why does the inequality sign have to be flipped when dividing by a negative number?

Answer:

its subtraction property of equality

Step-by-step explanation:

it shows that the 3/4 next to the 16 was subtracted on both sides to cancel out on of the other 3/4 on the other side...

i uploaded a pic just incase u didnt understand

Hope this helps!!!

Answer:

Domain is All Real x.

Range is f(x) ≥ 2.

Step-by-step explanation:

The vertical lines about the x - 1 means the Absolute value ( always positive).

|x - 1| will always be positive or 0 and it's graph is  shaped like a V with the vertex at (1, 0)

The + 2 will move the graph up 2 units so the vertex becomes (1, 2).

Yes, a hole in a function is considered a type of discontinuity. A hole occurs when a point is missing from the graph of a function, which causes the graph to have a break in it.

A discontinuity is a break or jump in the graph of a function. A hole in a function is a type of discontinuity where a point is missing from the graph, causing the graph to have a break in it. This type of discontinuity is usually caused by a function having a denominator that is equal to zero, as this creates an undefined point on the graph. This can also occur when two parts of the function are not connected, causing an open gap in the graph. In both cases, the graph is not continuous and has a discontinuity at the point where the hole is present.

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Yes, the function has a hole in discontinuity.

The term function in math is called as a rule that gives value of a dependent variable that corresponds to specified values of one or more independent variables.

Here we to identify is a hole in a function a discontinuity.

the term discontinuity is defined as is discontinuous at a point if it becomes undefined or the limit at that point does not exist. And whether this point is known as the point of discontinuity.

While we looking the hole on a graph looks like a hollow circle. And which  represents the fact that the function approaches the point, here it is not actually defined on that precise value. Where the major reason why this function is not defined at is because is not in the domain of the function.

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Answer:

14.12 × 2 + 5.93 = 34.17

40$ - 34.17 = 5.83$

Answer:

$14.12+$14.12=$28.24+$5.93=$34.17

Change is $6.83

The Giapetto problem is a linear programming problem that involves maximizing profit from producing two types of wooden toys. In response to the questions:

a. The dual of the Giapetto problem can be obtained by interchanging the roles of the variables and constraints. The objective of the dual problem is to minimize the sum of the dual variables (representing the costs) subject to the constraints defined by the coefficients of the original primal problem.

b. To determine the optimal dual solution, we can examine the optimal tableau of the Giapetto problem. The dual solution is obtained by considering the dual variables associated with the constraints. These variables represent the shadow prices or the marginal values of the resources in the primal problem. By analyzing the optimal tableau, we can identify the values of the dual variables and determine the optimal dual solution.

c. In this instance, we can verify that the Dual Theorem holds. The Dual Theorem states that the optimal value of the dual problem is equal to the optimal value of the primal problem. By comparing the optimal solutions obtained in parts (a) and (b), we can confirm whether they are equal. If the optimal values match, it confirms the validity of the Dual Theorem, indicating a duality relationship between the primal and dual problems. The dual of the Giapetto problem involves minimizing costs instead of maximizing profit. By examining the optimal tableau, we can determine the optimal dual solution. Lastly, by comparing the optimal solutions of the primal and dual problems, we can verify the Dual Theorem's validity, which states that the optimal values of both problems are equal, demonstrating their duality relationship.

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Answer:

2 4/5

Step-by-step explanation:

2/5 x 2 = 4/5 + 2 = 2 4/5

_______________

Hope this helps :)

The resulting graph of g(x) will resemble the graph of f(x), but it will be stretched vertically and pushed leftward by three units.

Each element of a set (referred to as the domain) is mapped by a rule known as a function to a particular element of this other set (called the range). A function is, in other words, a connection between two subsets in which every member of the domain has a unique relationship to every element of the range. One popular approach to write a function is via function notation, which entails writing the function name surrounded by the incoming signal in parentheses, as in the following example: f (x). For instance, the formula f(x) = 2x + 1 takes the input x and produces the result 2x + 1.

given,

The fundamental quadratic function f(x) = x² serves as the parent function for g(x) = (x + 3)².

