Q10 Q2.) Find the standard form of the equation of the parabola satisfying the given conditions.
Answers
1. You have that the standard form of the equation of the parabola must satisfy the following conditions given in the exercise above:
Focus: (-1,4) and Directrix: y=2
2. Therefore you have:
√(x0-(-1))²+(y0-4)²=|y0-2|
(x0+1)²+(y0-4)²=(y0-2)²
3. When you simplify the expression above and clear y0, you obtain:
y0=y
y=1/4(x²+2x+13)
y=(x²/4)+(x/2)+(13/4)
Therefore, the answer is: y=(x²/4)+(x/2)+(13/4)
Related Questions
78 million in scientific notation
Answers
Answer:
[tex]78\ million=7.80\times 10^7[/tex]
Step-by-step explanation:
A number N can be written in scientific notation as :
[tex]N=p{\circ}0\times 10^q[/tex]
Where
p is the any real number
q is any integer
Here, the given number is 78 million. Firstly, we must know meaning of 1 million.
Since, [tex]1\ million=10^6[/tex]
[tex]78\ million=78.0\times 10^6[/tex]
To convert the above number in scientific notation, we can shift the decimal before 8 such that,
[tex]78\ million=7.80\times 10^7[/tex]
Hence, this is the required solution.
The service plan for edith's cell phone charges her $29.50 a month for 300 minutes and 10¢ a minute for each additional minute over the 300 minutes. if edith uses 400 minutes this month, how much money will she have to pay?
Answers
The expression 5(F-32) divided by 9 yes the Celsius temperature for a Fahrenheit temperature of F degrees C noon Fahrenheit temperature in Centerville was 86° what was the temperature in degrees Celsius
Answers
5(86 -32)/9 = 5(54/9) = 5(6) = 30
The temperature was 30 °C.
Answer:
30°C
Step-by-step explanation:
The following expression can be used to convert Farenheit degrees (°F) to Celsius degrees (°C).
°C = 5 . (°F - 32) / 9
If the temperature in Centerville is 86°F, we can replace this value in the previous expression to find its value in the Celsius scale.
°C = 5 . (°F - 32) / 9
°C = 5 . (86 - 32) / 9
°C = 5 . (54) / 9
°C = 270 / 9
°C = 30°C
Two positive numbers have a difference of four and a product of 96 what are the numbers
Answers
Answer:
The two positive numbers are 12 and 8.
Explanation:
The first phrase in the sentence tells us the difference between numbers equals 4, which can be represented a - b = 4
The second phrase tells us when multiplied together, it equals 96, which can be represented by the ab = 96, or a(b) = 96
So, first step is to list the factors of 96. I prefer to list them as pairs:
1, 96; 2, 48; 3, 32; 4, 24; 6, 16; and 8, 12
Now we plug each these pairs into the first equation to see if they satisfy the equation.
96 - 1 = 95 24 - 4 = 20
95 > 4 20 > 4
48 - 2 = 46 16 - 6 = 10
46 > 4 10 > 4
32 - 3 = 29 12 - 8 = 4
29 > 4 4 = 4
Because a = 12 and b = 8 satisfies both equations that represent the given sentence, the two positive numbers are 12 and 8.
if a plane leave the ski resort every hour. the first plane leaves at 10 and the second plane leaves at 4 how man planes leave each day
Answers
https://brainly.com/question/9934382
John plays a game in which he throws a baseball java questions
Answers
which of the following best describes the English expression the product of two and a number minus eleven
Answers
2n -11
_____
It is somewhat ambiguous, so could also be interpreted to mean
2(n -11)
Wording could be changed to remove the ambiguity, if one were interested in doing that.
Lance lived in Portugal and Brazil for a total of 14 months to learn Portuguese. He learned an average of 130 words per month when he lived in Portugal, and an average of 150 new words per month when he lived in Brazil. In total, he learned 1920 new words write a system of equations to represent this situation. Use x to represent Portugal, and y to represent Brazil.
