The equation of the parabola is (x - 3)² = 20(y - k)
Given data ,
To write the equation of a parabola given its directrix and focus, we can use the standard form for a parabola with a vertical axis of symmetry:
(x - h)² = 4p(y - k)
where (h, k) represents the vertex of the parabola, and the distance between the vertex and the focus is equal to the distance between the vertex and the directrix.
In this case, the directrix is x = -2 and the focus is located at (8, -8). Since the directrix is a vertical line, the parabola has a horizontal axis of symmetry.
And , the vertex lies on the axis of symmetry, which is the line equidistant between the directrix and the focus. In this case, the axis of symmetry is the vertical line x = (8 + (-2)) / 2 = 3.
So, the vertex of the parabola is (3, k), where k is yet to be determined
Next, we need to find the value of p, which represents the distance between the vertex and the focus. Since the focus is at (8, -8), and the vertex is at (3, k), the distance between them is given by
p = 8 - 3 = 5
Now, substituting the values into the standard form equation, we have:
(x - 3)² = 4(5)(y - k)
Simplifying further:
(x - 3)² = 20(y - k)
Hence , the equation of the parabola is (x - 3)^2 = 20(y - k), where k is the y-coordinate of the vertex
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csc² 0 - cot²0 - sin² 0 = cos² 0
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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Someone help me please. The net signed area in the above graph can be written as……
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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if the measure of boa=44 and the radius of circle o is 4 what is the length plesa HURRY
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:
Find the average value of f(x)=……..
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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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
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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[tex]x-\frac{1}{2} =\sqrt\frac{1}{4} x[/tex]
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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what is 37 and 1/4 x 24
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?
Area and perimeter of a circle with a 13 ft radius
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!
figure A is a dilated from point E the center of dilation which figure is a dilation of figure A
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.
Y=x-5
x+y=-1
What is the solution to the system of equations
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
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
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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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.
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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I need help with this as well please same thing
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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75% of what number is 18?
Answer: So the number is 24.
Step-by-step explanation:
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
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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If you roll a die, what is the probability of not
rolling a 4? Write your answer as a fraction.
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
Rewrite the following in the form log(c). 2log(5)
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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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!
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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Write the polynomial as the product of linear factors and list all the zeros of the function:
f(x) = x^4 - 16
[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]
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?
If triangle has a side 16.5 side 29 and side x What is value of x
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.
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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100 Points! Algebra question. Sketch the angle. Then find its reference angle. Show your calculations. Photo attached. Thank you!
Answer:reference angle shoudl be 156 degrees srry if im wrong :)
Step-by-step explanation:
Find the surface area of a cylinder with a height of 9 ft and diameter of 4
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
What is x-3(9+7)x-(-3x)
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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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
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.
You jump 3 1/2 feet. How far do
you jump in inches?
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
¿Cual es la longitud del lado de un cuadrado de ´área 441 cm2 ?
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.
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?
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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