During renovation, a pillar is supported by two braces as shown in the diagram. Based on the diagram, at what height should the short brace touch the pillar to ensure that the short brace is parallel to the long brace?
 
10 feet

12 feet

15 feet

17 feet

Answer:

the answer to this question is 4x - 3(12x + 4) = -6 hope this helps

Answer:

[tex]h(x)=\frac{x}{2}-\frac{1}{2}[/tex]

Step-by-step explanation:

Hello

Step1

Let f(x)=y

f(x) = 2x + 1

(1)y= 2x + 1  

to find the inverse of f(x)

Replace every x with a y and replace every y with an x

y= 2x + 1

replacing  

x=2y+1

Step 2

Now solve the equation for y

x=2y+1

subtract 1 on both sides

x-1=2y+1-1

x-1=2y

divide boths dies by 2

(x-1)/2=2y/y

[tex]\frac{x-1}{2} =\frac{2y}{2} \\y=\frac{x-1}{2}[/tex]

let this last equation h(x)= inverse of f(x)

[tex]h(x)=\frac{x-1}{2}\\h(x)=\frac{x}{2}-\frac{1}{2}[/tex]

Have a great day

The cone of dimension 4.5 inches height and 1.5 inches radius can hold 9.425 inches^3 of ice cream.

A sugar cone can be seen as a three-dimensional object, specifically a cone, which has a known formula for calculating its volume.

Volume of a cone: (1/3) x π x radius2 x height

Substituting the given values: (1/3) x π x 1.52 x 4.5 = 9.425 inches^3.

The inverse Laplace transform of (2s+5)/(s^2+6s+34) is found by completing the square in the denominator and then matching the result to a known form in the Laplace transform table.

The question asks for the inverse Laplace transform of the function (2s+5)/(s^2+6s+34). To find the inverse Laplace transform, we usually decompose the given function into a form that matches entries in the Laplace transform table. A common technique involves completing the square for the quadratic denominator, which enables us to match the form with the inverse transform for exponential or trigonometric functions as per standard Laplace tables.

In this case, the denominator can be rewritten as (s+3)^2 + (5^2 - 3^2) to make it resemble the denominator of the Laplace transform of a damped sine or cosine function. Next, we would separate the original function into partial fractions if necessary or directly find a corresponding entry in the Laplace transform table. Unfortunately, without further simplification, we cannot provide the exact inverse Laplace transform but you should use the approaches mentioned along with your extended Laplace table or use the convolution theorem if the function can be expressed as a product of functions.

Answer:  D. [tex]\pi=\dfrac{C}{2r}[/tex]

Step-by-step explanation:

Given : The formula to find the circumference is given by :-

[tex]C=2\pi r[/tex], where r is the radius of the circle.

To find the formula for [tex]\pi[/tex] , we need to divide 2r on both of the sides in the above equation, we get

[tex]\pi=\dfrac{C}{2r}[/tex] , where  r is the radius of the circle.

Hence, the correct formula for [tex]\pi[/tex] : Option D [tex]\pi=\dfrac{C}{2r}[/tex]

The revenue function is R = -1/20x^2 + 1060x and the profit function is P = -1/20x^2 + 940x - 5000. The value of x that maximizes profit is 9400, and the maximum profit is calculated by substituting this value into the profit function. The price to charge to maximize profit is $590.

a) To express revenue (R) as a function of x, we multiply the price (p) by the quantity (x):

R = p * x

Substituting the demand equation (p = -1/20x + 1060):

R = (-1/20x + 1060) * x

Simplifying:

R = -1/20x^2 + 1060x

b) Profit (P) is given by subtracting the cost (c(x)) from the revenue (R):

P = R - c(x)

Substituting the expressions for R and c(x):

P = (-1/20x^2 + 1060x) - (120x + 5000)

Simplifying:

P = -1/20x^2 + 940x - 5000

c) To find the value of x that maximizes profit, we take the derivative of the profit function with respect to x and set it equal to zero:

dP/dx = -1/10x + 940

Solving for x:

-1/10x + 940 = 0

x = 9400

d) To find the price that maximizes profit, we substitute the value of x (9400) into the demand equation:

p = -1/20(9400) + 1060

simplifying:

p = 1060 - 470

p = $590

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a) First, we must express the revenue, denoted as 'R'. Revenue is simply the price per item multiplied by the quantity of items sold. Given the demand equation 'p', we can express the revenue as follows:

R = p * x = ( -1/20 * x + 1060 ) * x

This simplifies to:

R = x * (1060 - 0.05*x)

b) Profit is revenue minus cost. We use the revenue equation from part a) and the given cost equation 'c = 120x + 5000'. Plug these into the profit equation:

P = R - c = ( x * (1060 - 0.05*x) ) - ( 120x + 5000 )

This simplifies to

P = x * (1060 - 0.05*x) - 120*x - 5000

c) To maximize profit, we need to find the derivative of the profit function and then solve for x when this derivative is equal to zero (this will find the quantity that maximizes profit). After doing this, we find that the quantity that maximizes profit is x = 9400.

If we substitute x = 9400 into the profit function, we get the maximum profit which turns out to be 4413000.

d) The price that should be charged to maximize profit is found by substituting the value of x that gave us the maximum profit into the price function. In this case, substituting x = 9400 gives us the price = 590.

Therefore, in order to maximize profit, 9400 lawnmowers should be produced and sold at a price of 590 per lawnmower, which will yield a profit of 4413000.

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Answer:

The arc's length is 1.8 ft

Step-by-step explanation:

For calcaulate the arc length S we used the formula below:

[tex] S=\frac{\pi.\alpha(\º)}{180}*R[/tex]

Here alpha is the arc angle in degrees and R is the circle radius. Thus, if alpha is equal to 26 and R equals to 4 ft:

[tex] S=\frac{\pi.26}{180}\ *\ 4ft[/tex]

[tex] S=0.45\ *\ 4ft[/tex]

[tex] S=1.8\ ft[/tex]

Final answer:

To calculate the number of different responses in the survey, we multiply the number of potential responses for each issue. With 5 options for each of the 3 issues, there are 5 x 5 x 5 = 125 different possible combinations.

Explanation:

To determine the number of different responses to the survey conducted by a union, we need to calculate the total possible combinations that can occur when members are asked to rate the importance of three issues: (1) job security, (2) increased fringe benefits, and (3) improved working conditions. Since there are five different responses allowed for each issue, we would use a combination formula.

Each member can choose from 5 different responses for each of the 3 issues. This is a situation where we use the 'fundamental counting principle' where you multiply the number of options for each independent choice to get the total number of possibilities:

The total number of different responses to the survey is 5 x 5 x 5, which equals 125.

So, members have 125 different ways to respond to the survey based on how they rate the importance of each issue.

Answer:

1st one : A′(-3, 3), B′(-1, 1), C′(-2, 3)

Step-by-step explanation:

below

The fifth root of -32 is -2. To find it, think of a number that, when raised to the power of 5, gives the original number.

The fifth root of -32 is -2. To find the fifth root of a number, we can think of it as finding a number that, when raised to the power of 5, gives us the original number. In this case, -2 * -2 * -2 * -2 * -2 = -32.

Answer:

t = 11

Step-by-step explanation:

From the equation that gives, the number of games you can get the number t of players who participated in the ronund-robin tormeo, is:

[tex]N = \frac{t ^ 2-t}{2}[/tex]

[tex]55 = \frac{t ^ 2-t}{2}[/tex]

[tex]110 = t ^ 2-t[/tex]

[tex]t ^ 2-t -110 = 0[/tex]

[tex](t-11) (t + 10) = 0[/tex].  Then

[tex]t - 11 = 0\\t = 11\\t + 10 = 0\\t = -10[/tex]

Since t cannot take negative values, then t = 11.

Domain:{−2,7,2}

Range:{7,2}

Answer:

LM= 4

Step-by-step explanation:

In the triangle KLM, ON is the mid segment of KLM

WE use triangle Mid segment theorem

MN= twice of ON

MN= 2 times of ON

4x= 2(x+1)

distribute 2 inside the parenthesis

4x= 2x+2

Subtract 2x on both sides

4x-2x= 2x+2-2x

2x= 2

divide by 2 on both sides

x= 1

To find length of MN, we plug in 1 for x

MN= 4x= 4(1)= 4

The surface area of an open-ended pipe with a radius of 6 inches and a height of 18 inches is 678.24 square inches. The calculation is based on the formula for the circumference of the circle, which is multiplied by the height of the cylinder.

To calculate the surface area of a pipe that is open at both ends, we need to find the area of the outer surface. Since the pipe is a cylinder without the top and bottom circles, the surface area is simply the circumference of the circle (which is the edge of the openings) times the height of the cylinder. The formula for the circumference of a circle is C = 2πr, where r is the radius.

The radius is given as 6 inches and the height is 18 inches, therefore:

Final answer:

The greatest common factor of the monomials 16x and 36x is 4x, obtained by finding the common prime factors of 16 and 36 and including the variable x, which is present in both monomials.

Explanation:

To find the greatest common factor of the monomials 16x and 36x, we need to break each monomial into its prime factors and compare them.

Prime factors of 16 are 2 x 2 x 2 x 2.

Prime factors of 36 are 2 x 2 x 3 x 3.

Both 16 and 36 have two 2's in common.

Therefore, the GCF of 16 and 36 is 2 x 2 = 4. Since x is present in both monomials, x is also part of their GCF.

The greatest common factor of the monomials 16x and 36x is therefore 4x.