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Answer:

The area of the square is the side × side

We have the area

\(A = x^2-12x+36\\A = (x-6)^2\\A = (x-6)(x-6)\)

The length of one side of the square represents \(x -6\)

Step-by-step explanation:

total angle= 360°.

sides = 360/36 = 10 (decagon).

total angle= 360°

sides = 360/120 = 3(triangle).

hope this helps you to.

Elena plans on running a total of 5 miles.

Mile, any of several distance measurements, such as the statutory mile (5,280 ft) (1.609 km). It comes from of the Romans lire passus, also referred as the "1000 steps," which was equal to 5,000 Romans feet. Unit of length is a related topic. See all relevant material The "old London" mile was eight furlongs when it was first established in 1500.

The term mille passus, which translates to "a hundred paces" in Latin and meant a length of 1,000 rates of speed or 5,000 Rome feet, was originally used by the Romans. It is equivalent to around 1,480 metres, or 1,618 contemporary yards.

We are aware that she has covered 2 miles, or 40% of a total distance, in her run thus far:

\(2=0.4x\)

To find x,

\(2=0.4x\)

\(x=\frac{2}{0.4}\)

\(x=5\)

Therefore, Elena plans to run a total distance of 5 miles.

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In order of smallest to largest.

1) -7.1

2) -4 1/3

3) -4/5

4) .889753

5) 11/12

6) 0

7) π

8) 3.28

The possible dimensions (length and width) of the field are:(10 m × 13 m) or (13 m × 10 m) and (11 m × 12 m) or (12 m × 11 m).

Given that Aaron has 47m of fencing to build a three-sided fence around a rectangular plot of land that sits on a riverbank. The fourth side of the enclosure would be the river.

The area of the land is 266 square meters.To find the possible dimensions (length and width) of the field, we can use the given information.The length of fencing required = 47 m.

Since the fence needs to be built on three sides of the rectangular plot, the total length of the sides would be 2l + w = 47.1. When l = 10 and w = 13, we have:

Length of the field, l = 10 m Width of the field, w = 13 mArea of the field = l × w = 10 × 13 = 130 sq. m2. When l = 11 and w = 12,

we have:Length of the field, l = 11 m

Width of the field, w = 12 m

Area of the field = l × w = 11 × 12 = 132 sq. m

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To find the linearization of the function f(x, y) = xy at the point (-8, 4), we can use the formula for linearization:

L(x, y) = f(a, b) + f_x(a, b)(x - a) + f_y(a, b)(y - b)
where (a, b) is the point of linearization and f_x and f_y are the partial derivatives of f with respect to x and y, respectively.
In this case, a = -8, b = 4, and f(x, y) = xy.
To find the partial derivatives, we differentiate f(x, y) with respect to x and y:
f_x(x, y) = y
f_y(x, y) = x
Plugging these values into the formula, we get:
L(x, y) = f(-8, 4) + f_x(-8, 4)(x - (-8)) + f_y(-8, 4)(y - 4)
       = (-8)(4) + 4(x + 8) + (-8)(y - 4)
       = -32 + 4x + 32 - 8y + 32
       = 4x - 8y + 32
Therefore, the linearization of the function f(x, y) = xy at the point (-8, 4) is L(x, y) = 4x - 8y + 32.

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The value of function fg(x) is -x^4-4x^3.

What is a function?

A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and co-domain or range. A function is generally denoted by f(x) where x is the input. The general representation of a function is y = f(x).

There are several types of functions in math. Some important types are:

Injective function or One to one function: When there is mapping for a range for each domain between two sets.

Surjective functions or Onto function: When there is more than one element mapped from domain to range.

Polynomial function: The function which consists of polynomials.

Inverse Functions: The function which can invert another function.

Now,

given functions are f(x)=-x^3 and g(x)=x+4

        so,   fg(x)=f(x)*g(x)=-x^3(x+4)

Therefore, the value of

                fg(x)  = -x^4-4x^3

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The value of function fg(x) is -x^4-4x^3.

What is a function?

A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and co-domain or range. A function is generally denoted by f(x) where x is the input. The general representation of a function is y = f(x).

There are several types of functions in math. Some important types are:

Injective function or One to one function: When there is mapping for a range for each domain between two sets.

Surjective functions or Onto function: When there is more than one element mapped from domain to range.

Polynomial function: The function which consists of polynomials.

Inverse Functions: The function which can invert another function.

Now,

given functions are f(x)=-x^3 and g(x)=x+4

       so,   fg(x)=f(x)*g(x)=-x^3(x+4)

Therefore, the value of

              fg(x)  = -x^4-4x^3

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The minimum value of y is -1. This can be answered by the concept from equation of a circle.

To find the minimum value of y, we need to rewrite the given equation in terms of y. Completing the square, we have:

x² - 14x + y² - 48y = 0
(x² - 14x + 49) + (y² - 48y + 576) = 49 + 576
(x - 7)² + (y - 24)² = 625

This is the equation of a circle with center (7,24) and radius 25. The minimum value of y occurs at the bottom of the circle, which is the point (7,24-25).

Therefore, the minimum value of y is -1.

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According to the given information \(C\left(x^2+(y-10)^2=225\right.\\\) is the sprinkler's covered boundary is represented by equation.

The reference system is a two-dimensional surface created by combining two number lines. A single beam number line makes up the x-axis. The title of the vertically x axis, which is the other figure line, is the y-axis. The intersection of the two axes is the origin. To chart lines, arrows, and other objects, utilize the coordinate plane.

The convergence of the x-axis, a horizontally number line, and the y-axis, a horizontal figure line, creates a coordinate plane. The origin of something like the coordinate plane is the vertical intersection of a three axes (plural for axis).

\(\begin{aligned}& (x+k_1)^2+\left(y+k_2\right)^2=h \\& (0,10) . \quad k_1=0, \quad k_2=-10 \\& x^2+(y-10)^2=h \\& \text { to, } 25, \quad(0,-5) \\&\Rightarrow h=225 \quad \\& x^2+(y-10)^2=225\end{aligned}\)

Hence, the equation is \(C\left(x^2+(y-10)^2=225\right.\\\).

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The polar form of the quantity will be  100.83 L 76.47°.

Given X = 5 L 40'andY = 20 L -30°(X + Y)X* .The expression (X + Y)X* can be simplified as: X * X + Y * X* =X² + Y * X* .Now, we need to find the polar form of the quantity (X + Y)X*.That is, we need to representX² + Y * X* in polar form. By using rectangular to polar conversion, we can convert the above expression to polar form.

Using the formula:

r² = x² + y²... Equation 1

θ = tan⁻¹(y / x)... Eq 2 (Where,x = real part of the expression)

x = X² = 5² = 25... Eq 3 (y = imaginary part of the expression)

y = Y * X*... Eq 4

Therefore, Y

Y * X* = 20 L -30° * 5 L 40'20 L -30° * 5 L 40' = 100 L 10°... Eq5

y = 100 L 10°.

Substituting the values of x and y in equations 1 and 2, we get:r² = x² + y²r² = 25² + 100²r² = 10025 + 100²r = 100.83θ = tan⁻¹(y / x)θ = tan⁻¹(100 L 10° / 25)θ = tan⁻¹(4 L 10°)θ = 76.47°

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To find the point on the surface 6x = y^2 + z^2 where its tangent plane is parallel to a given plane, we need to find a point on the surface and determine the normal vector of the surface at that point.

Then, we can compare the normal vector of the surface to the normal vector of the given plane to check if they are parallel.

Let's first find a point on the surface by substituting a value for either y or z and solving for x. Let's choose y = 0:

6x = 0^2 + z^2

6x = z^2

x = z^2/6

So, one point on the surface is (z^2/6, 0, z).

To find the normal vector of the surface at this point, we can calculate the partial derivatives with respect to x, y, and z:

∂/∂x (6x) = 6

∂/∂y (y^2 + z^2) = 0

∂/∂z (y^2 + z^2) = 2z

The normal vector is then N = (6, 0, 2z) = (6, 0, 2z) / ||(6, 0, 2z)||, where ||N|| represents the magnitude of N.

To determine if the tangent plane is parallel to a given plane, we compare the normal vector of the surface to the normal vector of the given plane. If they are parallel, their direction vectors should be proportional.

If the given plane is parallel to the xy-plane and has a normal vector N_1 = (0, 0, 1), we can compare it to the normal vector of the surface. In this case, we see that the z-component of N (2z) is not proportional to the z-component of N_1 (1). Therefore, the tangent plane of the surface at the chosen point is not parallel to the given plane.

To find a point on the surface where its tangent plane is parallel to the given plane, we would need to choose a different point on the surface such that the normal vector of the surface at that point is parallel to the given plane's normal vector.

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Answer: here it is!

Step-by-step explanation :

peter griffin is in fortnight thats the answer we all need

Answer: an intiger is a whole number, positive or negative. It has no decimals.

Step-by-step explanation:

Answer:

put one point at (2, -4) and the other at (0, -1)

you can find the second point using the slope -3/2

Answer:

The rate change between these points is 3.

Step-by-step explanation:

Answer:

Rate of Change is 3

Step-by-step explanation:

The rate of change between two points is called the 'slope'.

x1-x2         -6-8          -14

____  =      ____  =   ___  = Divide  = 3

y1-y2      -20 - 22      -42

The probability of picking 4 aces in 4 tries in a deck of 1 cards contains 4 aces is 1.

Probability is the likelihood of an event

Since deck of 4 cards contains 4 aces the probability of picking 4 aces in 4 tries.

After each try, the card is put back and the cards are reshuffled.

To find this probability, we proceed as follows.

Let P(A) = probability of picking an ace

P(A) = number of aces/total number of cards

Since we have 4 aces and 4 cards, we have that

P(A) = 4/4 = 1/1 = 1

Now, we want the find the probability of picking 4 aces after 4 tries when each card is returned and reshuffled.

Let P(4 aces) = probability of picking 4 aces

Now, since the probability of picking one ace in each of the 4 tries is independent, we have that

P(4 aces) = P(A) × P(A) × P(A) × P(A)

                = [P(A)]⁴

So, substituting the value of the variable into the equation, we have that

P(4 aces) =  [P(A)]⁴ =  [1]⁴ = 1

Therefore, the probability is 1.

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Answer:

2/3 π ³+ πr²(h-r)

Step-by-step explanation:

The weighted-average unit contribution margin is $46.20.

The weighted-average unit contribution margin can be calculated by multiplying the unit contribution margin of each model by its respective sales mix percentage, and then summing up the results.

To find the weighted-average unit contribution margin, we first calculate the unit contribution margin for each model by subtracting the unit variable costs from the selling price:

For Model A12:

Unit contribution margin = Selling price - Unit variable cost

                     = $60 - $42

                     = $18

For Model B22:

Unit contribution margin = Selling price - Unit variable cost

                     = $120 - $84

                     = $36

For Model C124:

Unit contribution margin = Selling price - Unit variable cost

                     = $480 - $360

                     = $120

Next, we multiply each unit contribution margin by its respective sales mix percentage:

Weighted contribution margin for Model A12 = 60% * $18 = $10.80

Weighted contribution margin for Model B22 = 15% * $36 = $5.40

Weighted contribution margin for Model C124 = 25% * $120 = $30.00

Finally, we sum up the weighted contribution margins:

Weighted-average unit contribution margin = $10.80 + $5.40 + $30.00 = $46.20. Therefore, the weighted-average unit contribution margin is $46.20.

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Answer:

If you're trying to evaluate 6x + 9 + (-6), then the answer would be ↓

Step-by-step explanation:

6x + 3

Answer:

If you're trying to evaluate 6x + 9 + (-6), then the answer would be ↓

Step-by-step explanation:

6x + 3

The greatest common divisor of the pair of integers 19 and 1919 is 19.

the greatest common divisor (GCD) of the pair of integers you provided. The pair of integers in question is 19 and 1919.

To find the GCD, you can use the Euclidean algorithm:

1. Divide the larger integer (1919) by the smaller integer (19) and find the remainder.
  1919 ÷ 19 = 101 with a remainder of 0.

2. Since there is no remainder, the smaller integer (19) is the greatest common divisor.

So, the greatest common divisor of the pair of integers 19 and 1919 is 19.

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The average time required for a passenger to pass through security screening is found to be approximately 0.0612 minutes.

(a) The operating characteristics for the screening facility with two screening stations open are as follows:

P0 = 0.0196

Lq = 0.3922

L = 0.4902

Wq = 0.0490 min

W = 0.0612 min

Pw = 0.0909

(b) The two-screening-station system will not be able to meet the facility manager's goal of limiting the average number of passengers waiting in line to 10 or fewer.

