The function f(x) is shown on the graph.

The graph shows a downward opening parabola with a vertex at 3 comma 25, a point at negative 2 comma 0, a point at 8 comma 0, a point at 0 comma 16, and a point at 6 comma 16.

What is the standard form of the equation of f(x)?
f(x) = x2 − 6x + 16
f(x) = x2 + 6x + 16
f(x) = −x2 − 6x + 16
f(x) = −x2 + 6x + 16

Answer:

-2, 2

-4

Step-by-step explanation:

The x-intercept is the point where the graph crosses the x-axis. At that point, the y-coordinate equals zero. At the x-intercept, f(x) = 0.

Look below f(x) and find where f(x) = 0. Which x values correspond to f(x) = 0?

There are two x values: x = -2, and x = 2

The x-intercepts shown in the table are -2 and 2.

The y-intercept is the point where the graph crosses the y-axis. At that point, the x-coordinate equals zero. At the y-intercept, x = 0.

Look below x and find where x = 0. Which f(x) value corresponds to x = 0?

There is one f(x) value: f(x) = -4

The y-intercept shown in the table is -4.

The difference of the two polynomials is 7x^(4) - 9x - 23.

The difference of the two polynomials (19x^(4)-17x-18)-(12x^(4)-8x+5) can be found by subtracting the corresponding terms of the two polynomials.

Subtract the first term of the second polynomial from the first term of the first polynomial: 19x^(4) - 12x^(4) = 7x^(4)

Subtract the second term of the second polynomial from the second term of the first polynomial: -17x - (-8x) = -17x + 8x = -9x

Subtract the third term of the second polynomial from the third term of the first polynomial: -18 - 5 = -23

Write the resulting polynomial by combining the terms  7x^(4) - 9x - 23

Therefore, the difference of the two polynomials is 7x^(4) - 9x - 23.

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Answer: six hundred nine thousandths

Step-by-step explanation:

Answer:

34%

Step-by-step explanation:

495 is 66% of 750 so 66% - 100% is 34%

Answer:

34

Step-by-step explanation:

TB is both one-to-one and onto, it is an isomorphism.

To prove that TB is an isomorphism, we need to show that it is both one-to-one and onto.

One-to-one: Assume TB(A) = TB(C) for some A, C EM nxn(K). Then, BAB-¹ = CBC-¹. Multiplying both sides by B-¹ on the left and B on the right gives B-¹BAB = B-¹CBC. Since B is invertible, B-¹B = I and we have A = C. Therefore, TB is one-to-one.

Onto: Let D EM nxn(K). Then, we can define A = B-¹DB. Since B is invertible, A EM nxn(K) and TB(A) = BAB-¹ = B(B-¹DB)B-¹ = D. Therefore, TB is onto.

Since TB is both one-to-one and onto, it is an isomorphism.

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Answer:

70.5

In Maths, two angles are said to be complementary, when the angles add up to 90 degrees. The complementary angle need not be adjacent to each other, but its sum should be equal to 90 degrees. For example, 47° and 43° are complementary angles.

Example:

To find out another angle if one of the complementary angles is 60°

Solution:

We know that the sum of complementary angles is 90

Let the unknown angle be x

Thus,

60° + x = 90°

X = 90° – 60°

X = 30°

Hence, the unknown angle is 30°

To find the mean and standard deviation of the distribution, we can use the z-scores for the given percentages and the corresponding spending amounts.  The mean of the distribution is $46.63 and the standard deviation is $2.63.

By using the z-scores for the specified percentages and related spending amounts, we can determine the mean and standard deviation of the distribution. The z-score for 10% is 1.28 and the z-score for 30% is 0.52. Using the formula

z = (x - mean)/standard deviation, we can set up two equations:

1.28 = ($50 - mean)/standard deviation

0.52 = ($48 - mean)/standard deviation

We can rearrange the equations to solve for the mean and standard deviation:

mean = $50 - (1.28)(standard deviation)

mean = $48 - (0.52)(standard deviation)

Subtracting the second equation from the first gives us:

0 = $2 - (0.76)(standard deviation)

Solving for standard deviation gives us:

standard deviation = $2/0.76 = $2.63

Plugging this back into the first equation gives us:

mean = $50 - (1.28)($2.63) = $46.63

Therefore, the mean of the distribution is $46.63 and the standard deviation is $2.63.

