Encuentra la ecuación de la parábola y los elementos que se solicitan, sabiendo que su vértice está en el origen y su foco está en F (0, -15).
Answers
The equation of parabola for the given statement is: [tex]x^{2} = -60y[/tex]
What is Parabola ?The locus of points where point moves under a restriction that its distance from a fixed point Focus(F) and fixed line Directrix always remain constant
Solution: here focus of parabola is on -ve y axis so we will take general equation of parabola whose focus is on -ve y axis and directrix will be above x axisi.e[tex]x^{2} =-4ay[/tex]
here a is the distance between vertex and focus and here vertex is origin so by distance formula it comes out to be a = 15
put back in above equation we get its equation[tex]x^{2} = -60y[/tex]which is our required equation of parabola.
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Related Questions
Suppose $30,000 is invested into an account where interest is compounded quarterly. After 30 years the balance is $149,519.
What was the interest rate as a percent?
Round the answer to the nearest hundredth of a percent.
Interest Rate ≈
Answers
The interest rate as a percentage is 5.39% per year.
How to solve compound interest?$30,000 is invested into an account where interest is compounded quarterly. After 30 years the balance is $149,519.
The interest rate as a percent can be calculated as follows:
[tex]r = n((\frac{A}{P} )^{\frac{1}{nt} } -1)[/tex]
where
P = principalA = amount n = number of timest = time in yearsP = 30000
A = 149519
n = 4
t = 30 years
r = ?
[tex]r = 4((\frac{149519}{30000})^{\frac{1}{4(30)} } - 1 )[/tex]
[tex]r = 4((\frac{149519}{30000})^{\frac{1}{120} } - 1 )[/tex]
r = 0.0539008
Then convert r to R as a percentage
R = r * 100
R = 0.0539008 * 100
R = 5.39% per year
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PLS HELP THIS IS HARDER THAN COUNTING 10000000 DOTA A DAY!!
at the bottom “is a bit covered”
Answers
Answer:
List Price: 1750
Sale Price: 1400
Step-by-step explanation:
If 20% = 350, we can just multiply it by 5 to get the list price.
Because:
= 20% / 100%
= 20 / 100
= 2 / 10
= 1 / 5
= 1 / 5 * 5 = 1
= 350 * 5 = 1750 (list price)
To get the sale price, we subtract 350 from 1750
1750 - 350 = 1400
1400 is 80% of full price, which is what it was purchased for.
A one-way data table summarizes
A. a single input's impact on the output of interest
B. values of the input cells that will cause the single output value to equal zero
C. multiple input's impact on a single output of interest
D. values of cells when not all of the model is observable on the screen
Answers
Answer:
A
Step-by-step explanation:
hope this helps! :) Hope you have. a great day
PLEASE HELP ASAP!!! I WILL GIVE YOU BRAINLIST PLEASE Due in like 10 minutes
Which algebraic rule describes the translation of quadrilateral HIJK to quadrilateral H'I'J'K'?
Answers
The algebraic rule describes the translation of quadrilateral HIJK to quadrilateral H'I'J'K' is (x, y) => (x+1, y-8)
How to determine the algebraic rule that describes the translation of quadrilateral?Translation is defined as the movement on a straight line
Given: quadrilateral HIJK to that translated H'I'J'K'
To determine the algebraic rule, we need to get the coordinates of HIJK and H'I'J'K' and then subtract them to get the translation:
H => (x, y) = (4, 6) | H' => (x, y) = (5, -2)
I => (x, y) = (6, 4) | I' => (x, y) = (7, -4)
J => (x, y) = (4, 2) | J' => (x, y) = (5, -6)
K => (x, y) = (4, 2) | K' => (x, y) = (3, -6)
Using points H and H' (you can use any point):
The difference in x is 5-4 = +1 => x+1
The difference in y is -2-6 = -8 => y-8
Therefore, the algebraic rule describes the translation is (x, y) => (x+1, y-8). Option C is the answer
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Answer:
(x, y) => (x+1, y-8)
Step-by-step explanation:
what are the next numbers in the series 1, 2, 3, 0, 1, 2, -1
Answers
Answer:
Step-by-step explanation:
the pattern is x+1+1-3 so
1+(1)=2
2+(1)=3
3-(3)=0
Alright now the next numbers (assuming the next 3 numbers?)
-2,-3,-4
I’m so sorry if I’m incorrect but I hope this helps
Convert 93 ft to yards
Answers
Answer:
31 yards
Step-by-step explanation:
Since there are 3ft in 1 yard,
93 ft / 3 ft = 31 yards
Answer:
31 yards
Step-by-step explanation:
1 ft is 1/3 yard
So 93 ft = 93/3
= 31 yards
OR
1 ft is 0.333 yard
93 × 0.333 = 31 yard.
