we can infer that the missing numbers are: 9, 4, 19, 30, 84, 16, 8, 22, and 40.

To complete the table correctly we must identify the columns or rows with more data. These will be the easiest to complete. First of all, we must fill in those that already have a number in the total box because we can add the available numbers and later subtract them from the total to identify the missing number.

We can also find the numbers in the total cells by adding all the numbers in a column or row to find this result. Finally, the boxes that are being completed serve as clues to complete the others.

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Answer:

(C) The sum of the measures of ∠P, ∠Q, and ∠R is 180°

Step-by-step explanation:

All triangles, when their three angles are added up, gets us 180°.

This goes without saying, even with scalene triangles.

Additionally, the angles in squares add up to 360°, the angles in a pentagon add up to 540°.

Hope this helped!

Answer: Inferential

Step-by-step explanation:

Inferential statistics, has to do with taking data from the samples that the researcher has and then making generalizations about the population through the sample gotten.

Through Inferential statistics, one can draw conclusion about a particular phenomenon. Therefore, the answer to the above question is Inferential statistics

.

The process of finding distances using similar triangles is called "indirect measurement." This technique is commonly used in fields such as engineering, architecture, and surveying.

Indirect measurement involves creating a scale drawing of the object or space in question, using known dimensions and ratios to create a proportional representation. This drawing is then used to create similar triangles, which can be used to calculate distances and other measurements.

For example, if you want to measure the height of a building, you can create a scale drawing of the building and its surroundings, and use trigonometry to calculate the height of the building based on the length of its shadow and the angle of the sun.

Indirect measurement can be a powerful tool for solving complex problems and making accurate measurements in situations where direct measurement is not possible. However, it does require a strong understanding of geometry and mathematical concepts, as well as careful attention to detail and accuracy in creating the scale drawing.

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Answer:

Step-by-step explanation:

line RPN = 180 = 4y - 10 + 90 + y

180 - 90 + 10= 5y

100 = 5y

y = 100/5

y = 20

The function F(x, y) has a local maximum at (-2, -3), saddle points at (2, -3) and (-2, 1), and a local minimum at (2, 1).

To find the critical points and classify them as local maxima, local minima, or saddle points, we need to find the partial derivatives of the function F(x, y) and evaluate them at each critical point.

Given the function F(x, y) = x³ - 12x + y³ + 3y² - 9y, let's find the partial derivatives:

∂F/∂x = 3x² - 12

∂F/∂y = 3y² + 6y - 9

To find the critical points, we set both partial derivatives equal to zero and solve the resulting system of equations:

3x² - 12 = 0 --> x² = 4 --> x = ±2

3y² + 6y - 9 = 0 --> y² + 2y - 3 = 0 --> (y + 3)(y - 1) = 0 --> y = -3 or y = 1

Therefore, the critical points are (-2, -3), (2, -3), and (-2, 1).

To classify these critical points, we use the second partial derivatives test. The second partial derivatives are:

∂²F/∂x² = 6x

∂²F/∂y² = 6y + 6

Now, let's evaluate the second partial derivatives at each critical point:

At (-2, -3):

∂²F/∂x² = 6(-2) = -12 (negative)

∂²F/∂y² = 6(-3) + 6 = -12 (negative)

Since both second partial derivatives are negative, the point (-2, -3) corresponds to a local maximum.

At (2, -3):

∂²F/∂x² = 6(2) = 12 (positive)

∂²F/∂y² = 6(-3) + 6 = -12 (negative)

Since the second partial derivative with respect to x is positive and the second partial derivative with respect to y is negative, the point (2, -3) corresponds to a saddle point.

At (-2, 1):

∂²F/∂x² = 6(-2) = -12 (negative)

∂²F/∂y² = 6(1) + 6 = 12 (positive)

Since the second partial derivative with respect to x is negative and the second partial derivative with respect to y is positive, the point (-2, 1) corresponds to a saddle point.

Therefore, the critical points are classified as follows:

Local maximum: (-2, -3)

Saddle points: (2, -3) and (-2, 1)

Local minimum: (2, 1)

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Step-by-step explanation:

The area of a rectangle is given by the formula:

Area = length * width

In this case, the length of the rectangle is given by x + 3 and the width is given by x - 4.

Therefore, the area of the rectangle is:

Area = (x + 3) * (x - 4)

The perimeter of a rectangle is given by the formula:

Perimeter = 2 * (length + width)

In this case, the length of the rectangle is given by x + 3 and the width is given by x - 4.

Therefore, the perimeter of the rectangle is:

Perimeter = 2 * ((x + 3) + (x - 4)) = 2x - 2

So the area of the rectangle is (x + 3)(x - 4) and the perimeter is 2x - 2.

give me brainlist

Answer: Area= x^2-x-12  ,  Perimeter = 4x-2

Step-by-step explanation: According to the question,

Length = x+3

Breadth = x-4

Area of a rectangle = Length * breadth

Area = (x+3)(x-4)

Area = x^2-x-12

Perimeter of rectangle = 2*(length+ breadth)

Perimeter = 2* (x+3+x-4)

                 = 2*(2x-1)

                 = 4x-2

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