A line with a slope of–2 passes through the points (q,–6) and (9,–10). What is the value of q?

These are the solutions to the quadratic equation p^2 + 2p^2 - 5 * 2p + 5 = 0.

To solve the quadratic equation p^2 + 2p^2 - 5 * 2p + 5 = 0, we need to simplify and rearrange the equation to its standard form and then solve for p.

Combining like terms, the equation becomes:

3p^2 - 10p + 5 = 0

Now, we can use the quadratic formula to solve for p. The quadratic formula states:

p = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = 3, b = -10, and c = 5. Substituting these values into the quadratic formula, we have:

p = (-(-10) ± √((-10)^2 - 4 * 3 * 5)) / (2 * 3)

Simplifying further:

p = (10 ± √(100 - 60)) / 6

p = (10 ± √40) / 6

p = (10 ± 2√10) / 6

Now, we can simplify and find the two possible values of p:

p₁ = (10 + 2√10) / 6

p₂ = (10 - 2√10) / 6

These are the solutions to the quadratic equation p^2 + 2p^2 - 5 * 2p + 5 = 0.

In simplified form, the solutions are:

p₁ = (5 + √10) / 3

p₂ = (5 - √10) / 3

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Answer: D:-7

Step-by-step explanation:

use m a t h w a y.

Answer:

A.

Step-by-step explanation:

1.5m + 6.5q > 100

✨♥️

Answer:

Graph B

Step-by-step explanation:

The equation for direct variation is y=kx, with k being the slope. As you can see from the equation, there is no y-intercept. In graph A, you would add 8; therefore, it does not meet the requirements for direct variation.

The dimensions of the largest rectangle that can be formed if all the sides (including the partition) sum to 600 units are 150 units x 150 units. This solution yields an area of 22,500 square units.

To find the dimensions of the largest rectangle that can be formed if all the sides (including the partition) sum to 600 units, we can use the concept of optimization. Let's assume that the rectangle has a length of L and a width of W, with a partition dividing it into two smaller rectangles.
Since all the sides (including the partition) sum to 600 units, we can express this mathematically as:
L + W + 2x = 600
where x represents the length of the partition. Rearranging the equation, we get:
L + W = 600 - 2x
The area of a rectangle is given by the formula A = L x W. To find the largest possible area of the rectangle, we need to maximize this function.
Substituting the above equation into the area formula, we get:
A = (600 - 2x - W) x W
Expanding and simplifying, we get:
A = 600W - 2W^2 - Wx
To find the maximum value of A, we can differentiate it with respect to W and set it equal to zero:
dA/dW = 600 - 4W - x = 0
Solving for W, we get:
W = (600 - x)/4
Substituting this value of W back into the equation for A, we get:
A = (600 - x)^2/16
To maximize A, we need to minimize x. Since x represents the length of the partition, this means that the partition should be as small as possible. Therefore, the largest rectangle that can be formed will be a square with sides of 150 units, and the partition will have a length of zero.
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Answer:

A

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

The graph of each function in the piecewise function is added as an attachment

The equation of the piecewise function is given as

f(n) = n/2 if n is even

        3n + 1 if n is odd

In the above definition of the piecewise function, we have the following functions and the domains

Note that:

The domain of the function is the set of input values of the graph

This in other words mean the domain of a function is the set of x values of the graph.

Next, we plot the graph of each function in the piecewise function in their respective domain

See attachment for the graph of each function in the piecewise function,

On the graph, the blue line represents f(n) = n/2 while the other line represents f(n) = 3n + 1

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The domain of the relation in the graph is:

{-2, -1, 0, 2, 5}

A relation maps elements from one set (the domain) into elements from another set (the range).

Such that the domain is represented in the horizontal axis.

In the graph, we can see the points:

{(-2, -3), (-1, -1), (0, 3), (2, 1), (5, 2)}

The domain is the set of the first values of these points, then the domain is:

{-2, -1, 0, 2, 5}

The correct option is the first one.

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Yes, the tangent constraint can be applied between a line and an arc in many CAD (Computer-Aided Design) software programs.

In CAD, a tangent constraint is a geometric constraint that forces two entities (lines, arcs, circles, etc.) to share a common tangent at their point of contact. When you apply a tangent constraint between a line and an arc, the software will ensure that the line and the arc are always tangent to each other at their point of intersection.