Susan paid $15.84 for a 7.48 - kg bag of dog food. A few weeks later, she paid $16.58 for a 7.94 - kg bag at a different store.
Find the unit price for each bag. Then state which bag is the better buy based on the unit price.
Round your answers to the nearest cent.
Unit price for the 7.48 - kg bag:
Unit price for the 7.94 - kg bag:
The better buy:
- 7.48
- 7.94
- Neither
Answers
The unit price for the 7.48 is $2 kg per bag and the unit price for the 7.94 is $2 per kg bag, there is no difference in unit rates of both the bag.
What is unit rate?A unit rate means a rate for one of something.
Given that, Susan paid $15.84 for a 7.48 kg bag of dog food. A few weeks later, she paid $16.58 for a 7.94 kg bag at a different store.
15.48/7.48 = $2/kg
16.58/7.94 = $2/kg
Hence, there is no difference in between both the bags, hence either of them are better.
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On a recent trip to the convenience store, you picked up 3 gallons of milk, 4 bottles of water, and 7 snack-size bags of
chips. Your total bill (before tax) was $23.40. If a bottle of water costs twice as much as a bag of chips, and a gallon of
milk costs $2.20 more than a bottle of water, how much does each item cost?
Answers
Answer:
bottle of water: $1.60
gallon of milk: $3.80
bag of chips: $0.80
Step-by-step explanation:
First, the amount of groceries bought can be represented as:
[tex]3m + 4w + 7c = \$ 23.40[/tex]
where [tex]m[/tex] represents the cost of one gallon of milk, [tex]w[/tex] represents the cost of a bottle of water, [tex]c[/tex] represents the cost of one bag of chips.
We can form a system of equation by constructing another equation to substitute into the first using the other pieces of information given.
"a bottle of water costs twice as much as a bag of chips"
[tex]w = 2c[/tex] → [tex]c = \dfrac{w}{2}[/tex]
"milk costs $2.20 more than a bottle of water"
[tex]m = w + \$ 2.20[/tex]
Now, substitute these into the first equation and solve for w in terms of c.
[tex]3(w + 2.20) + 4w + 7\cdot \dfrac{w}{2} = 23.40[/tex]
[tex]3w + 6.60 + 4w + \dfrac{7}{2} \, w = 23.40[/tex]
[tex]\dfrac{21}{2} \, w = 16.80[/tex]
[tex]21w = 33.60[/tex]
[tex]w = 1.60[/tex]
So, one bottle of water costs $1.60.
To solve for the other items, plug the solved value into the 2-variable equations.
[tex]m = 1.60 + 2.20[/tex]
[tex]m = 3.80[/tex]
So, one gallon of milk costs $3.80.
[tex]c = \dfrac{1.60}{2}[/tex]
[tex]c = 0.80[/tex]
So, one bag of chips costs $0.80.
4. Emily, Ashley and Peter can clean a warehouse in 2 hours. If Emily does the job alone, she can finish it in 6 hours. If Ashley does the job alone she can finish it in 8 hours.
How long will it take for Peter to finish the job alone?
How long will it take for Emily and Peter to finish the job together.
Answers
According to the unitary method,
A) The time taken for Peter to finish the job alone is 4 hours, 48 minutes.
B) The time taken for Emily and Peter to finish the job together is 2 hours, 36 minutes.
Unitary method:
In math, unitary method refers the process of finding the value of a single unit, and based on this value.
Given,
Emily, Ashley and Peter can clean a warehouse in 2 hours. If Emily does the job alone, she can finish it in 6 hours. If Ashley does the job alone she can finish it in 8 hours.
Here we need to find the following:
A) The time take for Peter to finish the job alone
B) The time taken for Emily and Peter to finish the job together
Let us consider x be the time taken for Peter to finish the job alone.
So, based on the given question we can write it as,
=> 1/6 + 1/8 + 1/x = 1/2
=> (8 + 6)/48 + 1/x = 1/2
=> 14/48 + 1/x = 1/2
=> 7/24 + 1/x = 1/2
=> 1/x = 1/2 - 7/24
=> 1/x = 12 -7/24
=> 1/x = 5/24
=> x = 24/5
=> x = 4.8
So, the time taken for Peter to finish the job alone is 4 hours, 48 minutes.
Then the time taken for Emily and Peter to finish the job together is calculated as,
=> 5/24 + 1/6
=> 5 + 4/ 24
=> 9/24
=> 3/8
Therefore, the time taken for Emily and Peter to finish the job together 2 hours, 36 minutes.
