Find the standard form of the parabola
with vertex: (- 2,5) and directrix: x = 3.
Answers
Check the picture below, so the parabola looks more or less like so, the "p" distance is negative, because the horizontal parabola is opening to the left-hand-side, so
[tex]\textit{horizontal parabola vertex form with focus point distance} \\\\ 4p(x- h)=(y- k)^2 \qquad \begin{cases} \stackrel{vertex}{(h,k)}\qquad \stackrel{focus~point}{(h+p,k)}\qquad \stackrel{directrix}{x=h-p}\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ \stackrel{"p"~is~negative}{op ens~\supset}\qquad \stackrel{"p"~is~positive}{op ens~\subset} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\begin{cases} h=-2\\ k=5\\ p=-5 \end{cases}\implies 4(-5)( ~~ x-(-2) ~~ )=(y-5)^2 \implies -20(x+2)=(y-5)^2 \\\\\\ x+2=-\cfrac{1}{20}(y-5)^2\implies {\Large \begin{array}{llll} x=-\cfrac{1}{20}(y-5)^2-2 \end{array}}[/tex]
Related Questions
Suppose Tom borrows $4000 at an interest rate of 3% compounded each year.
Assume that no payments are made on the loan.
Follow the instructions below. Do not do any rounding.
(a) Find the amount owed at the end of 1 year.
(b) Find the amount owed at the end of 2 years.
Answers
The amount owed at the end of 1 year is $4120 and by the end of 2 years, $4243.60 when Tom borrows $4000 at an interest rate of 3% compounded each year.
What is compound interest?The interest you earn on interest is known as compound interest. Simple math can be used to demonstrate this: if you have $100 and it earns 5% interest annually, you will have $105 at the end of the first year. You will end up with $110.25 at the end of the second year. In order to calculate compound interest, multiply the principal of the original loan by the annual interest rate multiplied by the number of compound periods minus one.
Here,
principle amount=$4000
rate of interest=3%
For first year,
A=P(1+r/n)^(nt)
A=4000(1+3/12)^12*1
A=$4,120.00
For first year,
A=P(1+r/n)^(nt)
A=4120(1+3/12)^12*1
A=$4,243.60
When Tom borrows $4000 at an interest rate of 3% compounded annually, the total amount due at the end of one year is $4120, and at the end of two years, it is $4243.60.
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4. Can the output of f(x) = 5 ever be a negative number? Why
a
or why not?
Answers
There is not any chance of getting negative number in answer.
What is Function?In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.
Given:
f(x) = 5
Here, f(x) = 5 shows that whatever is the value of x the result value will be 5.
As, there is no variable x in the defined function and only having a constant 5 which is positive in nature.
So, whatever be the value of x is we will get 5 only.
Thus, there is not any chance of getting negative number in answer.
For example, f(1)= 5, f(3)= 5, f(-5)= 5
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What is the absolute value of -330?
Answers
Answer:
Why is | 330 | the absolute value of the number 330?
The absolute value of a number is how far away the number is from zero. The absolute value is ALWAYS positive.
What is the absolute value of -330?
The negative version of the number is also | 330 |
More Examples
Here are more examples of even and odd numbers in sequence:
Number 328 329 331 332
Absolute Value 328 329 331 332
A guy wire used to support a tower is 200 feet long. The guy wire is attached to the top of the tower and is anchored to the ground 150 feet away from the base. How tall is the tower?
Answers
The height of the tower that was supported with the wire is 132.29 feet.
What is the height of the tower?The tower, the wire and the ground would form a right triangle. A right triangle is a polygon that has three sides. The longest side is the hypotenuse. The other two sides are the length and the base.
In this question, the wire is the hypotenuse, the tower is the length and the ground is the base. Pythagoras theorem would be used to determine the height of the tower.
The Pythagoras theorem: a² + b² = c²
where:
a = length
b = base
c = hypotenuse
a² + 150² = 200²
a² + 22,500 = 40,000
a² = 40,000 - 22,500
a² = 17,500
a = √17,500
a = 132.29 feet
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Kirsty makes orange-strawberry punch. The table shows how many parts orange juice and strawberry juice to make one batch.
Orange-Strawberry Punch
Parts Orange Juice
4
Parts Strawberry Juice
5
Kirsty decides to increase the strawberry juice by one part. What is the new ratio of strawberry juice to orange juice?
For every 4 parts orange juice there are 4 parts strawberry juice.
For every 5 parts orange juice there are 4 parts strawberry juice.
For every 4 parts orange juice there are 6 parts strawberry juice.
For every 5 parts orange juice there are 6 parts strawberry juice.
Answers
Answer:
2nd one, hope this helps
Step-by-step explanation:
Answer:
It is C.