Since the argument of the function (x + 3) is x shifted left by 3 units, the graph of f(x) is horizontally displaced to the left by 3 units.

Given that the coefficient of the squared term is 1, the graph of the resulting function is shifted up by a factor of 1.

As a result, the transformation can be represented as a 3 unit horizontal shift and a 1 unit vertical stretch.

The resulting graph of g(x) will resemble the graph of f(x), but it will be stretched vertically and pushed leftward by three units.

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Answer:

B

Step-by-step explanation:

pretty sure im on the same part as u

The equation of the function h(x) in terms of g(x) is h(x) = g(x) + 5

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

g(x) = 2|x + 4| - 3

Then we have

The graph of h(x)

An absolute value function is represented as

y = a|x - h| + k

Where

Vertex = (h, k)

From the graph, we have

Vertex = (h, k) = (-4, 2)

So, we have

h(x) = a|x + 4| + 2

Using the points on the graph, we have

a|-5 + 4| + 2 = 4

So, we have

a = 2

This gives

h(x) = 2|x + 4| + 2

Recall that

g(x) = 2|x + 4| - 3

This means that

h(x) = g(x) + 5

Hence, the function h(x) is h(x) = g(x) + 5

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Complete question

The function h(x) which is graphed below, and the function g(x) = 2|x + 4| - 3. Which is the the formula for h?

Answer:

x = 10, ∠ EHF = 110°

Step-by-step explanation:

7x and 11x are adjacent angles and sum to 180° , then

7x + 11x = 180

18x = 180 ( divide both sides by 18 )

x = 10

∠ EHF = 11x = 11(10) = 110°

Answer:

EHF = 110 deg

Step-by-step explanation:

From what it looks like 7x and 11x are being used as units of measurment. I can asssume a full circle adds up to 36x because 180deg adds up to 18deg.

If there were a number that was supposed to fill in for x it could be 0 because if the angles in this problem were 110 deg and 70 deg they would make 180 deg which is the straight line that the problem has.

mean = 4

Median = 3

Mode = 1

Step-by-step explanation:

first let’s arrange the numbers from least to highest:

1 , 1 , 1 , 2 , 3 , 3 , 5 , 5 , 15

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

The median is the number that’s comes in the middle of the data set ⇒ median = 3  ( the fifth number in the data set)

1 , 1 , 1 , 2 , 3, 3 , 5 , 5 , 15

________________________

The mode is the number that repeats the most ⇒ mode = 1  (repeated 3 times)

____________________________________

\(\text{the mean} =\frac{1+1+1+2+3+3+5+5+15}{9} = \frac{36}{9}=4\)

The absolute maximum value of f(t) is approximately -0.1213 at t = 9/4, and the absolute minimum value is -2 at t = 4.

To find the absolute maximum and absolute minimum values of f on the given interval [−1, 4], we first need to find the critical points of the function f(t) = t − 3√t.
Taking the derivative of f(t) with respect to t, we get:
f'(t) = 1 - (3/2)t^(-1/2)
Setting f'(t) = 0 to find critical points, we get:
0 = 1 - (3/2)t^(-1/2)
(3/2)t^(-1/2) = 1
t^(-1/2) = 2/3
t = (2/3)^(-2) = 2.25
So the only critical point of f(t) on the interval [−1, 4] is t = 2.25.
Now we need to evaluate f(t) at the endpoints of the interval and at the critical point to determine the absolute maximum and minimum values of f on the interval:
f(-1) = -1 - 3√(-1) = -1 - 3i
f(4) = 4 - 3√4 = 4 - 6 = -2
f(2.25) = 2.25 - 3√2.25 = 2.25 - 3(1.5) = -2.25
Therefore, the absolute maximum value of f on the interval [−1, 4] is f(-1) = -1 - 3i, and the absolute minimum value of f on the interval is f(4) = -2.
To find the absolute maximum and minimum values of f(t) = t - 3√t on the interval [-1, 4], we need to evaluate the function at its critical points and endpoints.
First, we find the critical points by taking the derivative of the function and setting it to zero:
f'(t) = 1 - (3/2)t^(-1/2)
To solve for critical points, set f'(t) = 0:
0 = 1 - (3/2)t^(-1/2)
(3/2)t^(-1/2) = 1
t^(-1/2) = 2/3
t = (2/3)^(-2) = 9/4
Since 9/4 is within the interval [-1, 4], it is a valid critical point.
Now, evaluate the function at the critical point and the endpoints:
f(-1) = -1 - 3√(-1)