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a biology text editor spent 10.5 hour making telephone calls, writing email, and attending meetings. he spent thrice as much time attending meeting as making telephone calls and 0.5 hour longer writing emails than making telephone calls. how many hour did he spent on each task?
Answers
Answer:
telephone calls = 2 hours ; attending meeting = 6 hours ; writing email= 2.5 hours
Step-by-step explanation:
t + e + m = 10.5
3t = m
e = 0.5 + t
t + 0.5 + t + 3t = 10.5
5t = 10.5 - 0.5
5t = 10
5/5 t = 10/5
t = 2
e = 0.5 + 2
e = 2.5
m = 3 (2)
m = 6
A newspaper conducted a statewide survey concerning the 1998 race for state senator. The newspaper took a SRS of n=1200 n=1200
registered voters and found that 620 would vote for the Republican candidate. Let p represent the proportion of registered voters in the state who would vote for the Republican candidate.
We test
H0:p=.50
H0:p>.50
Answers
The value of z = 1.15
The value of the p value is 0.124. vWe would fail to reject the null hypothesis
How to solve for the z statisticWe have to find the sample proportion
This is given as x / n
where
x = 620
n = 1200
620 / 1200
= 0.516667
The null hypothesis that is to be tested is H0:p=.50
The alternative hypothesis that is to be tested as well is H1:p>.50
We are to test for the value of Z as well as P value through the use minitab software and make conclusions with the results.
In the result, the
1. The value of z is solved to be 1.15
2. The P value is 0.124. The value of the P value is very high, the decision would be for us to fail to reject the null hypothesis.
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Complete question
A newspaper conducted a statewide survey concerning the 1998 race for state senator. The newspaper took a SRS of n=1200 registered voters and found that 620 would vote for the Republican candidate. Let p represent the proportion of registered voters in the state who would vote for the Republican candidate.
We test
H0:p=.50
Ha:p>.50
(a) What is the z-statistic for this test?____.
(b) What is the P-value of the test?_____.
Answer:
620÷2=310 50% is half of 620
Step-by-step explanation:
3. The expression 0.12 x+(x-35) models the final price of a scooter with an instant rebate in a state that charges sales tax.
- Which part of the expression represents the discounted price before tax?
- Which part of the expression represent the amount of sales tax, in dollars (not the tax rate, the amount of sales tax paid)?
Answers
The expression x - 35 represents the discounted price before tax. The expression 0.12x represent the amount of sales tax.
What is an expression?Expressions are defined as mathematical statements that have a minimum of two terms containing variables or numbers.
The expression given which models the final price of a scooter with an instant rebate in a state that charges sales tax is:
⇒ 0.12x + (x - 35)
As per the given expression,
The discounted price before tax = x - 35
The amount of sales tax = 0.12x
Thus, the expression x - 35 represents the discounted price before tax and the expression 0.12x represent the amount of sales tax.
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Seth mowed his neighbor's lawn m times. He earned 15 dollars each time. Choose the expression that shows how many dollars Seth earned.
Answers
The expression that shows how many dollars Seth earned is 15m.
What is an expression?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.
Since Seth mowed his neighbor's lawn m times and earned 15 dollars each time.
The amount made will be:
= Cost for each mowing × Number of times
= 15 × m
= 15m
The expression is 15m.
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Answer:
15m
Step-by-step explanation:
HELP PLEASE!!
Write the equation of the line that is perpendicular to the line below and passes through the point (4,-6) write your equation in point-slope form.
Answers
y+6=-4/3x+16/3 is equation of the line that is perpendicular to the line below and passes through the point (4,-6)
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
We need to find the slope of given line.
The line is passing through points (4, 0) and (0, -3)
m=-3-0/0-4
m=3/4
The slope of perpendicular lines is -1.
m.3/4=-1
m=-4/3
the equation of the line that is perpendicular to the line below and passes through the point (4,-6)
y-y₁=m(x-x₁)
y-(-6)=-4/3(x-4)
y+6=-4/3x+16/3
Hence, y+6=-4/3x+16/3 is the point slope form of line passing through (4,-6)
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What graph would best display the data shown in the frequency table?
A. line plot
B. vertex-edge graph
C. histogram
D. stem-and-leaf graph
Answers
Answer:
histogram
Step-by-step explanation:
Answer the questions below. I need letter b and letter c
Answers
Answer:
b: mean
c: mode
Step-by-step explanation:
I say mean for b because to find average of how many sodas they drink in a month
For c I say mode because they want to find the most common year and mode is where it chooses which year appears the most
Hopes this helps please mark brainliest
find the sum of the AP 1 + 3 ½/2 +6.... 101
Answers
Answer:
2091
Step-by-step explanation:
[tex]1+3.5+6+\cdots+101 \\ \\ n=\frac{101-1}{2.5}+1=41 \\ \\ a=1 \\ \\ d=2.5 \\ \\ S=\frac{41}{2}[2(1)+(41-1)(2.5)] \\ \\ =2091[/tex]
Explain whether the recipe will make enough for Lucy and 3 friends to each have at least 1 cup of smoothie. If it does not make enough, explain how to change the recipe to make enough.
Answers
The recipe will be enough for Lucy and her friends to make smoothie.
How to illustrate the information?From the information, they are making smoothie. This will be illustrated as:
1 1/3 cups of banana = 4/3 cups
1 1/2 cup of yoghurt = 3/2 cups
1 cup of strawberry.
3/4 cup of orange juice.
Based on the information, we've to find the total quantity of smoothie. This will be:
= 4/3 + 3/2 + 1 + 3/4
= 4 7/12
Therefore, the recipe will be enough for Lucy.
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Complete question
Lucy is making a smoothie by following the recipe below
Sunshine smoothie
1 1/3 cups banana
1/2 cup yogurt
1 cup strawberries
3/4 cup orange juice
Will this recipe make enough for Lucy and 3 friends to have 1 cup of smoothie? Explain.
what should i say to this. like it’s okay, that was in the past???
Answers
Answer: You got roasted sir. Leave it alone.
Step-by-step explanation:
Covert 225g to kilograms using unit fractions ?
Answers
Answer:
.225 kg
Step-by-step explanation:
[tex]\frac{225 grams}{1}[/tex] x [tex]\frac{1kg}{1000grams}[/tex] = .225 kg
Solve the system of equations by substitution
x=-4
x+5y=2
Answers
You roll two dice as part of a casino game. Express your answers as reduced fractions.Find the probability of rolling a sum of 6, 7, or 8.
Answers
==================================================
Explanation:
Let's list the ways to roll a 6.
1+5 = 62+4 = 63+3 = 64+2 = 65+1 = 6There are A = 5 items listed above.
Now let's list the ways to roll a sum of 7.
1+6 = 72+5 = 73+4 = 74+3 = 75+2 = 76+1 = 7There are B = 6 items listed above.
Lastly, let's list the ways to roll a sum of 8.
2+6 = 83+5 = 84+4 = 85+3 = 86+2 = 8There are C = 5 items listed above.
-------------
Summary so far:
We found there are
A = 5 ways to roll a "6"B = 6 ways to roll a "7"C = 5 ways to roll an "8"Therefore, we have A+B+C = 6+7+8 = 21 ways to roll either of those three sums. Each event is mutually exclusive.
This is out of 6*6 = 36 ways to roll two dice (whether we get those sums or not).
21/36 = (7*3)/(12*3) = 7/12 is the probability of getting any of those three sums mentioned.
7/12 = 0.5833 = 58.33% approximately
Examine the following typical corporate bond listing:
In the name column, NYTel is the abbreviated name of the company (New York Telephone) issuing the bond. What was the closing price of the bond? What was the dollar amount? (See attachments)
a. 101 3/4; $101,750
b. 7 1/4; $7250
c. 101 3/4; $1017.50
d. 107 1/4; $1072.50
Answers
Answer:
C. 101 3/4; $1017.50
Step-by-step explanation:
Correct on E2020!
Which statement are true about the linear inequality y>3/4x-2 select three options
Answers
The graph of linear inequality y > 3/4x - 2 is attached below and it's properties are the graph passes through the x - axis at 2.67, the graph passes through the y - axis at -2 and the graph has a straight broken line to denote the ">" inequality sign.
Linear InequalityLinear inequalities are inequalities that involve at least one linear algebraic expression, that is, a polynomial of degree 1 is compared with another algebraic expression of degree less than or equal to 1. There are several ways to represent various kinds of linear inequalities.
In the inequality given, we can represent this on a graph and discuss it's properties.
The graph of y > 3/4x - 2 shows these properties
The graph passes through the x - axis at 2.67The graph passes through the y - axis at -2 The graph has a straight broken line to denote the ">" inequality sign.Kindly find the attached graph below
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Complete Question:
Which of the statement are true about the linear inequality y > 3/4x - 2
I. The graph has a broken line
II. The graph has an unbroken line
III. The graph passes through y - axis at -2
IV. The graph passes through the x - axis at 2.67
How much should be deposited in an account paying 3.5% interest, compounded semiannually, in order to have a balance of $ 6,000 after 17 years and 6 months?
