Prove the following,in a semigroup:

The correct option is (b) i.e. the total perimeter of the fence is 7x + y − 4 feet.

What is Perimeter?

Perimeter is the total length of the boundary or outer edge of a two-dimensional shape, such as a polygon, circle, or ellipse. It is the sum of the lengths of all the sides or arcs that make up the shape. For example, the perimeter of a square is the sum of the lengths of all its sides, while the perimeter of a circle is the circumference, which is the distance around the circle. The perimeter is often measured in units such as centimeters, meters, or feet, depending on the context of the problem.

Given : sides of the fence

            s₁ = 4x + 5

            s₂ =  y − 7

            s₃ = 3x − 2

We know that, perimeter of a triangle is sum of all three sides.

So, Perimeter of the fence =  s₁+ s₂+ s₃

                                            = 4x + 5 + y − 7 + 3x − 2

                                            = 7x + y - 4 ft.

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The length of the bar is doubled because it was stretched to twice the length of the original bar.

A multiplication equation that shows how the length is scaled is 2 × 8 = 16.

The length of the bar is halved because it was compressed to one-half the length of the original bar.

A multiplication equation that shows how the length is scaled is 1/2 × 8 = 4.

In Mathematics and Geometry, the scale factor of a geometric figure can be calculated by dividing the length of the image (new figure) by the length of the pre-image (original figure):

Since the original bar has a length of 8 units, we can logically deduce that its length became doubled because it was expanded to twice the length of the original bar. Therefore, a multiplication equation to model this expansion is given by:

2 × 8 = 16.

Conversely, the original bar has a length of 4 units, we can logically deduce that its length was halved because it was shrunk to one-half the length of the original bar. Therefore, a multiplication equation to model this compression is given by:

1/2 × 8 = 4.

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The statement that could be true for g is D. g(-13) = 20.

We are given that the function g has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45, and we also know that g(0) = -2 and g(-9) = 6.

We can use this information to eliminate the statements that are not true and find the one that could be true for g.

Therefore, g(-13) is greater than g(-9) and could be 20, so this statement could be true.

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Therefore , the solution of the given problem of graphs comes out to be curve of y = 4x – 3 can be plot by y=4x graph.

Graphs are used by theoretical physicists to analytically and graphically display assertions rather than values. Typically, a graph coordinate point shows the relationship between several distinct objects. A graph is a particular kind of pas e carrier construction composed of groups and lines. The borders, also known as the channels, should be joined together with glue.

Here,

The methods below can be used to plot y = log4 x - 3 as a graph:

Move the y-axis of the graph of

=>  y = log4 x down 3 units, making the horizontal asymptote y = -3 the new x-axis.

To acquire the graph of

=> y = log4 x – 3, reflect the resulting graph across the line y = x.

Here is a detailed explanation of how to plot y = log4 x - 3:

Diagram y equals 4x:

Plot the following y = 4x key locations first:

=> Y = 40 = 1 when x = 0.

=> If x = 1, then y = 41 = 4.

=> Y = 4-1 = 1/4 when x = -1.

The graph of y = 4x can be easily drawn using just these three values.

The curve of y = 4x is now 3 units lower:

To do this, take each y-coordinate and deduct 3 from it spots on the y = 4x graph. We now have the curve of y = 4x – 3:

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Answer:

Jeriel would have to pay $17

Step-by-step explanation:

t= hours

$3 per t hour +$8 fee

t=3

3(3)+8= $17

How much would Jeriel have to pay if he left his car in the lot for t hours:

3t+8

How much total money would Jeriel have to pay for parking if he left his car in the lot for 3 hours?

