Write the equation of each parabola based on the given information. Focus = 3,6Directrix y=8
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To write the equation of a parabola, we are given the following information;
\(\begin{gathered} \text{Focus}=(3,6) \\ \text{Directrix;} \\ y=8 \end{gathered}\)We shall begin by taking any point on the parabola which would be point;
\((x_1,y_1)\)The distance between the focus and this random point can be calculated as follows;
\(d=\sqrt[]{(x_1-3)^2+(y_1-6)^2}\)Similarly, the distance between the directrix and this random point is;
\(|y_1-8|\)Note that the directrix is given as
\(\begin{gathered} y=8 \\ \text{Therefore;} \\ The\text{ two y-coordinates would be;} \\ y_1\text{ and} \\ y=8 \\ \text{The distance therefore is, } \\ y_1-8 \end{gathered}\)This is expressed in absolute value because the distance cannot be a negative.
We now equate both distances and we can begin to simplify;
\(\begin{gathered} \sqrt[]{(x_1-3)^2+(y_1-6)^2}=|y_1-8| \\ \text{Square both sides of the equation to eliminate the radical;} \\ (x_1-3)^2+(y_1-6)^2=(y_1-8)^2 \\ \end{gathered}\)We can now simplify all parenthesis;
\(x^2_1-6x_1+9+y^2_1-12y_1+36=y^2_1-16y_1+64\)We now move all terms to one side and we now have;
\(\begin{gathered} x^2_1-6x_1+9-64+y^2_1-y^2_1-12y_1+16y_1=0 \\ x^2_1-6x_1-55+4y_1=0 \end{gathered}\)Next step, we make y the subject of the formula;
\(\begin{gathered} 4y_1=-x^2_1+6x_1+55 \\ \text{Divide all through by 4;} \\ y_1=-\frac{1}{4}x^2_1+\frac{3}{2}x_1+\frac{55}{4} \end{gathered}\)We can now re-write for (x, y) as follows;
ANSWER:
\(y=-\frac{x^2}{4}+\frac{3x}{2}+\frac{55}{4}\)Related Questions
what additional information is needed to show that abc def by asa
Answers
To prove congruence using SAS Theorem, you must understand that pairs of two angles are congruent as well as the pair of sides that are next to one of the specified angles.
What is triangle?In Euclidean geometry, any three points that are not collinear produce a singular triangle and a singular plane (i.e. a two-dimensional Euclidean space). In other words, every triangle is contained in a plane, and there is only one plane that contains that triangle.
All triangles are contained in a single plane if all geometry is on the Euclidean plane, but in higher-dimensional Euclidean spaces, this is no longer the case.
The definition of the terminology used to classify triangles can be found on the first page of Euclid's Elements, which dates back more than two thousand years. In modern classification, names are either directly transliterated from Euclid's Greek or translated from Latin.
Hence, To prove congruence using S Theorem, you must understand that pairs of two angles are congruent as well as the pair of sides that are next to one of the specified angles.
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The question is in the pic pls help
Answers
Answer:
pink
Step-by-step explanation:
Briannas semimonthly salary is $3,874. What would be her equivalent biweekly salary (in $)? Round answer to two decimal places.
Answers
ANSWER:
$3576
STEP-BY-STEP EXPLANATION:
The biweekly paychecks will be less money, but you will provide the two additional paychecks to make up the difference.
Let's say an employee earns $ 42,000.00 per year. If paid biweekly, their gross salary would be approximately $ 1,615.38 every two weeks ($ 42,000.00 / 26). If they are paid semimonthly, their gross salary would be $ 1,750.00 ($ 42,000.00 / 24).
In this case, would be:
\(\begin{gathered} 3874\cdot\frac{24}{26}=3576 \\ \end{gathered}\)Therefore the biweekly salary would be $3576
a silver dollar is dropped from the top of a building that is 1342 feet tall. use the position function below for free-falling objects. s(t)
Answers
A silver dollar falls from 1342 feet. We use position equation to find its position, velocity, average velocity, and impact velocity. Time to reach ground level is 9.808 seconds. Impact velocity is -158.4 ft/s.
(a) The position function for the coin is
\(s(t) = -16t^2 + v_ot + s_o\)
where \(s_o\) is the initial height of the coin and \(v_o\) is the initial velocity. Given that the initial height is 1342 feet, \(s_o = 1342\)
And since the coin is dropped from rest, the initial velocity is \(v_o = 0\) Hence, the position function for the coin is:
\(s(t) = -16t^2 + 1342\)
The velocity function for the coin is given by the derivative of the position function:
\(v(t) = -32t + 0 = -32t\)
(b) The average velocity over the interval [1,2] can be calculated using the formula:
average velocity \(= (v(2) - v(1)) / (2-1)\)
\(= (-32 * 2 - 32 * 1) / (2 - 1)\)
\(= -64\)
(c) The instantaneous velocity at t = 1 second is given by
\(v(1) = -32 * 1 = -3\)
The instantaneous velocity at t = 2 seconds is
\(v(2) = -32 * 2 = -64\)
(d) To find the time required for the coin to reach the ground level, we need to find the value of t when s(t) = 0. Solving for t, we get:
\(0 = -16t^2 + 1342\\16t^2 = 1342\\t^2 = 83.875\\t = 9.1\)(rounded to three decimal places)
Hence, the time required for the coin to reach the ground level is 9.1 seconds.
(e) The velocity of the coin at impact can be found using the velocity function, v(t), at the time t when the coin reaches the ground level:
\(v(9.1) = -32 * 9.1 = -281.2\) (rounded to three decimal places)
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The complete question is :
A silver dollar is dropped from the top of a building that is 1342 feet tall. Use the position function below for free-falling objects.
\(s(t) = -16t^2 + v_ot + s_o\)
(a) Determine the position and velocity functions for the coin.
(b) Determine the average velocity on the interval [1, 2].
(c) Find the instantaneous velocities when t = 1 second and t = 2 seconds.(d) Find the time required for the coin to reach the ground level. (Round your answer to three decimal places.)
(e) Find the velocity of the coin at impact. (Round your answer to three decimal places.)
What is a good practice to remember when adding transitions to a presentation?
Answers
A good practice to remember when adding transitions to a presentation is to ensure that they are purposeful, consistent, and enhance the overall flow of the presentation.
Purposeful: Use transitions to guide the audience through your key points and ideas, making sure they complement the content and contribute to the overall message.
Consistent: Maintain a consistent style of transitions throughout your presentation to maintain a cohesive look and feel. Avoid using too many different types of transitions, as this may be distracting.
Enhance flow: Transitions should help create a smooth flow between slides and ideas, making it easy for the audience to follow your presentation. Avoid using abrupt or overly flashy transitions that may interrupt the natural progression of your content.
finally, Test your presentation with the transitions to make sure they enhance the overall flow and comprehension of your message.
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Susie has 26 baskets of apples. Each basket can hold 12 apples. Can Susie fit all her apples in her baskets?
Answers
Answer: Yes, Susie can fit all her apples in her baskets.
Step-by-step explanation: If she has 26 baskets filled of apples and can hold 12 apples each, then she can fill 2 baskets with apples and have a remainder of 2 apples left.
What is the area of the square that measures 3.1 m on each side
Answers
The area of the square with a side length of 3.1 meters is 9.61 square meters.
To find the area of a square, we need to multiply the length of one side by itself. In this case, the square has a side length of 3.1 m.
Area of a square = side length × side length
Substituting the given side length into the formula:
Area = 3.1 m × 3.1 m
To perform the calculation:
Area = 9.61 m²
It's worth noting that when calculating the area, we are working with squared units. In this case, the side length is in meters, so the area is expressed in square meters (m²). The area represents the amount of space enclosed within the square.
Remember, to find the area of any square, you simply need to multiply the length of one side by itself.
The area of the square with a side length of 3.1 meters is 9.61 square meters.
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Select the correct similarity statement.
ASTR-ATQR
ASTR - ARST
O ASTR – ASQR
O ASTRARTO
Answers
Answer:
∆STR ~ ∆RTQ
Step-by-step explanation:
For two fugures to be considered similar, it means the corresponding sides are proportional, and as such, the ratio of their corresponding sides are equal.
However, the corresponding angles of two similar figures are the same and equal.
Taking a look at the figure of the triangle given, ∆STR is a right angle triangle, and it is similar to ∆RTQ as the angle formed at <T in ∆RTQ = 90°.
<T in ∆STR = <T in ∆RTQ.
Therefore, the correct similarity statement is ∆STR ~ ∆RTQ.
The last option is correct.
What is 7/11 x 1/4 in simplest form
Answers
Answer:
\(\frac{7}{11} * \frac{1}{4}\) = \(\frac{7}{44}\).
Cannot reduce it. Then it will make the numerator a decimal
Which cannot happen.
\(\frac{7}{44}\) is the answer then
Answer:
7/11 x 1/4 = 0.015
I hoped it helped you.
PLEASE HELP ILL GIVE BRAINLIEST PLEASE!!!!!
Answers
Step-by-step explanation:
OKAY, SO FIRST DIVIDE 43 BASE BY 36 AND IT WILL BE THE ANSWER OF THE ANGLE AND IF DAT TO HARD I THINK THE ANGLE IS 36 D
Which pair shows equivalent expressions?
