Find a quadratic function that includes the set of values below.
(0,7), (2,17), (3,16)
The equation of the parabola is

The transformations that change the domain of a function are given as follows:

The domain of a function is defined as the set containing all the values assumed by the independent variable x of the function, which are also all the input values assumed by the function.

Hence we must look at transformations that change the values of x of the function, which are given as follows:

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Answer:

\(tan(30) = \frac{A}{B}\)

Step-by-step explanation:

Given

The attached triangle

Required

Find tan(30)

Let the side opposite 30 degrees be A and the side adjacent 30 degrees be B

So [using tangent identity]:

\(tan(\theta) = \frac{Opposite}{Adjacent}\)

This gives:

\(tan(30) = \frac{A}{B}\)

Answer: C

she donates a for 12 months, the 12 in the a * 12=300. the a is the fixed amount, meaning she will donate a 12 times in a year.

The side length of the cube is 5.6 feet (rounded to the nearest tenth).

We can calculate the side length of a cube with a volume of 141 cubic feet using the formula for cube volume , which is \(V = s^3\), where V is the volume and s is the side length.

We can calculate s by taking the cube root of both sides of the equation:

\(s = (V)^{(1/3)\)

Substituting V = 141, we get:

\(s = (141)^{(1/3)\)

By using a calculator to evaluate this expression, we may determine:

s ≈ 5.6

As a result, the cube's side length is roughly 5.6 feet (rounded to the closest tenth). This indicates that if we increase the side length by three, it will become longer. (\(s^3\)), we will get the volume of the cube, which is 141 cubic feet.

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Answer:

Part A:

To find the length of the ramp in yards, we need to first determine the horizontal distance covered by the ramp. The slope of the ramp is 1/12, meaning that for every 12 inches of horizontal distance, the height of the ramp increases by 1 inch. Since the height of the ramp when it connects to the house is 9 inches, we can use this information to determine the horizontal distance covered by the ramp.

9 inches / (1/12) = 108 inches

To convert inches to yards, we divide by 36, so

108 inches / 36 inches/yard = 3 yards

Part B:

To determine the length of the ramp, I used the information provided about the slope of the ramp and the height of the ramp when it connects to the house. I used the slope of the ramp (1/12) to calculate the horizontal distance covered by the ramp. Then I converted the horizontal distance from inches to yards by dividing by 36. Finally, I obtained 3 yards as the length of the ramp.

Answer:

Part A = 3 yards

Part B = 9 x 12 = 108 inches = 9 feet = 3 yards

Step-by-step explanation:

Part A

1 inch height - 12 inches length

9 inches height - 9 x 12 = 108 inches length

36 inches = 1 yard

108 inches = 108/36 = 3 yards

Part B

Shown above

The ramp is 9 inches tall, so the length of the ramp is 9 x 12 = 108 inches.

1 feet = 12 inches

108 inches = 108/12 feet = 9 feet

1 yard = 3 feet

9 feet = 3 yards.

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There are no possible real values for the first term 'a' that satisfy both equations.

Let's denote the first term of the geometric progression as 'a' and the common ratio as 'r'.

The sum of the first two terms can be expressed as:

a + ar = 16

To find the sum to infinity, we can use the formula:

Sum to infinity = a / (1 - r)

Given that the sum to infinity is 25, we have:

25 = a / (1 - r)

We now have two equations:

a + ar = 16

a / (1 - r) = 25

We can solve these equations simultaneously to find the possible values of 'a'.

From the first equation, we can factor out 'a' to get:

a(1 + r) = 16

Dividing both sides of the second equation by 25, we have:

a / (1 - r) = 1

We can rearrange this equation to get:

a = 1 - r

Substituting this expression for 'a' in the first equation, we get:

(1 - r)(1 + r) = 16

Expanding the equation, we have:

1 - r^2 = 16

Rearranging the terms, we get:

r^2 = -15

Since we are dealing with a geometric progression, the common ratio 'r' must be a real number. However, we observe that r^2 = -15 has no real solutions. Therefore, there are no possible real values for the first term 'a' that satisfy both equations.

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The probability of drawing a king from a standard deck of 52 cards is 1/13.

In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.

To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).

The total number of possible outcomes is 52 because there are 52 cards in the deck.

The favorable outcomes, in this case, are the four kings.

Therefore, the probability of drawing a king is given by:

Probability = (Number of favorable outcomes) / (Number of possible outcomes)

= 4 / 52

= 1 / 13

Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.

This means that out of every 13 cards drawn, on average, one of them will be a king.

It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.

Each draw is independent, and the probability of drawing a king is constant.

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Answer:

68 degrees

Step-by-step explanation:

Supplementary angles have sum 180°

<A=

Answer:

26000 ft²

Step-by-step explanation:

The area of the unshaded part is calculated as

Area of outer rectangle - area of square - area of triangle

outer area = 300 × 150 = 45000 ft²

area of square = 100² = 10000 ft²

area of triangle = \(\frac{1}{2}\) × 120 × 150 = 60 × 150 = 9000 ft²

Thus

unshaded area = 45000 - 10000 - 9000 = 26000 ft²

Using the inverse of the function from the table, the value of f⁻¹(4) is 107/3

The inverse of a function is a new function that "undoes" the original function. It reverses the mapping of inputs and outputs, allowing you to find the original input value when you know the output value.

In this problem, we have to use the table to find the original function which is f(x) and use it to find the inverse of the function;

Taking two points from the table;

m = y₂ - y₁ / x₂ - x₁

m = 0 - (-3) / -9 - (-11)

m = 3 / 20

Using the slope and one point on the table;

y = mx + x

-3 = 3/20(-11) + c

-3 = -1.65 + c

c = -3 + 1.65

c = -1.35

Putting the slope and y - intercept together;

y = 3/20x - 1.35

y = 3/20x - 27/20

f(x) = 3/20x - 27/20

Taking the inverse of the function;

f⁻¹(x) = (20x + 27)/3

To find the value of f⁻¹(4), we just need to substituting the value of x in the function;

f⁻¹(4) = (20(4) + 27)/3

f⁻¹(4) = 107/3

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Based on the information, it should be noted that the value of tan(A-B) is 234/583.

Given:

tanA = 60/11

sinB = 45/53

A and B are in Quadrant I

We can use the following identity to find tan(A-B):

tan(A-B) = (tanA - tanB)/(1 + tanA*tanB)

Substituting the given values, we get:

tan(A-B) = (60/11 - 45/53)/(1 + (60/11)*(45/53))

= (15/53)/(295/583)

= 234/583

Therefore, the value of tan(A-B) is 234/583.

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Answer:

I think it is p= $60

By using normal distribution, we get probability of gains between 0kg to 3kg is 0.2547

What is normal distribution?

A probability distribution known as a "normal distribution" is symmetric about the mean and indicates that data that are close to the mean are more likely to occur than data that are far from the mean.

Given that:

μ= 1.4

σ=4.6

We know the formula of normal distribution is z = (x-μ)/σ

\(P(0 < x < 3)=P(x < 3)-P(x < 0)\)

For \(P(x < 3)\)

\(z=\frac{3-1.4}{4.6} \\z=0.35\)

By using the z-table \(P(x < 3)=0.6368\)

For \(P(x < 0)\)

\(z=\frac{0-1.4}{4.6}\\z=-0.30\)

By using the z-table \(P(x < 0)=0.3821\)

Substituting \(P(x < 3)\) and \(P(x < 0)\) in \(P(0 < x < 3)\)

we get,

\(P(0 < x < 3)=0.6368-0.3821\\P(0 < x < 3)=0.2547\)

Therefore, by using normal distribution, we get probability of gains between 0kg to 3kg is 0.2547

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The percent change in the number of water bottles the company manufactured from February to April is 19.5%, to the nearest percent.

A % is a quantity or ratio that, in mathematics, represents a portion of one hundred. A dimensionless relationship between two numbers can be represented in a variety of ways, such as through ratios, fractions, and decimals.

The total number of water bottles the company manufactured in February, March, and April.

In February, the company manufactured 4,100 water bottles. In March, the company manufactured 7% more water bottles than in February, which is 7/100 * 4,100 = 287 water bottles.

Therefore, the total number of water bottles the company manufactured in March is 4,100 + 287 = 4,387 water bottles. In April, the company manufactured 500 more water bottles than in March, which is 4,387 + 500 = 4,887 water bottles.

This is calculated as (4,887 - 4,100) / 4,100 = 0.195 or 19.5%.

Therefore, the percent change in the number of water bottles the company manufactured from February to April is 19.5%, to the nearest percent.

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Step 1: We have a line segment XZ, with point Y between X and Z.

Therefore, we have:

XY + YZ = XZ

Replacing with the values given:

7a + 5a = 6a + 24

Like terms:

7a + 5a - 6a = 24

6a = 24

Dividing by 6 at both sides:

6a/6 = 24/6

a = 4

Step 2: Now we can find the length of the line segment, this way:

YZ = 6a + 24

Replacing a by 4

YZ = You can finish the calculation

The turning points of the function y = x³ - 3x² - 9x + 4 are (3, -23) and (-1, 9).

To determine the turning points of the given function y = x³ - 3x² - 9x + 4, we need to find the critical points where the derivative of the function is equal to zero.

1. Find the derivative of the function:

  y' = 3x² - 6x - 9

2. Set the derivative equal to zero and solve for x:

  3x² - 6x - 9 = 0

3. Factorize the quadratic equation:

  3(x² - 2x - 3) = 0

4. Solve the quadratic equation by factoring or using the quadratic formula:

  (x - 3)(x + 1) = 0

  This gives us two possible values for x: x = 3 and x = -1.

5. Substitute these critical points back into the original function to find the corresponding y-values:

  For x = 3:

  y = (3)³ - 3(3)² - 9(3) + 4

    = 27 - 27 - 27 + 4

    = -23

  For x = -1:

  y = (-1)³ - 3(-1)² - 9(-1) + 4

    = -1 - 3 + 9 + 4

    = 9

6. Therefore, the turning points are (3, -23) and (-1, 9).

Note: It appears that there was a typo in the original equation, where the term "-9x" should have been "-3x²". The above solution assumes the corrected equation.

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Answer:

$37623.04

Step-by-step explanation:

The formula we'll use for this is the simple interest formula, or:

\(I=p*r*t\)

Where:

P is the principal amount, $1088.00.

r is the interest rate, 839.5% per year, or in decimal form, 839.5/100=8.395.

t is the time involved, 4....year(s) time periods.

So, t is 4....year time periods.

To find the simple interest, we multiply 1088 × 8.395 × 4 to get that:

The interest is: $36535.04

Usually now, the interest is added onto the principal to figure some new amount after 4 year(s),

or 1088.00 + 36535.04 = 37623.04.

Answer:

3 2/2

Step-by-step explanation:

Answer:

72.3 + (-39.1) = 70 + 2 + 0.3 + (-30) + (-9) + (-0.1)

Step-by-step explanation:

Answer:

arithmetic, divide by 2

Step-by-step explanation:

Answer:

This is a geometric sequence and the common ratio is equal to 1/2

Answer:

  91 lbs

Step-by-step explanation:

28/16 = 1.75 times as much force will lift 1.75 times as much weight:

  1.75 × 52 lbs = 91 lbs

The lever will lift 91 pounds if 28 pounds of force are used.

Answer:

4x² + 22x - 12

Step-by-step explanation:

A = bh/2

A = (4x - 2)(2x + 12)/2

A = (8x² + 48x - 4x - 24)/2

A = (8x² + 44x - 24)/2

A = 4x² + 22x - 12

Answer:

To convert a percentage to fractions: Percent means per hundred so say 5% is the same as 5/100 58% is like saying 58/100 or simplified 29/50

Step-by-step explanation:

Answer:

Just remeber Percent means"per hundred" so the answer woud

be 1/20 :) Hope this helps!!!!!!!

because  5% is the same as 5/100.

Step-by-step explanation:

Answer:

8 meters.

Step-by-step explanation:

the formula for the hypotenuse of a right triangle is: \(a^2 + b^2 = c^2\). Where C= hypotenuse and a and b = other sides. We can sub in a and c to get \(6^2 + x^2 = 10^2\\\). Simplify to \(36+x^2=100\). Subtract 36 from both sides to get x^2 = 64. \(\sqrt{64} =8\)

Answer: D) 7 3/4

Step-by-step explanation:

With averages, we add all the values and divide by the number of values. Here, we know three out of the four days, let's label the day we don't know x. There are four days, so we can divide by four. 7 1/4 is the average, so we can set the equation equal to 7 1/4.

7 1/4 = (7 1/2 + 7 3/8 + 6 3/8 + x) / 4

Let's multiply both sides by 4 to get rid of the fraction. Let's also add what is in the parentheses

29 = 21 1/4 + x

Now we can isolate x by subtracting 29-21 1/4

so

x = 7 3/4 thus the answer is D

Answer:

D) 7 3/4

Step-by-step explanation:

Let x = amount of last feeding.

7 1/4 = (7 1/2 + 7 3/8 + 6 3/8 + x)/4

4 × 7 1/4 = 7 1/2 + 7 3/8 + 6 3/8 + x

28 + 1 = 7 4/8 + 7 3/8 + 6 3/8 + x

29 = 20 10/8 + x

(20 10/8 is the same as 20 + 10/8 = 20 + 8/8 + 2/8 = 20 + 1 + 1/4 = 21 + 1/4 = 21 1/4)

29 = 21 2/8 + x

29 = 21 1/4 + x

x = 29 - 21 1/4

x = 28 4/4 - 21 1/4

x = 7 3/4

Answer: 7 3/4

Answer:

x-int: (-1, 0), (-11, 0)

y-int: (0, 11)

Step-by-step explanation:

To find x-int, set equation equal to 0:

x² + 12x + 11

(x + 1)(x + 11)

x = -11, -1

To find y-int, set x = 0

f(0) = 0² + 12(0) = 11

f(0) = 11

Answer:

Step-by-step explanation:

x - y = (6 - 5)(y - x) → False

(x - y) (6 - 5) = 1 → False

x- y = (1)(x - y) → True

x - y = 1 + (x - y) → No solution, False

x - y = (6 - 5)(x - y)  → True

Answer:

the answer its 16.15 hope helps you

Step-by-step explanation:

Answer:

16.15

Step-by-step explanation:

Remember the order of operations. Here, you do the parenthesis first, 1.6 + 2.4 = 4, 4 - 2.1 = 1.9. Lastly, 8.5*1.9. Which equals 16.15