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=
Answers
I did some research and found that for quadratic equations in the form of [tex]y = ax^2 + bx + c[/tex], you can find the minimum value using the equation [tex]$\text{minimum} = c - \frac{b^2}{4a}[/tex] .
We can substitute our given values in the formula and get the following: [tex]$37 = 118 - \frac{b^2}{4}$[/tex] .
We can go ahead and solve it, and get the following:
[tex]-81 = -\frac{b^{2}}{4}[/tex]
[tex]324 = b^2[/tex]
[tex]\pm{18} = b[/tex]
Now we know that the equation is either [tex]$f(x)=x^2+18x+118$[/tex] or [tex]$f(x)=x^2-18x+118$[/tex] .
We will solve using both equations, but we will solve the one with a positive b-value first. Substituting [tex]f(x)[/tex] for [tex]$37$[/tex], the minimum or y-value of the vertex, we can now solve for the x-value of the vertex.
We have:
[tex]37 = x^2+18x+118[/tex]
[tex]0=x^2+18x+81[/tex]
[tex]0=(x+9)^2[/tex]
[tex]x+9=0\\x=-9[/tex]
Doing the same thing with the second equation, we get:
[tex]37 = x^2-18x+118[/tex]
[tex]0=x^2-18x+81[/tex]
[tex]0=(x-9)^2[/tex]
[tex]x-9=0\\x=9[/tex]
After all of this, we know our vertex's x-values are either [tex]9[/tex] or [tex]-9[/tex], and that our y-value is [tex]37\\[/tex].
We can conclude that our k-value (y-value of the vertex in vertex form) is [tex]37[/tex], and our h-value (x-value of the vertex in vertex form) is [tex]9[/tex] or [tex]-9[/tex].
Conclusion: [tex]h = -9, 9[/tex]
[tex]k=37[/tex]
Related Questions
¿Cual es la longitud del lado de un cuadrado de ´área 441 cm2 ?
Answers
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.
Find the average value of f(x)=……..
Answers
The average value of the function over the interval is 0
Finding the average value of the functionFrom 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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[tex]x-\frac{1}{2} =\sqrt\frac{1}{4} x[/tex]
Answers
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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If you roll a die, what is the probability of not
rolling a 4? Write your answer as a fraction.
Answers
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
In a college, some courses contribute more towards an overall GPA than other courses. For example, a science class is worth 4 points; mathematics is worth 3 points; history is worth 2 points; and English is worth 3 points. The values of the grade letters are as follows, A= 4, B=3, C=2, D=1, F=0. What is the GPA of a student who made a “C” in Trigonometry, a “B” in American History, an “A” in Botany, and a “B” in Microbiology?
Answers
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.
How to find the valuesTo 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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I need help with this as well please same thing
Answers
The length of the variable are as follows;
x = 27.4 units
y = 12.7 units
How to find the variables in the tangent, secant and chord?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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Y=x-5
x+y=-1
What is the solution to the system of equations
Answers
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
Isabel went to the grocery store. She spent $15.91 on vegetables and $11.22 on fruit. She also bought some bread. If she paid with 3 ten dollar bills and got 45 cents back in change, how much did she spend on bread?
Answers
$15.91+$11.22=$27.13
$30-$0.45=$29.55
$29.55-$27.13=$2.42
You jump 3 1/2 feet. How far do
you jump in inches?
Answers
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
6. Suppose this preference schedule gives the results of an election among three candidates: Abe
(A), Benny (B), and Chloe (C). Which candidate, if any, wins using the plurality method?
number of votes 20 19 5
A|B|C
B CB
1st
2nd
3rd
CAA
O Abe (A)
OBenny (B)
O Chloe (C)
ONo candidate wins using the plurality method.
(1
Answers
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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Please help mee...
Please help make a pie chart from this data,,, It really really really helpful for me...please!!!! I'll give you Brainliest...
Btw I'm from Indonesia
If you answer incorrect,, and just play me I'll block and report you!
Answers
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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100 Points! Algebra question. Sketch the angle. Then find its reference angle. Show your calculations. Photo attached. Thank you!
Answers
Answer:reference angle shoudl be 156 degrees srry if im wrong :)
Step-by-step explanation:
Someone help me please. The net signed area in the above graph can be written as……
Answers
The net signed area in the above graph can be written as
(x² + 10x - 2√2)dx.
