The absolute value of the opposite of 7 is the same as the opposite of the absolute value of 7?

To find the day when daily ticket sales will peak and the number of tickets sold on that day, we can analyze the given quadratic equation [tex]\displaystyle\sf N = -0.5x^{2} + 15x + 11[/tex].

The equation is in the form of [tex]\displaystyle\sf y = ax^{2} + bx + c[/tex], where [tex]\displaystyle\sf a = -0.5[/tex], [tex]\displaystyle\sf b = 15[/tex], and [tex]\displaystyle\sf c = 11[/tex].

The peak of the quadratic function occurs at the vertex, which can be found using the formula [tex]\displaystyle\sf x = -\frac{b}{2a}[/tex].

Substituting the given values:

[tex]\displaystyle\sf x = -\frac{15}{2(-0.5)} = -\frac{15}{-1} = 15[/tex]

The peak day is 15 days since the concert was first announced.

To find the number of tickets sold on that day, we substitute [tex]\displaystyle\sf x = 15[/tex] into the equation:

[tex]\displaystyle\sf N = -0.5(15)^{2} + 15(15) + 11[/tex]

Simplifying the equation:

[tex]\displaystyle\sf N = -0.5(225) + 225 + 11[/tex]

[tex]\displaystyle\sf N = -112.5 + 225 + 11[/tex]

[tex]\displaystyle\sf N = 123.5[/tex]

Therefore, the daily ticket sales will peak on the 15th day, and 123.5 tickets (rounded to the nearest whole number) will be sold on that day.

Answer:

The daily ticket sales will peak on day 15.

The number of tickets sold that day will be 123.

Step-by-step explanation:

To find the day when the daily ticket sales peak and the number of tickets sold on that day, we need to determine the vertex of the quadratic function representing the ticket sales.

The quadratic function given for the number of tickets sold each day is:

[tex]N(x) = -0.5x^2 + 15x + 11[/tex]

The x-coordinate of the vertex of a quadratic function in the form of f(x) = ax² + bx + c can be found using the formula:

[tex]x = \dfrac{-b}{2a}[/tex]

For the given equation, a = -0.5 and b = 15.

Substitute these values into the formula:

[tex]x = \dfrac{-15}{2(-0.5)}[/tex]

[tex]x = \dfrac{-15}{-1}[/tex]

[tex]x=15[/tex]

Therefore, the x-coordinate of the vertex is x = 15.

As x is the the number of days since the concert was first announced, this means that the daily ticket sales peak is day 15.

To determine the number of tickets sold on that day, substitute the found value of x into the equation:

[tex]N = -0.5(15)^2 + 15(15) + 11[/tex]

[tex]N = -0.5(225) + 225 + 11[/tex]

[tex]N = -112.5 + 225 + 11[/tex]

[tex]N = 123.5[/tex]

Therefore, on the 15th day since the concert was first announced, the daily ticket sales will peak, and approximately 123.5 tickets will be sold on that day.

Since the number of tickets sold has to be a whole number, we can round this down to 123 tickets.

Given: The differential equation is (1 − cotx)y′′ − 2y′ + (1 + cotx)y = ex(cosecx − 2cosx), and we know that y1(x) = sinx and y2(x) = ex form a fundamental set of solutions for the homogeneous equation. So, the answer is (c) −ex(sinx−cosx).

We need to find the particular solution to the differential equation. There are two ways to solve the particular solution for a non-homogeneous differential equation: method of undetermined coefficients and variation of parameters.

The method of undetermined coefficients depends on the form of the non-homogeneous term, which includes polynomial, exponential, sine, cosine, and so on.

The form of the non-homogeneous term is ex(cosecx − 2cosx). Therefore, we use the following trial solution for the non-homogeneous part: yp(x) = Aexcosx + Bexsinx + Cexcosecx + Dexsinx cosx + Eex

Here's how to determine the coefficients: Find the first and second derivatives of yp(x), and then substitute them into the differential equation to obtain: Substitute the initial values of the equation to get the final solution. The final solution is as follows:yp(x) = -ex(sinx - cosx). Therefore, the answer is (c) −ex(sinx−cosx).

