50 POINTS TO BEST ANSWER

A function is shown below where b is a real number.
f(x)=x²+bx+118
The minimum of the function is 37.
Create an equivalent equation of the function in the form f(x)=(x-h)²+k.
Type your numerical answers below for h and k. Use the hyphen (-) for the negative sign if
necessary.
h=
k=

[tex]a^2-b^2=(a-b)(a+b)[/tex]

Therefore

[tex]f(x)=x^4-16\\f(x)=(x^2-4)(x^2+4)\\f(x)=(x-2)(x+2)(x^2+4)[/tex]

[tex](x-2)(x+2)(x^2+4)=0\\x=2 \vee x=-2[/tex]

A figure that is a dilation of figure A include the following: B. figure C.

In Geometry, a dilation is a type of transformation which typically transforms the dimension (size) or side lengths of a geometric object, without affecting its shape.

This ultimately implies that, the dimension (size) or side lengths of the dilated geometric object would be stretched or shrunk depending on the scale factor that is applied.

In this context, we can reasonably infer and logically deduce that both figure A and figure C are congruent to figure E because they all share a common center of dilation.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The data set is approximately periodic with a period of 3 and an amplitude of about 7.5.

The period is the length of time it takes for the data to repeat itself. In this case, the data repeats itself every 3 hours. The amplitude is the distance between the highest and lowest values in the data set. In this case, the amplitude is about 7.5 cars.

Hour | Number of cars

------- | --------

1     | 90

2     | 52

3     | 76

4     | 75

5     | 91

6     | 104

7     | 89

8     | 105

9     | 119

10    | 103

11    | 121

12    | 135

As you can see, the data repeats itself every 3 hours. The highest value in the data set is 135 cars, and the lowest value is 52 cars. The difference between these two values is 83 cars, which is about 7.5 times the average number of cars (90 cars). Therefore, the amplitude of the data set is about 7.5 cars.

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The average value of the function over the interval is 0

From the question, we have the following parameters that can be used in our computation:

f(x) = √(49 - x²)

The interval is given as

From x = 0 to x = 7

The function is a square root function

Calculating f(0) and f(7), we have

f(0) = √(49 - 0²) = 7

f(7) = √(49 - 7²) = 0

Next, we have

Average value = (7 * 0 + 0 * 7)/(0 + 7)

Evaluate

Average value = 0

Hence, the average value is 0

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Answer:

To determine the length you're referring to, we need more information about the specific configuration or diagram you're referring to. Please provide additional details or clarify your question so that I can assist you more accurately.

Step-by-step explanation:

Answer:

x = 2

y = -3

Step-by-step explanation:

y = x - 5

x + y = -1

To solve the given system of equations, we can use the method of substitution.

That is, you can replace y with ( x - 5 ).

x + y = -1

x + (x - 5 ) = -1

x + x - 5 = -1

Combine like terms.

2x - 5 = - 1

Add 5 to both sides.

2x = - 1 + 5

2x = 4

Divide both sides by 2.

x = 2

And now let us find the value of y by replacing x with 2.

y = x - 5

y = 2 - 5

y = -3

The expression 2log(5) can be rewritten as log(25) in the form log(c), representing the Logarithm to the base 10 that yields the value 25.

The expression 2log(5) in the form log(c), we can use the logarithmic property that states:

nlog(b) = log(b^n)

Applying this property, we can rewrite 2log(5) as:

2log(5) = log(5^2)

Simplifying further, we have:

2log(5) = log(25)

Therefore, the expression 2log(5) can be written in the form log(c) as log(25).

The logarithmic function log(c) represents the exponent to which a given base must be raised to obtain the value c. In this case, log(25) represents the exponent to which the base 10 must be raised to obtain the value 25.

In summary, the expression 2log(5) can be rewritten as log(25) in the form log(c), representing the logarithm to the base 10 that yields the value 25.

