Given:
The given equation is
[tex]y-3=(2-x)^2[/tex]
To find:
The vertex, focus, and directrix.
Solution:
The equation of a parabola is
[tex]y-k=a(x-h)^2[/tex] ...(i)
where, (h,k) is vertex, [tex]\left(h,k+\dfrac{1}{4a}\right)[/tex] and directrix is [tex]y=k-\dfrac{1}{4a}[/tex]
We have,
[tex]y-3=(2-x)^2[/tex]
It can be written as
[tex]y-3=(-(x-2))^2[/tex]
[tex]y-3=(x-2)^2[/tex] ...(ii)
On comparing (i) and (ii), we get
[tex]h=2,k=3,a=1[/tex]
Vertex of the parabola is (2,3).
[tex]Focus=\left(2,3+\dfrac{1}{4(1)}\right)[/tex]
[tex]Focus=\left(2,3+\dfrac{1}{4}\right)[/tex]
[tex]Focus=\left(2,\dfrac{13}{4}\right)[/tex]
Therefore, the focus of the parabola is [tex]\left(2,\dfrac{13}{4}\right)[/tex].
Directrix of the parabola is
[tex]y=3-\dfrac{1}{4(1)}[/tex]
[tex]y=3-\dfrac{1}{4}[/tex]
[tex]y=\dfrac{11}{4}[/tex]
Therefore, the directrix of the parabola is [tex]y=\dfrac{11}{4}[/tex].
Analyze the biconditional statement below and complete the instructions that follow.
A polygon is a pentagon if and only if it has five sides.
Express the given biconditional as the conjunction of two conditionals.
A.
If it is a pentagon, then it has five sides. If it is a polygon, then it is a pentagon.
B.
If it is a pentagon, then it is a polygon. If it is a polygon, then it is a pentagon.
C.
If it is a pentagon, then it is a polygon. If it is a polygon, then it has five sides.
D.
If it is a pentagon, then it has five sides. If the polygon has five sides, then it is a pentagon
Answer:
A polygon is a pentagon if and only if it has five sides."If this statement is true, then which of the follow… Get the ... The given statement is of the form
Step-by-step explanation:
hope it helps you
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Answer:
D. If it is a pentagon, then it has five sides. If the polygon has five sides, then it is a pentagon
Step-by-step explanation:
Given statements;
A polygon is a pentagon if and only if it has five sides.
From the statement we see that a pentagon has 5 sides. A body of this structure with 5 sides can be classified as a polygon.
Therefore, this bi-conditional statement is premised on two "if"s,
If it is a pentagon then we are dealing with a body with 5 sides.
And if such body has five sides, it is a polygon called pentagon
The correct option is D
Choice A, B and C are logically flawed.
A. If it is a pentagon, then it has five sides. If it is a polygon, then it is a pentagon.
The emboldened part we do not know.
B. If it is a pentagon, then it is a polygon. If it is a polygon, then it is a pentagon
The emboldened part is flawed.
C. If it is a pentagon, then it is a polygon. If it is a polygon, then it has five sides.
We do not know if all pentagons have 5 sides.
please help me!!! I will make you brainiest!!!
Answer:
C
Step-by-step explanation:
y-intercept is 3 down and slope is the same
Guadalupe Fue a la mercería a comprar 15.5 m de encaje blanco que necesitaba para la clase de costura. Si cada metro cuesta $5.60, ¿cuanto pago por todo el encaje que necesitaba?
Answer:
Costo total= $86.6
Step-by-step explanation:
Dada la siguiente información:
Guadalupe Fue a la mercería a comprar 15.5 m de encaje blanco que necesitaba para la clase de costura. Cada metro cuesta $5.60.
Si y= costo total, y x= cost por metro, entonces:
y= 5.6x
Para 15.5 metros:
y= 5.6*15.5= $86.8
You can factor a quadratic function using the completing the square method for any coefficient of the a term. True or false
Answer:
Step-by-step explanation:
Find the minimum or maximum value of the function y = -x– 4x - 2. Describe the domain and range of the function, and
where the function is increasing and decreasing.
Answer: How can this function have a max/min if it’s not a parabola?
When you graph this it’s a line.
313 multiplied by t is equal to 180
Answer:
t= 180/313 or 0.57507987
If m∠MNP = 107°, what is m∠MQP?
Answer:
180 - 107 = 73
Step-by-step explanation:
Which table represents a linear function?
Х
1
2.
3
4
y
3
7
11
15
o
Х
1
2.
3
4
у
3
8
15
21
х
1
2.
3
4
y
3
9
3
9
Х
1
2
3
у
3
9
27
Answer: D
I believe :0
The table which represents a linear function is table 4.
What is a function?
Function is a type of relation, or rule, that maps one input to specific single output.
In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable). In mathematics and the physical sciences, functions are indispensable for formulating physical relationships.
Linear function is a function whose graph is a straight line
We are given that;
The tables in the question
Now,
The table that represents a linear function is:
X Y
1 3
2 7
3 11
4 15
The reason this is a linear function is that for each increase in the input value of X by 1, the output value of Y increases by a constant amount of 4. In other words, the rate of change of Y with respect to X is constant at 4, indicating a linear relationship between the two variables.
Therefore, the answer of the function will be table 4.
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Question Details
What is the slope of a line that passes through the
points (-2, 12) and (-6, 8)?
Answer:
m = 1
Step-by-step explanation:
Use the given points to solve the slope formula.
(-2, 12) (-6, 8)
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
m is the slope, x is the first number in the given point, and y is the second. (It doesn't matter which point you choose to be x1,y1 or x2,y2)
[tex]m=\frac{8-12}{-6-(-2)}[/tex] (subtracting negative cancels out and becomes adding a positive)
[tex]m=\frac{-4}{-4}[/tex] (the negatives cancel out and become positive)
m = 1
I need to find the value of x
Answer:
I think I already gave the answers to you on your previous question to find the value of y. I gave the x and y answers.
Step-by-step explanation:
x = 98
what is 6 feet below sea level
Answer:
-6
Step-by-step explanation:
Answer:
-6
Step-by-step explanation:
sea level is 0 and below sea level would have to be a negative and you would takr the number of feet below sea level and that would be your answer in this case its -6
Divide x²-14× +45 by X-9
5/8 + (-7/8) how do i get the answer
Answer:
-0.25 = -1/4Step-by-step explanation:
The answer ( depending on what you're asking ) either fraction or decimal is this:
Decimal: -0.25
Fraction: -1/4
Hope this helps! <3
Answer:
Your answer is - 1/4
Step-by-step explanation:
I'm the best at math my grade is 100 so believe me
We want to decide whether to employ a human operator or buy a machine to paint steel beams with a rust inhibitor. Steel beams are produced at a constant rate of one every 14 minutes. A skilled human operator takes an average time of 700 seconds to paint a steel beam, with a standard deviation of 300 seconds. An automatic painter takes on average 40 seconds more than the human painter to paint a beam, but with a standard deviation of only 150 seconds. Estimate the expected waiting time in queue of a steel beam for each of the operators, as well as the expected number of steel beams waiting in queue in each of the two cases. Comment on the effect of variability in service time.
Answer:
Manual painter, expected waiting time = 0.085
Automatic painter expected waiting time = 0.031
Step-by-step explanation:
See attachment
Carlos buys a phone that costs $250. He pays a monthly rate of $75. Write a function f(×) for the total amount that Carlos pays for using the phone for x month
-x + 2 = x+4
help please!
Answer:
x=-2
Step-by-step explanation:
hope this helps
follow me
Answer:
-1
Step-by-step explanation:
-x + 2 = x+4
-x-x = 4-2
-2x = 2
x= 2/-2
x= -1
hope it will help......
The median starting salary for new law school graduates is determined by
log(salary) = B0 + B1 LSAT + B2 GPA + B3 log(libvol) + b4 log(cost) + B5 rank + u,
where LSAT is the median LSAT score for the graduating class, GPA is the median college. GPA for the class, libvol is the number of volumes in the law school library, cost is the annual cost of attending law school, and rank is a law school ranking (with rank = 1 being the best).
i. Explain why we expect b5 < 0.
ii. What signs do you expect for the other slope parameters? Justify your answers.
iii. Using the data in LAWSCH85.RAW, the estimated equation is log(salary ) = 8.34 + .0047 * LSAT + .248 GPA + .095 log(libvol) + .038 log(cost) - .0033 rank n = 136, R^2 = .842
What is the predicted ceteris paribus difference in salary for schools with a median GPA different by one point? (Report your answer as a percentage.)
iv. Interpret the coefficient on the variable log(libvol).
v. Would you say it is better to attend a higher ranked law school? How much is a difference in ranking of 20 worth in terms of predicted starting salary?.
Step-by-step explanation:
1) we would have the expectation that b₅ < 0 because b₅ shows how salary responds to law school ranking. As the rank of law school increases then median starting salary for new law school graduates declines. there is an inverse relation between salary and rank, Coefficient of rank, b5 will be negative since it is less than 0
ii) B₁ is going to be positive because as median LSAT score for the graduating class goes up, so does the salary of graduates. we have B1 >0
B₂ will be positive as college median GPA rises, so does graduate salary.
B₃ will be positive because if the more volumes of book in library, the greater possibility of getting higher salary, so B₃ >0.
B₄ >0 as if annual cost is high , then there would be indictaes more facilities of learning for students, leading to more chances of high salaries , hence B4 >0.
B5<0 this has been explained in 1.
iii) predicted ceteris paribus difference in salary for schools with a median GPA different by one point
= coefficient of GPA
=0.248
= this 24.8% in percentages B₂ tells us that when other factors are held constant,increasing median gpa by 1 would cause 24.8 percent increase in salary predicted.
iv)holding other variable factors constant, increasing the volume in the law library would bring about predicted salary increase by 0.095%
v) due to the inverse relationship between rank of law school and salary, it is better to attend a law school with lower rank than that with higher rank
difference in ranking of 20 = 20*(-0.0033)
= -0.066 x 100
= -6.6%
if rank is lower by 20 units , then we will have salary to be 6.6% higher
Which expression is equivalent to s - 0.78s +0.28s?
0.58
1.5s
O 1-0.55
s – 0.5
Answer:
0.5s
Step-by-step explanation:
Solve for equation x by graphing -4^x+1=3x-4
Answer:The answer is B
x=0.75
I’m not sure though
Step-by-step explanation:
According to the Bureau of Labor Statistics, citizens remain unemployed for an average of 15.9 weeks before finding their next job (June, 2008). Suppose you want to show that Louisiana has been effective in getting their unemployed back to work sooner. You take a random sample of 50 citizens who were unemployed six months earlier and ask them to report the duration. You find that the average time spent unemployed was 13.4 weeks. Which of the following statements is the correct alternative hypothesis?
a. -2.64
b. -2.32
c. -2.11
d. -1.28
e. none of these are correct
Complete Question
According to the Bureau of Labor Statistics, citizens remain unemployed for an average of 15.9 weeks before finding their next job (June, 2008). Suppose you want to show that Louisiana has been effective in getting their unemployed back to work sooner. You take a random sample of 50 citizens who were unemployed six months earlier and ask them to report the duration. You find that the average time spent unemployed was 13.4 weeks with a sample standard deviation of the time unemployed is 6.7 weeks.
1 Which of the following statements is the correct alternative hypothesis?
2 The test statistic for testing the hypothesis is
a. -2.64
b. -2.32
c. -2.11
d. -1.28
e. none of these are correct
Answer:
1
The alternative hypothesis [tex]H_a : \mu < 15.9[/tex]
2
The test statistics [tex]z = -2.64 [/tex]
Step-by-step explanation:
From the question we are told that
The population mean value for time citizens remain unemployed is [tex]\mu = 15.9 \ weeks[/tex]
The sample size is n = 50
The sample standard deviation is 6.7 weeks.
The sample mean value for time citizens remain unemployed is [tex]\mu = 15.9 \ weeks[/tex]
The null hypothesis is [tex]H_o : \mu \ge 15.9[/tex]
The alternative hypothesis [tex]H_a : \mu < 15.9[/tex]
Generally test statistics is mathematically represented as
[tex]z = \frac{ \= x - \mu }{ \frac{s}{\sqrt{n} } }[/tex]
=> [tex] z = \frac{13.4 - 15.9}{\frac{6.7}{\sqrt{50}}}[/tex]
=> [tex]z = -2.64 [/tex]
The ratio of people who prefer chocolate chip cookies to oatmeal cookies is 5:2. If there were a total of 56 people surveyed, how many people prefer chocolate chip cookies?
Answer:
40
Step-by-step explanation:
5 + 2 = 7
56 ÷ 7 = 8
8 × 5 = 40
75bdivided by 230 need this answer to
Answer:
0.32608696
Step-by-step explanation:
what is the value of ÷ 2 1/3
Answer:
6÷2 1/3
Step-by-step explanation:
Juan is paid a salary of $2400 biweekly. Find the Juan's earnings per year.
Answer:
2,400x26=62,400
Step-by-step explanation:
you times it by 26 because he gets paid biweekly
PLEASE HURRY 100 POINTS!
Graph x > 2.
Answer:
see below
Step-by-step explanation:
We know that x > 2 that means the line at x = 2 is dotted since there is no equals sign
We shade to the right since x is greater
Answer:
sea below
Step-by-step explanation:
Ken and Leo weighed the same and their total weight was above 130 kg. After a year, Ken has lost 8 kg and is below 60 kg now. How heavy was Ken one year ago?
Answer:
68 kg
Step-by-step explanation:
How to solve: -x=14.
Answer:
x=-14
Step-by-step explanation:
Multiply each term in − x = 14 by − 1
Answer:
-14
Step-by-step explanation:
The value of y is directly proportional to the value of x.If y=35 when x=140, what is the value of y when x=70
A ship travels 200 miles due west, then adjusts its course 30° north of west. The ship continues on this course for 30 miles. Approximately how far is the ship from where it began?
Answer:
The answers D on Edg
Step-by-step explanation:
Just finished the test
The distance of the ship from the beginning is 226.48 miles far apart.
What is a triangle?A triangle is a flat geometric figure that has three sides and three angles. The sum of the interior angles of a triangle is equal to 180°. The exterior angles sum up to 360°.
For the given situation,
The diagram below shows the travelling of ship from A to C.
Let sides a = 30 miles, c = 200 miles,
The measure of angle B is [tex]\angle CBA = 180-30[/tex] [∵ Supplementary angle]
⇒ [tex]\angle CBA = 150[/tex]
Here two sides and one angle of triangle are provided.
The other side of the triangle, that is the distance traveled by the ship can be found by using the law of cosines.
The formula of law of cosines,
[tex]b = \sqrt{a^{2}+c^{2}-2ac (cosB ) }[/tex]
On substituting the values,
⇒ [tex]b = \sqrt{30^{2}+200^{2}-2(30)(200) (cos150 ) }[/tex]
⇒ [tex]b = \sqrt{900+40000-12000(-0.8660 ) }[/tex]
⇒ [tex]b = \sqrt{40900+10392 }[/tex]
⇒ [tex]b = \sqrt{51292}[/tex]
⇒ [tex]b=226.477[/tex] ≈ [tex]226.48[/tex]
Hence we can conclude that the distance of the ship from the beginning is 226.48 miles far apart.
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What is the x intercept?
Look at the picture.
Answer:
-2
Step-by-step explanation:
the x-intercept is where the line of the slope crosses the x-axis
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