How do we know?The net signed area can be found by summing the areas of the three parts:
The three being
A line with slope 2 A Vertical line The area under the Parabolic curveHence 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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Use the law of cosines to find one angle and the law of sines to find a second angle. Then use either rule or other rules from geometry to calculate the third angle. Angles may be calculated in radians or degrees. All sides are 7.5 inches.
Answers
The value of all three angles, A , B and C is 60°
Using the cosine Rule :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]
Using Sine RuleFrom 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]
Using the Sum of Triangle RuleA + 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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Is the data set approximately periodic?
If so, what are its period and amplitude?
Hour
Number of cars
1 2 3
4
5
6
7 8 9 10 11 12
52 76 90 75 91 104 89 105 119 103 121 135
Answers
The data set is approximately periodic with a period of 3 and an amplitude of about 7.5.
How to explain the valueThe 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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csc² 0 - cot²0 - sin² 0 = cos² 0
Answers
Answer:
see below
Step-by-step explanation:
You want to show that csc²(θ) -cot²(θ) -sin²(θ) = cos²(θ).
ProofIt 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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Jack leaves home for school on his bike every day at 6 a.m., travelling at 32 km/h.
One day he forgot his homework, which his mother discovered in the car 15 minutes after he had left.
She immediately left home and chased after Jack, travelling at 52 km/h.
At what time did she catch up to him?
Answers
Let's break down the information given:
- Jack's speed: 32 km/h
- Jack left at 6 a.m.
- Jack's mother's speed: 52 km/h
- Jack's mother discovered the homework 15 minutes after Jack had left.
First, we need to convert the 15 minutes of delay into hours. There are 60 minutes in an hour, so 15 minutes is equal to 15/60 = 0.25 hours.
Now, let's calculate the time it took for Jack's mother to catch up to him:
Distance traveled by Jack in 0.25 hours = Jack's speed * time
Distance traveled by Jack in 0.25 hours = 32 km/h * 0.25 hours = 8 km
Since Jack's mother is traveling at a faster speed than Jack, she will cover this distance faster. To determine the time it takes for her to catch up, we divide the distance by her speed:
Time taken for Jack's mother to cover 8 km = Distance / Speed
Time taken for Jack's mother to cover 8 km = 8 km / 52 km/h ≈ 0.154 hours
Now, we can add this time to the initial delay of 0.25 hours to find out when Jack's mother catches up to him:
Time when Jack's mother catches up to him = 6 a.m. + 0.25 hours + 0.154 hours
To simplify the calculation, we can convert the minutes into hours:
0.25 hours + 0.154 hours = 0.404 hours
Converting back to minutes:
0.404 hours * 60 minutes/hour ≈ 24.24 minutes
Adding this to the initial time of 6 a.m.:
Time when Jack's mother catches up to him ≈ 6:24 a.m.
Therefore, Jack's mother catches up to him at approximately 6:24 a.m.
Find the surface area of a cylinder with a height of 9 ft and diameter of 4
Answers
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
if the measure of boa=44 and the radius of circle o is 4 what is the length plesa HURRY
Answers
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:
75% of what number is 18?
Answers
Answer: So the number is 24.
Step-by-step explanation:
Area and perimeter of a circle with a 13 ft radius
Answers
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!
What is x-3(9+7)x-(-3x)
Answers
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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Joe is working out by riding his bike. He starts by biking at a constant rate. Then he gradually picks up speed until he reaches his peak. He maintains this peak speed for the rest of the workout
Answers
The graph that represents the motion of Joe on his bike is: Graph D
How to Interpret Speed Time Graph?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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A rocket is launched upward with an initial velocity of 1960 m/s. After how many minutes does it fall to the ground? (in meter the formula h=rt-4.9t^2 is used
Answers
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.
what is 37 and 1/4 x 24
Answers
To solve this simply you can do 1/4 x 24 = 6, and then do 37 x 24 = 888. Add the two together to get 894. Can also simply plug 37.25 x 24 into a calculator, but the former solution is easier to do by hand.
Rewrite the following in the form log(c). 2log(5)
Answers
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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Write the polynomial as the product of linear factors and list all the zeros of the function:
f(x) = x^4 - 16
Answers
[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]
figure A is a dilated from point E the center of dilation which figure is a dilation of figure A
Answers
A figure that is a dilation of figure A include the following: B. figure C.
What is a dilation?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.
If triangle has a side 16.5 side 29 and side x What is value of x
Answers
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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A blood bank needs 8 people to help with a blood drive. 19 people have volunteered. Find how many different groups of 8 can be formed from the 19 volunteers.
Answers
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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