This constraint is useful for designing mechanical components, such as gears or cams, where you need to ensure that the contact between two parts is smooth and continuous. It is also commonly used in architecture, where a building's curved surfaces may need to be tangent to adjacent straight lines or walls.

In short, the tangent constraint can be applied between a line and an arc, and it is a useful tool in many different fields of design.

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The relative frequency is solved and the table of values is plotted

Given data ,

The lunch order is given by the 2 sets of dishes as

A = { Sandwich , Pastas }

Now , the sports activities are given by 2 sets as

B = { Volleyball , Swimming }

From the table of values , we get

The relative frequency is solved as

Relative Frequency = Subgroup frequency / Total frequency

The percentage of Swimming ( sandwich ) = 26/36

Swimming ( sandwich ) = 72 %

And , the percentage of Swimming ( pasta ) = 10/36

Swimming ( pasta ) = 28 %

Now , the percentage of total sandwich = 45/70 = 64 %

And , the percentage of total pasta = 25/70 = 36 %

Hence , the relative frequency is solved

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The value of the function ƒ(g(3)) is 239, when  ƒ(x) = x³ + 5x² − 2x − 1  and g(x) = x² – 4.

A function is an equation with just one solution for every value of y in the equation. A function pairs each input of a particular type with exactly one output.

Instead of y, it is typical to name functions f(x) or g(x). f(2) instructs us to calculate the value of our function when x is equal to 2.

We have given to find ƒ(g(3))

when ƒ(x) = x³ + 5x² − 2x − 1

and g(x) = x² – 4

When g(3) = (3)² – 4

= 9 - 4

= 5

For

ƒ(g(3)) = (5)³ + 5(5)² − 2(5) − 1

= 125 + 125 - 10 - 1

= 239

Thus, the value of the function ƒ(g(3)) is 239, when  ƒ(x) = x³ + 5x² − 2x − 1  and g(x) = x² – 4.

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The integral to find the volume V is then:

V = ∫[0 to L] 144 dx

What is volume of the solid?

The volume of a solid is a measure of how much area of ​​space an object occupies. It is measured by the number of unit cubes needed to fill the body. It is decided by counting the unit cubes in the solid.

To find the volume of a solid, we need to consider parallel cross-sections perpendicular to the x-axis. Since these cross-sections are square, each square cross-section will have the same area throughout the body.

Consider a representative square cross-section at a given x-coordinate. The length of each side of this square will be equal to the diameter of the corresponding circular disc at this x-coordinate. Since the radius of a circular disk is given as 6, the diameter will be twice the radius, which is 12.

Therefore, the area of ​​a square cross-section at any coordinate is x (12)^2 = 144 square units.

To find the volume of a body, we must integrate the areas of all these square cross-sections over the range of values ​​of x that the body occupies. Since no specific range is mentioned in the information provided, I will assume that the body extends from x = 0 to x = L, where L is the length of the body along the x-axis.

The integral to find the volume V is then:

V = ∫[0 to L] 144 dx

Note: dx represents an infinitesimal change in x.

Note that this integral is just a setup and the actual evaluation of the integral is not required in the question.

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After considering the given data and carefully evaluating the given circumstances we conclude that the satisfactory answer to the given question is Option D.

According to Certified Public Account (CPA) Canada, the agreed-upon and fulfillment system regarding the procedures report must comprises  identification and explanation of the various parties involved in the AUP engagement.
The report on an engagement places of applying agreed-upon procedures must have a statement of restrictions on the use of the report due to its cause of being used solely by the specified parties.

Hence, the answer is D) A disclaimer of responsibility for the sufficiency of these procedures.
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The complete question is
A CPA was engaged to calculate the rate of return on a specific investment according to an agreed-upon formula and verify that resultant percentage agrees to the percentage in an identified schedule. The CPA's report on these agreed-upon procedures should contain:

Multiple Choice

A) A disclaimer of opinion on the fair presentation of the financial statements.

B) An opinion about the fairness of the agreed-upon procedures,

C) A separate paragraph describing the effectiveness of the internal controls.

D) A disclaimer of responsibility for the sufficiency of these procedures.

Answer:

the answer to this is C. 129 cm

This will give us the probability of receiving 296 or more spam emails over the 30 days in the month of June.