$17

Answer: The height of Nasim's kite above the ground is 51.79 feet

Step-by-step explanation

Let h represent the height from Nasim hand to the kite, hence:

sin(28) = h / 105

h = 49.29

Kite height above the ground = 2.5 + 49.29 = 51.79 feet

The height of Nasim's kite above the ground is 51.79 feet

Answer:

The height of Nasim kite above the ground is 51.79 feet

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

Let h represent the height from Nasim hand to the kite, hence:

sin(28) = h / 105

h = 49.29

Kite height above the ground = 2.5 + 49.29 = 51.79 feet

The height of Nasim kite above the ground is 51.79 feet

Answer:

I’m pretty sure it’s Salma because hers is all positive na the graph is and the graph is in quadrant 1 which is all positive

The value of x is found by using the similarity theorem to create a proportion of the sides of the similar triangle, such that: x = 6 cm.

Both triangles in the image above are similar to each other based on the AA similarity theorem, which states if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. This means that the corresponding sides of the triangles are proportional.

Therefore, we will have:

x/42 = 4/28

Cross multiply:

28x = 168

x = 168/28

x = 6 cm

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The solution of the quadratic equation x² + 10x -4 found using the quadratic formula is: x = -5 ± √29.

Sometimes, factoring the quadratic, setting its factor equal to zero, but then solving each factor is the quickest way to find the answer to "ax² + bx + c = 0" given the value of x.

Yet, there are situations when the quadratic is too complicated, it just doesn't factor in anyway, or you might not feel like factoring at all. The Quadratic Formula also can provide the solutions for you even when factoring sometimes isn't going to be successful.

The given equation:

x² + 10x -4

The general quadratic equation can be written as:

ax² + bx +c

Then, roots of the equation can be found using quadratic formula:

x = -b±√(b²-4ac))/(2a)

a = 1, b = 10 and c = -4

Put the values:

x = [ -10 ± √(10²- 4*1*(-4))]/ (2*1)

x = [ -10 ± √(100 + 16)]/ 2

x = [-10 ± √116] / 2

x =  [-10 ± 2√29] / 2

x = -5 ± √29

Thus, the solution of the quadratic equation x² + 10x -4 found using the quadratic formula is: x = -5 ± √29.

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Answer:

18.8

Step-by-step explanation:

consider rounding off 7 that becomes 8

Answer:

18.8

Step-by-step explanation:

Yes...Thats the ans...

Taking the quantities by volume of each potion into consideration, we can respectively answer 250ml (A), 40 mL of red and 60 mL of blue potion (B), and no (C).

For question A: Let x be the amount of red potion (in mL) that must be added to 500 mL of blue potion to produce a potion that is 40% magical syrup by volume. The amount of magical syrup in the red potion is 0.6x, and the amount of magical syrup in the blue potion is 0.3(500) = 150. The total amount of syrup in the final mixture is 0.4(500 + x), and the amount of magical syrup in the final mixture is 0.4x + 150. We can set up the equation:

0.4x + 150 = 0.4(500 + x)

Solving for x, we get x = 250 mL. Therefore, 250 mL of red potion must be added to 500 mL of blue potion to produce a potion that is 40% magical syrup by volume.

For question B: Let x be the amount of red potion (in mL) and y be the amount of blue potion (in mL) that must be combined to produce 100 mL of a potion that is 54% magical syrup by volume. The amount of magical syrup in the red potion is 0.6x, and the amount of magical syrup in the blue potion is 0.3y. The total amount of syrup in the final mixture is x + y, and the amount of magical syrup in the final mixture is 0.6x + 0.3y. We can set up the equations:

x + y = 100 (equation 1)

0.6x + 0.3y = 0.54(100) (equation 2)

Solving for x and y, we get x = 40 mL and y = 60 mL. Therefore, 40 mL of red potion and 60 mL of blue potion must be combined to produce 100 mL of a potion that is 54% magical syrup by volume.

For question C: No, there does not exist a combination of red potion and blue potion that can produce a potion that is 75% magical syrup by volume. The amount of magical syrup in the red potion is 60%, which is more than twice the amount of magical syrup in the blue potion (30%). Therefore, any combination of the two potions will always have less than 60% magical syrup by volume.

