The table describes the quadratic function p(x).


x p(x)
−1 31
0 17
1 7
2 1
3 −1
4 1
5 7

What is the equation of p(x) in vertex form?
p(x) = 2(x − 3)2 − 1
p(x) = 2(x + 3)2 − 1
p(x) = 3(x − 3)2 − 1
p(x) = 3(x + 3)2 − 1

Answer:

Step-by-step explanation:

The volume for a right cylinder is

[tex]V=\pi r^2h[/tex]

We are given all the values except the radius, so we plug them in as follows:

[tex]18488=\pi r^2(23)[/tex]

Begin by dividing by 23π to get

255.8657603 = r²

and then take the square root of both sides to find that

r = 15.995 or 16 m

Answer:

The answer would not be 0, it would be -12, and here is why.

4x^4+ 16x+31x^2=62x-90.

In thia case i ignpored the variable, i think its a variable..

You woulkd add 62+16, you get 78.

78-90= -12

Answer: The transformations that occurred to create g(x) = -2(x-8)²-81+7 from f(x) = x are:

- Horizontal translation 8 units to the right: The term (x - 8) in the equation of g(x) means that the graph of g(x) has been shifted horizontally 8 units to the right compared to f(x) = x.

- Vertical stretch by a factor of 2: The coefficient -2 in front of the term (x - 8)² means that the graph of g(x) has been vertically stretched by a factor of 2 compared to f(x) = x.

- Vertical translation 81 units down and 7 units up: The terms -81 and +7 in the equation of g(x) mean that the graph of g(x) has been shifted vertically 81 units down and then 7 units up compared to f(x) = x.

Therefore, the correct answer is (a) vertical translation 7 units up.

Step-by-step explanation:

The quadratic equation written in vertex form is:

A(x) = x^2 - 4

Here we want to find the vertex form of the quadratic equation:

A(x) = (x + 2)*(x - 2)

Remember that for a quadratic equation with the vertex (h, k) and leading coefficient a is written as:

f(x) = a*(x - h)^2 + k

Now, notice that the zeros of the quadratic function are x = -2 and x = 2.

Then the vertex is just between these two, at x = 0.

Then h = 0, and the y-value of the vertex is what we get when we evaluate in x = 0.

k = (0 + 2)*(0 - 2) = 2*-2 = -4

Then the vertex is (0, -4) and the leading coefficient is 1, we can write the quadratic equation as:

A(x) = (x - 0)^2 -4

A(x) = x^2 - 4

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Answer:

189 chips are estimated to be in the bag.

Step-by-step explanation:

Mass of Chips = Mass of Chips + Bag - Mass of Bag

Mass of Chips = 369 g - 28 g

Mass of Chips = 341 g

Mass of 1 Chip = Mass of 25 Chips / 25

Mass of 1 Chip = 45 g / 25

Mass of 1 Chip = 1.8 g

Number of Chips = Mass of Chips / Mass of 1 Chip

Number of Chips = 341 g / 1.8 g

Number of Chips ≈ 189

Answer:

D.

Step-by-step explanation:

Nikolas did not make a mistake. The formula to calculate volume of a triangular prism is

[tex]V=Bh[/tex]

where B is the area of the base and h is the height.

The area of the triangular base is [tex](0/5)(5.8)(6.2) = 17.98[/tex].

[tex]Bh = 17.98 * 9.2 = 165.416 ft^3[/tex]

The area of the sector with a central angle of 180° as required to be determined in the task content is; 176.41 cm².

It follows from the task content that the sector in discuss has a central angle of 180° and a diameter of 21.2 cm.

Recall the area of a sector is;

Area, A = (theta/360) × πr²

where r = diameter / 2

r = 21.2/2

r = 10.6 cm.

A = (180/360) × 3.14 × 10.6²

Area, A = 176.41 cm².

Ultimately, the area of the sector is; 176.41 cm².

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Slope AB = slope CD = 1/1 and slope BC ≠ slope DA. Therefore, AB and CD are parallel sides, and ABCD is a trapezoid.

In geometry, a trapezoid (also known as a trapezium in some countries) is a quadrilateral with at least one pair of parallel sides. The parallel sides are called the bases of the trapezoid, and the other two sides are called the legs.

The trapezoid can be classified into three types based on the positions of the bases:

Isosceles trapezoid: A trapezoid in which the non-parallel sides are congruent.

Right trapezoid: A trapezoid in which one of the angles formed by the legs is a right angle.

Scalene trapezoid: A trapezoid in which none of the sides are congruent.

The area of a trapezoid can be calculated by the formula:

A = (b1 + b2)h/2

where b1 and b2 are the lengths of the bases and h is the height of the trapezoid (the perpendicular distance between the bases).

To show that ABCD is a trapezoid, we need to demonstrate that it has at least one pair of parallel sides. One way to do this is to calculate the slopes of the line segments that connect the vertices.

The slope of a line passing through two points (x1, y1) and (x2, y2) is given by:

slope = (y2 - y1) / (x2 - x1)

Using this formula, we can calculate the slopes of the four line segments:

slope AB = (4 - 1) / (2 - (-1)) = 3/3 = 1

slope BC = (1 - 4) / (3 - 2) = -3/1 = -3

slope CD = (-3 - 1) / (-3 - 3) = -4/-6 = 2/3

slope DA = (1 - (-3)) / (-1 - (-3)) = 4/2 = 2

We can see that slope AB = slope CD = 1/1 and slope BC ≠ slope DA. Therefore, AB and CD are parallel sides, and ABCD is a trapezoid.

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The probability that the number of defective bulbs in the sample is greater than 15 is  0.401, or 40.1%.

This is a binomial distribution problem with n=550 and p=0.035. We want to find the probability that the number of defective bulbs in the sample is greater than 15, which can be written as P(X > 15), where X is the number of defective bulbs in the sample.

Using the binomial probability formula, we have:

P(X > 15) = 1 - P(X ≤ 15)

P(X ≤ 15) = Σi=0¹⁵ (550 chooseᵃ) * 0.035ᵃ * (1-0.035)⁵⁵⁰⁻ᵃ

We can use software or a calculator with a binomial probability distribution function to find this sum, which is approximately 0.599.

Therefore, the probability that the number of defective bulbs in the sample is greater than 15 is:

P(X > 15) = 1 - P(X ≤ 15) ≈ 1 - 0.599 = 0.401

So the probability that more than 15 bulbs in the sample are defective is approximately 0.401, or 40.1%.

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The equivalent expression is 9b^6/a^4c^6

An equivalent expression is a mathematical expression that has the same value as another expression, even though it may be written differently. Equivalent expressions can be useful in simplifying complex mathematical expressions or in solving equations by replacing a complex expression with a simpler, equivalent one.

In algebra, two expressions are considered equivalent if they simplify to the same expression, or if they have the same solution set when solved.

We have that;

(-3ab^2c^-3/a^3b^-1)^2

9a^2b^4c^-6/a^6b^-2

9a^-4b^6c^-6

9b^6/a^4c^6

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The constant proportionality is 15, which means that for every box of candy, there are 15 pieces of candy. The equation is 15x.

A variable in mathematics is a sign that denotes a value that may vary, as opposed to a constant, which is a set number that never changes. Variables are used to represent unknown or changing quantities, such as time (t) or the distance (d) travelled by an item, whereas constants are used to represent fixed numerical values, such as pi or the speed of light (c). In contrast to variables, which are often represented by lowercase letters, constants are typically represented by capital letters. In mathematical equations and formulae, the distinction between constants and variables establishes which values are fixed and which values are subject to change.

The slope of line is given as:

m = (change in y) / (change in x)

Substitute the values from the table:

m = (135 - 150) / (9 - 10) = -15/-1 = 15

For the equation to be of the form y = mx we have:

y = mx + b

150 = 15(10) + b

b = 0

Substituting the values the equation is:

y = 15x

Hence, the constant proportionality is 15, which means that for every box of candy, there are 15 pieces of candy. The equation is 15x.

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Answer:

Step-by-step explanation:

Post a link to the paper then i will edit it and send it back and then give you the answers on the paper you share with me

The amplitude οf the functiοn is 1/2, the phase shift is (-π)/3, and the periοd is 2π/3.

Phase shift simply means that the twο signals are at different pοints οf their cycle at a given time.

The given functiοn is y = 2 – (1/2) cοs (3x+π).

We can see that the general fοrm οf this functiοn is y = A cοs (Bx - C) + D, where A is the amplitude, B is the frequency, C is the phase shift, and D is the verticaI shift.

Cοmparing the given functiοn with the general fοrm, we can see that:

A = 1/2

B = 3

C = -π

D = 2

Therefοre, the amplitude is |A| = 1/2.

The phase shift is given by C/B = (-π)/3.

The periοd οf the functiοn is given by T = 2π/B = 2π/3.

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Answer:

A. No Solution

B. Unique Solution (0,0)

Step-by-step explanation: When you are dealing with a system of equations and they have the same variables with the same coeffiencts adding up to different numbers, it is unsolvable and therefore has no-solution. When you are dealing with two y-values equaling different amounts of x-values, 0 satisfy both varaibles.

If you approach this from a graphing perspective, you can put both equations in the system into slope intercept form.

System A:

Line 1: 3x + 5y = 8

                  5y = -3x + 8

                    y = -3/5 x + 8/5

Line 2: 3x + 5y = 7

                  5y = -3x + 7

                    y = -3/5 x + 7/5

Because both lines have the same slope, but different y-intercepts, the lines are parallel and will never intersect.  This is why there is no solution to the system.

System B:

Line 1: y = 7x is in slope intercept form.

Line 1: y = 3x is in slope intercept form.

Since these lines have different slopes, they are guaranteed to intersect only once.  There is a single solution.

If you graph these lines, they will intersect at the origin, at (0,0), since that is a common point on both lines.

Answer:

x = 3[tex]\sqrt{2}[/tex] , y = [tex]\frac{3\sqrt{2} }{2}[/tex]

Step-by-step explanation:

this is a 90- 45- 45 isosceles triangle with legs congruent , that is

y = [tex]\frac{3\sqrt{2} }{2}[/tex]

using Pythagoras' identity in the right triangle

x² = ( [tex]\frac{3\sqrt{2} }{2}[/tex] )² + y²

   = ( [tex]\frac{3\sqrt{2} }{2}[/tex] )² + ( [tex]\frac{3\sqrt{2} }{2}[/tex] )² = 9 + 9 = 18 ( take square root of both sides )

x = [tex]\sqrt{18}[/tex] = [tex]\sqrt{9(2)}[/tex] = [tex]\sqrt{9}[/tex] × [tex]\sqrt{2}[/tex] = 3[tex]\sqrt{2}[/tex]

The equation for c in terms of p is c = (9/7)p. To obtain this equation, we use the given values of C and p to find the constant of proportionality.

We know that c and p are directly proportional, which means that c = kp for some constant k. We can find k by plugging in the given values:

We can solve this system of equations for k by using elimination or substitution. Solving for k, we get

Thus, the equation for c in terms of p is

c = (9/7)p.

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The points (7,9), (9,7), (0,6), (3,8), (7,5), (8,3), (6,0), (9,10), (5,2), and (2,5) can be represented in a table with two columns - one for the x-coordinate and one for the y-coordinate. This format is useful for organizing and manipulating data, but it does not provide a visual representation of the location of the points.

On the other hand, a coordinate plane is a visual tool that allows us to plot and view the location of points in two-dimensional space. The x-axis and y-axis intersect at the origin (0,0), and each point is represented by a unique combination of x and y coordinates. This format is particularly useful for understanding the relationships and patterns among the points.

A table lists the coordinates of points in a tabular format, a coordinate plane allows us to plot and visualize the location of points in two-dimensional space.

Representing points in a table and in a coordinate plane are two common ways to visually display data. While a table lists the coordinates of points in a tabular format, a coordinate plane is a graphical representation that allows us to plot and visualize the location of points in two-dimensional space.

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Therefore , the solution of the given problem of area comes out to be 4-cm by 8-cm rectangle, we can keep adding rows of four-square units.

Its total size can be determined by figuring out how much room would be required to completely cover the outside. The surroundings are also taken into consideration when determining this same surface that has a trapezoidal shape. Something's total dimensions are determined by its surface area. The volume of water that a cuboid can contain inside depends on the number of edges that are present between its four trapezoidal extremities.

Here,

A 4-cm by 8-cm rectangle has an area

=> 4⋅8=32

square centimetres when its length and breadth are multiplied. Starting with a row of four tiny squares,

we can then layer another row of four tiny squares on top of it. We now have a total of 8 tiny squares, which together measure 4 by 2 centimetres.

Then, after the first two rows, add a third row of four little squares to complete the procedure.

We now have a total of 12 little squares, which together make a rectangle measuring 4 centimetre by 3 cm.

Up until we have 32 small squares in total, which make up the complete 4-cm by 8-cm rectangle, we can keep adding rows of four-square units.

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Therefore , the solution of the given problem of area comes out to be the cone has a 5 millimetre height.

Calculating how much space would be needed to fully cover the outside will reveal its overall size. When calculating a trapezoidal form's surface, the environs were also taken into account. The surface area of something determines its overall measurements. The amount of edges connecting each of a cuboid's four parallelogram ends reveals how much underground water it can hold.

Here,

Let's name the cone using the details provided:

Its base measures 25 mm2.

A parallel slice 6 mm from the vertex has a 36 mm2 surface.

We can use the fact that the area of a circular slice of a cone is proportional to the square of its distance from the vertex to build up a proportion:

(area of slice) / (base area) Equals (distance from vertex) / (height) 2/ (area from slice)

When we enter the numbers we are aware of, we obtain:

=> 36 / 25 = 6² / h²

If we simplify, we get:

=>  h² = (25 * 6²) / 36 = 25

When we square the two edges, we obtain:

=>  h = 5

As a result, the cone has a 5 millimetre height.

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Answer:

[tex]4t^{2}+4t-35[/tex]

Step-by-step explanation:

[tex](2t+7)(2t-5)\\4t^{2}-10t+14t-35\\4t^{2}+4t-35[/tex]

The expression [tex]-100^5 + 90[/tex] is completely factored as [tex]-(10^5 + 3)(10^5 - 3)[/tex].

Mathematical expressiοns cοnsist οf at least twο numbers οr variables, at least οne arithmetic οperatiοn, and a statement. It's pοssible tο multiply, divide, add, οr subtract with this mathematical οperatiοn.

The expression [tex]-100^5 + 90[/tex] can be factοred as follows -

Grοup the negative sign with the first term -

[tex]= -(100^5) + 90[/tex]

Evaluate [tex]100^5[/tex] as [tex](10^2)^5 = 10^{10}[/tex] -

[tex]= -(10^{10}) + 90[/tex]

Factor οut a negative sign -

[tex]= -(10^{10} - 90)[/tex]

Factor the difference of twο squares, where [tex]a = 10^5[/tex] and b = 3 -

[tex]= -(10^5 + 3)(10^5 - 3)[/tex]

Therefore, the expressiοn is factored as [tex]-(10^5 + 3)(10^5 - 3)[/tex].

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[tex]\textit{area of a semicircle}\\\\ A=\cfrac{\pi r^2}{2} ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ A=0.1413 \end{cases}\implies 0.1413=\cfrac{\pi r^2}{2}\implies 0.2826=\pi r^2 \\\\\\ \cfrac{0.2826}{\pi }=r^2\implies \sqrt{\cfrac{0.2826}{\pi }}=r\implies 0.30\approx r[/tex]

The coordinates of the new image are S(3, 6) →  (-6, 3), T(4,4) → (-4, 4), and U(5,1) → (-1, 5).

For describing a geometric transformation such a translation, rotation, scaling, or shearing, a matrix known as a transformation matrix is utilised. By multiplying the matrix by the column matrix of the original coordinates, the matrix is used to change the coordinates of points in a geometric figure. The modified figure is then drawn using the resultant transformed coordinates.

Given that the coordinates of the point are:

S(3, 6), T(4,4), and U(5,1)

When the figure is rotated by 90 degrees the resultant image has the following coordinates.

(x, y) → (-y, x)

Thus,

S(3, 6) →  (-6, 3)

T(4,4) → (-4, 4), and

U(5,1) → (-1, 5)

Hence, the coordinates of the new image are S(3, 6) →  (-6, 3), T(4,4) → (-4, 4), and U(5,1) → (-1, 5).

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yes, it is direct proportion becuz in direct proportion if the prize of one quantity increases the other too will have to increase. here in this question as you can see 5melons were costing 3.50 and on increasing it to 7 melons cost is too increasing soo it is a direct proportion.

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Answer:

-2b+12

Step-by-step explanation:

Answer:

-2b+12

Step-by-step explanation:

-2b-4(b+3)-4b

-2b+4b+12-4b

-2b+12

Triangle A″B″C″ is formed by a reflection over x = −1 and dilation by a scale factor of 4 from the origin. segment A double prime B double prime equals four segment BC ,equation shows the correct relationship between ΔABC and ΔA″B″C″

The equation that correctly shows the relationship between ΔABC and ΔA″B″C″ is C″A″/CA = 1/4. Triangle A″B″C″ is formed by reflecting triangle ABC over the line x = -1 and dilating it by a scale factor of 4. The reflection of a triangle preserves its angles and its sides are reversed, while the dilatation stretches the triangle out by a factor of 4. Therefore, the ratio between C″A″ and CA will be 1/4.

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Answer: Let's denote the two unknown angles as x and y.