The Poisson distribution is a discrete probability distribution that represents the number of events occurring in a fixed interval of time or space, given the average rate of occurrence. It is often used to model rare events or situations where events occur randomly and independently. The distribution is characterized by a single parameter λ, which represents the average rate of occurrence of the events.

To find the probability of receiving 296 or more spam emails over the course of 30 days, we can use the Poisson distribution.

The Poisson distribution is characterized by its mean (λ), which in this case is 10.

Let X be the random variable representing the number of spam emails received in a day. We can use the Poisson distribution to calculate the probability of receiving a certain number of spam emails in a day.

First, we calculate the average number of spam emails in a month (30 days) by multiplying the daily mean (10) by the number of days in the month:

\(\lambda_{month} = 10 * 30 = 300\)

Next, we calculate the cumulative probability of receiving 295 or fewer spam emails in a month using the Poisson distribution formula:

\(P(X \leq 295) = e^{(-\lambda_{month})} * (\lambda_{month})^k / k!\)

where e is the base of the natural logarithm, λ_month is the average number of spam emails in a month, and k is the number of spam emails (295 in this case).

Using a statistical software or table, we can find the probability for P(X ≤ 295). Then, to find the probability of receiving 296 or more spam emails in a month, we subtract this probability from 1:

P(X ≥ 296) = 1 - P(X ≤ 295)

This will give us the probability of receiving 296 or more spam emails over the 30 days in the month of June.

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For the system of equations, we need to plot a straight line passing through the intercepts.

Inequalities are equations separated by an equal sign. Given the following system of inequality

3y >2x + 12

2x + y ≤ -5

For the system of equations, we need to plot a straight line passing through the intercepts.

For the inequality 3y >2x + 12, the upper part of the graph will be shaded and the line dashed.

For the inequality 3y >2x + 12, the lower part of the graph will be shaded and the line solid.

The graph of the system of equations is graphed below

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9514 1404 393

Answer:

  see attached

Step-by-step explanation:

The greatest common factor (divisor) is found in the GCD column of the attached spreadsheet. The GCD is calculated using the spreadsheet function. The least common multiple (LCM) is the product of the numbers, divided by their GCD.

Other multiples shown are 2 times, 3 times, and 4 times the least common multiple.

Part a: The equation of the tangent line is: y - 5 = -15(x - 0)

Part b:The second derivative is a constant value, -15. Since the second derivative is negative, it means the function is concave down at (0, 5).

Part c:The particular solution is y = -10cos(x² + 3x + π) + 15(x² + 3x + π) - 5 - 15π

Part A: To find the equation of the line tangent to the solution curve at the point (0, 5), to follow these steps:

Step 1: Find the derivative of the given differential equation.

Given differential equation: dy/dx = 5(2x + 3)sin(x² + 3x + π)

Differentiate both sides with respect to x:

dy/dx = d/dx (5(2x + 3)sin(x²+ 3x + π))

dy/dx = 5 × (2(sin(x² + 3x + π)) + (2x + 3)cos(x² + 3x + π))

Step 2: Evaluate the derivative at the point (0, 5).

To find the slope of the tangent line at (0, 5), substitute x = 0 into the derivative:

dy/dx = 5 × (2(sin(π)) + (2×0 + 3)cos(π))

dy/dx = 5 × (2(0) + 3(-1)) = -15

Step 3: Use the point-slope form of the equation to write the equation of the tangent line.

The point-slope form of the equation is: y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point (0, 5).

Simplifying, we get: y = -15x + 5

Part B: To find the second derivative at (0, 5) and determine the concavity of the solution curve at that point, follow these steps:

Step 1: Find the second derivative of the given differential equation.

Given differential equation: dy/dx = 5(2x + 3)sin(x² + 3x + π)

Differentiate the previous result for dy/dx with respect to x to get the second derivative:

d²y/dx² = d/dx (-15x + 5)

d²y/dx² = -15

Step 2: Determine the concavity.

