Someone, please help me! I will give Brainliest!
Identify the key features of the parabola, 8(y + 4) = (x + 1)2:
Axis of Symmetry:
Vertex:
Focus:
Directrix:
Answers
Answer:
Step-by-step explanation:
8(y+4)=2(x+1)
divide by 8 y+4=1/4x+1/4 subtract 4 y=1/4x - 3 3/4 multiply by 4 y=1/4(x-15)
Answers:
Equation in standard form: [tex]y = \frac{1}{8}(x+1)^{2} -4[/tex]
Axis of Symmetry: x = -1
Vertex: (-1, -4)
Focus: (-1, -2)
Directrix: y = -6
Step-by-step explanation:
First, let's clean up some of the mess with the equation that we have been given in this question and put it in standard form so that we can find the features we've been asked to give.
Our initial equation is: [tex]8(y+4)=(x+1)^{2}[/tex]
In order to put our equation in standard form, we must isolate y, so that it is in terms of y.
First, we need to divide both sides by 8. When we do this, we get [tex]y+4=\frac{(x+1)^{2} }{8}[/tex] or [tex]y+4=\frac{1}{8}(x+1)^{2}[/tex]. Then we need to subtract 4 from both sides to get: [tex]y = \frac{1}{8}(x+1)^{2} -4[/tex].
Now, we can start to find the features of the parabola. Remember, the standard form of equations involving parabolas is [tex]y=a(x-h)+k[/tex] where [tex]a =\frac{1}{4p}[/tex].
The axis of symmetry is at [tex]x=h[/tex], in this case [tex]h=-1[/tex] so the axis of symmetry is [tex]x=-1[/tex].
The vertex is located at [tex](h, k)[/tex]. As we previously stated [tex]h=-1[/tex], but additionally, [tex]k=-4[/tex] making the vertex located at [tex](-1,-4)[/tex].
The focus is located at [tex](h, k+p)[/tex] and the directrix is located at [tex]y=k-p[/tex]. For this, we need to find p which we can find with the equation [tex]a =\frac{1}{4p}[/tex]. Substituting the value of “a” into the equation, we get [tex]\frac{1}{8} = \frac{1}{4p}[/tex]. We can cross-multiply to get the equation [tex]4p=8[/tex]. Dividing by 4 on both sides, we get [tex]p=2[/tex]. Now we can find the focus and directrix.
The focus is located at [tex](-1, [-4+2])[/tex] or [tex](-1,-2)[/tex] and the directrix is represented by the equation [tex]y=(-4-2)[/tex] or [tex]y=-6[/tex].
Hopefully this answered your question this time, and with this, I hope you are able to solve it without help the next time
Related Questions
Sharon Fox decided to buy a home in Marblehead, Massachusetts, for $282,000. Her bank requires a 20% down payment. Sue Willis, an attorney, has notified Sharon that besides the 20% down payment there will be the following additional costs:
Recording of the deed $ 37.00
A credit and appraisal report 162.00
Preparation of appropriate documents 55.00
In addition, there will be a transfer tax of 2% of the purchase price and a loan origination fee of 2% of the mortgage amount. Assume a 30-year mortgage at a rate of 10.5%.
a. What is the initial amount of cash Sharon will need? (Do not round intermediate calculations. Round your answer to the nearest cent.)
b. What is her monthly payment? (Do not round intermediate calculations. Round your answer to the nearest cent.)
c. What is the total cost of interest over the life of the mortgage? (Do not round intermediate calculations. Round your answer to the nearest cent.)
Answers
The initial amount of cash that Sharon will need in this scenario will be $67821.20.
How to calculate the payment?The initial amount of cash will be:
= ($282000 × 20%) + ($282000 × 2%) + ($276360 × 2%) + ($162) + ($37) + $55
= $56400 + $5640 + $5527.20 + $162 + $37 + $55
= $67821.20
Therefore, the the initial amount of cash Sharon will need is $67821.20.
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Solve the system of equations 6+4y=12 2x+3y=6
Answers
Answer:
x = 0.75 :: y = 1.5
Step-by-step explanation:
6 + 4y = 12
4y = 12 - 6
4y = 6
y = 1.5
_________
2x + 3(1.5) = 6
2x + 4.5 = 6
2x = 6 - 4.5
2x = 1.5
x = 0.75
Rewrite The following linear equations in slope intercept form y+2=4(x-3)
Answers
Answer:
the answer is y=4x-14
Step-by-step explanation:
I know that writing slope intercept form is extremely easy as you follow the y=mx+b formula. All that was really required was to simplify the equation and isolate the X and Y on separate sides of the equal. I hope this helps
At a factory, Joe assembles 12 parts each minute. He
has assembled 156 parts when Sheila starts on the line,
assembling at a pace of 15 parts per minute. If their
assembly rates continue, will Sheila ever catch up to Joe?
