Write the equation of the following parabolae in their canonical form and hence find their vertices, foci and directrix.
1.
[tex] {y}^{2} - 6y - 2x + 19 = 0[/tex]
2.
[tex] {x}^{2} + 4x + 4y + 16 = 0[/tex]
Given:
y² - 6y - 2x + 19 = 0This is a horizontal parabola.
Canonical form of horizontal parabola is:
4a(x - h) = (y - k)², where (h, k) is vertexFocus is:
F(h + a, k)Directrix is:
x = h - aConvert the equation:
y² - 6y - 2x + 19 = 0y² - 6y + 9 - 2x + 10 = 0(y - 3)² = 2x - 10(y - 3)² = 4(1/2)(x - 5)We got:
h = 5, k = 3, a = 1/2Focus is:
F(5 + 1/2, 3) = F(5.5, 3)Directrix is:
x = 5 - 1/2 = 4.5#2Given:
x² +4x + 4y + 16 = 0This is a vertical parabola.
Canonical form of vertical parabola is:
4a(y - k) = (x - h)², where (h, k) is vertexFocus is:
(h, k + a)Directrix is:
y = k - aConvert the equation:
x² + 4x + 4y + 16 = 0x² +4x + 4 + 4y + 12 = 0(x + 2)² = -4y - 12(x + 2)² = 4(-1) (y + 3)We got:
h = - 2, k = -3, a = - 1Focus is:
F(-2, -3 - 1) = F(-2, - 4)Directrix is:
y = -3 - (-1) = - 2Which function has the graph shown below? *
a. f(x) = x² - 4
b. f(x) = x² + 4
c. f(x) = (x + 4)²
d. f(x) = (x - 4)² opps dont forget to change the sign
Answer:
C
Step-by-step explanation:
yeah-ya......... right?
What is the next term in the sequence 58, 47, 36, 25,. ? –58 –8 14 69.
Answer:
14
Step-by-step explanation:
58, 47, 36, 25,. ?
Each term is 11 less than the preceding term
the term after 25 will be
25 - 11 = 14
express the function graphed on the axes below as piecewise function
for x<-4
for x>2
Answer:
<--------o o------------->
-4 2
Step-by-step explanation:
Because the sign in the inequalities is only greater than/ less than (not equal to), we know that there is an open dot on x=-4 and on x=2.
From there, we shade the area on the graph that is true to the function. So, we can test points.
First we will test x=-5
-5<-4 --> this is true, so we will shade to the left of x=-4
Now test x=0
0<-4 --> this is false
0>2 --> this is also false, so the area between the two open dots will not be shaded
Now test x=3
3>2 --> this is true, so we will shade to the right of x=3
HELP!!! IM CONFUSED
Answer:
2/3Step-by-step explanation:
If we want to find the slope, the most easiest way to find the slope is to use 'Rise/Run'. Two points are given, lets use those points and find the slope.
=> We see that the rise is 2. So 2 will be our numerator,
=> We can also see that the run is 3. So 3 will be our denominator.
What do we get?
We get 2/3 as our slope. Therefore, B is our answer. Hoped I helped.
the perimeter of rectangle is 2x² + 4x - 4y. its length is (2x - 3y). find the breadth of rectangle
plz help fast plz plz
Perimeter = 2 (l + b)
2x² + 4x - 4y = 2 {(2x - 3y) + b}
2x² + 4x - 4y = (4x - 6y) + 2b
2x² + 4x - 4y - (4x - 6y) = 2b
2x² + 4x - 4y - 4x + 6y = 2b
2x² + 2y = 2b
(2x² + 2y)/2 = b
x² + y = b
Breadth = x² + y
3x-8=3(1x-3)-2
whats the answer to that problem
Answer:
-3
Step-by-step explanation:
......................
solve pls brainliest
1) No, because it is a repeating decimal
2) Yes, because it is neither terminating nor repeating
3) Yes, because it is a terminating decimal
4) No, because it is a repeating decimal
Simplify.
x2+2x−3/
x−4/
2x2+5x−3/
x^2−16
x2−x−12/2x−3
x2−5x−4/2x−1
x2+3x−4/2x−1
x2+x−12/2x−3
Answer:
x^2 + 7x- 3/x - 3/x^2 -16
Step-by-step explanation:
Key: ( ^ ) means exponent
= x^2 + 2x- 3/x -2x^2 + 5x- 3/x^2 -16
= x^2 - 2x^2 + 2x+5x - 3/x- 3/x^2 -16
= x^2 - 2x^2 = -x^2
= -x^2 + 2x + 5x- 3/x- 3/x^2-16
As you see you add 2x and the 5x and got 7x
= Answer : x^2 + 7x- 3/x - 3/x^2 -16
Answer:
I think the answer is x^2+3x-4/2x-1
can anyone please help me asap? thanks in advance.
1. In three minutes Alex typed 120 words. At this rate, how long would it take him to type a 4800 word assignment?
2. The ratio of the length to the width of the Canadian flag is 2:1. What is the width of a 50 cm long Canadian flag?
3. A bulk nut mixture is priced at $1.14 per 100 grams. How much is 600g of this mixture?
please show ur work for each.
Answer:
1. 2 hours
2. 25cm
3. 6.84
Step-by-step explanation:
120÷3=40
4800÷40=120 so 2 hours
for the second one just divide 50 in half
for 3 just do $1.14×6
Answer:
1. 120 min
2. 25 cm
3. $6.84
Step-by-step explanation:
1. 120 words : 3min
multiply each side by 40 because 120 words times 4 is 4800 words
4800 words : 120min
2. 2 : 1 = length : width
multiply each side by 25 because 2 times 25 is 50 cm
50 cm : 25 cm
3. $1.14 : 100 grams
multiply each side by 6 because 100 grams times 6 is 600 grams
$6.84 : 600 grams
1428 rounded to the nearest thousandth
Answer:
1428- one is in the thousandth place
the number beside is lower than five so drop it and add zero to the end
1000 -is now your answer
Step-by-step explanation:
hope this helps if not then sorry goodluck and bye
The number 1428 to the nearest thousand is 1000.
When you round a number to a certain digit, you have to check the value of the digit before the place you want to round off to.
1. If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.
2. If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down.
Here, the question said the nearest thousand, so I had to look at the value in the hundred places which is 4 and less than 5.
Hence round the number down.
So, 1428 to the nearest thousand is 1000.
To learn more about rounding numbers visit:
brainly.com/question/27207159
#SPJ3
please help with statistic 20
Part A
p = 0.32 = probability of someone voting by internet
n = 13 = sample size
x = 10 = number of people who voted by internet
Apply the binomial probability formula.
[tex]P(x) = (_n C _x)*(p)^{x}*(1-p)^{n-x}\\\\P(10) = (_{13} C _{10})*(0.32)^{10}*(1-0.32)^{13-10}\\\\P(10) = (286)*(0.32)^{10}*(0.68)^{3}\\\\P(10) \approx 0.0010124942242\\\\P(10) \approx \textbf{0.00101}\\\\[/tex]
Note: the [tex]_n C_x[/tex] refers to the combination formula.
Answer: 0.00101=============================================================
Part B
We could apply the binomial theorem for the following values of x: {10,11,12,13}. Then would add up the results.
However, such a task is fairly tedious and it's more efficient to use computer software (or a graphing calculator). Also, there's the element of limited time that you'll need to consider. I showed the steps for part A above because your teacher may have wanted you to list them. Usually it's better to rely on software for that task as well. At the very least, it's useful to have software to check your answer.
Whichever method you use, you should find the following:
P(10) = 0.00101P(11) = 0.00013P(12) = 0.00001P(13) = 0The last value isn't exactly 0, but it's so small that it's effectively zero. This is because we only have 5 decimal places to work with.
Add up those four values to get:
[tex]P(x \ge 10) = P(10)+P(11)+P(12)+P(13)\\\\P(x \ge 10) \approx 0.00101+0.00013+0.00001+0\\\\P(x \ge 10) \approx 0.00115\\\\[/tex]
A faster shortcut is to use your calculator's binomCDF function.
This result of 0.00115 is fairly small. The usual distinction we make between whether a probability is small or not is to set up some kind of threshold. This threshold is known as the significance level. By default, it's set to 0.05 unless your teacher specifies otherwise. Another common significance level is 0.01, but it's usually mentioned.
Since 0.00115 is smaller than 0.05, and even 0.01, we consider the probability of getting 10 or more internet voters to be a significant event. It's fairly unusual to get 10 or more people voting by internet in this sample of n = 13 people.
Answer: Choice A) Yes, because the probability of 10 or more is 0.00115, which is low.=============================================================
Part C
Like with part B, we could find the binomial probability values for x = {1,2,3,...,11,12,13}. We could add up the values like I did, or use the binomCDF function which is faster.
Another approach is to use the complement of the event "at least 1". If x is some number in the set {0,1,2,..,12,13}, then either [tex]x = 0[/tex] or [tex]x \ge 1[/tex]
From this, we can say
[tex]P(x=0) + P(x \ge 1) = 1\\\\P(x \ge 1) = 1-P(x=0)\\\\P(x \ge 1) \approx 1-0.00665\\\\P(x \ge 1) \approx 0.99335\\\\[/tex]
This then rounds to 0.993
Answer: 0.993YES I WILL BE GIVING A BRANLIST
Which function has the greater rate of change? What is that value?
Answer:
To find the rate of change you use the formula, Y2-Y1/X2-X1.
Function A:
You can substitute in any two points. The points I will use are (0,0) and (1,1).
1-0/1-0
1/1
1
The rate of change for Function A is 1.
Function B:
The points I will use are (2,1) and (4,2).
2-1/4-2
1/2
The rate of change for Function B is 1/2.
Since 1 is larger than 1/2, Function A has a larger rate of change. The value is 1.
Hope this helps! :)
If A(2, 3) and B(-4, -6), find AB.--
[tex] \huge \bf༆ Answer ༄[/tex]
The distance between points can be solved using Distance formula (similar to Pythagoras theorem)
[tex] \boxed { \sf D = \sqrt{(x2 - x1) {}^{2} + {(y2 - y1) {}^{2} } }}[/tex]
Put the values : -
[tex] \sf D = \sqrt{ (2 - ( - 4)) {}^{2} + (3 - ( - 6)) {}^{2} } [/tex][tex] \sf \: D = \sqrt{ {(6)}^{2} + (9) {}^{2} } [/tex][tex] \sf D = \sqrt{36 + 81} [/tex][tex] \sf D = \sqrt{117} [/tex][tex] \sf D = 3 \sqrt{13} [/tex]Distance between the points = 3√13 units
[tex]꧁ \: \large \frak{Eternal \: Being } \: ꧂[/tex]
Answer:
If you are trying to find the line, simply use a graph.
Step-by-step explanation:
How do you make chicken napoleon page 145
In this exercise we have to use the knowledge of polygon areas to calculate the area of each of the informed objects, so we have to:
1) [tex]h = 19.1 in[/tex]
2) [tex]a = 6.7 ft[/tex]
3) [tex]e = 2.3 m[/tex]
4) [tex]y = 9.8 cm[/tex]
5) [tex]o = 71.6 ft[/tex]
6) [tex]e = 15.3 in[/tex]
7) [tex]y = 41.5 m[/tex]
8) [tex]o = 13.7 cm[/tex]
9) [tex]p = 18.5 ft[/tex]
10) [tex]s = 25.8 in[/tex]
11) [tex]b = 61.3 m[/tex]
12) [tex]n = 6.2 cm[/tex]
Then each of the figures will have its own area formula that corresponds to:
1) For the rectangle we find that:
[tex]14/11 = h/15\\h = 19.1 in[/tex]
2) For the rectangle we find that:
[tex]5/a = 9/12\\a = 6.7 ft[/tex]
3)For the rectangle we find that:
[tex]3.7/6.5 = e/4.0\\e = 2.3 m[/tex]
4) For the triangle we find that:
[tex]10/8 = s/13\\s = 16.3 cm\\6/8 = y/13\\y = 9.8 cm[/tex]
5) For the triangle we find that:
[tex]n/70 = 53/88\\n = 42.2 ft\\o/70 = 90/88\\o = 71.6 ft[/tex]
6) For the triangle we find that:
[tex]t/9.1 = 11.2/5.7\\t = 17.9 in\\e/9.1 = 9.6/5.7\\e = 15.3 in[/tex]
7) For the triangle we find that:
[tex]u/48 = 43/74\\u = 27.9 m\\y/48 = 64/74\\y = 41.5 m[/tex]
8) For the triangle we find that:
[tex]6.2/11.8 = t/10.1\\t = 5.3 cm\\o/10.1 = 16.0/11.8\\o = 13.7 cm[/tex]
9) For the triangle we find that:
[tex]30/p = 13/8\\p = 18.5 ft[/tex]
10) For the trapezoid we find that:
[tex]20/s = 12/15.5\\s = 25.8 in[/tex]
11)For the triangle we find that:
[tex]l/46 = 125/75\\l = 76.7 m\\b/46 = 100/75\\b = 61.3 m[/tex]
12)For the triangle we find that:
[tex]5.1/4.3 = r/9.8\\r = 11.6 cm\\n/9.8 = 2.7/4.3\\n = 6.2 cm[/tex]
See more about areas at brainly.com/question/1631786
what is the solution to the system of equations
HELP DUE IN 1 MINUTE 5x^3 + 20x^2-160x
hi please help me with part b and can you see if i did a correctly pls?
a is right its 58
and in my opinion i think b would be 58*5=290 cents, since nickel is worth 5 cents.
but gotta check other people's answers
What is the value of y=3x−1 when x=4?
Answer:
11
Step-by-step explanation:
y=(3 x 4)-1
y=12-1
y=11
Answer:
y = 11
Step-by-step explanation:
Substitute the value for x.
[tex]y=3x-1\\y=3(4)-1\\y=12-1\\y=11[/tex]
A line that passes trough the point (7,3) with slope of -1 ( answer plesse I need help )
Answer:
Slope-Intercept Form:
The equation of a line in slope-intercept form is y=mx+b. Since we know that the slope is -1, the equation so far is y=-x+b. To find the value of b, substitute in the given point.
3=-7+b
Add 7 to both sides.
10=b
The equation of the line is slope intercept form is y=-x-10.
Point-Slope Form:
The equation of a line in point-slope form is y-y1=m(x-x1). Substituting in the given point and slope, the equation is y-3=-(x-7).
Hope this helps! :)
Answer:
y= -x + 10
Step-by-step explanation:
3 = -1(7) + b
3 = -7 + b
10 = b
Since the slope is -1, that means it's just -x
So y = -x + 10
WILL GIVE BRAINLIEST
PLEASE HELP
(LINKS/WRONG ANSWERS/WANNA BE FUNNY ANSWERS/NO ANSWERS/. WILL BE REPORTED!!!
Sully built a shelf 8 5/8 inches wide for his DVD collection. If each DVD is 3/8 inches
wide, how many can he fit on the new shelf?
Answer:
23
Step-by-step explanation:
8 5/8 = 69/8
Each DVD is 3/8 inches
Ignore the denominators
We have 69 and 3
69 is 23 times bigger than 3, so 23 DVD's can fit
A t-shirt increased in price by 1/4. After the increase, it was priced at £65. What was the original price of the t-shirt?
Answer:
52
Step-by-step explanation:
Given:
1/4
Price at 65
Solution:
Let x be the original price
Based on the given conditions, formulate: [tex]x[/tex] ×[tex](1+\frac{1}{4} )=65[/tex]
Apply Multiplicative Distribution Law: [tex]x+\frac{x}{4} =65[/tex]
Multiply both sides of the equation by the common denominator: [tex]x[/tex]×[tex]4+\frac{x X4}{4} =65 X 4[/tex]
Reduce the fraction: x×4+x=65×4
Multiply the monomials: 4x+x=65×4
Combine like terms: 5x= 65×4
Calculate the product or quotient: 5x= 260
Divide both sides of the equation by the coefficient of variable: x = [tex]\frac{260}{5}[/tex]
Calculate the product or quotient: x = 52
get the result: x = 52
Answer: x = 52
Please complete this for me
ohmygod help
10, 10, 18, 18, 10, 5, 12, 13
Find the median and mean number of hours for these students.
If necessary, round your answers to the nearest tenth.
Step-by-step explanation:
The mean (average) of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set.
The median is the middle value when a data set is ordered from least to greatest.
If there is an even number of items in the data set, then the median is found by taking the mean (average) of the two middlemost numbers.
so, the mean value is
(10+10+18+18+10+5+12+13)/8 = 96/8 = 12
the median is first not clear when ordering the data set, as we have an even number of elements.
5 10 10 10 12 13 18 18
so, we have to take the mean or average between the 2 middle numbers : 10 and 12.
(10+12)/2 = 22/2 = 11
the median is 11.
A place kicker expects to make 75% of his field goal attempts this season.If he attempts 36 feild goals this season how many is he exspected to make? show your work
Answer:
27
Step-by-step explanation:
75 % of 36 is 27. The place kicker expects he that will make 27 field goals. 36 − 27 = 9 The place kicker expects that he will miss 9 field goals.
Represent the following expressions as a power of the number a (a≠0): (a^2*a^2*a^2)^3
Guided Practice
Type your answer and then click or tap Done.
Use the ^ symbol (Shift+6 on the keyboard) to signify an exponent. For example, for 2 to the third power, enter 2^3.
Identify the quadratic term in the function.
f(x)=2x^2−3x+5
Answer:
2x^2
Step-by-step explanation:
Q:
identify the quadratic term in the function f(x)=2x^2-3x+5
A:
The quadratic term is 2x^2.
Answer:
2x2-3x-5=0
Step-by-step explanation:
(2x2 - 3x) - 5 = 0
Answer:
The quadratic term in the function is
Step-by-step explanation:
Given : Function
To find : Identify the quadratic term in the function ?
Solution :
The quadratic form of the function is
Where, is quadratic term.
On comparing with given function,
is the quadratic term.
Therefore, the quadratic term in the function is
what is the correct Answer?!
Answer:
B
Step-by-step explanation:
2⁶
2³
2⁶
2³
then add the ⁶+³+⁶+³ =18
2¹⁸
Jessica and her brother collects stamps. When Jessica gives her brother 1% of her stamps, she has 2,475 stamps left. Calculate how many stamps Jessica had originally.
Answer:
2500
Step-by-step explanation:
2475 stamps is 99% of her original number of stamps.
SO,
[tex]2475 \div 99\% = 2500[/tex]
She originally had 2500 stamps
