find the vertex, focus and equation of the directrix for the conic given by (x + 1)^2 = -20(y - 3).
sketch a graph of this conic
Answers
Hello,
The conic is a parabola ,
vertex (-1,3)
focus : (-1,-2)
directrix: y=8
equation: y= - 1/20x²-1/10*x+59/20
solution in picture
The vertex is v(-1,3) , focus is f(-1,8) and the equation of directrix is y = -2.
What is a parabola?A parabola is a plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed line. The equidistant from a fixed point called the focus (F), and the fixed-line is called the directrix (x + a = 0).
For the given situation,
The standard form of equation of parabola is given by, [tex]y=\frac{1}{4p}(x-h)^{2}+k[/tex]
The vertex is given by [tex]v(h,k)[/tex]
The focus is given by [tex]f(h,k-p)[/tex]
The equation of directrix is given by [tex]y=k+p[/tex]
The given equation is [tex](x+1)^{2} =-20(y-3)[/tex]
On rearranging the given equation in standard form,
⇒ [tex](x+1)^{2} =-20y+60[/tex]
⇒ [tex](x+1)^{2} -60=-20y[/tex]
Divide by 20 on both sides,
⇒ [tex]\frac{(x+1)^{2}}{20} +4 = y[/tex]
⇒ [tex]y=\frac{-1}{(4)(5)} (x+1)^{2} +3[/tex]
On comparing the above equation with the standard form,we get
[tex]p=-5, h=-1, k=3[/tex]
⇒ [tex]k-p=3-(-5)\ =8[/tex]
Hence we can conclude that the vertex is v(-1,3), focus is f(-1,8) and equation of directrix is y=-2.
Learn more about a parabola here
https://brainly.com/question/7492359
#SPJ2
Related Questions
Mr smith owns a bike store and typically marks up the bikes 20% over the price that the bikes cost him. The bikes cost him 69.95.
Need answer asap pls help will mark as brainliest!!
Answers
Answer: $83.94
Step-by-step explanation:
20% = 0.269.95 + 69.95(0.2) = 69.95(1 + 0.2) = 69.95(1.2) = 83.94
Find the integral of x(4x² + 1) from 0 to 2. a. 18 c. 22 b. 16 d. 20
Answers
Answer:
a. 18
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightDistributive Property
Algebra I
Terms/CoefficientsCalculus
Integrals
Definite IntegralsIntegration Rule [Reverse Power Rule]: [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Rule [Fundamental Theorem of Calculus 1]: [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]
Integration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
Integration Property [Addition/Subtraction]: [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle \int\limits^2_0 {x(4x^2 + 1)} \, dx[/tex]
Step 2: Integrate
[Integrand] Distribute x [Distributive Property]: [tex]\displaystyle \int\limits^2_0 {(4x^3 + x)} \, dx[/tex]Rewrite Integral [Integration Property - Addition/Subtraction]: [tex]\displaystyle \int\limits^2_0 {4x^3} \, dx + \int\limits^2_0 {x} \, dx[/tex]Rewrite 1st Integral [Integration Property - Multiplied Constant]: [tex]\displaystyle 4\int\limits^2_0 {x^3} \, dx + \int\limits^2_0 {x} \, dx[/tex][Integrals] Reverse Power Rule: [tex]\displaystyle 4(\frac{x^4}{4}) \bigg| \limits^2_0 + (\frac{x^2}{2}) \bigg| \limits^2_0[/tex]Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]: [tex]\displaystyle 4(4) + 2[/tex]Evaluate: [tex]\displaystyle 18[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
Book: College Calculus 10e
18x-108
-----------
6x-54
simplify the expression
A.
B.
C.
D.
Answers
Answer:
3x-2
---------
x-1
Step-by-step explanation:
simplify 18x/6x = 3x/1x
simplify 108/54 = 2/1
pls help im begging u..