Explain and show all work.
Answers
Answer:
yes, after 52 minutes
Step-by-step explanation:
If t represents the time in minutes each person is working after Sheila arrives, then the number of parts produced is ...
Eric: 156 +12t
Sheila: 15t
These values are equal when ...
156t +12t = 15t . . . . . Eric's part count is equal to Sheila's part count
156 = 3t . . . . subtract 12t
52 = t . . . . divide by 3
Sheila will catch up to Joe after 52 minutes.
The Great Pyramid of Giza in Egypt is a square pyramid. The height is approximately 450 feet, and the side length of the base is approximately 750 feet. What is the lateral surface area of the pyramid rounded to the nearest thousandth?
A. 563,000 square feet
B. 1,312,000 square feet
C. 1,441,000 square feet
D. 879,000 square feet
Answers
879,000 square feet is the lateral surface area of the pyramid
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
The lateral surface area of a square pyramid can be calculated using the formula L = (1/2)Pl
where P is the perimeter of the base and l is the slant height of the pyramid.
Since the base of the pyramid is a square, the perimeter is 4 times the length of one side, or 4 × 750 = 3000 feet.
To find the slant height, we can use the Pythagorean theorem with one leg equal to half the length of the base (375 feet) and the other leg equal to the height (450 feet):
l =√375² + (450)²
= 583.095 feet
Therefore, the lateral surface area is:
L = (1/2) × 3000 × 583.095
= 879,000 square feet
Hence,879,000 square feet is the lateral surface area of the pyramid
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Please help!!!!!!!!!!!!!
Answers
Answer:
G
Step-by-step explanation:
when x = -1 the two equations equal the same thing -2
so they both go thru the point (-1,-2)
Which of the following best describes a problem that occurs when the majority criterion is observed?
A) The majority criterion cannot be upheld with the Condorcet method.
B) The majority criterion only considers the first-place votes.
C) The majority criterion must be used for first place, second place, third place, and so on to be valid.
D) The majority criterion never applies when the plurality method is used.
Answers
Answer:
i belive its A if you get it wrong im sorrry
Step-by-step explanation:
Option C is the statement that best describes a problem that occurs when the majority criterion is observed. This is because the majority criterion is a single-winner system.
Majority criterion:This criterion states that "if one candidate is ranked first by a majority, then that candidate must win".This method complies with the other criteria like the Condorcet method and Plurality method etc.This is applied in such a situation where one person has to be selected.Given information:It is given that all the options except option C are true about the majority criterion.
Option C - "The majority criterion must be used for first place, second place, third place, and so on to be valid" is not correct because this criterion is used only for choosing the first place.
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i need help 9th grade math
Answers
Answer:
$ 6875.05
Step-by-step explanation:
Check out the attached photo
You graph the number of times you go to the movies as one variable and the total amount of money you spend on movie tickets as the other variable. What type of slope would you expect the trend line to have?
Answers
Using linear function concepts, it is found that the trend line would be expected to have a positive slope.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.In this problem, the more times you go to the movies, the more money you are expected to spend, hence the variables are direct proportional and the trend line would be expected to have a positive slope.
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He notices a lumberjack cutting one down what is the probability that the lumberjack is cutting down a mature tree given it is a pine?
Answers
Answer:
The second one is correct.
Step-by-step explanation: if you add together all the numbers you get 563 so now if you divide 166 by 563 you get 0.2948
The polynomial equation x superscript 6 baseline minus 16 x squared = 4 x superscript 4 baseline minus 64 has complex roots plus-or-minus 2 i. what are the other roots? use a graphing calculator and a system of equations. –64, 0 –2, 2 –1, 1 0, 64
Answers
The other roots of the given polynomial equation are 2 and -2.
Given polynomial equation is:
[tex]x^{6} -16x^{2} =4x^{4} -64[/tex].....(1)
What is a polynomial?A polynomial is the sum of monomials of the form axⁿ where n is a whole number.
Rewriting the (1) as:
[tex]x^{6} -4x^{4} -16x^{2} +64=0[/tex]
[tex]x^{4} (x^{2} -4)-16(x^{2} -4)=0[/tex]
[tex](x^{2} -4)(x^{4} -16)=0[/tex]
[tex]x^{2} -4=0[/tex]
[tex]x^{2} =4[/tex]
[tex]x=2[/tex]
[tex]x=-2[/tex]
So, the other roots are 2 and -2.