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Answer:

Step-by-step explanation:

area of a circle = πr²

perimeter of a circle = 2πr

all we have to do is substitute the value into the formula:

area of this circle = 22/7 × 13² =  531.14 ..

perimeter of this circle = 2 × 22/7 × 13 = 81.71 ..

hope this helps!

The value of all three angles, A , B and C is 60°

All sides , a,b, and c are 7.5 inches

From Cosine Rule :

CosA = (b² + c² - a²)/(2bc)

CosA = (7.5² + 7.5² - 7.5²)/(2 × 7.5 × 7.5)

CosA = 56.25/112.5

CosA = 0.5

A =

[tex] {cos}^{ - 1} (0.5) = 60[/tex]

From Sine Rule a/sinA = b/sinB

7.5/Sin60° = 7.5/SinB

cross multiply

7.5SinB = 7.5(Sin60°)

sinB= 6.495/7.5

SinB = 0.866

B =

[tex] {sin}^{ - 1} (0.866) = 60[/tex]

A + B + C = 180

60 + 60 + C = 180

C = 180 - 120

C = 60°

Therefore , all three angles A,B and C are 60° each.

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Answer:21 cm.

Step-by-step explanation:

Para encontrar la longitud del lado de un cuadrado con un área de 441 cm², podemos usar la fórmula del área de un cuadrado.

El área de un cuadrado se calcula elevando al cuadrado la longitud de uno de sus lados, es decir, A = L², donde A es el área y L es la longitud del lado.

Dado que el área del cuadrado es 441 cm², podemos escribir la ecuación:

441 = L²

Para encontrar L, podemos tomar la raíz cuadrada de ambos lados de la ecuación:

√441 = √L²

21 = L

Por lo tanto, la longitud del lado de un cuadrado con un área de 441 cm² es de 21 cm.

The length of the variable are as follows;

x = 27.4 units

y = 12.7 units

When two secants intersect outside a circle, the circle divides the secants into segments that are proportional with each other.

Therefore,

5(x + 5) = 6(21 + 6)

5x + 25 = 126 + 36

5x + 25 = 162

5x = 162 - 25

5x = 137

x = 137 / 5

x = 27.4 units

Let's find variable y as follows;

If a secant and a tangent are drawn to a circle from the same external point, the product of the length of the secant and its external segment equals the square of the tangent segment.

Therefore,

y² = (21 + 6)6

y² = 27 × 6

y² = 162

y = √162

y = 12.7279220614

y = 12.7 units

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x - 3(9+7)x-(-3x) equals -43x, which is the answer we get after applying the order of operations.

To simplify this expression, we need to use the order of operations, which is PEMDAS (parentheses, exponents, multiplication and division, and addition and subtraction). We can simplify the expression step-by-step, following the rules of PEMDAS.
First, we need to simplify the parentheses, which contain an addition operation. We have:
x - 3(9 + 7)x - (-3x)
= x - 3(16)x + 3x   (remember that -(-3x) is the same as +3x)
= x - 48x + 3x     (multiplying 3 by 16 gives us 48)
= -44x + x
= -43x

Therefore, the expression x - 3(9+7)x-(-3x) simplifies to -43x.
In summary, x - 3(9+7)x-(-3x) equals -43x, which is the answer we get after applying the order of operations. Remember to follow the rules of PEMDAS carefully, and take your time simplifying each part of the expression.

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Answer:

3.33 minutes

Step-by-step explanation:

h = rt - 4.9t^2

In this case, the rocket is launched upward, so the initial velocity (r) is positive 1960 m/s. The rocket will fall to the ground when the height (h) becomes zero.

0 = 1960t - 4.9t^2

To solve this quadratic equation, we can set it equal to zero and use the quadratic formula:

4.9t^2 - 1960t = 0

Using the quadratic formula:

t = (-b ± √(b^2 - 4ac)) / (2a)

Here, a = 4.9, b = -1960, and c = 0. Plugging in these values:

t = (-(-1960) ± √((-1960)^2 - 4 * 4.9 * 0)) / (2 * 4.9)

Simplifying further:

t = (1960 ± √(3841600)) / 9.8

t = (1960 ± 1960) / 9.8

t = 1960 / 9.8 = 200

So, the rocket will fall to the ground after 200 seconds. To convert this to minutes, divide by 60:

200 seconds / 60 = 3.33 minutes (approximately)

Therefore, the rocket will fall to the ground after approximately 3.33 minutes.