Part C: To find the particular solution y = f(x) with the initial condition f(0) = 5,  to integrate the given differential equation:

dy/dx = 5(2x + 3)sin(x² + 3x + π)

Step 1: Integrate the equation with respect to x:

∫dy = ∫5(2x + 3)sin(x² + 3x + π) dx

y = ∫(10x + 15)sin(x² + 3x + π) dx

Step 2: Use u-substitution:

Let u = x² + 3x + π, then du = (2x + 3) dx

Now the integral becomes:

y = ∫(10x + 15)sin(u) du

Step 3: Integrate with respect to u:

y = -10cos(u) + 15u + C

Step 4: Substitute back for u:

y = -10cos(x² + 3x + π) + 15(x² + 3x + π) + C

Step 5: Apply the initial condition f(0) = 5:

Substitute x = 0 and y = 5 into the equation:

5 = -10cos(π) + 15(0² + 3(0) + π) + C

5 = 10 + 15π + C

Simplifying,

C = 5 - 10 - 15π

C = -5 - 15π

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Answer:

A = 20°

AC = 6.6

BC = 2.4

Step-by-step explanation:

Given:

B = 70°

C = right angle = 90°

AB = 7

Required:

A, AC, and BC

Solution:

✔️A = 180 - (90 + 70) (sum of triangle)

A = 20°

✔️Use trigonometric function to find AC:

Refernce angle = 70°

Opp = AC

Hypotenuse = 7

Apply SOH,

sin 70 = Opp/Hyp

sin 70 = AC/7

7 * sin 70 = AC

6.57784835 = AC

AC = 6.6 (nearest tenth)

✔️Use trigonometric function to find Bc:

Refernce angle = 70°

Adj = BC

Hypotenuse = 7

Apply CAH,

cos 70 = Adj/Hyp

cos 70 = BC/7

7 * cos 70 = BC

2.394141 = BC

BC = 2.4 (nearest tenth)

Answer:

sowkdiwdjs

help me

Step-by-step explanation:

please lol

The absolute minimum value of the function is 120 which occurs at x = -8. To find the absolute maximum and minimum values of the function f(x) = x^3 + 6x^2 - 63x + 8 over the interval [-8, 0], you need to first find the critical points by taking the first derivative and setting it to zero, and then evaluate the function at the critical points and the endpoints of the interval.

1. Take the derivative of f(x):
f'(x) = 3x^2 + 12x - 63

2. Set f'(x) to zero and solve for x:
3x^2 + 12x - 63 = 0
Divide by 3:
x^2 + 4x - 21 = 0
Factor:
(x+7)(x-3) = 0
So, the critical points are x = -7 and x = 3.

However, only x = -7 is within the interval [-8, 0].

3. Evaluate f(x) at the critical point x = -7 and at the endpoints of the interval, x = -8 and x = 0:
f(-7) = (-7)^3 + 6(-7)^2 - 63(-7) + 8 = 120
f(-8) = (-8)^3 + 6(-8)^2 - 63(-8) + 8 = 64
f(0) = 0^3 + 6(0)^2 - 63(0) + 8 = 8

Comparing the values of f(x) at these points, we find:
Absolute maximum: f(-7) = 120
Absolute minimum: f(0) = 8

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A recursive formula is an equation that is defined in terms of itself. The recursive formula is used to determine the next term in the sequence, as each term in the sequence is generated based on the preceding term's value.

The following is the recursive formula for the sequence 5, 18, 31, 44, 57:`a_n = a_{n-1} + 13` where `a_n` represents the nth term in the sequence. To find the next term, substitute n = 6 into the formula: `a_6 = a_{6-1} + 13 = a_5 + 13 = 57 + 13 = 70`Therefore, the next term in the sequence is 70.

The recursive formula can be used to find any term in the sequence by substituting the appropriate value of n. This is how you can write a recursive formula for the sequence 5, 18, 31, 44, 57 and find the next term.

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Answer:

12÷5= 2.4 miles per hour

Step-by-step explanation:

(144÷12)÷(15÷3)

= 12÷5

=2.4

If f is continuous at x0 = 0, then f is continuous and there exists c ∈ R such that f(x) = cx.

1. To show that f(0) = 0, we can use the property of the function given. Let's choose x = 0 and y = 0.

According to the property, f(x + y) = f(x) + f(y). Plugging in the values, we get f(0 + 0) = f(0) + f(0).

Simplifying this equation, we have f(0) = 2f(0). Since 2f(0) is equal to f(0), we can conclude that f(0) = 0.

2. To show that f(-x) = -f(x), we can choose x = 0 and y = -x. According to the property, f(x + y) = f(x) + f(y).

Plugging in the values, we get f(0 + -x) = f(0) + f(-x).

Simplifying this equation, we have f(-x) = -f(x).

3. To show that f(x - y) = f(x) - f(y), we can use the property of the function given. Let's choose x = x and y = -y.

According to the property, f(x + y) = f(x) + f(y).

Plugging in the values, we get f(x + -y) = f(x) + f(-y).

Simplifying this equation, we have f(x - y) = f(x) - f(y).

4. To show that f(nx) = nf(x) and f(n/x) = (1/n)f(x) for all x, we can use mathematical induction.

For the base case, n = 1, it is trivial to see that f(x) = f(x). Now, assuming f(kx) = kf(x), we need to prove that f((k+1)x) = (k+1)f(x).

Using the property, we have f((k+1)x) = f(kx + x) = f(kx) + f(x) = kf(x) + f(x) = (k+1)f(x).

Thus, by induction, f(nx) = nf(x) for all n ∈ N.

5. To show that f(rx) = rf(x) for all x, we can choose r = p/q, where p and q are integers and q ≠ 0.

Using the property, we have f(rx) = f((p/q)x) = f((1/q)(px)) = (1/q)f(px) = (1/q)(pf(x)) = rf(x).

6. To show that if f is continuous at x0 = 0, then f is continuous, we need to prove that for any ε > 0, there exists a δ > 0 such that |f(x) - f(0)| < ε whenever |x - 0| < δ.

Since f(0) = 0 (as shown in part 1), we have to prove that for any ε > 0, there exists a δ > 0 such that |f(x)| < ε whenever |x| < δ. Since f is continuous at x0 = 0, we can choose δ = ε.

Therefore, for any ε > 0, if |x| < δ = ε, then |f(x)| < ε. Hence, f is continuous.

7. To show that if f is continuous, then there exists c ∈ R such that f(x) = cx, we can choose c = f(1). By the property, f(n) = nf(1) for all n ∈ N. Also, f(0) = 0 (as shown in part 1).

Therefore, for any x ∈ R, we can write x = nx0 + m, where n ∈ N, x0 = 1, and m ∈ R.

Using the property, we have f(x) = f(nx0 + m) = f(nx0) + f(m) = nf(x0) + f(m) = nf(1) + f(m) = cf(1) + f(m) = cf(1) + f(0) = cf(1). Thus, there exists c ∈ R such that f(x) = cx.

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Answer:

A

Step-by-step explanation:

Answer: 112°

Step-by-step explanation:

The angles are supplementary so add to 180°

(2x) + (3x + 10) = 180

Combine Like Terms leaves:

5x + 10 = 180

Subtract 10 from each side:

5x = 170

Divide 5 on each side:

x = 34

Plug x into the large angle

3(34) + 10

Solve:

102 + 10 = 112

The large angle is 112°

Hope this helps!

Answer:

(4,4)

Step-by-step explanation:

The solution set of the system of equations can be found by setting the two equations equal to each other and solving for x.

x^2 - 6x + 12 = 2x - 4

x^2 - 8x + 16 = 0

(x - 4)^2 = 0

x = 4

Since both equations in the system are equal to y, we can substitute x = 4 into either equation to find the corresponding value of y.

y = 2x - 4 = 2(4) - 4 = 4

Therefore, the solution of this system of equations is (4, 4).

Therefore, the correct answer is (4, 4).

Answer:

To solve this equation, we will first simplify the left-hand side using the fact that the square root of a number squared is equal to the absolute value of that number.

So, we have:

| x - 4 | = 4 - x

We can now split this equation into two cases, depending on whether x - 4 is positive or negative:

Case 1: x - 4 ≥ 0

In this case, | x - 4 | = x - 4, so we have:

x - 4 = 4 - x

Simplifying this equation, we get:

2x = 8

x = 4

However, we must check this solution to make sure it satisfies the original equation. Plugging x = 4 back into the original equation, we get:

√(4 - 4)^2 = 4 - 4

√0 = 0

So, x = 4 is a valid solution.

Case 2: x - 4 < 0

In this case, | x - 4 | = -(x - 4), so we have:

-(x - 4) = 4 - x

Simplifying this equation, we get:

-2x + 8 = 4

-2x = -4

x = 2

Again, we must check this solution to make sure it satisfies the original equation. Plugging x = 2 back into the original equation, we get:

√(2 - 4)^2 = 4 - 2

√4 = 2

This is a valid solution.

Therefore, the equation has two solutions: x = 4 and x = 2.

Answer: Bro x = 4

Step-by-step explanation: