The recursive formula An+1 = 2∙An number of people with a virus in a school each week. If there are 96 people infected with the virus after 3 weeks, how many people will be infected after 6 weeks? What is the explicit formula?

Answer:

x = 6

Step-by-step explanation:

The given equation is [tex]f(x)=-(x+9)(x-21)[/tex]

We write the equation in standard form of parabola [tex]f(x)=ax^2+bx+c[/tex] using FOIL

[tex]f(x)=-(x+9)(x-21)\\\\f(x)=-(x^2-21x+9x-189)\\\\f(x)=-x^2+12x+189[/tex]

Now, we know that the axis of symmetry passes through the vertex. Hence, in order to find the vertex of the parabola, we find the x coordinate of the vertex.

x coordinate of the vertex is [tex]-\frac{b}{2a}[/tex]

Here, a = -1 b = 12

[tex]-\frac{b}{2a}\\\\=-\frac{12}{2\cdot(-1)}\\\\=-(-6)\\\\=6[/tex]

Therefore, the axis of symmetry is x = 6

Answer:

the real answer is -18 if ur k12

Step-by-step explanation:

Answer:

-40

Step-by-step explanation:

To simplify √24, we find its prime factors, pair them up, and bring one number from each pair outside the square root. The remaining numbers stay under the square root. The correct answer is 2√6. The options provided in the question are all incorrect.

The problem is asking us to simplify √24, which is a typical Mathematics question in Middle School. Here are the steps we need to take:

Therefore, √24 simplifies to 2√6.

All the options provided (A √38, B √212, C √26, D √46) are incorrect.

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Answer:

The correct option is:   C.  Add the two bags together, multiply by .80, and then subtract $1.00.

Step-by-step explanation:

First you need to add the prices of two bags for getting the total sales price.

Now, the store is offering 20% off, that means you need to pay 80% of the total sales price. For finding the amount, we need to multiply the total sales price by 0.80

Then, you have a manufacturers coupon for a $1.00 off. So, for fining the final price, you need to subtract that $1.00 from the last result.

Thus, the correct option will be......

C. Add the two bags together, multiply by .80, and then subtract $1.00.

The volume of the cylindrical water tank with a radius of 5.5 feet and a height of 8 feet is 760 cubic feet after rounding to the nearest whole number.

To calculate the volume of a cylindrical water tank, we use the formula V = , where V represents volume, is the constant Pi, approximately equal to 3.14, r is the radius of the cylinder, and h is its height.

Given that the radius r is 5.5 feet and the height h is 8 feet, substituting these values into the formula gives us:

V = 3.14 * (5.5ft) * 8ft

First calculate the radius squared:

5.5ft * 5.5ft = 30.25ft

Now, calculate the volume:

V = 3.14 * 30.25ft * 8ft = 3.14 * 242ft = 759.88ft

After rounding to the nearest whole number, the volume is 760 cubic feet.

Answer:

Solution is (2,1)

Step-by-step explanation:

In order to graph both lines ,we need to find the X and Y intercepts for both equations

Lets take equation  y =2x -3

               To find y intercept ,we plug x =0 ,we get y =2(0)-3 = 0-3 =-3

                         Y intercept is (0,-3) Which is point  'C' in the graph

              To find X intercept ,we plug y =0 ,we get 0 = 2x-3 or x = 3/2 or 1.5

                        X intercept is (1.5,0) Which is point D in the graph.

Lets take equation y =-2x+5

                   To find y intercept ,we plug x =0 ,we get y = -2(0)+5 = 0+5 = 5

                       Y intercept is (0,5) which is point A in the graph .

              To find X intercept ,we plug y =0 ,we get 0 =-2x+5 or x = 5/2 or 2.5

                     X intercept is (2.5,0) which is point B on the graph

         After getting intercept of both lines ,we plot both lines

In the graph Blue line shows  y=2x-3 and Red line shows y =-2x+5

both lines intersect at point E which is called the solution of both equation

which is given to be (2,1)

Note:

Images with coordinates or original and translated triangles are attached.

Answer:

The coordinates for the given triangle are A(6,3), B(6,-3) and C(-2,-3), respectively.

Let us translate this triangle by -6 units along the x-axis and +3 units along the y-axis. This means that 6 will be subtracted from each of the abcissas (x-points) and 3 will be added to each ordinates (y-points). Hence, our translated triangle will have the following coordinates: A'(0,6), B'(0,0) and C'(-8,0), respectively.

Now to prove that both triangles are congruent, we use the SSS postulate, which states that:

"If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent."

Distance between two point P1 and P2 will be:

[tex]|P_1P_2|=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Now using distance formula to find sides of triangle ABC and triangle A'B'C'.

For Triangle ABC:

|AB| = [tex]\sqrt{(6-6)^2+(-3-3)^2} =\;6\;units[/tex]

|AC| = [tex]\sqrt{(-2-6)^2+(-3-3)^2} =\;10\;units[/tex]

|BC| = [tex]\sqrt{(-2-6)^2+[-3-(-3)]^2} =\;8\;units[/tex]

For Triangle A'B'C':

|A'B'| = [tex]\sqrt{(0-0)^2+(0-6)^2} =\;6\;units[/tex]

|A'C'| = [tex]\sqrt{(-8-0)^2+(0-6)^2} =\;10\;units[/tex]

|B'C'| = [tex]\sqrt{(-8-0)^2+(0-0)^2} =\;8\;units[/tex]

Hence, as the distances are equal, the two triangles are congruent by SSS postulate.

Answer:

Option C is correct

[tex]x+y = 425[/tex]

[tex]y = 2x-70[/tex]

Step-by-step explanation:

Here, x represents Kathryn's score and y represents Michael's score.

As per the statement:

Michael and Kathryn bowl together and their combined total score for one game was 425 points.

⇒[tex]x+y = 425[/tex]

It is also given that Michael's score was 70 less than twice Kathryn's.

⇒[tex]y = 2x-70[/tex]

Therefore, the system of equations models the problem is:

[tex]x+y = 425[/tex]

[tex]y = 2x-70[/tex]

Answer:

Step-by-step explanation:

Given that there is a cone and cylinder with equal radius and height.

Recall volume formula for cone and cylinder as

Volume of cone = [tex]\frac{1}{3} \pi r^2 h[/tex]

Volume of cylinder =[tex]\pi r^2 h[/tex]

Thus we find that cylinder has a greater volume and ratio is 3:1

Hence 3 times if filled up with a cone the cylinder will be completely full

Definition: A transversal is a line that crosses at least two other lines.

Main properties:

Answer: true are options A, C and E.

A transversal in Mathematics is a line that intersects two or more lines at different points, but does not necessarily have to be parallel or bisect these lines. It can, however, be perpendicular to them.

In the subject of Mathematics, a transversal refers to a line that intersects two or more coplanar lines at different points. Therefore, the statement 'It is a line' and 'It intersects two or more coplanar lines' are true for a transversal.

The term transversal doesn't necessitate that it be parallel to other coplanar lines, nor does it indicate that it bisects line segments, so these statements are false. However, a transversal can be perpendicular to other lines if it intersects them at 90-degree angles.

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To find the number of white pieces when the ratio of black pieces to white pieces is known, set up a proportion and solve for the missing variable. In this case, the number of white pieces is 9.

To find the number of white pieces, we can use the proportion 3/4 = W/12, where W represents the number of white pieces.

Cross multiply to get 3*12 = 4*W

Therefore, 36 = 4W

Divide by 4 to find that W = 9.

The equation relating W to T is W = 600 + 25T.

Given:

The initial amount of water in the pond is 600 liters.

The water is being added at a rate of 25 liters per minute.

As time (T) increases, the amount of water in the pond (W) will increase due to the constant addition of 25 liters per minute.

The equation can be written as follows:

W = 600 + 25T

In this equation, 600 represents the initial amount of water in the pond (at T = 0), and 25T represents the additional water added for each minute of time (T).

Learn more about Linear Equation here:

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