Answer:50.2654812288

Step-by-step explanation:

The two circles :

Sa  = πr²

     = π x 2²

     = 12.5663706144

     = 12.5663706144 x 2

     = 25.1327412288

The rectangle :

C x h = 2πr

= 25.13274

= 25.13274 + 25.1327412288

= 50.2654812288

Step-by-step explanation:

50.2654858683848

because it is equivalent to this. Also I can tutor you

75,582 different groups of 8 can be formed from the 19 volunteers.

In this case, we want to calculate C(19, 8), which represents the number of ways to choose 8 volunteers from a set of 19 volunteers.

The formula for combinations is given by:

C(n, r) = n! / (r!(n-r)!)

Using this formula,

C(19, 8) = 19! / (8!(19-8)!)

C(19, 8) = 19! / (8!11!)

C( 19, 8) = 19 x 18 x 17 x 16 x 15 x 14 x 13 x 12 / 8 x7 x6 x 5x 4 x 3 x 2

C( 19, 8) = 75,582

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The third side of the triangle 12.5

A triangle is a polygon with three edges and three vertices. The important property of a triangle is that the sum of the internal angles of a triangle is equal to 180 degrees. This property is called angle sum property of triangle.

we the measurements of given two sides of the triangle 16.5 and 29

In a triangle, the sum of any two sides should be greater than the third side and the difference between any two sides should be lesser than that of the third side.

The sum of two sides rule

[tex]x + 16.5 > 29\\ x > 29 - 16.5\\ x > 12.5\\[/tex]

The difference between the two sides rule

[tex]29 - 16.5 < x \\ 12.5 < x[/tex]

Therefore, the value of x is 12.5

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Answer:

  see below

Step-by-step explanation:

You want to show that csc²(θ) -cot²(θ) -sin²(θ) = cos²(θ).

It often works well to express the trig functions in terms of sine and cosine. The identity sin²(θ) +cos²(θ) = 1 is also useful.

  [tex]\csc^2\theta-\cot^2\theta-\sin^2\theta=\cos^2\theta\\\\\dfrac{1}{\sin^2\theta}-\dfrac{\cos^2\theta}{\sin^2\theta}-\sin^2\theta=\cos^2\theta\\\\\\\dfrac{1-\cos^2\theta}{\sin^2\theta}-\sin^2\theta=\cos^2\theta\\\\\\\dfrac{\sin^2\theta}{\sin^2\theta}-\sin^2\theta=\cos^2\theta\\\\\\1-\sin^2\theta=\cos^2\theta\\\\\cos^2\theta=\cos^2\theta\qquad\text{Q.E.D.}[/tex]

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Answer: So the number is 24.

Step-by-step explanation:

The net signed area in the above graph can be written as

(x² + 10x - 2√2)dx.

The net signed area can be found by summing the areas of the three parts:

The three being

Hence the area

: 48 + 0 + 8 = 56

We now calculate values:

of c, d, a, and b:

c = 8 - (-2) = 10

d = 3 - 2 = 1

a = 2 + 8 = 10

b = -2√2

It is important to  note that since the area under the x-axis is negative hence the reason value of b is negative.

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The pie chart for the data is given below.

To create a pie chart from the given data, we first need to determine the percentage of each score in relation to the total frequency. Here's the calculation:

Score                    Frequency                        Percentage

60                           2 (2/24) x 100                    = 8.33%

63                            2 (2/24) x 100                     = 8.33%

65                            1 (1/24) x 100                     = 4.17%

67                            1 (1/24) x 100                     = 4.17%

71                            1 (1/24) x 100                     = 4.17%

72                            1 (1/24) x 100                     = 4.17%

73                            2 (2/24) x 100                     = 8.33%

74                            2 (2/24) x 100                     = 8.33%

75                            2 (2/24) x 100                     = 8.33%

76                            1 (1/24) x 100                     = 4.17%

78                            1 (1/24) x 100                     = 4.17%

79                            2 (2/24) x 100                     = 8.33%

80                            1 (1/24) x 100                     = 4.17%

81                            2 (2/24) x 100                     = 8.33%

82                            1 (1/24) x 100                     = 4.17%

84                            1 (1/24) x 100                     = 4.17%

85                            1 (1/24) x 100                     = 4.17%

87                            1 (1/24) x 100                     = 4.17%

88                            1 (1/24) x 100                     = 4.17%

89                            1 (1/24) x 100                     = 4.17%

90                            1 (1/24) x 100                     = 4.17%

92                            1 (1/24) x 100                     = 4.17%

94                            1 (1/24) x 100                     = 4.17%

Now, we can use this information to create a pie chart. The chart will have 24 segments, each representing one score. The size of each segment will correspond to the percentage calculated above.

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The graph that represents the motion of Joe on his bike is: Graph D

A speed time graph is defined as a graph that shows the motion of an object against time. They can also be referred to as even a velocity-time graph.

In a speed-time graph, we note that the speed is always plotted on the vertical axis and time is always plotted on the horizontal

Now, since Joe started at a constant rate, then it means that the line will be horizontal.

When he picks up the pace, the graph line will ascend upwards and when he maintains the peak speed, it means that the graph line remains horizontal.

Thus, option D is the correct option.

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Benny (B) would win the election using the plurality method.

To determine the winner using the plurality method, we need to calculate the total number of first-place votes for each candidate and see which candidate receives the most votes.

According to the given preference schedule, the number of first-place votes for each candidate is as follows:

Abe (A): 1st - 20 votes, 3rd - 2 votes (from the 2nd preference of voter 1)

Benny (B): 1st - 19 votes, 2nd - 5 votes

Chloe (C): 1st - 5 votes, 2nd - 19 votes, 3rd - 3 votes (from the 1st and 2nd preferences of voter 1)

Now, let's calculate the total number of first-place votes for each candidate:

Abe (A): 20 + 2 = 22 votes

Benny (B): 19 + 5 = 24 votes

Chloe (C): 5 + 0 + 3 = 8 votes

Based on the plurality method, the candidate with the highest number of first-place votes wins.

In this case, Benny (B) received the most first-place votes with a total of 24 votes.

Therefore, Benny (B) would win the election using the plurality method.

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The GPA of the student who earned a "C" in Trigonometry, a "B" in American History, an "A" in Botany, and a "B" in Microbiology is 3.

To calculate the GPA, we need to assign point values to each grade and then calculate the weighted average.

Given:

Trigonometry (C) = 2 points

American History (B) = 3 points

Botany (A) = 4 points

Microbiology (B) = 3 points

To calculate the GPA, we'll sum the total points earned and divide by the total number of courses:

Total Points = 2 + 3 + 4 + 3 = 12

Total Courses = 4

GPA = Total Points / Total Courses = 12 / 4 = 3

Therefore, the GPA of the student who earned a "C" in Trigonometry, a "B" in American History, an "A" in Botany, and a "B" in Microbiology is 3.

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Answer:reference angle shoudl be 156 degrees srry if im wrong :)

Step-by-step explanation:

Answer:  42 inches

Step-by-step explanation: Simple Math.

Answer: 42 inches

Step-by-step explanation:

There is 12 inches per foot and 6 inches for every 1/2 a foot so 12 x 3 = 36 + 6 = 42 inches

The value of the expression is 1.

Given is an expression we need to solve it,

x - 1/2 = √1/4 x

x - 1/2 = 1/2 x

x - 1/2 x = 1/2

1/2 x = 1/2

x = 1

Hence the value of the expression is 1.

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Step-by-step explanation:

NOT rolling a four means out of six posssible rols you can roll a 1.2.3.5 or 6

 or      5 / 6