Hence, the other roots of the given polynomial equation are 2 and -2.
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Answer:
its b
Step-by-step explanation:
took it
What is the completely factored form of 3x5 – 7x4 6x2 – 14x? (x superscript 4 baseline 2 x) (3 x minus 7) x superscript 4 baseline (3 x minus 7) (2 x minus 1) x (x cubed 2) (3 x minus 7) x (3 x superscript 4 baseline minus 7 x cubed 6 x minus 14)
Answers
A polynomial is an expression. The completely factored form of the polynomial 3x⁵-7x⁴+6x²-14x is (x⁴+2x)(3x-7).
What are polynomial?Polynomial is an expression that consists of indeterminates(variable) and coefficient, it involves mathematical operations such as addition, subtraction, multiplication, etc, and non-negative integer exponentials.
The completely factored form of the polynomial can be done in the following manner,
[tex]3x^5-7x^4+6x^2-14x\\\\= x^4(3x-7)+2x(3x-7)\\\\=(x^4+2x)(3x-7)[/tex]
Hence, the completely factored form of the polynomial 3x⁵-7x⁴+6x²-14x is (x⁴+2x)(3x-7).
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Answer:
A on edge
Step-by-step explanation:
I passed the test!
Which equation is true?
A) 3 x (5 + 1) = 3+ (5 x 1)
B) 5 x (2+8)= 10 +8
C) 8 x (2+9)= (8 x 2) + (8 x 9)
D) 4+ (2 +9)= (4 + 2) + (4 +9)
Answers
Answer:
C. 8 x (2 + 9) = (8 x 2) + (8 x 9)
Step-by-step explanation:
Let's solve to see!
Solve using PEMDAS:
Parenthesis
Exponents
Mulitplication/Division (depending on which one comes first - starting from left to right)
Addition/Subtraction (depending on which one comes first - starting from left to right)
A)
3 x (5 + 1) = 3 + (5 x 1) <== parenthesis first
3(6) = 3 + 5 <== multiply and add
18 = 8
False
B)
5 x (2 + 8) = 10 + 8 <== parenthesis first
5(10) = 10 + 8 <== multiply and add
50 = 18
False
C)
8 x (2 + 9) = (8 x 2) + (8 x 9) <== parenthesis first
8(11) = 16 + 72 <== multiply and add
88 = 88
True
D)
4 + (2 + 9) = (4 + 2) + (4 + 9) <== parenthesis first
4 + 11 = 6 + 13 <== add
15 = 19
False
Therefore, the correct answer is C.
Hope this helps!
685 x8483 - 3846 +483
Answers
Answer:
Step-by-step explanation:
i have no idea
(30 points and Brainliest)
If the value of a in the quadratic function f(x) = ax^2 + bx + c is 4, the function will_____.
A)open down and have a minimum
B)open up and have a minimum
C)open down and have a maximum
D)open up and have a maximum
Answers
Answer:
I honestly believe it's B I'm sorry if it's wrong
A school collects money for the local shelter. If the students collect $275 in the first month, $210 in the second month, and $136 in the third month, how much do they collect altogether?
Answers
Answer:
$621
Step-by-step explanation:
To find the total amount they collected, sum the amounts collected in each month.
[tex]\begin{tabular}{c l} & 275\\+ & 210\\+ & 136\\\cline{1-2} & 621\\\cline{1-2} & ^1^1\\\end{tabular}[/tex]
if A and B are two distinct points on the plane then distance between them is
A)zero
B)1
C)negative
D)positive
Answers
By definition, the distance between two points is always positive, so the correct option is D.
How to get the distance between two points?
Let's say that our plane has rectangular coordinates, so it would be something like a xy-plane.
Each point has 2 coordinates, so we can write:
A = (x₁, y₁)
B = (x₂, y₂)
The distance between the points is given by:
[tex]D = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
As you can see, the distance is defined as positive (indifferent of the coordinates of the points).
So the correct option is D, the distance is always positive.
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If you borrow $1425 for 9 years at an interest rate of 4%, how much interest will you pay?
Answers
Answer:
You would pay $242 in total interest over the life of this loan.
Step-by-step explanation:
In ________ simulation, one or more of the independent variables follows certain probability distributions, which can be either discrete distributions or continuous distributions.
Answers
In probabilistic simulation, one or more of the independent variables follows certain probability distributions.
What is simulation?This is also known as Probabilistic Analysis. It is an analysis that tells or gives room for network assessment that is done using probabilistic input data.
Note that it is vital when there is input parameters known to be random and as such, one or more of its independent variables follows a specific probability distributions.
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How do I do this fraction with Distributive Property???
Answers
Answer:
[tex]3a - 1[/tex]
Explanation:
[tex] \frac{9a - 3}{3} [/tex]
Factor out 3
[tex] \frac{3(3a - 1)}{3} [/tex]
Cancel out the common factor 3
[tex]3a - 1[/tex]
The product of two numbers is 26 and one of the numbers is one larger than six times the other number. find the numbers.
Answers
The numbers that the product is 26 and one of the numbers is one larger than six times the other number are 2 and 13.
How to form equation and solve for the variable?The product of two numbers is 26.
let the two numbers be x and y.
Therefore,
xy = 26
One of the numbers is one larger than six times the other number. Therefore,
x = 1 + 6y
Hence,
xy = 26
(1 + 6y)y = 26
y + 6y² = 26
6y² + y - 26 = 0
using quadratic formula,
[tex]\frac{-b + \sqrt{b^{2} -4ac } }{2a}[/tex]
where
a = 6
b = 1
c = - 26
Therefore,
y = 2 or - 13 / 6
We can only use the positive value.
Hence,
2x = 26
x = 26 / 2
x = 13
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question says : are these triangles congruent
Answers
Answer:
No.
Step-by-step explanation:
The triangles aren't congruent because the value of C is unsaid.
Someone help me please!
*not a test or quiz*
Answers
whenever you see this kind of question you don't need to start doing all the expressions, but look at the first and last numbers of the answer, the ones that cannot be changed (have no x or y or have those that cannot be changed in this expression):
the answer can't be a or c because in the given expression we can find 3x²y² and that's the only number where we can find x²y², so it cannot be changed. (you'll have 3x²y² in the answer)
now let's look at the last digit, that doesn't have a x or a y:
in b and d we can find 2 different results so this can determine which answer is correct:
let's look back at the given expression: -7+4= -3
so the answer is b
Which irrational number can be multiplied by –StartRoot 41 EndRoot to get a product that equals 1?
a) StartRoot StartFraction 1 Over 41 EndFraction EndRoot Negative
b) StartRoot 41 EndRoot Negative StartRoot
c) StartFraction 1 Over 41 EndFraction EndRoot
d) StartRoot 41 EndRoot
Answers
Answer:
D. 41
Step-by-step explanation:
Answer:
The answer is C
Step-by-step explanation:
First, convert - 1/41 to a decimal - 1/41 as a decimal which is just 1 divided by 41 which = 0.024390243902439 now multiply that by -41 and you get your answer.
Int the number 78.9 what digit is the ones place
Answers
Below is a rhombus with an equilateral triangle. Find the measure of a.
Answers
Answer:
a = 80°
Step-by-step explanation:
In order to solve this figure, we need to find a useful relationship between the various angles. We can use the straight angle at the upper left vertex of the equilateral triangle.
__
The sum of angles there is ...
a + 60° +(a/2) = 180°
3/2a = 120° . . . . . . . . . . subtract 60°, collect terms
a = 80° . . . . . . . . multiply by 2/3
_____
Additional comment
All triangles are isosceles, because they all have 2 (or more) sides the same length. That means the base angles are half the supplement of the a.pex angle. Of course, adjacent vertices of a rhombus have supplementary angles.
352, 345,338,...
352,345,338,...
\text{Find the 43rd term.}
Find the 43rd term.
Answers
Answer:
317
Step-by-step explanation:
The numbers change by -7 each step in the sequence. Let n be the position in the sequence, starting with n=0 for the first point. The value of a number at the nth position is (352 - 7*n).
The 43th position has the value 317.
n # Dif 352 -7n
0 352 352
1 345 -7 345
2 338 -7 338
3 331 -7 331
4 324 -7 324
43 317 -7 51Eric has a project. He will make a model of a pyramid out of cardboard. How much cardboard will he need if the base measures 20 cm and the height 18 cm?
Answers
Answer:
the area is equal to 180cm
Step-by-step explanation:
Area = (heigh x base) / 2
Area = (18 x 20) / 2 = 180
Kevin works 2 hours more than Emily each time they work together. Using this information, complete the table
Answers
Answer:
we cannot see the table, did u attach any photo before asking the question?
How do we find the difference between principal and interest?
Answers
Answer:
Principal is the money that you originally agreed to pay back. Interest is the cost of borrowing the principal.
Step-by-step explanation:
First, calculate the interest portion of the payment by multiplying the mortgage balance by the annual interest rate. Then divide the result by 12, for the number of months in the year: