1v=9. Which equation represents the equation of theparabola with focus (-3,3) and directrix y = 7?A),= (x+3)2 – 5B) y = 5(? – 3)2 +5C) y=-( + 3)2 +5D) y=-2 (2-3)2 +5
Answers
SOLUTION
From the focus (-3, 3) and the directrix y = 7 given, note that the vertex is usually between the focus and the directrix.
So, the vertex will have the same x-coordinate as the focus, which is -3, and the y-coordinate of the vertex becomes
[tex]\begin{gathered} \frac{3+7}{2} \\ that\text{ is 3 from the y-coordinate of the focus and 7 from the directrix} \\ y=7 \\ \frac{3+7}{2}=\frac{10}{2}=5 \end{gathered}[/tex]Hence coordinate of the vertex is (-3, 5)
Now, equation of a parabola is given as
[tex]\begin{gathered} (x-h)^2=4p(y-k) \\ where\text{ \lparen h, k\rparen is the coordinate of the vertex and p is the focal length} \\ y=k-p,\text{ so we have } \\ 7=5-p \\ p=5-7=-2 \end{gathered}[/tex]So putting in the values of h, k and p into the equation, we have
[tex]\begin{gathered} (x-h)^{2}=4p(y-k) \\ (x-(-3)^2=4(-2)(y-5) \\ (x+3)^2=-8(y-5) \\ -\frac{1}{8}(x+3)^2=y-5\text{ that is dividing through by -8} \\ making\text{ y the subject, we have } \\ y=-\frac{1}{8}(x+3)^2+5 \end{gathered}[/tex]Hence the answer is
[tex]y=-\frac{1}{8}(x+3)^{2}+5[/tex]Related Questions
As a janitor you make a cleaning solution by mixing 30 g of concentrated powdered cleanser into 2 L of water how much powder will you need for 5L of water?
Answers
30g - 2L
For 5L of water
[tex]\frac{5L\cdot30g}{2L}=75g[/tex]ANSWER
For 5L of water, we will need 75 g of concentrated powdered cleanser
[tex]y {}^{2} + 5y - 24[/tex]Help to do this problem by Factoring triinomials by Box Method. please
Answers
Factor the trinomial
[tex]y^2+5y-24[/tex]by the box method.
The multiplication gives -24y^2. Now we need to find two factor that gives 5x. It should be creal that this factor are 8y and -3y. Then:
Now we find the common factor for each column and row:
Therefore:
[tex]y^2+5y-24=(y-3)(y+8)[/tex]Distributive property to solve-4(s-4)
Answers
The distributive property can be applied in the following form:
[tex]a(b-c)=a\times b-a\times c[/tex]Now, the given values are: a=-4, b=s and c=4.
Let's replace them in the equation and solve:
[tex]\begin{gathered} -4(s-4)=(-4)\cdot(s)-(-4)\cdot(4) \\ By\text{ the law of signs -}\cdot-=+and-\cdot+=-\text{ thus:} \\ -4(s-4)=-4s+16 \end{gathered}[/tex]Then, the answer is -4s+16
I need help please!!
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Ok, well, I think I need to the see previous problem. But from the information given, I think the right choices are:
a) tenth
b) 31.8
c) 32
I need help question
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The domain is all values of x except 1
the range is all values of y < -1
domain (-∞,1)U(1,∞)
range (-∞,-1)
Find the roots of each quadratic equation by factoring. X² - 8x + 15
Answers
Given,
[tex]x^2-8x+15=0[/tex]To find the roots
[tex]\begin{gathered} x^2-8x+15=x^2-3x-5x+15 \\ =x(x-3)-5(x-3) \\ =(x-3)(x-5) \end{gathered}[/tex]The required roots are,
[tex](x-3)(x-5)[/tex]The graph represents a quadratic function. Write an equation of the function in standard form. PLEASE HELP ME
Answers
Explanation:
Standard form is Ax + By = C
Known points are (-3, 6) and (-1.5, 6.75)
Find the slope:
6.75-6/-1.5+3 = 0.75/1.5 = 0.5
Put in point slope form first: y - y1 = m (x-x1)
y - 6 = 0.5 (x + 3)
Then rewrite to standard form:
y - 6 = 0.5x + 1.5
-0.5x + y = 1.5 +6
-0.5x +y = 7.5
Lacie pays a babysitter an initial fee of $30 in addition to $7 per hour. When trying to solve this problem,Juan created the function y = 30x + 7. Explain his error.Juan assigned the wrong coefficient to x. He should have written the equation
Answers
he should have written the equation y=7x+30 because 30 is the fixed initial value and 7 is the value that increase with the number of hours