Answers
Number of months that Lance lived in Brazil: y
Lance lived in Portugal and Brazil for a total of 14 months to learn Portuguese:
(1) x+y=14
He learned an average of 130 words per month when he lived in Portugal:
Number of words that Lance learned in Portugal: 130x
and an average of 150 new words per month when he lived in Brazil:
Number of words that Lance learned in Brazil: 150y
In total, he learned 1920 new words:
(2) 130x+150y=1920
Write a system of equations to represent this situation:
(1) x+y=14
(2) 130x+150y=1920
A right rectangular prism is shown. What shape best describes the cross section cut perpendicular to the base of a right rectangular prism? Parallelogram Trapezoid Rectangle Square
Answers
Rectangle
_____
That rectangle may be a square, but is not required to be.
The shape that best describes the cross-section cut perpendicular to the base of a right rectangular prism is a rectangle.
A cross-section cut perpendicular to the base of a right rectangular prism will always result in a rectangular shape.
This is because a rectangular prism has six faces, and the base of the prism is one of those faces.
When you make a cross-section cut perpendicular to the base, you are essentially slicing through the prism parallel to one of its other faces.
Since the base is a rectangle, the cross-section will also be a rectangle.
In summary, the cross-section cut of a right rectangular prism perpendicular to its base will consistently yield a rectangular shape due to the inherent geometry of the prism.
for such more questions on perpendicular
https://brainly.com/question/1091880
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Which number is not in scientific notation?
A: 1.10 ⋅ 103
B: 4.0 ⋅ 1016
C: 7.03 ⋅ 10−2
D: 350 ⋅ 102
Answers
the anser would be c fo it to be in scientific notation you have to have an exponet
Complete the inequality. 9% ___ 0.4
Answers
write parametric equations of the line 2x+3y=11
Answers
1. You have the following equation of the line given in the problem above: 2x+3y=11.
2. Therefore, you have:
x=t
3. When you substitute x=t into 2x+3y=11, you obtain:
2t+3y=11
4. Now, solve for y, as below:
3y=11-2t
y=(11/3)-(2t/3)
Therefore, the answer is:
x=t
y=(11/3)-(2t/3)
Answer:
C
Step-by-step explanation:
If youre doing the test ;)
limit approaches infinity of 3^n / 3n+1
Answers
If y varies inversely as the square of x, and y=7/4/ when x=1, find y when x=3
Answers
[tex]y= \frac{k}{ x^{2} } [/tex]
where k is a constant of proportionality. It is given that y = 7/4 when x = 1.
Using these values, we can write:
[tex] \frac{7}{4}= \frac{k}{1} \\ \\ k= \frac{7}{4}[/tex]
So, now the equation in terms of x and y can be written as:
[tex]y= \frac{7}{4 x^{2} } [/tex]
We are to find y when x = 3. So we can write:
[tex]y= \frac{7}{4(9)}=\frac{7}{36} [/tex]
Thus, for x= 3 value of y will be 7/36
what is the factored form of a fourth degree polynomial function with coefficients that has -3,1and 1+5i
Answers
(x +3)(x -1)(x -1 -5i)(x -1 +5i)
If you want the complex factors combined to a real factor, the factorization is
(x +3)(x -1)(x² -2x +26)
If sinø= 4/7, what is cosø?
Answers
arc sine (4/7) = theta
theta = 34.85 Degrees
cosine (34.85) = 0.82065
stella received a package in the shape of rectangular prism. the box has a length of 21/2 feet, a width of 11/2 feet, and a height of 4 feet. stella wants to cover the box with wrapping paper. how much paper will sge need?
Answers
The dimensions of the box are as follows:
length=21/2 ft
width=11/2 ft
height=4 ft
Area of the box is given by the formula:
SA=2lw+2lh+2hw
SA=2(21/2×11/2)+2(21/2×4)+2(11/2×4)
SA=2(231/4)+2(42)+2(11/2×4)
SA=115.5+84+44
SA=243.5 ft²
Stella will need 243.5 ft²
Answer:
Step-by-step explanation:
To get the amount of paper required to cover the box, we find the area of the box. The dimensions of the box are as follows:length=21/2 ftwidth=11/2 ftheight=4 ftArea of the box is given by the formula:SA=2lw+2lh+2hwSA=2(21/2×11/2)+2(21/2×4)+2(11/2×4)SA=2(231/4)+2(42)+2(11/2×4)SA=115.5+84+44SA=243.5 ft²Stella will need 243.5 ft²
Q # 15 find the volume of the sphere
Answers
[tex]4 \times 5 \times 5 \times 5 \times \pi \times \frac{1}{3} = \frac{500\pi}{3} \\ = \frac{1570}{ 3} = 523.33[/tex]
good luck
Area = (4/3)πr³
Where r ⇒ radius of the sphere
π=3.14
Area = (4/3)× 3.14 ×5³
=523.33333 in³
To the nearest cubic, the answer is 523 in³
Please Help: 25 Points!
Jeremy constructed this solid by combining two rectangular prisms and a square pyramid. What is the surface area of this figure?
Answers
A1 = (1/2) * (6) * (7)
A1 = 21
Rectangle area of the base:
A2 = (14) * (6)
A2 = 84
Area of the posterior rectangle:
A3 = (5) * (6)
A3 = 30
Area of the frontal rectangle:
A4 = (6) * (2)
A4 = 12
Area of the rectangle parallel to the base:
A5 = (8) * (6)
A5 = 48
Rectangle area located between posterior and front rectangles:
A6 = (3) * (6)
A6 = 18
Area of the side walls of the figure:
A7 = (14) * (2) + (3) * (6)
A7 = 28 + 18
A7 = 46
Superficial area:
A = 4 * A1 + A2 + A3 + A4 + A5 + A6 + 2 * A7
A = 4 * 21 + 84 + 30 + 12 + 48 + 18 + 2 * 46
A = 368
Answer:
A = 368 m ^ 2
Answer:
368
Step-by-step explanation:
The formula for finding the horsepower of a vehicle is: Horsepower = weight × ( velocity 234 ) 3 Weight is the total weight of the vehicle, driver and any passengers. Velocity is determined by the speed at the end of a quarter mile run. The newest hybrid auto weighs 2200 pounds and the driver is 180 pounds. At the end of the quarter mile run, the speed is 98 miles per hour.
What is the horsepower of the car rounded to the nearest whole number?
161 hp
175 hp
209 hp
417 hp
Answers
Power = 175 hp
The correct formula to calculate the power is:
Power = weight * (speed / 234) ³
Where the weight is that of the vehicle plus the driver's
Therefore the calculation is as follows:
Power = (2200 + 180) * (98/234) ³
Power = 174.8266 hp
Rounding ...
Power = 175 hp
A bag of marbles contains 12 red marbles 8 blue marbles and 5 green marbles. If three marbles are pulled out find each of the probabilities. Find the probability of pulling three green marbles out with replacement
Answers
[tex] |\Omega|=25\cdot24\cdot23=13800\\
|A|=5\cdot4\cdot3=60\\\\
P(A)=\dfrac{60}{13800}=\dfrac{1}{230}\approx0.4\% [/tex]
The probability of an event is calculated as = [tex] \frac{Favorable outcomes}{Total number of outcomes} [/tex]
Here, the total number of outcomes = 12 red marbles + 8 blue marbles + 5 green marbles
So, total marbles = 25 marbles
Number of favorable or green marbles = 5 marbles
Probability of three green marbles if drawn with replacement = [tex] \frac{Number of favorable or green marbles}{Total number of marbles} [/tex] ×[tex] \frac{Number of favorable or green marbles}{Total number of marbles} [/tex] × [tex] \frac{Number of favorable or green marbles}{Total number of marbles} [/tex]
Probability of three green marbles if drawn with replacement = [tex] \frac{5}{25} [/tex] × [tex] \frac{5}{25} [/tex] × [tex] \frac{5}{25} [/tex]
Probability of three green marbles if drawn with replacement = [tex] \frac{1}{125} [/tex]
3x < 12 what is this in the interval notation
Answers
x < 4
Interval notation uses parentheses around the lower and upper limit of the interval. Here, the lower limit is -∞ and the upper limit is 4. The parentheses are round ( ) if the limits are NOT included as part of the interval. They are square brackets [ ] if the limits are included in the interval.
Here, since -∞ is not an actual number, we use the round bracket on that end of the interval. Since the solution space does not include 4, we use the round bracket on that end of the interval as well.
The solution to your inequality is ...
(-∞, 4)
A school conference room can seat a maximum of 83 people. The principal and two counselors need to meet with the school’s student athletes to discuss eligibility requirements. If each student must bring a parent with them, what is the maximum number of students that can attend each meeting?
Answers
After subtracting the principal and two counselors from the 83-person room capacity, dividing the remaining space by two shows that a maximum of 40 student-athletes can attend the meeting with their parents.
The maximum number of student-athletes that can attend a meeting in a conference room that has a capacity of 83 people while also accounting for their accompanying parents. Given that the principal and two counselors will also be in attendance, we need to subtract three from the total capacity to accommodate them, leaving us with 80 seats available. Since each student will bring a parent, we divide the remaining seats by two. Therefore, the maximum number of student-athletes that can attend each meeting is 40 students, with each accompanied by a parent.
The Frostburg-Truth bus travels on a straight road from Frostburg Mall to Sojourner Truth Park. The mall is 3 miles west and 4 miles south of the City Center. The park is 3 miles east and 5 miles north of the Center. How far is it from the mall to the park to the nearest tenth of a mile/12482564/8273204d?utm_source=registration
Answers
√(6² +9²) = √117 ≈ 10.8
Trip bought an icecream cone that is 4 inches tall with a radius of 2 inches
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keeping in mind that in 1 US ounce there are 1.805 in³, then in 35 ounces there are 63.175 in³, and in 3 oz there are 5.415 in³.
so the volume of the cone content alone will be, the 63.175 in³ when filled up, minus the topping and minus the 5.415 in³ from the cookie shell.
[tex]\bf \stackrel{\stackrel{volume}{\textit{when filled up}}}{63.175}~~-~~\stackrel{\stackrel{volume}{\textit{of hemisphere}}}{\cfrac{2\pi r^3}{3}} ~~-~~\stackrel{\stackrel{volume}{\textit{of cookie shell}}}{5.415} \\\\\\ \stackrel{\stackrel{volume}{\textit{when filled up}}}{63.175}~~-~~\stackrel{\stackrel{volume}{\textit{of hemisphere}}}{\cfrac{2\pi (2)^3}{3}} ~~-~~\stackrel{\stackrel{volume}{\textit{of cookie shell}}}{5.415}\\\\\\ 63.175-\cfrac{16\pi }{3}-5.415[/tex]
Please please help me with this
Answers
n=2→an=a2 (second term) = 4 (on the graph for n=2)→Second term = 4
ratio=(Second term)/(First term)=a2/a1=4/16
Simplifying the fraction dividing the numerator (4) by 4 and the denominator (16) by 4:
ratio=(4/4)/(16/4)→ratio=1/4
Answer: Option A. First term = 16, ratio = 1/4
Suppose the spread of a direct contact disease in a school is modeled by the exponential function P(t) =
2,000
1 + e3 − t
where P(t) is the total number of people infected after t hours. What does 2,000 represent in equation?
A) the rate at which the disease spreads
B) the number of the people in the school
C) the expected change in number of people infected
Eliminate
D) the total number of people infected after t hours
Answers
triangle abc and triangle bcd have vertices A(-6, -7), B(-6, 4), C(2, -7), D(8, 4) what is the area in square units of trapezoid ABCD which is formed by the two triangles?
Answers
According to the attached graph AC||BD, AB⊥BD and AB⊥AC.
|BD|=14; |AB|=11; |AC|=8.
All the details are in the attachment.
answer: 121 (sq.units).
What is the equation of the line that passes through the points (-1,2) and (6,3) in slope intercept form
Answers
[tex]\bf \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ &&(~ -1 &,& 2~) &&(~ 6 &,& 3~) \end{array} \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{3-2}{6-(-1)}\implies \cfrac{3-2}{6+1}\implies \cfrac{1}{7} \\\\\\ \stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-2=\cfrac{1}{7}[x-(-1)]\implies y-2=\cfrac{1}{7}(x+1) \\\\\\ y-2=\cfrac{1}{7}x+\cfrac{1}{7}\implies y=\cfrac{1}{7}x+\cfrac{1}{7}+2\implies y=\cfrac{1}{7}x+\cfrac{15}{7}[/tex]
Answer:
Step 1: Choose (x1, y1). (6,3)
Step 2: x2= -1 y2=2
Step 3: 1/7
Step 4: b= 15/7
What is the equation of the line in slope-intercept form?
B) y=1/7x+15/7
Step-by-step explanation:
The bold numbers are the answers.
( I need mo pts)
You scored the following grades on your first three math tests: 71, 78, 81. You only have one test remaining. What is the highest possible test average you can get?
Answers
Highest possible total scores for 4 tests = 71 + 78 + 81 + 100 = 330
Highest possible average score for 4 tests = 330 ÷ 4 = 82.5
Answer: 82.5