Step-by-step explanation:
Do not listen to top answer
I got it right on unit test review ….
Given <2=13, which lines, if any, must be parallel based on
the given information? Justify your conclusion.
Answers
Answer:
a parallel to b
Step-by-step explanation:
The illustration represents the positions of two planes on a radar screen at an airport control tower. The control tower is located at the origin. The radii of the circles are in miles.
Due to a problem on the ground, the pilots have been told to continue circling the airport and to maintain the same airspeed. The planes are located at the same altitude. Determine the equation of the circle on which the two planes are flying.
Answers
Answer:
0, 08Step-by-step explanation:
You want the equation of the circle shown on the radar screen as having a radius of 8 miles, centered at the origin.
Equation of a circleThe equation of a circle with center (h, k) and radius r is ...
(x -h)² +(y -k)² = r²
ApplicationYour circle is shown as having a radius of 8 miles. It is centered at the same origin where the control tower is located. That means we have ...
(h, k) = (0, 0)
r = 8
Using these values in the circle equation gives ...
(x -0)² +(y -0)² = 8²
Write an equation for the nth term of the arithmetic sequence
Answers
The equation for the nth term of the arithmetic sequence is [tex]a_{n}[/tex] = 25 - 4n
The nth term of the arithmetic sequence:An arithmetic sequence or arithmetic progression is a series of numbers with a common difference. For example 1, 2, 3, 4... is an Arithmetic sequence with a common difference 1. In an Arithmetic sequence, the difference between every two consecutive terms will be equal.
The formula for the nth term of a sequence is given below
=> [tex]a_{n}[/tex] = a + (n-1)d
where a is the first term and d is a common difference.
Here we have
21, 17, 13 ... is the arithmetic sequence
Where first term a = 21
and common difference d = term2 - term1 = 17 - 21 = - 4
As we know the nth term of AP, [tex]a_{n}[/tex] = a + (n-1)d
=> [tex]a_{n}[/tex] = 21 + (n-1)(-4)
=> [tex]a_{n}[/tex] = 21 - 4n + 4
=> [tex]a_{n}[/tex] = 25 - 4n
Therefore,
The equation for the nth term of the arithmetic sequence is [tex]a_{n}[/tex] = 25 - 4n
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what is the sum of the first 80
Consecutive odd numbers?
Answers
help, please the question in the picture
Answers
The probability that the advertising firm chosen at random has less than $1 million in revenue is 0.56.
The probability that the advertising firm chosen at random has an income between $1 million and $20 million or over $20 million is 0.44.
The rule used is the rule of addition only.
What are the probabilities?Probability is used in statistics to calculate the likelihood that a random event would take place. The likelihood that the random event occurs has a probability value that lies between 0 and 1.
The more likely it is that the event would occur, the closer the probability value would be to 1. The more unlikely it is that the event would not happen, the closer the probability value would be to 0.
The rules of addition is used to determine the probability that either of two events would occur.
Probability that the advertising firm chosen at random has less than $1 million in revenue = total number of firms that have a revenue that is less than 1 million / total number of firms surveyed
Probability that the advertising firm chosen at random has less than $1 million in revenue = 148 / 264 = 0.56
Probability that the advertising firm chosen at random has an income between $1 million and $20 million or over $20 million = (number of firms that have an income between $1 million and $20 million / total number of firms) + (number of firms that have an income over $20 million / total number of firms)
= (67 / 264) + (49 / 264)
= 116 / 264 = 0.44
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un ciclista recorre 300 metros por minuto. ¿cuantos kilómetros recorre en una hora?
Answers
Answer:
El ciclista recorre en una hora:
18 kilómetros.
Step-by-step explanation:
1 hora = 60 minutos
1 minuto = 1/60 = 0.01667 horas
1 kilómetro = 1000 metros
300 metros = 300/1000 = 0.3 kilómetros
Entonces:
300 metros por minuto = 300metros/minuto
300 metros / minuto = 0.3kilómetros / 0.01667 horas
= 0.3/0.01667
= 18 kilómetros/hora
El ciclista recorre 18 kilómetros cada hora
Find the slope (2, -7) and (5, -4)
Answers
the slope is 1 because 3/3
Answer:
1
Step-by-step explanation:
When two points are given;
Slope =y2-y1/x2-x1= -4-(-7)/5-2
= -4+7/3
= 3/3
=1
you want to obtain a sample to estimate a population proportion. based on the previous evidence, you believe the population proportion is approximately 76%. you would like to be 95% confident that your estimate is within 4.5% of the true population proportion. how large of a sample size is required?
n=
Answers
A proportion is an equation in which two ratios are set equal to each other and the large sample size required is [tex]0.75[/tex].