The operating characteristics for the screening facility with two screening stations open are calculated as follows:

P0 = 0.0196, Lq = 0.3922, L = 0.4902, Wq = 0.0490 min, W = 0.0612 min, Pw = 0.0909.

Based on these calculations, the two-screening-station system will not be able to meet the facility manager's goal of limiting the average number of passengers waiting in line to 10 or fewer.

(c) The average time required for a passenger to pass through security screening is 0.0612 minutes.

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The solution for the equation AB=BC is A = B(CB⁻¹), given that B is invertible.To solve the equation AB=BC for A, assuming that A, B, and C are square matrices and B is invertible, follow these steps:

1. Since B is invertible, it means it has an inverse matrix, denoted as B⁻¹.
2. To isolate A, you can multiply both sides of the equation by the inverse of B.
3. Multiply B⁻¹ to the right side of both equations: (AB)B⁻¹= (BC)B⁻¹.

4. Remember that matrix multiplication is associative, so you can rearrange the parentheses: A(BB⁻¹) = B(CB⁻¹).
5. Since the product of a matrix and its inverse is the identity matrix (I), we have AI = B(CB⁻¹).
6. As multiplying by the identity matrix doesn't change the original matrix, we can simplify the equation to A = B(CB⁻¹).
Now, you have isolated A, and the solution for the equation AB=BC is A = B(CB⁻¹).

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Answer:

7/24

Step-by-step explanation:

Total people in the studio = 24

3/8 are lifting weights
==> Number of people lifting weights  = 3/8 x 24 = 9

1/3 are cross training
==> Number of people cross training = 1/3 x 24 = 8

Therefore the remaining people who are running = 24 - (9 +8)

= 24 - 17

= 7

As a fraction of the total people, this would be

7/24

Mr. McGill's equation y = 10x + 5 is erroneous because it presumes the John reads 5 additional page every day following the first day, which isn't the case. Instead, y = 5x + 5, and Mr. McGill's solution y = 10x + 5 is .

An equation is an algebraic assertion that proves two mathematical expressions were equal in algebra, and this is how it is most commonly used. For instance, the equation 3x + 5 = 14 contains two expressions, 3x + 5 and 14, which are separated by the 'equal' sign.

In order to calculate John's total page readings depending on the number of days, we really have to find an expression. To demonstrate this, we might note that he reads 10 pages on day, and then 10 pages on each subsequent day.

5(x-1)

Therefore, the correct equation for the total number of pages y that John reads after x days is:

y = 10 + 5(x-1)

Simplifying this equation, we get:

y = 5x + 5

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d = rt

d/r  rt/r

d/r = t

Answer:

B. Point A is the center of the circle that passes through points X, Y, and Z.

C. ZA=YA

E. AX=AY

Step-by-step explanation:

Took the test got it right...

Answer:

2, 3, 5

Step-by-step explanation:

edge2020

a. The distribution of the sample mean time will follow a normal distribution, as the sample size is greater than 30 and the population standard deviation is known.

b. The standard error of the mean time can be calculated using the formula:

SE = σ/√n

Where σ is the population standard deviation and n is the sample size. Substituting the given values, we get:

SE = 2/√12 ≈ 0.577 seconds.

c. To find the percentage of sample means greater than 31.25 seconds, we need to standardize the sample mean using the formula:

z = (x^- - μ) / (σ/√n)

Where x^- is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

Substituting the given values, we get:

z = (31.25 - 24) / (2/√12) ≈ 5.42

Using a standard normal table or calculator, we can find that the percentage of sample means greater than 31.25 seconds is very close to 0%.

d. Similarly, to find the percentage of sample means greater than 28.25 seconds, we can use the same formula:

z = (28.25 - 24) / (2/√12) ≈ 2.04

Using a standard normal table or calculator, we can find that the percentage of sample means greater than 28.25 seconds is approximately 2.21%.

e. To find the percentage of sample means greater than 28.25 but less than 31.25 seconds, we need to find the area between these two values on the standard normal distribution. Using the same formula as before, we can find the z-score for each value:

z1 = (28.25 - 24) / (2/√12) ≈ 2.04

z2 = (31.25 - 24) / (2/√12) ≈ 5.42

Using a standard normal table or calculator, we can find the area to the left of z1 and subtract it from the area to the left of z2 to get the percentage of sample means between 28.25 and 31.25 seconds. This works out to approximately 1.65%.

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