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Therefore , the solution of the given problem of graph comes out to be option A f(n) = 7 - 2(n-1)

Theoretical physicists use graphs to analytically chart or visually represent claims rather than values. A graph point typically depicts the relationship between any number of things. A specific type of non-linear train assembly made up of clusters and lines is known as a graph. Glue should be used to connect the networks, also referred as the boundaries. In this network, the nodes had the numbers 1, 2, 3, and 5, whilst edges had the numbers 1, 2, 3, and 4, as well as the numbers (2.5), (3.5), (4.5), and yet also (4.5). (4.5).

Here,

We can use the following method to determine the general term of an arithmetic series:

=> f(n) = a + (n-1)d

where the usual difference is "d" and "a" is the first term.

Since the series begins at 7, "a" is 7, as shown by the graph. Additionally, since each term reduces by 2, we can see that the common difference is 2.

Consequently, the following is the arithmetic sequence's stated rule:

A) f(n) = 7 - 2(n-1)

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3525

The next term in the arithmetic sequence that increases by 21, starting at 55, is 76. The next two terms of the Fibonacci sequence are 67 and 109, and the 72nd term is 3525.

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Answer:

8.9

Step-by-step explanation:

9.0-0.1= 8.9

which is one-tenth less than 9

The reciprocal of 5/11 is: 11/5

The reciprocal of 20 is: since 20=20/1 so the reciprocal is 1/20

Answer: 11/5, 1/20

Step-by-step explanation:

The reciprocal of a value is the numerator and denominator of that value switched.

When you look at 5/11, we see that 5 is the numerator and 11 is the denominator. The reciprocal(switch numerator and denominator) is 11/5.

The reciprocal of 20 can be tricky because it isn't written with a denominator. But we know intuitively that 20 is also equal to 20/1.

Therefore we apply the same steps as in the first instance and we get that the reciprocal of 20/1 is 1/20.

Answer:$999

Step-by-step explanation:

You are going to want to multiply 75 by 12 since you are giving 75 dollars 12 times- then you are going to add $99 for the down payment- and you’ve got your answer!

Answer:

999

Step-by-step explanation:

of means "x"

12 monthly payments of $75

12 x 75 = total for 12 payments

then add down-payment

u get total cost

The total number of miles Rowan runs over the first ten weeks of training is found as 58 miles.

In mathematics, a geometric series is an infinite series with the formula a + ar + ar2 + ar3 +, where r is referred as the common ratio.

In the question:

Let 'x' be the miles that Rowan runs in 1st week.

Xn for the nth week.

x1 = 15 (given)

x2 = 15*(1 + 3%) = 15*1.03

Xn = 15*(1 + 3%0ⁿ⁻¹ = 15*(1.03ⁿ⁻¹)

Let 'S' be the total miles.

S = x1 + x2+ .....+ xn

S = 15 + 15 *1.03 + 15*1.03² + ...+ 15*1.03⁹

On solving the series:

S = 15 × 1.(1.03¹⁰ - 1)/0.03

S = 57.31

S = 58

Thus, the total number of miles Rowan runs over the first ten weeks of training is found as 58 miles.

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The number of degrees for each part of the museum visitors graph would be Age 18 and under: 108 degrees, Age 19 – 44: 180 degrees, Age 45 – 64: 54 degrees, and Age 65 and over: 18 degrees.

To find the number of degrees for each part of the museum visitors graph, we need to know the total number of visitors for that month. Let's assume that the total number of visitors for the month is 10,000.

Age 18 and under:

Let's assume that the number of visitors aged 18 and under is 3,000. To find the number of degrees for this section of the graph, we need to use the formula: (Number of visitors in the age group / Total number of visitors) x 360 degrees. So, (3000/10000) x 360 = 108 degrees.

Age 19 – 44:

Let's assume that the number of visitors aged 19-44 is 5,000. Using the same formula as above, we get (5000/10000) x 360 = 180 degrees.

Age 45 – 64:

Let's assume that the number of visitors aged 45-64 is 1,500. Using the same formula as above, we get (1500/10000) x 360 = 54 degrees.

Age 65 and over:

Let's assume that the number of visitors aged 65 and over is 500. Using the same formula as above, we get (500/10000) x 360 = 18 degrees.

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Answer:

28 and 152 degrees

Step-by-step explanation:

Using sine inverse, the answer is 28 or 152 degrees.

Answer:48.87°

Step-by-step explanation:

The area of the trapezoid is 65.16 metres squared.

The area of a trapezoid can be found as follows:

area of a trapezoid = 1 / 2 (a + b)h

where

Therefore,

a = 5metres

b = 13.1 metres

h = 7.2 metres

Hence,

area of a trapezoid = 1 / 2 (5 + 13.1) 7.2

area of a trapezoid = 1 / 2 (18.1)7.2

area of a trapezoid = 130.32 / 2

Therefore,

area of a trapezoid = 65.16 metres squared

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The solution to the system of equations using elimination is:

x = 1058/1890

y = 26/90

To solve this system of equations using elimination, we will add the two equations together and rearrange the terms.

2y = x - 5

2y = x + 5

Add the equations together:

2y + 2y = x - 5 + x + 5

4y = 2x + 0

Rearrange the terms:

4y - 2x = 0

We will now use this equation and the equation x + 2y = 13 to solve for x and y.

Substitute 4y - 2x = 0 into x + 2y = 13:

x + 2(4y - 2x) = 13

x + 8y - 4x = 13

Rearrange the terms:

5x + 8y = 13

Substitute 4y - 2x = 0 into 5x + 8y = 13:

5x + 8(4y - 2x) = 13

5x + 32y - 16x = 13

Rearrange the terms:

21x + 32y = 13

Divide by 21:

x + (32/21)y = 13/21

Rearrange the terms:

x = 13/21 - (32/21)y

Substitute x = 13/21 - (32/21)y into 4y - 2x = 0:

4y - 2(13/21 - (32/21)y) = 0

4y - (26/21) + (64/21)y = 0

Rearrange the terms:

(90/21)y = 26/21

y = (26/21) / (90/21)

y = 26/90

Substitute y = 26/90 into x = 13/21 - (32/21)y:

x = 13/21 - (32/21)(26/90)

x = 13/21 - (832/1890)

x = 1058/1890

The solution to the system of equations is:

x = 1058/1890

y = 26/90

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The following values represent the rollercoaster graph scenario most accurately:

is, Red (x) = 6+4 × cos(πx/6) if 0 ≤ x < 6

Green (x) = -2.5 × cos (π(x - 6)/4) + 4.5

Purple (x) = 3.5 - 3.5 × sin (π(x - 12.5)/5)

For Red (x) = 6 + 4 × cos(πx/6) if 0 ≤ x < 6

The graph is simply a structured representation of the data. It facilitates our understanding of the facts. The numerical information gathered through observation is referred to as data.

The Latin word Datum, which meaning "something provided," is where the word data first appeared.

In the question, where at x = 0, Red(x) = 10,

at x = 5, Red(x) = 2.5

For Green (x) = -2.5 × cos (π(x - 6)/4) + 4.5       if    6 ≤ x < 10

Given, where at x = 10, Green (x) = 7,

So, at x = 6, Green (x) = 2.0

For Purple (x) = 3.5 - 3.5 × sin (π(x - 12.5)/5) if 10 ≤ x ≤ 15

Given, where at x = 10, Purple (x) = 7,

at x = 15, Purple (x) = 0

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The complete question is:

The above rollercoaster graph needs a function to go with it. Select the correct functions that begins at (0,12) and ends at (12,0) with a local minimum at (5,1) and a local maximum at (9,6). You need to select one function for the red piece, one function for the green piece, and one function for the purple piece.

The distance between Jason's school and his house is 8 miles.

What is the Cartesian system?

Any point can be located using a Cartesian coordinate system or coordinate system, and that point can be plotted as an ordered pair (x, y) known as Coordinates. The origin, symbolized by the letter "O," is the point where the two number lines intersect. The horizontal number line is known as the X-axis, and the vertical number line is known as the Y-axis.

Given that the coordinates of Jason's house is (-4,-5). The coordinates of his school is  (-10,-11).

The formula distance between two points (x₁, y₁) and (x₂, y₂) is √[(x₂ - x₁)² + (y₂ - y₁)²].

Here, x₁ = -4, y₁ = -5,x₂= -10, y₂ = -11

The distance between points is

√[(-10-(-4))² + (-11 - (-5))²]

=√(6² + 6²)

= √(36+36)

= √72

= 6√2

= 8.48

≈ 8 miles

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Step-by-step explanation:

Refer to pic...........

The sample size that would be required to estimate the confidence interval with a margin of error of 1% is given as follows:

n = 9604.

A confidence interval of proportions has the bounds given by the rule presented as follows:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which the variables used to calculated these bounds are listed as follows:

The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

The margin of error is modeled as follows:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

We have no estimate of the proportion, hence it is used as follows:

[tex]\pi = 0.5[/tex]

The margin of error is of M = 0.01, hence the sample size is obtained as follows:

[tex]0.01 = 1.96\sqrt{\frac{0.5(0.5)}{n}}[/tex]

[tex]0.01\sqrt{n} = 1.96 \times 0.5[/tex]

[tex]\sqrt{n} = 98[/tex]

n = 98²

n = 9604.

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The value of λ and μ for which the system of equations x+y+z=6,x+2y+3z=10 and x+2y+λz=μ  are none of this. The correct answer is option D, None of these.

To find the value of λ and μ for which the system of equations has no solution, we can use the determinant method. The determinant of a system of equations is given by:

| a1 b1 c1 |
| a2 b2 c2 | = a1(b2c3 - b3c2) - b1(a2c3 - a3c2) + c1(a2b3 - a3b2)
| a3 b3 c3 |

For the given system of equations, the determinant is:

| 1 1 1 |
| 1 2 3 | = 1(2λ - 3μ) - 1(3 - 3) + 1(2 - 2)
| 1 2 λ |

Simplifying, we get:

2λ - 3μ = 0

For the system of equations to have no solution, the determinant must be equal to 0. Therefore, we need to find the values of λ and μ that satisfy the equation 2λ - 3μ = 0.

None of the given options satisfy this equation, therefore the correct answer is option D, None of these.

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Answer:

Step-by-step explanation:

Given: Length of the building = 78 ft

Scale = 1 in : 8 ft

To find: Length of the building in the drawing

Now we have the scale where

8 ft = 1 inch

So using unit rule

1 ft = (1/8) in

So

78 ft = (1/8)(78) in = 9.75 inch

So length of the building in the drawing is 9.75 inch.

The length of the drawing is 9.75 inches.

To calculate the length of the drawing, find out how many inches correspond to 78 feet using the scale provided.

Since the scale is 1in:8ft, this means that 1 inch on the drawing represents 8 feet in real life.

To determine the length of the drawing, divide the length of the building by the scale factor:

Length of drawing = Length of building / Scale factor

Length of drawing = 78 ft / 8

Length of drawing = 9.75 inches

Hence, the drawing is 9.75 inches long.

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To calculate the probability that a randomly selected person has at least 2 TV's, you would first calculate the probability of a person having more than 2 TV's:

Then, you would calculate the probability of a person having less than 2 TV's:

Finally, you would calculate the probability of a person having exactly 2 TV's:

Therefore, the probability that a randomly selected person has at least 2 TV's is:

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The polynomial expressions are P(x) = x(x - 5)(x - 2), P(x) = (x + 3)(x + 5)(x - 3)(x + 1), P(x) = (x + 5)(x² - 4x + 5) and P(x) = (x + 5)(x² + 4)

Zeros (1): 0, 5, 2

This means that

Roots: x = 0, x = 5 and x = 2

The equation can be represented as

P(x) = (x - root)

So, we have

P(x) = (x - 0)(x - 5)(x - 2)

Evaluate

P(x) = x(x - 5)(x - 2)

Zeros (2): 0, 5, 2

Here, we have

Roots: x = -3, x = -5, x = 3 and x = -1

Using the form in (a), we have

P(x) = (x + 3)(x + 5)(x - 3)(x + 1)

Zeros (3): 0, 5, 2

Here, we have

Roots: x = -5, x = 2 + i

Using the form used abov]e, we have

P(x) = (x + 5)(x - 2 - i)(x - 2 + i)

Expand

P(x) = (x + 5)((x - 2)² + 1)

So, we have

P(x) = (x + 5)(x² - 4x + 5)

Zeros (4): -1 and 2i

Here, we have

Roots: x = -1, x = 2i

Using the form used abov]e, we have

P(x) = (x + 1)(x - 2i)(x + 2i)

Expand

P(x) = (x + 5)(x² + 4)

Zeros (5):2 mult.2, -4

The zeros here are not clear

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