What is population proportion?
A fraction is represented in the form of [tex]\frac{a}{b}[/tex], a while ratio [tex]a:b[/tex], then a proportion states that two ratios are equal. Here, [tex]a[/tex] and [tex]b[/tex] are any two integers.
Here, we are determining the minimum sample size for the determination of the population proportion. So, the general formula is of the form is:-
[tex]n=(\frac{z_\frac{x}{2}.x}{E})^{2}[/tex]
Here given values are:-
σ[tex]=76[/tex], population standard deviation
[tex]1-x=0.95\\[/tex], Confidence level
[tex]E=4.5[/tex], Error
Determining the critical value, we get
[tex]z_\frac{x}{2}\\P(z\leq z_\frac{x}{2})=1-\frac{x}{2}\\1-x=0.95\\x=1-0.95\\x=0.05\\\frac{x}{2}=\frac{0.5}{2}\\\frac{x}{2}=0.25\\1-\frac{x}{2}=1-0.25\\\\=0.75[/tex]
Hence, a large sample size is required is [tex]0.75[/tex].
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What is the solution to the system of equations?
-2x + 5y = -16
3x - 4y = 17
Answers
The solution of the system of equations is , x= -16 - 10/2 = 13
What is equations?There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. Mathematical algebraic equations typically have one or more variables.A linear equation may have more than one variable. A linear equation is an equation in which the highest power of the variable is always 1.This is a second-order equation. In quadratic equations, at least one of the variables should be raised to exponent 2.According to our question-
-2x + 5y = -16 (3) = -6x + 15y = -48
3x - 4y = 17 (2) = 6x - 8y = 34
7y = -14
y= -14/7 = 2
-2x + 5(2) = -16
-2x + 10 = -16
x= -16 - 10/2 = 13
hence,The solution of the system of equations is , x= -16 - 10/2 = 13
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The growth of the world's population can be described by the equation A=Age, where time t is measure in years, A, is the population of the world at t=0, r is the annual growth rate, and A is the population at time t. Assume that r= 3% per year. How long will it take a
population of 8 billion to increase to 9 billion.
_ years, round to the nearest whole number
Answers
It will take 37.5 years.
From the question, we have
A_0 = 8 billion
A = 9 billion.
r= 3% per year
A = A_0*e^rt
9 = 8*e^3t/100
9/8 = e^3t/100
Taking log_e both sides,
log_e 9/8 = log_e e^3t/100
9/8 = 3t/100
t = (9*100)/(8*3)
t = 37.5 years
Multiplication:
Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious. In mathematics, the repeated addition of one number in relation to another is represented by the multiplication of two numbers. These figures can be fractions, integers, whole numbers, natural numbers, etc. When m is multiplied by n, either m is added to itself 'n' times or the other way around.
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Which of the statements are true about the image?
Answers
Answer:
which image
Step-by-step explanation:
if you tell me I will answer the question
Answer:
image not found
you can send the image privately
If your car gets 35 miles per gallon, how much does it cost to drive 420 miles when gasoline costs $2.50 per gallon?
The cost is $
(Simplify your answer. Round to the nearest cent as needed.)
Answers
Answer: 30$
Step-by-step explanation:
first you divide 420 by 35 and you get 12 times 2.50$ equals 30$
Kathy invested $3000 at a rate of 7% for 4 years and 6 months. Find the amount she got back.
Answers
The amount that Kathy got back after 4 years and 6 months is $3945 .
In the question ,
it is given that ,
the amount invested by Kathy(P) = $3000
the rate at which the amount is invested (r) = 7% per annum
time for which the amount is invested (t) = 4 years and 6 month = 4.5 years
the simple interest calculated by
Simple Interest = ( 3000 × 7 × 4.5)/100
= 94500/100
= 945
So , the interest is $945 .
So , the amount that Kathy get = Principle + Interest
= 3000 + 945
= 3945
Therefore , amount that Kathy got back after 4 years and 6 months is $3945 .
The given question is incomplete , the complete question is
Kathy invested $3000 at a rate of 7% simple interest for 4 years and 6 months. Find the amount she got back.
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7. In 2009, the national average price for milk was $3.11
and in 2011 it rose again to $3.57 per gallon.
Was the percent increase in cost greater from 2009
your answer.
Answers
The percentage increase in cost greater from 2009 is 14.79%
The average price of milk in 2009 = $3.11
The average of price of milk in 2011 = $3.57
The increase in price = The average of price of milk in 2011 - The average price of milk in 2009
Substitute the values in the equation
The increase in price = 3.57 - 3.11
= $0.46
The percentage increase = The increase in price / The average price of milk in 2009 × 100
Substitute the values in the equation
The percentage increase = ( 0.46 / 3.11 )×100
= 14.79%
Hence, the percentage increase in cost greater from 2009 is 14.79%
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what is the quotient of -0.75 0.4 please help
Answers
The quotient of -0.75 /0.4 is approximately -1.88.
What is the quotient?
This refers to the value you get after division operation has been carried out.
given in the question:
-0.75/0.4 = -1.875
≈ -1.88
Recall, according to the sign rule in mathematics:
Any negative number divided by a positive number gives a negative value.
hence the quotient of -0.75/0.4= -1.875
≈ -1.88
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find m
a. 14
b. 39
c. 51
d. 90
Answers
I WILL USE SUM OF INTERIOR ANGLES OF A TRIANGLE TO GET x
[tex](2x + 11) + (4x - 5) + 90 = 180 \\ 2x + 4x + 11 - 5 + 90 = 180 \\ 6x + 96 = 180 \\ 6x = 180 - 96 \\ 6x = 84 \\ \frac{6x}{6} = \frac{84}{6} \\ x = 14[/tex]
THE ANSWER IS OPTION a
X=14°
A die is rolled. Find the probability of the given event.
(a) The number showing is a 6;
The probability is :
(b) The number showing is an even number;
The probability is :
(c) The number showing is greater than 1;
The probability is :
4
Answers
b. Probability is 3/6 (or 1/2 simplified) since 2,4,6 are the possible options
c. Probability of greater number than 1 is 5/6
Put these numbers in order from least to greatest
Answers
By writing the fractions as decimals, we will see that the numbers ordered from least to greatest are:
-5, 2/16, 23/40
How to order the numbers?The 3 numbers given are:
-5
23/40
2/16
The numbers should be ordered as they appear on a number line (from left to right)
The smaller number is, obviously, the negative one, so the thing that we need to check now is what of the two fractions is smaller.
To do so, we can write them as decimals:
23/40 = 0.575
2/16 = 0.125
So the smaller one is 2/16 and then comes 23/40
Then the numbers ordered from smaller to larger are:
-5, 2/16, 23/40
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IXL Please Help Fast!
Answers
Answer:
[tex]y=2x-1[/tex]
Step-by-step explanation:
Take a look at the attachment...
Hope this helps! :)
solve for x
m = -12bx - 3 + 9x
Answers
Answer:
Below
Step-by-step explanation:
m = x ( -12b+9) - 3
m+ 3 = x (-12b+9)
x = (m+3) / ( -12b+9) 0r (m+3) / (9-12b)
Which expression is equivalent to 6^-6 x 6^6
Answers
Answer:
Step-by-step explanation:
x^-3 * x^-3
Explain how you could estimate 22% of 78 to check if your answer is reasonable.
Answers
In outer space, the distant an object travels varies directly with the amount of time it travels. If an asteroid travels 3000 miles in 6 hours, how far could the asteroid travel in 9 hours?
Answers
Unit rate is the quantity of an amount of something at a rate of one of another quantity.
3000 miles = 6 hours
4500 miles = 9 hours
The distance asteroid travel in 9 hours is 4500 miles
What is a unit rate?Unit rate is the quantity of an amount of something at a rate of one of another quantity.
In 2 hours, a man can walk for 6 miles
In 1 hour, a man will walk for 3 miles.
We have,
3000 miles = 6 hours
Divide both sides by 6.
500 miles = 1 hour
Multiply 9 on both sides.
9 x 500 miles = 9 hours
9 hours = 4500 miles
Thus,
The distance asteroid travel in 9 hours is 4500 miles
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Find the exact value of the given expression.
cos(2tan^-1(24/7))
Answers
Which of the following are solutions to the inequality 2y+3<7? Mark all that are solutions.
[_] 2
[_] 0
[_] -1
[_] 1
Answers
y<2 is the solution to the inequality
What is Linear Inequality?
The mathematical expression with unequal sides is known as an inequality in mathematics. Inequality is referred to in mathematics when a relationship results in a non-equal comparison between two expressions or two numbers. In this instance, any of the inequality symbols, such as greater than symbol (>), less than symbol (), greater than or equal to symbol (), less than or equal to symbol (), or not equal to symbol (), is used in place of the equal sign "=" in the expression. Polynomial inequality, rational inequality, and absolute value inequality are the various types of inequalities that can exist in mathematics.
The symbols "" and ">" signify tight inequalities, while "" and "" signify slack inequalities. A linear inequality looks precisely like a linear equation, but the symbol connecting two expressions is different.
According to the question
2y+3<7
subtracting 3 from both sides
we get,
2y<4
dividing both sides with 2
we get,
y<2
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