Help quick please!
Answers
Answer:
i think A
Step-by-step explanation:
SAT verbal scores are normally distributed with a mean of 430 and a standard deviation of 120 (based on the data from the College Board ATP). If a sample of 15 students is selected randomly, find the probability that the sample mean is above 500. Does the central limit theorem apply for this problem?
Answers
Answer:
The value is \(P(X > 500 ) = 0.011942\)
Step-by-step explanation:
From the question we are told that
The mean is \(\mu = 430\)
The standard deviation is \(\sigma = 120\)
The sample size is n = 15
Generally the probability that the sample mean is above 500
Gnerally the standard error of mean is mathematically represented as
\(s = \frac{\sigma }{ \sqrt{n} }\)
=> \(s = \frac{ 120 }{ \sqrt{15} }\)
=> \(s = 30.984\)
Generally the probability that the sample mean is above 500
\(P(X > 500 ) = P( \frac{X - \mu }{\sigma_x} > \frac{500 - 430 }{ 30.984 } )\)
\(\frac{X -\mu}{\sigma } = Z (The \ standardized \ value\ of \ X )\)
\(P(X > 500 ) = P( Z > 2.259 )\)
=> \(P(X > 500 ) = P( Z > 2.259 )\)
From the z table the area under the normal curve to the right corresponding to 2.259 is
\(P( Z > 2.259 ) = 0.011942\)
=> \(P(X > 500 ) = 0.011942\)
Can someone answer this question?
Answers
The graph of the polynomial function y = f(x) in the xy plane could be the first graph.
Given a polynomial function f.
Range of the polynomial function is the set of all the real numbers less than or equal to 4.
So y values are y ≤ 4
So the vertex of the function will be at y = 4 and other value are less than 4.
So parabola is downwards.
Two options are there with the parabola folded downwards.
Now the zeroes of f are at -3 and 1.
Zeroes of f are the values of x where the function touches the X axis.
Hence the correct graph is first one.
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150 copies will cost $15.00. How many copies can be made for $6.00?
Answers
Answer:
60 copies
Step-by-step explanation:
$15/150 = 0.1 each copy costs 1 cent
$6/$0.1 = 60 copies
Answer:
60 copies
Step-by-step explanation:
After using Unitary Method, We find that one copy costs 0.1 dollar. So divide 6.00 dollars by 0.1 and we find 60
For checking, we can multiply 60 by 0.1 and we get the same answer
Find the midpoint of the segment with the following endpoints.
(-4,-9) and (4, -1)
Answers
Answer:
\((0,-5)\)
General Formulas and Concepts:
Pre-Alg
Order of Operations: BPEMDASAlg I
Midpoint Formula: \((\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})\)Step-by-step explanation:
Step 1: Define
Point (-4, -9)
Point (4, -1)
Step 2: Find midpoint
Substitute: \((\frac{-4+4}{2},\frac{-9-1}{2})\)Add/Subtract: \((\frac{0}{2},\frac{-10}{2})\)Divide: \((0,-5)\)Use the figure to find the measures of the
numbered angles.
1/2
a
107°
b
Answers
Answer:
∠1 = 107
∠2 = 73
Step-by-step explanation:
Lily received 50 postcards. 16% of them were from Thailand. After he received ostcards from Thailand, the percentage of Thailand postcard increased to 30%. How many Thailand postcards did he receive?
Answers
Answer:
Step-by-step explanation:
Final answer: Lily received 10 postcards from Thailand.
Explanation: Number of postcards=50
Percentage of postcards from thailand= 16
Number of postcards from Thailand= 16/100*50= 8
Now, he received some postcards from Thailand. Let the number of postcards received from Thailand be x. Therefore,
Number of postcards=50+x
Number of postcards from Thailand= 8+x
We know that the percentage of postcards from Thailand now is 30.
Therefore,
30=(8+x/50+x)*100
0.3(50+x)=8+x
15+0.3x=8+x
0.7x=7
x=10
Therefore, he received 10 postcards from Thailand.
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what is inequalities
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Inequalities are used in various branches of mathematics, as well as in real-world applications such as economics, physics, and social sciences, to describe relationships, make comparisons, and analyze data.
Inequalities are mathematical statements that describe a relationship between two values or expressions, indicating that one is greater than, less than, or not equal to the other. Inequalities are used to compare quantities and express their relative sizes or order.
The most common symbols used in inequalities are:
">" (greater than): indicates that the value on the left side is larger than the value on the right side.
"<" (less than): indicates that the value on the left side is smaller than the value on the right side.
"≥" (greater than or equal to): indicates that the value on the left side is greater than or equal to the value on the right side.
"≤" (less than or equal to): indicates that the value on the left side is less than or equal to the value on the right side.
