Gigi graphs the parabola (x+1)2=2(y−3).
How does she proceed?
Drag a value, coordinates, equation, or word to the boxes to correctly complete the statements.
Answers
After graphing the parabola [tex](x+1)^2=2(y-3)[/tex], she can fill the boxes as follows:
Gigi identifies that the vertex of the parabola is [tex](-1, 3)[/tex]. The parabola opens up, and the focus is [tex]\frac{1}{2}[/tex] unit away from the vertex. The directrix is [tex]1[/tex] unit from the focus. The focus is the point [tex](-1, \frac{7}{2})[/tex]. The directrix of the equation is [tex]y=\frac{5}{2}[/tex].
Since Gigi's parabola has the x-term squared, then the parabola has the general formula
[tex](x-h)^2=4p(y-k)[/tex]
So,
[tex]x-h=x+1 \implies h=-1[/tex]
[tex]y-k=y-3\implies k=3[/tex]
The vertex is
[tex](h,k)=(-1,3)[/tex]
The focus is
[tex](h,k+p)=(-1,3+\frac{1}{2})\\=(-1,\frac{7}{2})[/tex]
The directrix is
[tex]y=k-p=3-\frac{1}{2}=\frac{5}{2}[/tex]
The other values can be computed as follows;
Direction the parabola opens: Since the value of p is positive, the parabola opens up.
Distance of focus from vertex: The focus and vertex both have the same x position, so the distance will be in terms of the y-coordinates only. The distance from the focus to the vertex is
[tex]\frac{7}{2}-3=\frac{1}{2}\text{ unit}[/tex]
Distance of directrix to focus: The directrix is the line [tex]y=2.5[/tex]. The distance of the directrix to the focus will be
[tex]\frac{7}{2}-\frac{5}{2}=1 \text{ unit}[/tex]
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Answer:
I took the quiz.
Step-by-step explanation:
Related Questions
George bought 2.45 pounds of tofu and 1.62 pounds of fish. How many more pounds of tofu did he buy than fish.
Answers
Answer:
0.83 pounds
Step-by-step explanation:
2.45 take away 1.62
Find the number that makes the ratio equivalent to 99:66
:6
Answers
Answer:
9
Step-by-step explanation:
99 : 66 ( divide both parts by 11 )
= 9 : 6
What is the value of x? If necessary leave your answer in the simplest radical form.
Answers
Explanation:
This is a 30-60-90 triangle as shown by the angles. These types of triangles have their shortest leg opposite the smallest angle, and the connection between the short and long legs is
long = short*sqrt(3)
We see that the long leg is 16*sqrt(3) units long, which must mean the short leg is 16 units. This doubles to 32 when we go from short leg to hypotenuse
hypotenuse = short*2
Francesca tried to evaluate an expression. Here is her work: 3(5)2–18÷3 = 3(25)–18÷3 = 75–18÷3 = 57÷3 = 19 Is Francesca's work correct?
Answers
Answer:
Nope. Moltiplication (and thus divisions) has to be done before any addition or subtractions, unless parenthesis indicate otherwise.
[tex]3(5)^2 - 18\div 3 = 3(25) - 6 = 75-6=69[/tex]
the sum of three consecutive integers is forty -two. find the three numbers
Answers
Answer:
13, 14, 15 right?
Step-by-step explanation:
hsbhjbhfbghwebfhdfbghef gbhbr ghb erhjtgb
Answers
Answer:
the answer to hsbhjbhfbghwebfhdfbghef gbhbr ghb erhjtgb is hdshdjsh df ejnjg grkejfiejfirnigjre
Step-by-step explanation:
you have to multiply hsbhjbhfbghwebfhdfbghef gbhbr ghb erhjtgb by skjdkahdjhs to get jskhijdfkjd then multiply it by sijdikjakdj9uie. the answer would be hdshdjsh df ejnjg grkejfiejfirnigjre.
Un pilón de riego está lleno en sus cuatro séptimas partes y contiene 1 600 m3 de agua. ¿Cuántos metros cúbicos caben en el pilón?
Answers
Veremos que el volumen total que cabe en el pilón es 2,800 m^3
Sabemos que el pilón tiene una capacidad máxima V.
Tambíen sabemos que de momento, el pilón tiene 1,600 m^3 de agua, y esto es equivalente a 4/7 de la capacidad máxima.
Entonces podemos plantear:
(4/7)*V = 1,600m^3
Podemos resolver esta ecuación para V si multiplicamos ambos lados por (7/4), así obtenemos:
V = (7/4)*1,600m^3 = 2,800 m^3
Es decir, el volumen total que cabe en el pilon es 2,800m^3
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A group of 40 people goes to a football game. Each ticket to the game costs $55. Each person pays $8 for transportation to and from the game. What is the total cost for the 40 people to go to the game?
Answers
2200 + 320
$2520
Which of these are ways to measure a resting heart rate?
Select all that apply.
Answers
Answer:
Place the index and middle fingers on the neck to the side of the windpipe to find the pulse.
Place two fingers between the bone and the tendon over the radial artery of the wrist to find the pulse.
Step-by-step explanation:
I did a test and that was a correct answer.
Haley invested $750 into a mutual fund that paid 3.5% interest
each year compounded annually. Find the value of the mutual
fund in 15 years.
Answers
The future value of the mutual fund after 15 years is equal to $1,256.55.
Given the following data:
Principal = $5,000Interest = 3.5% = 0.035Time = 15 years
To find the future value of the mutual fund after 15 years:
Mathematically, compound interest is given by the formula:
[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]
Where;
A is the future value.P is the principal or starting amount.r is annual interest rate.n is the number of times the interest is compounded in a year.t is the number of years for the compound interest.Substituting the given parameters into the formula, we have;
[tex]A = 750(1 + 0.035)^{15}\\\\A = 750(1.035)^{15}\\\\A = 750(1.6754)[/tex]
Future value, A = $1,256.55
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Help me out I need it be great
Answers
Answer:
A.
How many tiles will you put in each row? 9
How many rows will you make? 3
B.
9x3=27
C.
9 models the amount of tiles in each row
3 models the amount of rows
27 models the total number of chairs/tiles
Step-by-step explanation:
Help me with this very confused
Answers
Answer:
[tex] \frac{3 - 5x}{2} [/tex]
Step-by-step explanation:
Set g(x)=y
y=-2/5x+3
5y=-2x+3
2x=3-5y
x=3-5y/2
So g^-1(x)=
[tex] \frac{3 - 5x}{2} [/tex]
Guys please help asap i don't want to fail
Consider the sequence shown.
Answers
Answer:
The answer is option D
Step-by-step explanation:
f (n)=-2. (-5)^n-1. Jesus loves you
I Jose' Altuve is currently hitting 2 home runs for each 25 times at bat. If he continues at this rate, how many home runs will he hit in a season in which he bats 550 times?
Answers
Answer:
44 home runs
Step-by-step explanation:
550 ÷ 25
= 22
22 x 2
= 44
solve pls brainliest
Answers
Answer:
Step-by-step explanation:
|x|=x,if x>0
|x|=-x,if x<0
(a)
|7-9|=|-2|=-(-2)=2
(b)
|7|-9=7-9=-2
find the total surface area of this triangular prism PLEASE HELP
Answers
Answer:
Step-by-step explanation:
Surface area = (Perimeter of the base × Length of the prism) + (2 × Base Area) = (S1 + S2+ S3)L + bh
S.A=(help me)
(4)/(12)= ()/(3) what makes this equivalent
Answers
Answer:
1/3
Step-by-step explanation:
4/12 divide by 4 to the top and bottom you get 1/3
[tex]\dfrac 4{12} = \dfrac{ 4 \times \tfrac 14 }{12 \times \tfrac 14} = \dfrac 13\\\\\\\\\text{Hence the answer is 1}[/tex]
The quotient of a number, divided by 3, equals-8
Answers
Answer:
x / 3 = -8
Step-by-step explanation:
given f(x)=2x^3+kx-9 and x-1is a factor of f(x), then what is the value of k?
Answers
When it says the "x - 1 " is the factor of that function means when you find the root of the phrase x - 1 which is x = 1 , put it in the function then you have to get zero for the answer :
thus :
[tex]f(1) = 0[/tex]
Thus :
[tex]2 \times {1}^{3} + k(1) - 9 = 0[/tex]
So :
[tex]2 + k - 9 = 0[/tex]
[tex]k - 7 = 0[/tex]
Add both sides 7
[tex]k - 7 + 7 = 0 + 7[/tex]
[tex]k = 7[/tex]
There you go...
Have a great day ❤
Deon's gas tank is 1/5 full. After he buys 13 gallons of gas, it is 7/10 full. How many gallons can Deon's tank hold?
Answers
Answer/Step-by-step explanation:
We start with the variable "x". Let's call "x" Dan's full tank.
So we know that right now he has 1/5x or 1/5 of a full tank.
After adding 13 gallons, at the end, he has 7/10x, or 7/10 of a full tank
So we start with
(1/5)x + 13 = 7/10x
Let's subtract 1/5x from both sides
13 = 7/10x - 1/5x
Remember, we need to use common denominators to subtract, so 1/3 becomes 2/10
13 = 7/10-2/10x
Now we simplify to get
13 = 5/10x
Multiply the reciprocal of 5/10 to both sides which is 10/5
13 * 10/5= x
Answer is 26 gallons.