We know that the sum of the three angles in a triangle is 180 degrees. So we can set up the following equation:

10 + 3x + 14x = 180

Simplifying the equation:

17x = 170

x = 10

Now we can use the ratio of the other two angles to find the value of y:

3:14 can be simplified as 3x:14x or x:4.67x

So y is 4.67 times larger than x:

y = 4.67x = 4.67(10) = 46.7

Therefore, the measures of the two unknown angles are x = 10 degrees and y = 46.7 degrees.

Step-by-step explanation:

The measure of the remaining two angles are 46.7

The angle sum property of a triangle states that the sum of interior angles of a triangle is 180°

Given here, One angle of a triangle measures 100°. the other two angles are in a ratio of 3:14. Then let the measure of the angles be 3x and 14x

thus using the angle sum property we have

[tex]3x+14x=80[/tex]

[tex]17x= 80[/tex]

[tex]x = 46.7[/tex]

Hence, The measure of the remaining two angles are 46.7

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By using trigοnοmetric functiοns, the sizes οf β and γ, tο the nearest 0.1, are β ≈ 24.0 degrees and γ ≈ 63.4 degrees

The basic trigοnοmetric functiοns are:

Sine (sin): the ratiο οf the length οf the side οppοsite an angle tο the length οf the hypοtenuse οf the triangle.

Cοsine (cοs): the ratiο οf the length οf the side adjacent tο an angle tο the length οf the hypοtenuse οf the triangle.

Tangent (tan): the ratiο οf the length οf the side οppοsite an angle tο the length οf the side adjacent tο the angle.

Fοr the first right triangle:

Using the trigοnοmetric functiοn tangent, we have:

tan(β) = οppοsite side / adjacent side

tan(β) = 9/20

Taking the inverse tangent οf bοth sides, we get:

β = tan⁻¹(9/20)

Using a calculatοr, we can find that:

β ≈ 24.0 degrees

Fοr the secοnd right triangle:

Using the trigοnοmetric functiοn cοsine, we have:

cοs(γ) = adjacent side / hypοtenuse

cοs(γ) = 6/15

Taking the inverse cοsine οf bοth sides, we get:

γ = cοs⁻¹(6/15)

Using a calculatοr, we can find that:

γ ≈ 63.4 degrees

Therefοre, the sizes οf β and γ, tο the nearest 0.1, are:

β ≈ 24.0 degrees

γ ≈ 63.4 degrees

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4

The rank of a matrix can be determined by converting it to its reduced row echelon form. It is also known as the row reduced echelon form or simply the reduced echelon form. The rank of a matrix is the number of non-zero rows in its reduced row echelon form. The given matrix is,

`A=[[2,3,-1,-1],[1,-1,-2,-4],[3,1,3,-2],[6,3,0,-7]]`

We need to convert the given matrix to its reduced row echelon form. It is done by applying elementary row operations on the matrix. The elementary row operations are as follows:

- Interchange the order of two rows.
- Multiply a row by a non-zero scalar.
- Add a multiple of one row to another row.

Let us apply these operations on the given matrix,

`[[2,3,-1,-1],[1,-1,-2,-4],[3,1,3,-2],[6,3,0,-7]]`

`= [R1, R2, R3, R4]`

`R1 → R1 - R2/2` (subtract half of R2 from R1)
`R2 → R2 - R1/2` (subtract half of R1 from R2)
`R3 → R3 - 3R1/2` (subtract three times half of R1 from R3)

`[[1,5/2,1/2,1/2],[0,-3/2,-5/2,-9/2],[0,-7/2,3/2,-7/2],[0,0,-3,-6]]`

`= [R1, R2, R3, R4]`

`R2 → -R2/3` (multiply R2 by -1/3 to make its first entry as 1)
`R3 → R3 - 7R2/3` (subtract 7 times -1/3 of R2 from R3)
`R4 → -R4/3` (multiply R4 by -1/3 to make its first entry as 1)

`[[1,5/2,1/2,1/2],[0,1,5/3,3/2],[0,0,-4/3,-4],[0,0,1,2]]`

`= [R1, R2, R3, R4]`

`R3 → -3R3/4` (multiply R3 by -3/4 to make its third entry as 1)

`[[1,5/2,1/2,1/2],[0,1,5/3,3/2],[0,0,1,1],[0,0,1,2]]`

`= [R1, R2, R3, R4]`

`R4 → R4 - R3` (subtract R3 from R4 to make its third entry as 0)

`[[1,5/2,1/2,1/2],[0,1,5/3,3/2],[0,0,1,1],[0,0,0,1]]`

`= [R1, R2, R3, R4]`

The given matrix is converted to its reduced row echelon form. The last row contains only a single non-zero entry, hence the rank of the matrix is 4.

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