Answers
what is 1/4 of the H.C.F of 24,16,48
Answers
Answer:
2
Step-by-step explanation:
What is 1/4 of the H.C.F of 24,16,48
Your answer
GIven data
24,16,48
let us find the HCF of the above numbers
24=2*2*2*3
16= 2*2*2*2
48=2*2*2*2*3
Hence the HCF is 2*2*2= 8
Let us find 1/4 of the HCF
=1/4*8= 2
Hence the final answer is 2
1). What is the equation of the line that is perpendicular to y= -3x+1 that passes through the point (9,0)?
2). What is the equation of the line that is parallel to y= -3x+1 that passes through the point (9,0)?
Answers
Answer:
Step-by-step explanation:
1) Slope of the given line = -3
slope of the perpendicular line = 1/3
y - 0 = 1/3(x-9)
y = 1/3x - 3
2) slope of the parallel line = -3
y - 0 = -3(x-9)
y = -3x + 27
Answer:
1). y = 1/3x - 3 2).y = -3x + 27
Step-by-step explanation:
1). y = 1/3x + b
0 = 1/3(9) + b
0 = 3 + b
-3 = b
y = 1/3x - 3
2)/ y = -3x + b
0 = -3(9) + b
0 = -27 + b
27 = b
y = -3x + 27
17:56 Dawn is trying to find out how much weight she can push across the room. She is really trying to find her __________.
Answers
Drag the tiles to the boxes to form correct pairs
Multiply the sets of numbers and match them with their products.
Answers
[tex]( - \frac{3}{4} )( \frac{7}{8} )[/tex]
[tex] = \frac{ - 3}{4} \times \frac{7}{8} [/tex]
[tex] = \frac{ - 21}{32} [/tex]
_______________________________________
[tex]( \frac{2}{3} )( - 4)(9)[/tex]
[tex] = \frac{2}{3} \times - 4 \times 9[/tex]
[tex] = \frac{ - 72}{3} [/tex]
[tex] = - 24[/tex]
_______________________________________
[tex]( \frac{5}{16} )( - 2)( - 4)( - \frac{4}{5} )[/tex]
[tex] = \frac{5}{16} \times - 2 \times - 4 \times \frac{ - 4}{5} [/tex]
[tex] = \frac{ - 160}{80} [/tex]
[tex] = \frac{ - 16}{8} [/tex]
[tex] = - 2[/tex]
_______________________________________
[tex](2 \frac{3}{5} )( \frac{7}{9} )[/tex]
[tex] = \frac{13}{5} \times \frac{7}{9} [/tex]
[tex] = \frac{91}{45} [/tex]
I hate this, I’m not sure how to do these
Answers
Answer:its B....sorry i didnt read the qn properly earlier
Answer:
tanθ = 9/40
Step-by-step explanation:
Can someone help me with this question please. I've been struggling.
Write the equation of the line of reflection
Answers
Answer:
y=-1
Step-by-step explanation:
Since we see an overlap, the line must cross through the original image.We can solve the equation of the line of reflection by realizing there is no slope because the reflection is parallel to the x-axis.The pie chart represents the results when 120 people in a shopping centre were asked which country they were born in. Uk:84 What fraction of people were born in the UK? Give your answer in its simplest form.
Answers
Answer:
22 people were born in the uk (66 ÷ 360) × 120=22
Step-by-step explanation:
Using the pie chart, the fraction of people born in the UK, is: 7/30.
What is a Pie Chart?A pie chart is a graphical representation used to describe the composition of a data using degrees or percentages.
84° is given as the number of people that were born in the UK.
That's about: 84/360 × 120 = 28 people.
28 out of 120 people would give us a fraction of: 28/120 = 7/30.
Learn more about pie chart on:
https://brainly.com/question/26851221
#SPJ2
Hans withdrew 40 dollars from his checking account write a signed number to represent this change in his account
Answers
Answer:
-40
Step-by-step explanation:
I assume a signed number means a number with a positive or negative sign in front of it. If you withdraw cash from your checking account, your checking account amount decreases, so it would be like subtracting 40 dollars, or -40.
Hope this helps (●'◡'●)
Ben has twenty-six coins in her pocket are all dollars(1$ coins) and quarters, and they add up to seventeen dollars in value. How many of each coin does he have
Answers
Answer:
14 $1 coin
12 quarter coin
Step-by-step explanation:
Let :
x = $1 dollar coin
y = $0.25 (1 quarter) coin
x + y = 26 - - - (1)
1x + 0.25y = 17 - - - - (2)
From (1) :
x = 26 - y
Put x = 26 - y in (2)
1(26 - y) + 0.25y = 17
26 - y + 0.25y = 17
-y + 0.25y = 17 - 26
-0.75y = - 9
Divide both sides by - 0.75
-0.75y /- 0.75 = - 9 / - 0.75
y = 12
Put y = 12 in (1)
x = 26 - 12
x = 14
What is a counterexample to this claim?
All quadrilaterals are parallelograms.
OA a rectangle
OB.
a rhombus
ОС. .
a square
OD.
a trapezoid
Answers
Answer:
The answer is D.
Step-by-step explanation:
Which of the following numbers does not have
factors that include the smallest factor (other
than 1) of 119 ?
A. 28
B. 35
C. 40
D. 63
Answers
Answer:
C. 40
Step-by-step explanation:
The smallest factor of 119 (other than 1) is 7.
28/7 = 4,
35/7 = 5,
40/7 = 5 5/7
63/7 = 9
So it is 40
What is the slope of the line shown in the graph?
A coordinate plane is shown. Points are graphed at −3 comma 2 and −1 comma −1. The points are connected by a line.
−3 over 2
−1 over 2
3 over 2
Undefined
Answers
plisss help me in thiss
Answers
Answer:
x=80
Step-by-step explanation:
The angle of a line is 180*.
The equation would be (x+20)+x=180
Subtract 20 from both sides: 2x=160
Divide by 2: x=80
That's your answer!
I hope this helps!
Answer:
x=80
Step-by-step explanation:
I cant explain well but edge 2021 never lie's!
help me to solve this question please faster thankyouu
Answers
Answer:
Step-by-step explanation:
u799
Solve for x. Round to the nearest tenth of a degree, if necessary.
Answers
Answer:
49.6°Step-by-step explanation:
tangent = opposite / adjacenttan x = 40/34x = arctan (40/34)x ≈ 49.6°Step-by-step explanation:
[tex] \rm{tangent \: = \: opposite \:/ adjacent} \\ \rm{tan \: x \: = \: 40 \:/ 34} \\ \rm \: x \: = arctan \: (40 \:/ 34) \\ \: \rm {x \: = \boxed{49. \: 60°}}[/tex]
a right triangle is 18 inches long and a hypotenuse that is 30 inches long. what is the perimeter, in inches, of this triangle?
Answers
Answer:
The perimeter is 72 inches
Step-by-step explanation:
using the pythagorean theorem we can solve for the missing leg by plugging in the values we know.
[tex]a^{2} + b^{2} = c^{2} \\18^{2} + b^{2} = 30^{2} \\324 + b^{2} = 900\\ b^{2} = 900-324\\b^{2} = \sqrt{576} \\b= 24[/tex]
now you just add the values, 30 + 24 + 18
The triangle below is isosceles. Find the length of side xx in simplest radical form with a rational denominator.
Answers
Answer:
Solution given:
Since the given triangle is isosceles and right angled triangle
perpendicular [p]=base[b]=x
hypotenuse [h]=6
we have
by using Pythagoras law
p²+b²=h²
x²+x²=6²
2x²=36
x²=36/2
x²=18
x=[tex]\sqrt{18}[/tex]
x=[tex]\bold{3\sqrt{2}}[/tex]
The length of side x in simplest radical form with a rational denominator is [tex]3\sqrt{2}[/tex]
Let the perpendicular base be x.Given the following data:
Hypotenuse = 6 units.To determine the length of side x in simplest radical form with a rational denominator, we would apply Pythagorean's Theorem:
What is the Pythagorean Theorem?Mathematically, Pythagorean's Theorem is given by this formula:
[tex]c^2 = a^2 + b^2[/tex]
Substituting the given parameters into the formula, we have:
[tex]6^2 = x^2 + x^2\\\\36=2x^2\\\\18=x^2\\\\x=\sqrt{18} \\\\x=3\sqrt{2}[/tex]
Read more on Pythagorean Theorem here: https://brainly.com/question/16176867
f(x) = x5 – 9x3 Choose all of the zeroes of f(x)
Answers
Answer:
[tex]x^{3} (x^{2} -9)[/tex]
[tex]x^{3} (x+3)(x-3)[/tex]
zeros at : 0,3,-3
Step-by-step explanation:
URGENT PLS ANSWER QUICKLY
Answers
Answer:
5 is 14cm . 14 is 2pie r. 6 is 120
Answer:
Question 5 = 14
Question 6 = 120
I hope this helped!
Tony is 3 years older than Marie. This can be modeled with the following equation
Answers
Answer:
M = T - 3
Step-by-step explanation:
Given
T = M + 3 ( subtract 3 from both sides )
T - 3 = M , that is
M = T - 3
Answer:
[tex] \small \sf \: M = { \fbox { \green{T} } } - 3[/tex]
Step-by-step explanation:
T = M + 3
Swap the sides of of equations .
M + 3 = T
subtract 3 from both side
M + 3 - 3 = T - 3
M = T - 3
Aflati al 2013 lea termen al unei progresii aritmetice cu termenul al treilea egal cu 12 si diferenta a doi termeni consecutivi, 4.
Answers
Răspuns:
8052
Explicație pas cu pas:
Al treilea termen al unei progresii aritmetice:
T (n) = a + (n - 1) d
Unde ;
a = primul termen; d = diferență comună = 4; n = al treilea termen (numărul termenului)
Al treilea (3) termen:
T (3) = a + (3-1) 4
T (3) = 12
12 = a + 2 (4)
12 = a + 8
12 - 8 = a
4 = a
Prin urmare, primul termen = a
Al 2013-lea mandat;
T (2013) = a + (2013-1) d
T (2013) = 4 + (2012) 4
T (2013) = 4 + 8048
= 8052
Simplify:
a.5³×5‐²×5⁴.
b.a⁴×a‐²×x³.
c.(x⁵)²×(y⁵)³
__________
(x³)³×(y²)²
Answers
Answer:
a. 125 * 0.04 * 625 = 5 * 625 = 3125
b. a^2 * x^3
c. x^10 * x^ y^15
Last one: x^9 * y^4
Step-by-step explanation:
Because yes.
what is the value of x?
Answers
Answer:
x°=70°{ vertically opposite angle are equal}hope it helps.stay safe healthy and happy..We know that,
Vertically opposite angles are equal,
So, x° = 70°
=> x = 70
HELP! Use the elimination method to solve the system of equations.
A. (0,8)
B. (-4,0)
C. (-2,4)
D. (0,3)
Answers
Answer:
B, (-4,0)
Step-by-step explanation:
2(4x - 2y = -16) 8x - 4y = -32
8x - 4y = -32
+ -3x + 4y = 12
5x = -20
x = -4
4(-4) - 2y = -16
-16 - 2y = -16
-2y = 0
y = 0
Simplify the expression by combining like
terms:
2b + 7b2 - 2 + 3b - 1 + b
Answers
Answer:
[tex]7b^2+6b-3[/tex]
Step-by-step explanation:
Given:
[tex]2b+7b^2-2+3b-1+b[/tex]
Combine like terms.
[tex]7b^2+6b-3[/tex]
Hope this helps.
i need help with this!!!!
Answers
Answer:
Tomas
Step-by-step explanation:
Divide Distance by Time
[tex]\frac{distance}{time}[/tex] = speed
Answer:
Tomas is the fastest
Step-by-step explanation:
To find out who is the fastest, divide the distance by the time to get the unit rate. (The amount they drove each hour.)
Maren: 60 / 1 = 60
Safiya: 120 / 3 = 40
Tomas: 84 / 1.2 = 70
Cam: 75 / 1.5 = 50
Tomas has the largest unit rate therefore he is the fastest.