Therefore, Deon's tank can hold 26 gallons.
Answer:
26 gallons.
Step-by-step explanation:
7/10 - 1/5
= 7/10 - 2/10
= 5/10 = 1/2.
So the tank holds 2*13 = 26 gallons.
Find the area of the composite figure made up of a square and a semicircle. Use 3.14 as an approximate for pi and give your nearest square inch. Enter only the number.
Answers
Answer:
200.52 in^2
Step-by-step explanation:
to find the area of a circle, you square 6 and multiply it by pi in this case 3.14.
that gives you 113.04 but because this is only a half circle, it is 56.52 in^2.
Next, you need to find the rectangle. multiply 12(length) by 12(Width) to get 144 add 144 to 56.52 to get 200.52.
Hope this helped if it did please give me brainliest it helps me a lot. :)
Hope this helped!
Celine is making a special gelatin dessert for the Constellation Club meeting. She plans to fill
a large moon-shaped mold with 8 ounces of gelatin. She wants to use the rest of the gelatin
to fill small star-shaped molds. Each star-shaped mold holds 2 ounces, and the package of
gelatin she bought makes 48 ounces in all. How many star-shaped molds can Celine fill?
Answers
Answer:
Celine can fill 20 stars i believe
Step-by-step explanation:
(48-8)÷2=20
The number of star-shaped molds that Celine can fill will be 20.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.
For the Constellation Club meeting, Celine is preparing an exclusive gelatin dessert. She intends to use 8 ounces of gelatin to fill a large moon-shaped mold. She plans to fill little star-shaped molds with the remaining gelatin. The bag of gelatin she purchased yields 48 ounces in total, with each star-shaped mold holding 2 ounces.
⇒ (48 - 8) ÷ 2
⇒ 40 / 2
⇒ 20
Then the number of star-shaped molds that Celine can fill will be 20.
More about the Algebra link is given below.
https://brainly.com/question/953809
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lacie is making bracelets. if each has 11 beads, and each bead has 2 colors, red and green, how many different bracelets can lacie make if the bracelet can be rotated without losing its uniqueness but cant be flipped
Answers
Answer:24
Step-by-step explanation:
the Arizona Cardinals won 10 games out of 16 games during the 2009 regular season. At this rate, how many games do they need to play to win 50 games?
Answers
For every 10 games they won they lost 6:
50 wins/ 10 wins = 5
5 x 6 loses = 30 loses
50 wins + 30 loses = 80 total games
Answer: 80
SUPER EASY! FRACTIONS PLS HELP!
a kindergraten teacher has a bucket of 51 crayons and another bucket of 5 redpencils,14 blue pencils and 6 green pencils.the bucket of crayons contains 19 red crayons ,17 blue crayons 9 green crayons and 6 yellow crayons.
1.what is the fraction of green crayons to the total number of crayons written in simplest form
2.the teacher places the crayons and pencils in one bucket what is the fraction of yellow crayons and green pencils wriiten in simplest form
3.penicls come in boxes of 6 the number of boxes of blu pencils in the bucket can be represented by the mixed numeral 2 2/6 what is the number of boxes in simplest form?
Answers
Answer:
1: 1/3
2: 3/19
3: 7/3
Step-by-step explanation:
Use the graph to complete the statements.
The car gets
30
miles to the gallon.
After the car has traveled?
miles, 2 and two-thirds how many gallons of gas have been consumed.
Answers
Answer:
The answer is 80 miles 2/23
Step-by-step explanation:
I hope this helps
What is the greatest common factor of 42 and 48?
Answers
Answer:
The greatest common factor is 6
Step-by-step explanation:
There are 4 common factors of 42 and 48, that are 1, 2, 3, and 6. Therefore, the greatest common factor of 42 and 48 is 6.
hope this helps
Find the slope of the line that passes through the point (-3,20), (12,15)
Answers
Carefully evaluate f (1)
Answers
Answer:
it should be f
Step-by-step explanation:
Hey y’all pls help me , what’s the answer :))
Answers
Answer:
r — 7.5 > -8
Step-by-step explanation:
r — 7.5 < —8 is r < - 0.5
—r — 7.5 > -8 is r < 0.5
—r — 7.5 > 8 is r < -15.5
r — 7.5 > -8 is r > -0.5
If you replace r with 17 the only that would be true is r — 7.5 > -8 cause 17 - 7.5 > -8 = 9.5 > -8 making the sentence true.