"≠" (not equal to): indicates that the values on both sides are not equal.
Inequalities can be represented using variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. Solutions to inequalities are often expressed as intervals or sets of values that satisfy the given inequality.
Inequalities are used in various branches of mathematics, as well as in real-world applications such as economics, physics, and social sciences, to describe relationships, make comparisons, and analyze data.
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what is the answer to (f+g)(x)
Answers
Answer:
fx + gx
Step-by-step explanation:
\((f + g)(x) = (f + g)x\)
multiply every terms in brackets with x
\(\boxed{\green{ = fx + gx}}\)
What is the distance between A(-8, 4) and B(4, -1)?
Answers
Answer:
10.908
Step-by-step explanation:
Match the subtraction expressions to their correct answers. -12.48-(-2.99)-5.62 -353.92-(-283.56)-131.29 837–108– (-99) -15.11 -201.65 74 -199
Answers
We have the following:
1.
\(-6\frac{4}{9}-3\frac{2}{9}-8\frac{2}{9}=-6\frac{2\cdot2}{9}-3\frac{2}{9}-8\frac{2}{9}=-12\frac{2}{9}-3\frac{2}{9}-8\frac{2}{9}=-23\frac{2}{9}=-17\frac{8}{9}\)2.
\(-12.48-(-2.99)-5.62=-12.48+2.99-5.62=-15.11\)3.
\(-19\frac{2}{9}-4\frac{1}{9}-(-3\frac{4}{9})=-19\frac{2}{9}-\frac{4}{9}+3\frac{4}{9}=-19\frac{8}{9}\)4.
\(-353.92-(-283.56)-131.29=-353.92+283.56-131.29=-201.65\)5.
\(83\frac{1}{5}-108\frac{2}{5}-(-99\frac{1}{5})=83\frac{1}{5}-108\frac{2}{5}+99\frac{1}{5}=74\)
Can y’all tell me which one is a function and which ones is not ?
Answers
the ones with straight lines are functions the ones that are curved is not a function
Answer:
Ones that have 2 values of y for a single value of x
(vertical line, sideways v shape are not functions)
Step-by-step explanation:
In a function, each input (x) can have only one output (y)
There cannot be two ys for one x
the minimum sustained wind speed of a Category 1 hurricane is 74 miles per hour. The maximum sustained wind speed is 95 miles per hour. Write an absolute value equation that represents the minimum and maximum speeds. Let v represent the wind speed
Answers
Answer:
you must read good luck
Answer:
|v – 84.5| = 10.5
Step-by-step explanation:
|v – average| = range
|v – 84.5| = 10.5
Please help. I’ll mark you as brainliest if correct!!!!!
Answers
\(x^2+14x+40=0\\x^2+14x+40+9-9=0\\x^2+14x+49=9\\(x+7)^2=9\\\\D=7\\E=9\)
Answer:
x^2+14x+40=0\\x^2+14x+40+9-9=0\\x^2+14x+49=9\\(x+7)^2=9\\\\D=7\\E=9
Step-by-step explanation:
Solve Y/5.6 = 12 for y
Answers
Y=12*5.6
Y=67.2 is the correct answer
Answer:
y = 67.19
Step-by-step explanation:
y/5.6 = 12
=> y = 12(5.6)
=> y = 67.19
in a classroom, there are 20 boys to 25 girls. Write the ratio of boys to girls as a simplified fraction.
Answers
Answer:
Pretty sure its 4/5
Step-by-step explanation:
Ratio is 20:25 simply it by dividing 5 its 4:5 then as a fraction it's 4/5
The hanger image below represents a balanced equation.
Answers
Answer:
\( \frac{1}{5} + z = \frac{3}{5} \)
Answer:
1/5+z=3/5
Step-by-step explanation:
i'm a little bit confused about this question.
Answers
Answer:
4
Step-by-step explanation:
1 3 4 . 0
thousand hundred ones
Anyone can help me ?? Pleaseeee
Answers
C
that's the answer
enjoy
\(\boxed{\underline{\bf \: ANSWER}}\)⇨
\( \sf \frac{x}{27} = \frac{4}{9} \\ \)
Use the cross-multiplication method. Then,..
\( \sf \frac{x}{27} = \frac{4}{9} \\ \sf 4 \times 27 = 9x \\ \sf 108 = 9x \\ \sf 108 \div 9 = x \\ \boxed{ \bf \: 12 = x}\)
So, the correct value of x is 12 (option C.)
_____
Hope it helps.
Help me out please???
Answers
9514 1404 393
Answer:
x = 5
Step-by-step explanation:
DE being a midsegment means that D is a midpoint. Then BD = DA, or x = 5.