(Note: This value is complex, and we're looking for absolute max/min in the real domain, so we'll ignore this endpoint)
f(9/4) = (9/4) - 3√(9/4) ≈ -0.1213
f(4) = 4 - 3√4 = -2
So, the absolute maximum value of f(t) is approximately -0.1213 at t = 9/4, and the absolute minimum value is -2 at t = 4.

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Answer:

perimeter is 36 cm

Step-by-step explanation:

The surge tank is a vital component of a system in which the flow rate fluctuates significantly. The flow rate entering the tank varies significantly, causing the fluid level in the tank to fluctuate as a result of the compressibility of the liquid. The surge tank is utilized to reduce pressure variations generated by a rapidly fluctspace uating pump flow rate. To determine the matrices A,B,C, and D using state-space notation, here are the steps:State representation is given by:dx/dt = Ax + Bu; y = Cx + DuWhere: x represents the state variablesA represents the state matrixB represents the input matrixC represents the output matrixD represents the direct transmission matrixThe equation can be written asA = [ -1/R₁ 0; 1/R₁ -1/R₂]B = [1/A₁; 0]C = [0 1/R₂]D = 0Thus, the matrices A,B,C and D assuming that the level deviations are the state variables: h'₁ and h'₂. The input variable is q'ᵢ, and the output variable is the flow rate deviation, q'₂ are given by A = [ -1/R₁ 0; 1/R₁ -1/R₂]B = [1/A₁; 0]C = [0 1/R₂]D = 0.Hence, the required matrices are A = [ -1/R₁ 0; 1/R₁ -1/R₂], B = [1/A₁; 0], C = [0 1/R₂], and D = 0 using state-space notation for the given system of equations for two liquid surge tanks.

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The standardized distribution known as the T distribution is a member of the one-parameter family. The degrees of freedom are the only input for the t distribution.

A measure of the distribution of a set of data points is called population variance. It measures the mean squared departure from the mean, specifically. As a result, the variance will be minimal if all of the data points are very near to the mean. The variation will be high if the data points are dispersed throughout a wide range.

The standardized distribution known as the T distribution is a member of the one-parameter family. The degrees of freedom are the only input for the t distribution. Because sample size is used to assess this degree of freedom, degrees of freedom are dependent on sample size.

The t distribution tends to follow a normal distribution as sample size rises. The degree of freedom is ultimately determined by the sample size, so as the degree of freedom rises, the t distribution tends to be a normal distribution.

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Answer:0

Step-by-step explanation:0x0=0

Answer:

(x,y) = (8,-3)

Step-by-step explanation:

hope this helps.

Answer:

see below

Step-by-step explanation:

a^5*(a^3)^2

We know that a^b^c = a^(b*c)

a^5*a^(3*2)

a^5*(a^6)

We know a^b * a^c = a^(b+c)

a^(5+6)

a^11

There will be only 6  cubes with only one side painted red.

Cube : A cube is a 3D shape having 6 equal square sides. it has 6 faces , 8 vertices and 12 edges.

According to the question

A 3 cm cube is divided into one centimeter cube.

Every face will have 9 cube each and from that 9 cube there will be only one 1 cube that will have one side painted red.

Since there are 6 faces,

cubes painted one side red = 6x1=6.

Therefore , There will be only 6  cubes with only one side painted red.

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Function for which x -intercepts is at 4 and -6 is given by

y = k (x - 4)( x + 6).

As given in the question,

Let us consider f(x) be the required function.

y = f(x)

Standard form of a function whose x- intercepts is defined as x = a and

x = b is given by ;

f(x) = k (x - a ) ( x -b)

⇒ y =  k (x - a ) ( x -b)

Where 'k' is constant which can be evaluate when quadratic function  passes through point ( x₁ , y₁).

Here x - intercept is  at 4 and -6

a = 4 and b = -6

Function for which x -intercepts is at 4 and -6 is given by :

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

⇒ y = k ( x - 4 ) ( x+ 6 )

Therefore, function for which x -intercepts is at 4 and -6 is given by

y = k (x - 4)( x + 6).

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Answer:

1. ΔA'B'C' = A' = (1, 1), B'(-1, 1), and C'(1, 4)

2. ΔA''B''C'' = A''(-7 1), B''(-15 1), and C''(-7, 4)

Step-by-step explanation:

1. The coordinates of the triangle ΔABC are; A(3, 1), B(5, 1), and C(3, 4)

The reflection of a line across the line x = 2, is given as follows

The distance between the x-coordinate of the preimage and the line of reflection which is parallel to the x-axis = The distance of the x-coordinate of the preimage from the line of reflection but opposite in sign

The distance from A(3, 1) from x = 2 is 3 - 2 = 1, therefore, the x-coordinate of the image, A' = 2 - 1 = 1, therefore, we have;

The coordinate of A' = (1, 1)

Similarly, we have; B(5, 1) (reflection across x = 2) → B'(-1, 1)

C(3, 4) (reflection across x = 2) → C'(1, 4)

Therefore when we reflect ABC across the line x = 2, we get ΔA'B'C', with A' = (1, 1), B'(-1, 1), and C'(1, 4)

2. Reflection of A'B'C' across the line x = -3, gives;

A'(1, 1) (reflection across x = -3) → A''(-7 1)

B'(-1, 1) (reflection across x = -3) → B''(-15 1)

C'(1, 4) (reflection across x = -3) → C''(-7, 4)

The coordinates of the reflection of ΔA'B'C' across the line x = -3 is ΔA''B''C'' = A''(-7 1), B''(-15 1), and C''(-7, 4)

Answer:

the value of x will be 9

x = 9

Therefore, the given integrals are ∫Ye^(7y^2)dy = (1/14)*e^(7y^2) + C and ∫Y^3e^(7y^2)dy = (1/14)*e^(7y^2) + C.

integral is ∫Y*e^(7y^2) dy.(A) Evaluate the given integral.

To solve the given integral,Let 7y^2 = u   ⇒ 14ydy = du⇒ dy = du/14y

Let's plug the values to the integral= (1/14) ∫ e^udu= (1/14)*e^u + C= (1/14)*e^(7y^2) + C

Thus, ∫Ye^(7y^2)dy = (1/14)*e^(7y^2) + C(B)

Evaluate the given integral.To solve the given integral,

Let 7y^2 = u   ⇒ 14ydy = du⇒ dy = du/14yLet's plug the values to the integral= (1/14) ∫ Y^3 e^udu= (1/14)*e^u + C= (1/14)*e^(7y^2) + C

Thus, ∫Y^3e^(7y^2)dy = (1/14)*e^(7y^2) + C

Therefore, the given integrals are ∫Ye^(7y^2)dy = (1/14)*e^(7y^2) + C and ∫Y^3e^(7y^2)dy = (1/14)*e^(7y^2) + C.

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Answer:

iiiiiiiipppppppppppp

Yosef finished the mile in 9 minutes.

Distance = 1 mile

Demetrius' speed = 7.5 miles per hour

Demetrius' time = Distance/speed

= 8 minutes

Demetrius finished the mile first by taking 1 minute less than Yosef's finishing time.

The factor that does NOT control the stability of a slope is the angle of repose for intact bedrock. The angle of repose refers to the steepest angle at which a pile of loose material remains stable without sliding. It is mainly applicable to loose materials like soil and granular substances, not intact bedrock.

Bedrock stability depends on factors such as its strength, fracturing, and geological properties, rather than the angle of repose. Factors that control the stability of a slope include whether the slope is rock or soil. Rock slopes tend to be more stable than soil slopes due to the cohesive nature of intact rock.

The amount of water in the soil also affects slope stability, as excessive water can increase pore pressure and reduce the shear strength of the soil, leading to slope failure. Additionally, the orientation of fractures, cleavage, and bedding in the rock can influence slope stability by creating planes of weakness or strength.

To summarize, while the angle of repose is a significant factor in slope stability, it is not applicable to intact bedrock. The stability of a slope is influenced by the type of material (rock or soil), the presence of water, and the orientation of fractures and bedding.

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The cylinder should make approximately 0.3097 revolutions per second in order for the clothes to lose contact with the wall at an angle of 54.0°.

To determine the required number of revolutions per second for the cylinder in order for the clothes to lose contact with the wall at a specific angle, we can use the concept of centripetal acceleration.

The centripetal acceleration experienced by an object moving in a circular path of radius r at a speed v is given by the formula:

\(a = v^2 / r\)

In this case, when the clothes lose contact with the wall, the net force acting on them is the gravitational force pulling them downward, which can be expressed as:

mg = m * g

Since the gravitational force provides the centripetal force for the clothes, we can equate the centripetal acceleration to the gravitational acceleration:

v^2 / r = g

To solve for the speed v, we need to find the circumference of the circular path. The circumference C can be calculated as:

C = 2πr

Substituting this into the equation above, we have:

v^2 / (2πr) = g

Now, we need to find the required speed v when the clothes lose contact with the wall at an angle of θ = 54.0°. We can use the angle θ to find the arc length traveled by the clothes on the circular path.

The arc length s can be calculated as:

s = θ * r

Substituting the given values, we have:

s = (54.0°) * (0.512 m)

Next, we can calculate the time it takes for the clothes to traverse the arc length s at the required speed v. The time t can be calculated as:

t = s / v

Now, since we want to find the number of revolutions per second, we need to convert the time t into seconds per revolution (s/rev). Since each revolution covers the circumference C, the time for one revolution is:

t_rev = C / v

Finally, the number of revolutions per second is given by the reciprocal of the time for one revolution:

Rev/s = 1 / t_rev

Let's calculate the required number of revolutions per second using the given values. Assuming the acceleration due to gravity is approximately 9.8 m/s²:

r = 0.512 m (radius)

θ = 54.0° (angle)

g = 9.8 m/s² (acceleration due to gravity)

First, calculate the arc length s:

s = (54.0°) * (0.512 m) = 27.648 m

Next, calculate the required speed v using the centripetal acceleration equation:

v^2 / (2πr) = g

v^2 / (2π * 0.512 m) = 9.8 m/s²

v^2 = (2π * 0.512 m) * (9.8 m/s²)

v^2 = 10.0384 m²/s²

v ≈ 3.1687 m/s

Now, calculate the time for one revolution:

t_rev = (2π * 0.512 m) / (3.1687 m/s) ≈ 3.2321 s/rev

Finally, calculate the number of revolutions per second:

Rev/s = 1 / (3.2321 s/rev) ≈ 0.3097 rev/s

Therefore, the cylinder should make approximately 0.3097 revolutions per second in order for the clothes to lose contact with the wall at an angle of 54.0°.

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For the simple harmonic motion equation d=2 sin(pi/3t), the period is 6 seconds.

The period of a simple harmonic motion is the time taken for one complete cycle of the motion. In this equation, d represents the displacement or position of the object at time t. The equation is in the form of sin function with the argument (pi/3)t. The general form of the equation for simple harmonic motion is d=A sin(ωt+φ), where A is the amplitude, ω is the angular frequency, and φ is the phase angle. To determine the period of this motion, we can use the formula T=2π/ω, where T is the period and ω is the angular frequency. In this case, ω=pi/3, so the period is T=2π/(pi/3)=6 seconds (rounded to the nearest second). Therefore, the object completes one full cycle of motion every 6 seconds.

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