Enter the answer in dollars and cents, and round to the nearest cent, if needed. Do not include the dollar sign. For example, if the answer is $0.61, only the number 0.61 should be entered.
Principal ≈ $
Answers
The principal that was deposited is $3326.45 .
What is the principal?The principal has to do with the amount that has been deposited in the bank and after a while we would have the amount which is the summation of the principal and the interest that accrues.
Given that;
A = P(1 + r/n)^nt
A = amount
P = principal
r = rate
n = number of times compounded
t = time
Then;
6,000 = P(1 + 0.035/2)^2 * 17
P = 6000/(1 + 0.035/2)^2 * 17
P = $3326.45
At the beginning the money that was deposited is $3326.45 .
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Write the symbol for every chemical element that has atomic number less than 5 and atomic mass greater than 8.5 u.
Answers
Answer:
Be - Beryllium
Find all values of m for which the equation has two real solutions.
3x² + 7x - (m + 1) = 0
ñ
Answers
Given equation to us is , [tex]3x^2+7x-(m+1)=0[/tex] .
The given equation is a quadratic equation and it has two real solutions if it's discriminant is greater than or equal to 0 .
For a quadratic equation in standard form of [tex]ax ^{2} + bx + c = 0[/tex]
the discriminant is given by b² - 4ac .
On comparing wrt to Standard form, we have ;
[tex]a = 3[/tex][tex]b = 7[/tex][tex]c = - (m+1)[/tex]Hence we have,
[tex]\longrightarrow b^2-4ac \geq 0\\ [/tex]
[tex]\longrightarrow 7^2-4(3)-(m+1)\geq 0\\[/tex]
[tex]\longrightarrow 49 +12(m+1)\geq 0\\ [/tex]
[tex]\longrightarrow 49 +12m+12\geq 0 \\ [/tex]
[tex]\longrightarrow 12m \geq -61\\[/tex]
[tex]\longrightarrow \underline{\underline{m \geq \dfrac{-61}{12}}} [/tex]
Therefore the given quadratic equation will have real solutions for values of m greater than or equal to -61/12 .
And we are done!
Sampling distributions for the mean follow many rules. Which of the rules listed below is false? Two of the options listed are false. Sampling distributions get wider (I.e. have greater variability) with increasing sample size Sampling distributions of size n > 30 are typically bell-shaped Sampling distributions are composed of statistics from many, many samples. All of the options listed are false. Sampling distributions are centered over the true population parameter. Three of the options listed are false.
Answers
Option B. The rule of sampling distribution that is listed here that can be said to be false is Sampling distributions get wider (I.e. have greater variability) with increasing sample size.
What is meant by sampling distribution?The probability distribution of a statistic that is acquired by repeated sampling of a particular population is called the sampling distribution. It outlines a variety of potential possibilities for a statistic, such as the mean or mode of a population's mean or mode of some variable.
It could be regarded as the statistical distribution for all feasible samples drawn from the same population with a particular sample size. The population's underlying distribution, the statistic under consideration, the sampling technique utilized, and the sample size used all have an impact on the sampling distribution.
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The —-
of a quadratic equation is ax² +bx+c = 0, where a 0 and a, b, and care integers
Answers
The degree of the quadratic equation, ax² +bx+c = 0 will be 2.
What is a quadratic equation?Any equation of the form ax² +bx+c = 0 where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation. Any function of the form of the given form where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic function.
It is given that the equation is,
ax² +bx+c = 0
The highest power of the quadratic equation is the degree to that quadratic equation. The highest power of the given quadratic equation is 2.
Thus, the degree of the quadratic equation, ax² +bx+c = 0 will be 2.
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need help pls thank you
Answers
a) The value of b if the total number of students is 55 is; b = 8
b)i) Probability that the student passed both french and german is 19/55
ii) Probability that the student passed exactly one of the two subjects is; 36/55
How to interpret Venn Diagrams?A venn diagram is used to compare and contrast two different ideas.
We are given that;
Number of students that passed French only = 17
Number of students that passed German only = 11
Number of students that passed both French and German = 19
Number of students that did not pass any of the 2 subjects = b
Total number of students = 55
Thus;
a) To get the value of b that will represent the number of students who didn't pass any of the 2 subjects will be calculated as;
b = 55 - (17 + 11 + 19)
b = 8
b)i) To get the probability that the student passed both french and german is given by the formula;
P(Paased french and german) = Number that passed french and german/Total number of students = 19/55
ii) To get the Probability that tells us the student passed exactly one of the two subjects is;
(17/55) + (19/55) = 36/55
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