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So , b = 240 - 240 = 0So, the linear model that represents the total cost, C as a function of t is:C = 80t + 0 which can be simplified as C = 80t.

Let C be the total cost and t be the time of membership in months. After 3 months of membership, the new member paid a total of $240. Therefore, the cost per month, m can be calculated as:

m = 240/3 = $80

After 7 months, the new member paid a total of $400.Therefore, the total cost, C as a function of t can be expressed as:

C = mt + b,

where b is the initial cost of membership. Substituting the value of m and b, we get,

C = 80t + b When t = 0, C = b.

But we don't know the value of b. To find b, we can substitute the value of C and t from one of the given points.

(3, 240) = 80(3) + b240 = 240 + bT.

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By looking at the domain we can see that the correct option is A.

On the right side, we can see the graphs of functions G and F.

We can see that at x = 8 G has a maximum at:

G(8) = 5

And F has a minimum at:

F(8) = -1

Then in G - F, we should see that when x = 8, the value of the function must be:

5 - (-1) = 6

Also, notice that the difference must be restricted to the shared domain between both functios, which is: 3 < x < 11

Taking that in account, the only graph where we can see that is graph A.

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Answer:

The other term is 2ab

Step-by-step explanation:

To find the other term, you must divide the product 6a²b² by the given term 3ab.

(6a²b²) / (3ab)

You can simplify this expression by dividing each component separately:

(6/3) * (a²/a) * (b²/b)

This would simplify to 2 * a * b

Therefore, the other term is 2ab.

The total number of students on the honor roll decreased by approximately 17.1% this year.

To find the percentage decrease in the total number of students on the honor roll, we need to compare the total number of students last year with the total number of students this year.

Last year, there were 140 boys and 100 girls on the honor roll, making a total of 240 students on the honor roll.

This year, the number of boys on the honor roll decreased by 25%. To find the new number of boys on the honor roll, we multiply the original number of boys by (1 - 0.25) or 0.75:

New number of boys = 140 * 0.75 = 105

Similarly, the number of girls on the honor roll decreased by 6%. To find the new number of girls on the honor roll, we multiply the original number of girls by (1 - 0.06) or 0.94:

New number of girls = 100 * 0.94 = 94

The total number of students on the honor roll this year is the sum of the new number of boys and the new number of girls:

Total number of students this year = 105 + 94 = 199

To find the percentage decrease, we need to compare the total number of students this year with the total number of students last year:

Percentage decrease = [(Total number of students last year - Total number of students this year) / Total number of students last year] * 100

Percentage decrease = [(240 - 199) / 240] * 100

Percentage decrease = (41 / 240) * 100

Percentage decrease ≈ 17.1%

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The value of the point is given as follows:

x = 31,622.78.

The point is exactly at the halfway point between 4 and 5, hence it is given as follows:

p = 4.5.

However, the graph has a logarithmic scale, meaning that the actual value of each point is given by the point elevated to the power of 10.

Hence the value of the point is given as follows:

[tex]x = 10^{4.5} = 31,622.78[/tex]

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The area of the science fair poster in square feet is 6 sq ft.

A science fair poster is a rectangle 36 inches long and 24 inches wide. Some of the entry rules for the fair refer to the area of the poster in square feet. Using the given information, we need to find the area of the poster in square feet. We know that:1 yard (yd) = 36 inches (in)So, 1 yard = 36 × 36 square inches (sq in) = 1,296 sq inAlso, we know that 1 foot (ft) = 12 inches (in)So, 1 sq ft = 12 × 12 sq in = 144 sq inUsing the above information,

we can find the area of the poster in square feet as follows:Length of the poster = 36 inchesWidth of the poster = 24 inches Area of the poster in sq in = length × width = 36 × 24 = 864 sq inArea of the poster in sq ft = Area in sq in ÷ 144= 864 ÷ 144 = 6 sq ft

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The first possible location of O is approximately (2.038, 2.981).The second possible location of O is approximately (-4.038

To find the possible locations of point O, we need to divide the line segment MN into two parts with lengths in a ratio of 5:2.

Let's calculate the distance between points M and N first using the distance formula:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

For points M(-8, 8) and N(6, 1):

d = sqrt((6 - (-8))^2 + (1 - 8)^2)

 = sqrt(14^2 + (-7)^2)

 = sqrt(196 + 49)

 = sqrt(245)

 ≈ 15.65 (approximated to two decimal places)

Now, we can determine the lengths of the two parts using the given ratio.

Length of the first part: (5 / (5 + 2)) * d

Length of the second part: (2 / (5 + 2)) * d

Length of the first part: (5 / 7) * 15.65

                     ≈ 11.22 (approximated to two decimal places)

Length of the second part: (2 / 7) * 15.65

                      ≈ 4.43 (approximated to two decimal places)

Now, we need to find the coordinates of the point O that divides the line segment MN into two parts with lengths approximately 11.22 and 4.43.

First possible location of O:

We start from point M(-8, 8) and move along the line segment MN in the direction of point N(6, 1) by a distance of approximately 11.22 units. To calculate the coordinates of O, we use the following formula:

O(x) = M(x) + ((length of the first part) / d) * (N(x) - M(x))

O(y) = M(y) + ((length of the first part) / d) * (N(y) - M(y))

O(x) = -8 + (11.22 / 15.65) * (6 - (-8))

    ≈ -8 + (0.717) * (14)

    ≈ -8 + 10.038

    ≈ 2.038 (approximated to three decimal places)

O(y) = 8 + (11.22 / 15.65) * (1 - 8)

    ≈ 8 + (0.717) * (-7)

    ≈ 8 - 5.019

    ≈ 2.981 (approximated to three decimal places)

Second possible location of O:

We start from point M(-8, 8) and move along the line segment MN in the direction of point N(6, 1) by a distance of approximately 4.43 units. To calculate the coordinates of O, we use the same formula as above:

O(x) = -8 + (4.43 / 15.65) * (6 - (-8))

    ≈ -8 + (0.283) * (14)

    ≈ -8 + 3.962

    ≈ -4.038 (approximated to three decimal places)

O(y) = 8 + (4.43 / 15.65) * (1 - 8)

    ≈ 8 + (0.283) * (-7)

    ≈ 8 - 1.981

    ≈ 6.019 (approximated to three decimal places)

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Answer:

996 in³

Step-by-step explanation:

Volume of pentagon pyramid:5/2*apothem*side* height

here

apothem =8.3 in

height =4 in

side length=12 in

Now

substituting value in above formula

Volume of pentagon pyramid:5/2*8.3*4*12=996 in³

Answer:

996 in³

Step-by-step explanation:

The given figure is a regular pentagonal prism.

To find its volume, we first need to find the area of its pentagonal base.

From inspection of the given diagram, the parameters of the pentagonal base are:

Substitute these values into the area of a regular polygon formula to find the area of the base of the prism.

[tex]\boxed{\begin{minipage}{6cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{n\cdot s\cdot a}{2}$\\\\where:\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\ \phantom{ww}$\bullet$ $s$ is the length of one side.\\ \phantom{ww}$\bullet$ $a$ is the apothem.\\\end{minipage}}[/tex]

Therefore:

[tex]\begin{aligned}\textsf{Base\;area}&=\dfrac{5 \cdot 12 \cdot 8.3}{2}\\\\&= \dfrac{498}{2}\\\\&=249\; \sf in^2\end{aligned}[/tex]

To find the volume of the prism, multiply the base area by the prism's height:

[tex]\begin{aligned}\textsf{Volume}&=\sf Base\;area \times height\\\\&=249 \times 4\\\\&=996\; \sf in^3\end{aligned}[/tex]

Therefore, the volume of the prism is 996 in³.

To find the particular solution of the system [tex]\displaystyle\sf x' = 4x - 3y[/tex] and [tex]\displaystyle\sf y' = 6x - 7y[/tex] that satisfies the initial conditions [tex]\displaystyle\sf x(0) = 2[/tex] and [tex]\displaystyle\sf y(0) = -1[/tex], we can use the method of solving a system of linear differential equations.

Let's first find the general solution of the system by solving the differential equations. We can rewrite the system in matrix form as follows:

[tex]\displaystyle\sf \begin{bmatrix} x' \\ y' \end{bmatrix} = \begin{bmatrix} 4 & -3 \\ 6 & -7 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix}[/tex].

The coefficient matrix [tex]\displaystyle\sf A[/tex] is [tex]\displaystyle\sf \begin{bmatrix} 4 & -3 \\ 6 & -7 \end{bmatrix}[/tex], and the vector [tex]\displaystyle\sf X[/tex] is [tex]\displaystyle\sf \begin{bmatrix} x \\ y \end{bmatrix}[/tex].

To find the general solution, we need to find the eigenvalues and eigenvectors of matrix [tex]\displaystyle\sf A[/tex].

By solving [tex]\displaystyle\sf \det(A-\lambda I) = 0[/tex], where [tex]\displaystyle\sf \lambda[/tex] is the eigenvalue and [tex]\displaystyle\sf I[/tex] is the identity matrix, we can find the eigenvalues.

Solving [tex]\displaystyle\sf \det(A-\lambda I) = \det\left(\begin{bmatrix} 4 & -3 \\ 6 & -7 \end{bmatrix} - \begin{bmatrix} \lambda & 0 \\ 0 & \lambda \end{bmatrix}\right) = 0[/tex], we get [tex]\displaystyle\sf \lambda^{2} - (-3-6)\lambda + (4\cdot -7 - 3\cdot 6) = \lambda^{2} + 9\lambda - 54 = 0[/tex].

Solving the quadratic equation, we find [tex]\displaystyle\sf \lambda = -12[/tex] and [tex]\displaystyle\sf \lambda = 3[/tex].

Next, we find the corresponding eigenvectors by solving [tex]\displaystyle\sf (A-\lambda I)X = 0[/tex] for each eigenvalue.

For [tex]\displaystyle\sf \lambda = -12[/tex], we have [tex]\displaystyle\sf (A-(-12)I)X = \begin{bmatrix} 16 & -3 \\ 6 & 5 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = 0[/tex]. By solving this system of equations, we find [tex]\displaystyle\sf X_{1} = \begin{bmatrix} 3 \\ 2 \end{bmatrix}[/tex].

For [tex]\displaystyle\sf \lambda = 3[/tex], we have [tex]\displaystyle\sf (A-(3)I)X = \begin{bmatrix} 1 & -3 \\ 6 & -10 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = 0[/tex]. By solving this system of equations, we find [tex]\displaystyle\sf X_{2} = \begin{bmatrix} 1 \\ 2 \end{bmatrix}[/tex].

The general solution of the system is given by [tex]\displaystyle\sf X = c_{1}e^{-12t}X_{1} + c_{2}e^{3t}X_{2}[/tex], where [tex]\displaystyle\sf c_{1}[/tex] and [tex]\displaystyle\sf c_{2}[/tex] are constants, and [tex]\displaystyle\sf X_{1}[/tex] and [tex]\displaystyle\sf X_{2}[/tex] are the eigenvectors corresponding to the eigenvalues -12 and 3, respectively.

To find the particular solution that satisfies the initial conditions [tex]\displaystyle\sf x(0) = 2[/tex] and [tex]\displaystyle\sf y(0) = -1[/tex], we substitute these values into the general solution and solve for the constants [tex]\displaystyle\sf c_{1}[/tex] and [tex]\displaystyle\sf c_{2}[/tex].

Substituting [tex]\displaystyle\sf t = 0[/tex], [tex]\displaystyle\sf x(0) = 2[/tex], and [tex]\displaystyle\sf y(0) = -1[/tex] into the general solution, we have:

[tex]\displaystyle\sf 2 = c_{1}e^{-12\cdot 0}(3) + c_{2}e^{3\cdot 0}(1)[/tex],

[tex]\displaystyle\sf -1 = c_{1}e^{-12\cdot 0}(2) + c_{2}e^{3\cdot 0}(2)[/tex].

Simplifying these equations, we get:

[tex]\displaystyle\sf 2 = 3c_{1} + c_{2}[/tex],

[tex]\displaystyle\sf -1 = 2c_{1} + 2c_{2}[/tex].

Solving this system of equations, we find [tex]\displaystyle\sf c_{1} = \frac{1}{5}[/tex] and [tex]\displaystyle\sf c_{2} = \frac{7}{5}[/tex].

Therefore, the particular solution of the system that satisfies the initial conditions is:

[tex]\displaystyle\sf X = \frac{1}{5}e^{-12t}\begin{bmatrix} 3 \\ 2 \end{bmatrix} + \frac{7}{5}e^{3t}\begin{bmatrix} 1 \\ 2 \end{bmatrix}[/tex].

The greatest common divisor of 5! and 7! is 840.

To find the greatest common divisor (GCD) of 5! and 7!, we need to calculate the prime factorization of both numbers.

First, let's calculate the prime factorization of 5!:

5! = 5 * 4 * 3 * 2 * 1 = 120.

The prime factorization of 120 is 2^3 * 3 * 5.

Now, let's calculate the prime factorization of 7!:

7! = 7 * 6 * 5! = 7 * 6 * 120 = 5040.

The prime factorization of 5040 is 2^4 * 3^2 * 5 * 7.

To find the GCD of 5! and 7!, we need to find the common factors in their prime factorizations. We take the smallest exponent for each prime factor that appears in both factorizations.

From the prime factorizations above, we can see that the common factors are 2^3, 3, 5, and 7. Multiplying these factors together gives us:

GCD(5!, 7!) = 2^3 * 3 * 5 * 7 = 8 * 3 * 5 * 7 = 840.

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The sum of the reciprocals of A and B is 40.

To solve this problem, let's break it down step by step.

The given equation is: A% of B + B% of A = 10% of (A + B)

To simplify the equation, we convert the percentages to their decimal forms by dividing them by 100:

(A/100) * B + (B/100) * A = (10/100) * (A + B)

Next, we can simplify the equation by multiplying both sides by 100 to remove the fractions:

A * B + B * A = 0.1 * (A + B)

Now, let's simplify further:

2AB = 0.1A + 0.1B

To make the equation easier to work with, we can move all terms to one side:

2AB - 0.1A - 0.1B = 0

Now, let's factor out common terms from the left side of the equation:

A(2B - 0.1) + B(2A - 0.1) = 0

At this point, we have two terms that involve A and B separately. To simplify further, we can equate each term to zero:

2B - 0.1 = 0 (Equation 1)

2A - 0.1 = 0 (Equation 2)

Solving Equation 1 for B:

2B = 0.1

B = 0.1 / 2

B = 0.05

Similarly, solving Equation 2 for A:

2A = 0.1

A = 0.1 / 2

A = 0.05

Now that we have the values of A and B, we can find their reciprocals:

1/A = 1/0.05 = 20

1/B = 1/0.05 = 20

The sum of the reciprocals of A and B is:

1/A + 1/B = 20 + 20 = 40

Therefore, the sum of the reciprocals of A and B is 40.

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Approximately 0.057 cubic meters of air was used to fill the spherical balloon.

To determine the amount of air used to fill a spherical balloon with a radius of 165 mm, we can calculate the volume of the balloon.

The volume of a sphere is given by the formula:

Volume = (4/3)π [tex]r^3[/tex]

where r is the radius of the sphere.

Given that the radius of the balloon is 165 mm, we can substitute this value into the formula:

Volume = (4/3)π [tex](165 mm)^3[/tex]

To simplify the calculation, we can convert the radius from millimeters to meters, as the volume will be in cubic meters.

One meter is equal to 1000 millimeters, so the radius in meters is 165 mm / 1000 = 0.165 m.

Now we can calculate the volume:

Volume = (4/3)π [tex](0.165 m)^3[/tex]

Using a calculator and rounding to 2 decimal points:

Volume ≈ 0.057 [tex]m^3[/tex]

Therefore, approximately 0.057 cubic meters of air was used to fill the spherical balloon.

It's worth noting that the volume calculation assumes a perfectly spherical shape for the balloon and does not account for any variations due to stretching or irregularities in the shape.

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Answer:

  69 ft²

Step-by-step explanation:

You want the surface area of a square pyramid with a slant height of 10 ft and a base edge of 3 ft.

The surface area is the sum of the area of the base and the areas of the four congruent triangles. The area formulas are ...

  A = 1/2bh . . . . area of triangle with base b and height h

  A = s² . . . . . . . area of square with side s

Then the area of the pyramid with b=s=3 ft and h=10 ft is ...

  A = s² +4(1/2)sh = s(s +2h) = (3 ft)(3 ft + 2×10 ft) = (3 ft)(23 ft)

  A = 69 ft²

The surface area of the pyramid is 69 square feet.

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• Temperature at 6pm = 8°C

• Temperature at 6am = 7°C

• Temperature fallen = The temperature has decreased by 1°C in 12 hours.

To solve the equation 3(____ + 15) = 36 + 45, we can follow these steps:

Distribute the 3 on the left side of the equation:

3 * ____ + 3 * 15 = 36 + 45

Simplify the equation:

3____ + 45 = 81

Subtract 45 from both sides of the equation:

3____ = 81 - 45

Simplify the right side of the equation:

3____ = 36

Divide both sides of the equation by 3 to solve for the blank:

____ = 36 / 3

Calculate the value of the blank:

____ = 12

Therefore, the value of the blank is 12.

Answer:     X  =  12

3( X  +  15 )   =   36   +  45

 Hence, X    =  12

     Evaluate:

     3( X  +  15)   =    36  +  45

     3x   +   45    =    36  +   45

              3(x   +     15)  =  81

        3x    +   45   =  81

        3x   =    81   -   45

                 3x           =   36

                 3x  *  1/3  =  36  *  1/3

                  3x   *   1/3  =   12

        3(12  +  15 )   =   36  +  45

             3  *   27    =     81

              81            =      81   BOTH SIDES ARE EQUAL

        X  =  12

I hope this helps you!

Answer: y = x³ + 4x² + 3x

Step-by-step explanation:

      We are given that this equation has the roots 0, -1, and -3. To write these as factors, we will write them like this:

        y = (x)(x + 1)(x + 3)

      Now, we will turn this into a polynomial equation by distributing the factors above out. This gives us a cubic polynomial equation.

        y = (x)(x + 1)(x + 3)

        y = (x² + x)(x + 3)

        y = x³ + 4x² + 3x

The following expression represents the rational function with the given characteristics:h(x) = (-15/14) * (x + 3) * (x - 4) / (x - 7) * x

A rational function is defined as the ratio of two polynomials. It is written as follows: f(x) = p(x) / q(x), where p(x) and q(x) are polynomials and q(x) is not zero. The function has the following characteristics if its degree of q(x) is greater than that of p(x):Vertical asymptotes: These are the points where q(x) is zero but p(x) is not. Because it indicates that the denominator is zero at that point, this creates a vertical asymptote. Let's assume that the vertical asymptotes are at x = -3 and x = 4. Therefore, q(x) is the product of (x + 3) and (x - 4).Horizontal asymptote: If the degree of the numerator (p(x)) is less than that of the denominator (q(x)), the function's horizontal asymptote is y = 0. When the degree of p(x) is equal to that of q(x), the horizontal asymptote is y = a/b,

where a is the leading coefficient of p(x) and b is the leading coefficient of q(x). Since the degree of q(x) is greater than that of p(x), the horizontal asymptote is y = 0 + 2, or y = 2. The following expression represents the function now:f(x) = k * (x + 3) * (x - 4) / (x - 7) * xIf we set k to 1, the function is complete.

However, the x-intercepts are not -6 and 7. We must adjust the value of k until the function has the desired x-intercepts. We substitute the values of x and y into the expression, and then solve the equations. Here's what it looks like in action:(x, y) = (-6, 0)(-6 + 3) * (-6 - 4) / ((-6 - 7) * -6) = k * (x + 3) * (x - 4) / (x - 7) * xWe can simplify this equation to -1 / 13k = 1 / 24 by canceling out common factors.(x, y) = (7, 0)(7 + 3) * (7 - 4) / ((7 - 7) * 7) = k * (x + 3) * (x - 4) / (x - 7) * xWe can simplify this equation to 2 / 3k = -1 / 15 by canceling out common factors.

We must solve this set of equations:1 / 24 = -6k / 91 / 15 = 28k / 21We can simplify these equations to k = -91/4 and k = -15/14, respectively. We must choose one of the values to ensure that the function has the desired x-intercepts. We choose k = -15/14 to ensure that the x-intercepts are (-6, 0), (7, 0), and (0, 7).

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A regular pentagon has five-fold symmetry, which means that it looks the same when rotated by 72 degrees, 144 degrees, 216 degrees, and 288 degrees.A regular pentagon is rotated about its center. The minimum number of degrees to carry the pentagon onto itself is 72 degrees.

?A regular pentagon is a polygon with five equal sides and five equal angles. The five angles of a regular pentagon measure 108 degrees each. There are five lines of symmetry in a regular pentagon.

When a regular pentagon is rotated about its center, it rotates by 72 degrees for each rotation. The minimum number of degrees to carry the pentagon onto itself is 72 degrees. Therefore, a regular pentagon has rotational symmetry of order 5.

A regular pentagon has five-fold symmetry, which means that it looks the same when rotated by 72 degrees, 144 degrees, 216 degrees, and 288 degrees.

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Answer:

To solve the system of equations:

x + y = 8

2x^2 - y = -5

We can use the method of substitution or elimination. Let's use the elimination method to solve this system.

First, let's multiply the first equation by 2 to match the coefficients of x^2:

2(x + y) = 2(8)

2x + 2y = 16

Now, we can subtract the second equation from this new equation:

2x + 2y - (2x^2 - y) = 16 - (-5)

2x + 2y - 2x^2 + y = 16 + 5

2y + y - 2x^2 + 2x = 21

Simplifying the equation:

3y - 2x^2 + 2x = 21

Now, let's rearrange this equation:

2x^2 - 2x - 3y = -21

This is a quadratic equation in terms of x. To further solve for x or y, we need another equation or more information.

If you have any additional equations or information related to the system, please provide them, and I will be happy to assist you further.

Step-by-step explanation:

Answer:

cat pens <60 and

dog runs <15

Step-by-step explanation:

shortly an equation of inequality to represent all of the combinations of cats and dogs that can board based on the given constraints would be written as,

possible space available is 360ft2

cat pens require space 6ft2

dog runs require space 24ft2

thus the maximum cats stored in the available storage would be <60, and

maximum dog runs stored in the given storage would be <15

Answer: 11/9

Step-by-step explanation:

you would cross out the two 4s(using butterfly method) and make them 1s. So 11 x 1 and 1 x 9 = 11/9

Answer:

11/4 times 4/9 is 11/9

Step-by-step explanation:

We have to find,

(11/4) times 4/9

[tex](11/4)(4/9) = (11*4/4*9)[/tex]

We can cancel the 4s from the numeratorand denominator to get,

[tex](11*4/4*9) = (11*1/1*9) = 11/9\\=11/9[/tex]

The answer is 11/9

The expression 8x²² represents a term where the variable x is raised to the power of 22 and multiplied by the constant coefficient 8.