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Answer:

It's 5

Step-by-step explanation:

i tootk the test

Step-by-step explanation:

To solve the system of equations:

3x - 4y = 16

2x + 3y = 5

We can use either substitution or elimination method. Here, we will use the elimination method:

Multiply the second equation by 4 to get:

8x + 12y = 20

Now we can add this equation to the first equation:

3x - 4y + 8x + 12y = 16 + 20

Simplifying the left side and adding the right side, we get:

11x = 36

Dividing both sides by 11, we get:

x = 36/11

Substituting this value of x into the second equation, we get:

2(36/11) + 3y = 5

Multiplying through by 11 to eliminate the fraction, we get:

72/11 + 3y = 55/11

Subtracting 72/11 from both sides, we get:

3y = -17/11

Dividing both sides by 3, we get:

y = -17/33

Therefore, the solution to the system of equations is:

x = 36/11, y = -17/33

or in decimal form,

x ≈ 3.27, y ≈ -0.52

Answer:

The taxable income is £3000 - £500 = £2500.

The tax paid at the rate of 5 penny per pound is:

0.05 x £2500 = £125

Therefore, the total tax paid by the man is £125. Answer: A. £125

Step-by-step explanation:

Answer:

hope this helps you a lot

She received 5 or more emails in the same time period with a probability of 0.05265.

Simply put, probability is the likelihood that something will occur.

When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes.

Statistics is the study of events that follow a probability distribution.

The higher the likelihood, the more likely it is that the event will take place.

So, the probability would be:

We know that λ = 2.

The formula for the poisson distribution states:

P(x = x) = (λˣ * e^⁻ˣ) / x!

P(x = 1) = (2¹ *e⁻²) / 1!

P(x = 1) = (2 * 0.1353352) = 0.2706

Then,

P(x ≥ 5) = 1 - P(x < 5)

1 - P(x < 5) = 1 - [p(x = 0) + p(x = 1) + p(x = 2) + p(x = 3) + p(x = 4)]

We gather the individual probabilities and combine them. We can use a Poisson distribution calculator to speed up computations:

1 - P(x < 5) = 1 - (0.13534+0.27067+0.27067+0.18045+0.09022)

1 - P(x < 5) = 1 - 0.94735 = 0.05265

P(x ≥ 5) = 1 - P(x < 5) = 0.05265

Therefore, she received 5 or more emails in the same time period with a probability of 0.05265.

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Correct question:

An internal study by the Technology Services department at Lahey Electronics revealed company employees receive an average of two emails per hour. Assume the arrival of these emails is approximated by the Poisson distribution. What is the probability she received 5 or more emails during the same period?

Answer:

Hi! x = 4

Step-by-step explanation:

the shape is a parallelogram!

so the opposite angles must be the same

therefore, you can equate angle L and angle N to find your x!

Hope this helps

Marjorie's profit for a week when she teaches no student lessons is $0.  Marjorie's profit for a week when she teaches 20 student lessons is $700. The slope of the equation P = 35s is 35

a. To find Marjorie's profit for a week when she teaches no student lessons, we substitute s = 0 into the equation P = 35s:

P = 35(0) = 0

Therefore, Marjorie's profit for a week when she teaches no student lessons is $0.

b. To find the profit for a week when she teaches 20 student lessons, we substitute

s = 20 into the equation

P = 35s:

P = 35(20) = 700

Therefore, Marjorie's profit for a week when she teaches 20 student lessons is $700.

c. The slope of the equation P = 35s is 35. This means that for each additional student lesson Marjorie teaches, her profit increases by $35.

The P-intercept of the equation is 0, which represents the profit Marjorie makes when she does not teach any student lessons.

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The first parentheses, (10-5), will calculate to 5. The second parentheses, (8-9.16), will calculate to -1.16.

The first parentheses, (3 + 6.8), will calculate to 9.8. The second parentheses, (6.3 x 15), will calculate to 94.

Parentheses are symbols used to group numbers or variables together, usually for the purpose of making calculations easier. Parentheses are commonly used to group numbers within an equation or expression and to indicate that certain operations should be performed before or after others. They are also used to clarify the meaning of a mathematical expression or to help identify the parts of an equation.

To create an expression with parentheses so that the value of the expression 32.6 ÷ 10-5 x 8-9.16 is 43.10, the following equation can be used: (32.6 ÷ (10-5)) x (8-9.16) = 43.10. The parentheses are used to ensure that the values within them are calculated first. The first parentheses, (10-5), will calculate to 5. The second parentheses, (8-9.16), will calculate to -1.16. Then the resulting equation will be 32.6 ÷ 5 x -1.16, which will equal -43.10.

To create an expression with parentheses so that the value of the expression 6.3 x 15 ÷ 3 + 6.8 - 28.09 is 46.25, the following equation can be used: (6.3 x 15) ÷ (3 + 6.8) - 28.09 = 46.25. The parentheses are used to ensure that the values within them are calculated first. The first parentheses, (3 + 6.8), will calculate to 9.8. The second parentheses, (6.3 x 15), will calculate to 94.

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Answer:

Step-by-step explanation:

We know that the area of the plane shape is given by A = (10x - 2) cm^2, and we also know that:

A is not greater than or equal to 12 cm^2 (i.e., A < 12), and

A is not less than 2 cm^2 (i.e., A > 2).

To find the smallest possible area of the shape, we need to find the smallest possible value of x that satisfies these conditions.

From the given conditions, we have:

10x - 2 < 12

10x < 14

x < 1.4

and

10x - 2 > 2

10x > 4

x > 0.4

Therefore, the smallest possible value of x that satisfies both conditions is:

0.4 < x < 1.4

To find the smallest possible area, we can substitute the lower bound of x into the area formula:

A = (10x - 2) cm^2

A = (10 × 0.4 - 2) cm^2

A = 2 cm^2

Therefore, the smallest possible area of the shape is 2 cm^2.

The correct statement is that the transfer of land by George to the corporation in exchange for stock should qualify for non-recognition of gain or loss under section 351 of the IRC, and each shareholder's basis in the stock received would depend on their respective contributions.

Fair market value is the amount that a product would sell for on the open market if all parties were acting in their own best interests, were not subject to excessive pressure, and were given a reasonable amount of time to complete the transaction (FMV).

The given scenario describes the formation of a corporation by Nancy and George, where Nancy contributes cash and George contributes land. The corporation issues shares of stock to Nancy and George in exchange for their respective contributions.

Section 351 of the Internal Revenue Code (IRC) provides rules for the non-recognition of gain or loss on the transfer of property to a corporation in exchange for its stock. To qualify for non-recognition, certain requirements must be met, including that the transfer must be made in exchange for stock, and the transferors must be in control of the corporation immediately after the exchange.

Assuming that the requirements of section 351 are met, the transfer of the land by George to the corporation in exchange for stock should not result in any immediate tax consequences. George's basis in the stock received would be equal to his basis in the land transferred. Nancy's contribution of cash would not affect her basis in the stock received.

Therefore, the correct statement is that the transfer of land by George to the corporation in exchange for stock should qualify for non-recognition of gain or loss under section 351 of the IRC, and each shareholder's basis in the stock received would depend on their respective contributions.

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Complete question is: Nancy and George form EB Corporation with the following investments: cash by Nancy of $ ; land by George (basis of $ and fair market value of $). EB Corporation issues shares of stock, each to Nancy and George. Thus, each receives stock in EB worth $.

a. the transfer of land by George to the corporation in exchange for stock should qualify for non-recognition of gain or loss

b. Basis of $ in the EB Corp stock (assuming Bluebird reduces its basis in the land to $).

c. Basis of $ in the EB Corp stock (assuming Bluebird reduces its basis in the land to $).

d. Basis of $ in the EB Corp stock (assuming Bluebird reduces its basis in the land to $).

e. Basis of $ in the EB Corp stock, because her basis exceeded the fair market value of the land she contributed.

Answer:

Step-by-step explanation:

Since PQR is a triangle with QR = PQ, we have:

∠PQR = ∠QPR (since the angles opposite to equal sides are equal)

Let x be the measure of ∠QPR. Then:

∠PQR + ∠QPR + ∠R = 180° (sum of angles in a triangle)

x + x + 50° = 180°

2x = 130°

x = 65°

Therefore, the measure of ∠QPR is 65°.