14 Select all that apple Which of these fractions are equivalent to ?
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the initial fraction es 1/4, so if we multiply the fraction by 2/2 it become:
[tex]\frac{2}{2}\cdot\frac{1}{4}=\frac{2}{8}[/tex]and if we multiply by 6/6
[tex]\frac{6}{6}\cdot\frac{1}{4}=\frac{6}{24}[/tex]So the solution is fraction 2/8 and fraction 6/24
Hello, can you help me find the solutions to this problem?
Answers
Given,
The expression is,
[tex]\begin{gathered} x^3=216 \\ x^3-216=0 \end{gathered}[/tex]The rational theorem tells that if the polynomial has the rational 0 then it must be a fraction p/q, where p is a factor of constant term and q is the factor of leading coefficient.
The constant term 216 with factors:
[tex]1,2,3,4,6,8,9,12,18,24,27,36,54,72,108\text{ }and\text{ }216.[/tex]The leading coefficient is 1, with a single factor of 1.
[tex]\begin{gathered} \frac{p}{q}=\frac{factor\text{ of 216}}{factor\text{ of 1}}=\pm\frac{1}{1},\operatorname{\pm}\frac{2}{1},\operatorname{\pm}\frac{3}{1},\operatorname{\pm}\frac{4}{1},\operatorname{\pm}\frac{6}{1},\operatorname{\pm}\frac{8}{1},\operatorname{\pm}\frac{9}{1},\operatorname{\pm}\frac{12}{1}, \\ \operatorname{\pm}\frac{18}{1},\operatorname{\pm}\frac{24}{1},\operatorname{\pm}\frac{27}{1},\operatorname{\pm}\frac{36}{1},\operatorname{\pm}\frac{54}{1},\operatorname{\pm}\frac{72}{1},\operatorname{\pm}\frac{108}{1},\operatorname{\pm}\frac{216}{1} \end{gathered}[/tex]Substitute the possible roots one by one into the polynomial to find the actual roots. Start first with the whole numbers.
p(6)=0 so x=6 is a root of a polynomial p(x).
Using factor theorem to find the remaining roots,
[tex]\begin{gathered} \frac{x^3-216}{x-6}=x^2+6x+36 \\ By\text{ formula method,} \\ x=\frac{-6\pm\sqrt{36-144}}{2} \\ x=\frac{-6\pm\sqrt{108}}{2} \\ x=\frac{-6\pm6\sqrt{-3}}{2} \\ x=-3\pm3\sqrt{3i} \end{gathered}[/tex]Hence, the roots are 6, -3-3sqrt(3)i, and -3+3sqrt(3)i. So, option A is correct.
David drank 10 fluid ounces of juice. how much is this in cups? write your answer as a whole number or a mixed number in simplest form. Include the correct unit in your answer.
Answers
Given
David drank 10 fluid ounces of juice.
Find
how much is this in cups?
Explanation
As we know
1 cup = 8 ounces
so , 8 ounces = 1 cup
then
12 ounces =
[tex]\frac{1}{8}\times12=\frac{3}{2}=1\frac{1}{2}cups[/tex]Final Answer
hence , the required answer is
[tex]1\frac{1}{2}cups[/tex]Which is greater, 1/2 or 2/7?
Answers
If we have two fractions a/b and c/d:
[tex]\frac{a}{b}(\text{ })\frac{c}{d}[/tex]To determine which one of them is greater we make the cross product:
[tex]ad(\text{ })bc[/tex]We have 3 cases:
- If ad is greater than bc, then a/b is greater than c/d
- If bc is greater than ad, then c/d is greater than a/b
- If ad is equal to bc, then a/b is equal to c/d
For 1/2 and 2/7:
[tex]\begin{gathered} \frac{1}{2}(\text{ })\frac{2}{7} \\ 7\cdot1(_{\square})2\cdot2 \\ 7>4 \\ \Rightarrow\frac{1}{2}>\frac{2}{7} \end{gathered}[/tex]Please help me with this quickly, the questions says to show work or explain but I want explanation, thank you!
Answers
Solution
- Experimental probability is the probability gotten from conducting experiments and it is different from theoretical probability which is derived from hypothetical situations.
- In this question, the hypothetical situation that leads to the theoretical probabilities of getting a red, an orange, and so on, is the fact that the question already said the smallest section of the circle is 1/16 and every other portion is a multiple of this.
- The experimental probabilities are gotten from the table and the formula for calculating this probability is given below:
[tex]\begin{gathered} Given\text{ Event \lparen E\rparen,} \\ P(E)=\frac{Number\text{ of times an event occurs}}{Total\text{ number of trials}} \end{gathered}[/tex]- Thus, we can proceed to find the experimental probabilities of finding any of these colors as follows:
Orange:
[tex]\begin{gathered} E=\text{ Event of spinning an Orange} \\ P(orange)=\frac{3}{30}=\frac{1}{10} \end{gathered}[/tex]Green:
[tex]P(green)=\frac{6}{30}=\frac{1}{5}[/tex]Blue:
[tex]P(blue)=\frac{5}{30}=\frac{1}{6}[/tex]estimate the quotient 612 and 60
Answers
612 is very close to 600 and 600 into 60 is 100
[tex]\frac{600}{60}=100[/tex]Also, we have 12 in front of 600 that makes it 612 and we know that 12 is not divisible by 60, and therefore, it will be the remainder.
Hence, the estimate of the quotient of 612 and 60 is 100
I have the answers to the question but I’m not sure how they got them?
Answers
Hello there. To solve this question, we'll have to use the data from the graph (dot plot) and determine the answers for each letter.
a) How many babies begin walking before 13 months of age?
For this, we have to add all the number of babies walking from the dot plot that are less than 13.
In this case, we add the values of babies walking with 9, 10, 11 and 12 months:
1 + 1 + 3 + 5 = 10
Therefore 10 babies have begun walking before 13 months of age.
b) What percent of babies begin walking at 12 months?
For this, we add the entire number of babies walking by age and calculate the ratio between the number of babies walking at 12 months and this result.
We have 25 babies at total and 5 of them began walking at 12 months of age, so now we take the ratio:
[tex]\frac{5}{25}=\frac{1}{5}=20\%[/tex]c) Which three ages combined account for less than 16% of the babies?
For this, we find how many is 16% of 25, that is, the total of babies:
[tex]0.16\cdot25=4[/tex]So we have to find which three ages combined gives us less than 4 babies.
Notice we cannot choose the ages 12, 13, 14 because their number of babies, alone, are already bigger than 4.
We cannot also choose 11, because it is equal to 3 and all the other options are bigger than or equal to 1, so adding it with something else already would be equal to 4.
The same happens to 15 and 16, because their assigned value is 2, so adding both together gives us 4 and since all the others are greater than or equal to 1, we could not add other two together with them.
That's why the final answer is 9, 10 and 17, because they are the only numbers left that add up to 3 and this is a number less than 4, that is, less than 16% of the babies.
you deposit $4000 each year into an account earning 3% interest compounded annually. How much will you have in the account and 35 years?
Answers
ANSWER:
$ 241848.33
STEP-BY-STEP EXPLANATION:
Given:
P = $4000
r = 3% = 3/100 = 0.03
n = 35 years
The formula for the future value is:
[tex]\begin{gathered} FV=P\mleft(\frac{\left(1+r\right)^n-1}{r}\mright) \\ \text{ replacing} \\ FV=4000\cdot\mleft(\frac{\mleft(1+0.03\mright)^{35}-1}{0.03}\mright) \\ FV=241848.33 \end{gathered}[/tex]Therefore, after 35 years, he would have $ 241848.33 in the account.
How can you write the expression with a rationalized denominator?See image
Answers
Okay, here we have this:
Considering the provided expression, we are going to rationalize the denominator, so we obtain the following:
[tex]\begin{gathered} \frac{\sqrt[3]{3}}{\sqrt[3]{4}} \\ =\frac{\sqrt[3]{3}\cdot\sqrt[3]{4^2}}{\sqrt[3]{4}\cdot\sqrt[3]{4^2}} \\ =\frac{\sqrt[3]{3}\cdot\sqrt[3]{2^4}}{4^{\frac{1}{3}+\frac{2}{3}}} \\ =\frac{\sqrt[3]{3}\cdot2^{\frac{4}{3}}}{2^2} \\ =\frac{\sqrt[3]{3}\sqrt[3]{2}}{2} \\ =\frac{\sqrt[3]{6}}{2} \end{gathered}[/tex]Finally we obtain that the correct answer is the second option.
lonny and mia each take out a 250,000 loan for a new house. each has to repay the loan in 25 years. lonny will pay an interest rate of 3.4% per year. his monthly payments will be $1250. because mia has a lower credit score she will have to pay an interest rate of 4.1% per year. her monthly payments will be $1360. how much more will a 250,000 loan cost mia than lonny?
Answers
Lonny takes a loan of 250000 and repays $1250 /month
in a year he pays 1250 x 12 =$15000
in 25 years he pays 15000 x 25 =$375000
mia pays 1360/ month. In a year she pays 1360 x 12 =$16320
in 25 years she pays 16320 x 25= $408000
difference in cost = 408000 -37500 = $33000
it will cost mia $33000 more for the loan.
what is the positve solution for this equation? 4x2 + 12 x= 135
Answers
We need to solve the following equation for x, and choose the positive solution
[tex]4x^2+12x=135[/tex]we substract 135 from both sides of the equation obtaining the canonical form of a quadratic equation, the we apply the quadratic formula with a=4, b=12 and c=-135 then x will be equal to:
[tex]x=\frac{-12+\sqrt[]{144-4(4)(-135)}}{8}=\frac{48-12}{8}=\frac{9}{2}=4.5[/tex]then the positive solution to the equation will be x=4.5the Santa Ana College theartre department sold 177 tickets to the spring play student tickets were sold for $7 each and general admission ticket were $9 if the total tickets sales were 1365 how many of each type of tickets were sold?
Answers
Let
x -----> number of play student tickets sold
y ----> number of general admission tickets sold
we have that
x+y=177 ------> x=177-y -----> equation A
7x+9y=1365 -----> equation B
solve the system
substitute equation A in equation B
7(177-y)+9y=1365
solve for y
1239-7y+9y=1365
2y=1365-1239
2y=126
y=63
Find the value of x
x=177-63
x=114
therefore
student tickets sold was 114general admission ticket sold was 63there are 117 staff members in your school. One third of them are going away for the Thanksgiving holiday. How many staff members are not traveling
Answers
78 members are not traveling
Explanation
Step1
we need to use fractions to find the number of memebers are going away, so the whole number (117) is represented by 1
then,Let
whole number=full staff= 117
One third of them are going away for the Thanksgiving holiday, to find the number of members just do:(fraction by number)
[tex]\begin{gathered} \text{Members are going away=}\frac{1}{3}\cdot117 \\ \text{Members are going away=}39 \end{gathered}[/tex]Step 2
now, let's use subtraction to find the number of members that are not traveling
[tex]\begin{gathered} \text{Members are not traveling=full staff -member are going away} \\ \text{Members are not traveling=117-39} \\ \text{Members are not traveling=}78 \end{gathered}[/tex]I hope this helps you
Answer:
78
Step-by-step explanation:
So, to solve this problem, we have to divide 117 by 3, because one third of the staff is going away. 117 divided by 3 equals 39, which is number of staff this is going away. Next we have to subtract 39 from 117, which will give us our answer. 117 - 39 = 78
Happy Holidays!
If the function fis defined by f(x) = x ^ 5 - 1 then the inverse, f ^ - 1 is defined by f ^ - 1 * (x) =
Answers
Given the function:
[tex]f(x)=x^5-1[/tex]We have that f(x) = y, so:
[tex]y=x^5-1[/tex]Substitute x with y:
[tex]x=y^5-1[/tex]And solve for y:
[tex]\begin{gathered} x+1=y^5-1+1 \\ x+1=y^5 \\ y=\sqrt[5]{x+1} \end{gathered}[/tex]Answer:
[tex]\sqrt[5]{x+1}[/tex]Suppose that $2700 borrowed for two years at an interest rate of 4.5% per year, compounded continuouslyFind the amount owed, assuming no payments are made until the end. not round any intermediate computations , and round your answer to the nearest cent
Answers
To find:
The amount owed.
Solution:
It is known that the amount owed when the money is compounding continuously at a rate of r per year for the time t years is given by:
[tex]A=Pe^{rt}[/tex]Here, P = 2700, r = 0.045, t = 2, so the amount is:
[tex]\begin{gathered} A=2700e^{(0.045\times2)} \\ =2700e^{0.09} \\ =2700(1.094) \\ =2954.27 \end{gathered}[/tex]Thus, the amount he owed after 2 years is $2954.27.
Find the length of x. Round answers to the nearest tenth if necessa 60° 30 у your answer
Answers
From our trig ratios, we can see that,
[tex]\begin{gathered} \frac{1}{x}\text{ =}\sin 30,\text{ x = }\frac{1}{\sin 30}\text{ = 2} \\ x=2 \end{gathered}[/tex]Solve the system of two equations in two variables. Y=1/4x+42x - 8y =9
Answers
The given system is
[tex]\mleft\{\begin{aligned}y=\frac{1}{4}x+4 \\ 2x-8y=9\end{aligned}\mright.[/tex]To solve this system, we substitute the first equation in the second one.
[tex]2x-8(\frac{1}{4}x+4)=9[/tex]Now, we solve for x.
[tex]\begin{gathered} 2x-\frac{8}{4}x-32=9 \\ 2x-2x=9+32 \\ 0=41 \end{gathered}[/tex]This means the system has no solutions.In other words, the system represents parallel lines.
6) What is the slope of the line represented in the table?02d)-112Choose
Answers
The equation of slope of the graph is,
[tex]Slope=\frac{y_2-y_1}{x_2-x_1}[/tex]Consider,
[tex]x_1=2,x_2=4,y_1=9,y_2=13[/tex]Then,
[tex]\text{Slope =}\frac{13-9}{4-2}=2[/tex]Therefore, the correct option is A
grading system 1. grading system 2test average-35% 45%final exam grade- 25% 15%projects-15% 15%homework-15% 10%class participation-10% 15%If your values are the following in your math class, which grading system would you prefer and why?test average=84final exam grade=72projects=68homework=88class participation=95
Answers
We have two grading systems, with different weights for different items.
We have to calculate, for a certain points of the different items, which grading systems gives a higher weighted average score.
To do so we multiply each percentage to each of the items points and add them all.
We start with grading system 1:
[tex]\begin{gathered} P1=0.35\cdot84+0.25\cdot72+0.15\cdot68+0.15\cdot88+0.1\cdot95 \\ P1=29.4+18+10.2+13.2+9.5 \\ P1=80.3 \end{gathered}[/tex]The grading system 1 gives an average score of 80.3.
We apply the grading system 2 coefficients and we get:
[tex]\begin{gathered} P2=0.45\cdot84+0.15\cdot72+0.15\cdot68+0.10\cdot88+0.15\cdot95 \\ P2=37.8+10.8+10.2+8.8+14.25 \\ P2=81.85 \end{gathered}[/tex]The grading system 2 gives an average score of 81.85.
With the grading system 2, the final score is a little higher than with grading system 1. So we would prefer the system 2.
A line has a slope of 8 and passes through the point (1,4). What is its equation in slope-intercept form? Show work
Answers
The equation of the line in slope intercept form is:
y = 8x - 4
Given, we have slope = 8
Point = (1,4)
Equation in slope intercept form is:
y = mx+c
let the point (1,4) ne (x₁,y₁)
and slope (m) = 8
y - y₁ = m(x-x₁)
y - 4 = 8(x - 1)
y - 4 = 8x - 8
y = 8x - 8 + 4
y = 8x - 4
Hence the equation in slope intercept form is y = 8x-4
Learn more about Coordinate geometry here:
brainly.com/question/7243416
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I need help please it’s due tomorrow For lines a and b identify which inverse operation should come first
Answers
Answer:
[tex]\begin{gathered} a\text{. }\frac{k}{7}=11+11\text{ Addition} \\ b\text{. }k=22\cdot7\text{ Multiplication} \\ c\text{. }k=154 \end{gathered}[/tex]Step-by-step explanation:
Solve the following equation:
[tex]\frac{k}{7}-11=11[/tex]To solve the following equation use inverse operations. Addition and subtraction are inverse operations, multiplication, and division too.
[tex]\begin{gathered} \frac{k}{7}-11=11 \\ \frac{k}{7}=11+11\text{ Addition} \\ k=22\cdot7\text{ Multiplication} \\ k=154 \end{gathered}[/tex]6. A local deli kept track of the sandwiches itsold for three months. The polynomialsbelow model the number of sandwiches sold, where s represents days.Ham and Cheese: 453-285 +33s + 250 Pastrami:-7.452 + 32s +180Write a polynomial that models the total number of these sandwiches that were sold.
Answers
ok
Total sandwiches = Hand and Cheese + Pastrami
= 4s^3 - 28s^2 + 33s + 250 - 7.4s^2 + 32s + 180
= 4s^3 - 35.4s^2 + 55s + 430
[tex]\text{ 4s}^3-35.4s^2\text{ + 55s + 430}[/tex]