The expression 8x²² represents a term with a variable x raised to the power of 22, multiplied by the constant coefficient 8.

Here's a breakdown of the expression:

Coefficient:

The coefficient is the constant multiplier of the variable term.

The coefficient is 8, meaning that the variable term is multiplied by 8.

Variable:

The variable in this expression is x, which represents an unknown quantity.

The variable is raised to the power of 22, indicating that it is multiplied by itself 22 times.

Exponent:

The exponent is the superscript number that denotes the power to which the variable is raised.

The exponent is 22, indicating that the variable x is multiplied by itself 22 times.

Simplification:

The expression 8x²² is already simplified, it can be further clarified by expanding the exponentiation.

To expand it, we can write it as 8 × (x × x × x × x × x × x × x × x × x × x × x × x × x × x × x × x × x × x × x × x × x × x).

It is important to note that without additional context or equations involving this expression, we cannot provide further analysis or determine specific values for x.

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Answer:

1 cm / 6 km = 4.8 cm / x km

x = 4.8 cm (6 km/cm) = 28.8 km

The correct answer is A.

Answer:

Vertex = (1, -6)

Focus = (2, -6)

Step-by-step explanation:

The standard form of a sideways parabola that opens left to right is:

[tex]\boxed{(y-k)^2=4p(x-h)}[/tex]

where:

Given equation:

[tex](x-1)=\dfrac{(y+6)^2}{4}[/tex]

Rearrange the given equation so that it is in standard form by multiplying both sides by 4:

[tex]4 \cdot (x-1)=4 \cdot \dfrac{(y+6)^2}{4}[/tex]

[tex]4(x-1)=(y+6)^2[/tex]

[tex]\boxed{(y+6)^2=4(x-1)}[/tex]

Comparing it with the standard form (y - k)² = 4p(x - h):

Therefore:

The vertex is the point where the curve changes direction. In a sideways parabola opening to the right, it is the point furthest to the left.

In a sideways parabola, the axis of symmetry is a horizontal line that passes through the vertex. This line divides the parabola into two symmetrical halves, and it is parallel to the x-axis.

The focus is a point that lies on the axis of symmetry and is equidistant from all points on the parabola. It is located inside the curve, so in a sideways parabola opening to the right, it is to the right of the vertex.

The directrix is a line perpendicular to the axis of symmetry. It is a vertical line located outside the curve and is equidistant from all the points on the parabola. In a sideways parabola opening to the right, it is to the left of the vertex.

To plot the graph using your graphical calculator, move the vertex to point (1, -6).  The other point (focus) should be at (2, -6).

Plot:

The expression can be rewritten as: 84c + 3c - 7 = 4c + 3c - 7.The expression that shows the use of the distributive property is: 84c + 3c - 7 = (4 + 3)c - 7.

The distributive property states that when we multiply a number or term outside parentheses by a sum or difference inside parentheses, we can distribute the multiplication to each term inside the parentheses.

In the given expression, we have the term (4 + 3)c. By applying the distributive property, we can multiply each term inside the parentheses by the coefficient outside. This gives us: (4 + 3)c = 4c + 3c.

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The main answer is that without specific values or elements for sets A and B, we cannot determine the result of A - B and B - A.

To find A - B, we need to subtract the elements in set B from set A. Similarly, to find B - A, we need to subtract the elements in set A from set B.

However, I need the specific values or elements of sets A and B to perform the calculations. Could you please provide the values or elements of the sets?In order to perform set subtraction, we need the specific elements or values of sets A and B. Set subtraction involves removing the common elements between the sets.

Let's say set A is {1, 2, 3} and set B is {2, 3, 4}. To find A - B, we remove the elements in set B from set A. Thus, A - B would be {1}.

To find B - A, we remove the elements in set A from set B. Therefore, B - A would be {4}.

Please provide the values or elements of sets A and B, and I will be able to calculate A - B and B - A accordingly.

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