Answer:

144inch^2

Step-by-step explanation:

8×8=64

64÷2=32

10×8=80

80+32+32=144

Answer:

144 in

Step-by-step explanation:

Area of a trapezoid: the large base plus the small base multiplied by the height divided by two

small base:10 in

large base: 10+8+8=26

(10+26)×8 = 36×8 = 144 in

2 2

Answer:

To get 9d^2 + 6d + 1 from (3d+1), you would need to multiply by 3d+1 again.

Expanding (3d+1)(3d+1), you get:

9d^2 + 3d + 3d + 1

Simplifying, you get:

9d^2 + 6d + 1

Therefore, you need to multiply (3d+1) by (3d+1) or (3d+1)^2 to get 9d^2 + 6d + 1.

The equation of the ellipse whose vertices are at (-3, -7), and (-3, 5), and focus is at (-3, 1) is; [tex]\frac{(x + 3}{8}+\frac{(y -2}{9} = 1[/tex]

The equation of an ellipse can be presented as follows;

[tex]\frac{(x - h)^2}{b^2} + \frac{(y-k)^2}{a^2} = 1[/tex]

Where;

(h, k) = The coordinates of the center of the ellipse

a = The semi major axis

b = The semi minor axis

(h, k ± a) = The vertex coordinates

(h ± b, k) = The covertex coordinates

(h, k ± c) = The coordinates of the foci

c² = a² - b²

The vertex of the specified ellipse are; (-3, -1) and (-3, 5)

The focus = (-3, 1)

Therefore;

k + a = 5

k - a = -1

2·k = 4

k = 4/2 = 2

k + a = 5

2 + a = 5

a = 5 - 2 = 3

k - c = 1

2 - c = 1

-c = 1 - 2 = -1

-c = -1

c = 1

c² = a² - b²

Therefore;

1² = 3² - b²

b² = 3² - 1² = 8

The equation of the ellipse is therefore;

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Answer:

7

Step-by-step explanation:

When you put a value for x in a function, it means that you substitute all terms of x for that value you just substitute for x=2. The x term in the function is x^2,  so that squared would be 4. You then add 3, yielding a total result of 7.

Answer:

f(2) = 7

Step-by-step:

Let f(x)=x^2+3. Find f(2)

[tex] \begin{gathered}{\longrightarrow{f(x)= {x}^{2} +3}}\end{gathered}[/tex]

[tex] \begin{gathered}{\longrightarrow{f(2)= {(2)}^{2} +3}}\end{gathered}[/tex]

[tex] \begin{gathered}{\longrightarrow{f(2)= {(2 \times 2)}+3}}\end{gathered}[/tex]

[tex] \begin{gathered}{\longrightarrow{f(2)= {(4)}+3}}\end{gathered}[/tex]

[tex] \begin{gathered}{\longrightarrow{f(2)= 4+3}}\end{gathered}[/tex]

[tex]\begin{gathered}{\longrightarrow{\underline{\underline{f(2)= 7}}}}\end{gathered}[/tex]

Hence, the value of f(2) is 7.

The sale tax fοr the cοmputer is $28.89.

A sales tax is a fee that is paid tο the gοvernment when certain gοοds and services are sοld. Typically, laws permit the seller tο charge the custοmer the tax at the time οf purchase. It is typically referred tο as a use tax when a tax οn gοοds οr services is paid directly tο a gοverning bοdy by a cοnsumer.

Yοur cοmputer purchase cοst $398.50 in tοtal. The sales tax is 7.25 percent.

The sale tax = cοst οf the prοduct × pecentage οf tax

Sales tax = 398.50 × 7.25%

Cοnvert percentages intο fractiοns:

Sales tax = 398.50 × (7.25/100)

Sales tax = 28.89125

sales tax  ≈ 28.89

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Answer:

(-7,2)

Step-by-step explanation: