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.
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]
Learn more about conic sections here: https://brainly.com/question/12854078
Answer:
I took the quiz.
Step-by-step explanation:
Laura is saving to buy a 10-speed bike that costs $189. For four weeks she saved part of her check in the amounts of $15, $39, $18 and $27. How much more does she need?
Answer:
90$
Step-by-step explanation:
Answer:
$90
Step-by-step explanation:
$15 + $39 + $18 + $27 = $99
$189 - $99 = $90
Hope this helps <3
What is the degree of angle o?
Show work
Ty factored 24a + 36c and got an answer of 3(8a + 12c). Did Ty factor correctly?
If not, explain what he did wrong and correct his mistake.
No he did not factor correctly. He needed to factor completely which would get 12(2a+3c)
I NEED THE ANSWR ASAP: Write the number as a power with a base of 5.
125^3
Answer:
5^9
Step-by-step explanation:
I had this question before.
A rectangular prism has dimensions of 8 cm by 9 cm by 10 cm. What is its volume? cubic centimeters
Answer: 288 cubic centimeters
Two architects bid for a small government project, both
charging a flat fee added to an hourly rate. Amazing
Designs bids $250 plus $45 per hour, while Super Structures
bids $100 plus $60 per hour. At what point in time will the
two companies charge exactly the same amount?
Answer:
10 hours
Step-by-step explanation:
let x be the total number of hours
Amazing design total charge = 45x+250
super structures total charge = 60x+100
both companies charge the same amount when both equation equals
45x+250=60x+100
60x-45x=250-100
15x=150
x=10
therefore at 10 hours both companies will charge the same amount
Camelle manages her soccer team. she needs to order 4 practice jerseys for each player. There are y players how many total practice jerseys does she need to order?
write and expression
Answer:
T= total # of jerseys to order
y= # of players
T= 4*y
Total equals 4 times # of players
T= 4y
If angle 1 is 110° what would the other angle measures have to be in order for m || n and q || p
Answer:
Angle 1 = 110
Angle 2 = 110
Angle 3 = 70
Angle 4 = 70
Step-by-step explanation:
Angles 1 and 2 are corresponding angles, and therefore congruent
Angles 2 and 3 are same-side interior angles, and therefore supplementary
Angles 3 and 4 are alternate interior angles, and therefore congruent.
Answer:
Angle 2: 110
Angle 3: 70
Angle 4: 70
Can someone please help me with this?
Hello,
Ali is right, Khamis is wrong. Why because Khamis forgot to put the negative sign in front of 5b, it should be wrote -5b in the second line and not 5b.
And then Khamis should have divided -5b by -5b.
Good Luck
There are 190 people on the beach. 110 are wearing sunglasses, 70 are wearing bathing suits, and 95 are wearing a hat. Everyone is wearing at least one of these items. 30 are wearing both bathing suits and sunglasses. 25 are wearing both bathing suits and a hat. 40 are wearing both sunglasses and a hat. How many people are wearing all three items
190=110+70+95−(30+25+40)+x190=110+70+95−(30+25+40)+x
Simplifying, we get that x=10x=10.
its 10
What does the degree of the polynomial tell you.
A degree in a polynomial function is the greatest exponent of that equation, which determines the most number of solutions that a function could have and the most number of times a function will cross the x-axis when graphed.
What is the product?
Enter your answer as a fraction, in simplified form, in the box.
3/8*(-36)
Answer:
-27/2
Step-by-step explanation:
3/8 × -36
(3×-36)/8
-108/8
-27/2
I just woke up i need help ;-;
Answer:
i think that the correct answer is 7/12
What is the second step in solving the equation
slm
+7= 5?
Subtract 7 from each side.
Divide each side by 3.
Add 7 to each side.ch
O Multiply each side by 3.
Answer:
subtract 7 from each side
Step-by-step explanation:
Answer:
Subtract 7 from each side.
Step-by-step explanation:
x+7 = 5x+7-7 = 5-7x = -2Here is an inequality -10+x÷4+5>7x-5÷3
Answer:
here is the answer x>1/2
-
1.) -x + 5y = 49
X =
X - 4y = - 39
-
=
Answer: (1,10)
Step-by-step explanation:
Assuming these are the correctly written equations:
-x + 5y = 49, and
x - 4y = -39
I'll rewrite them:
5y = x + 49
y = (1/5)x + (49/5)
-4y = -x -39
y = (1/4)x + (39/4)
=====
I'll assume the question is to find the point these two lines intersect (?).
See the attached graph. They intersect at (1,10).
Old McDonald's 3 hens lay the same number of eggs one week. This gives Old McDonald's wife enough eggs for two recipes. One recipe requires 10 eggs and the other recipe requires 2 eggs. How many eggs did each hen lay?
can someone please help me solve this!
Answer:
B
Step-by-step explanation:
[tex]4x^{2}-11x-3=0\\4x^{2}-12x+x-3=0\\4x(x-3) + (x-3) = 0\\(4x+1)(x-3)=0[/tex]
B is factorable through this method
find the three common multiple of
a)3 and 18
b)9 and 13
c)5 and 17
Answer:
I think these are the answers
a) 3
b) 1
c) 1
The times for running a 5K for a local charity event are Normally distributed with a mean time of 28 minutes and
standard deviation of 5.4 minutes. Which time represents the 60th percentile?
Find the z-table here.
A. 19.6 minutes
B. 26.6 minutes
C. 29.4 minutes
D. 36.4 minutes
Answer:
29.4 minutes represents the 60th percentile
Step-by-step explanation:
Given : The times for running a 5K for a local charity event are Normally distributed, with a mean time of 28 minutes and standard deviation of 5.4 minutes.
To Find : Which time represents the 60th percentile?
19.6 minutes
26.6 minutes
29.4 minutes
36.4 minutes
Solution:
time represents the 60th percentile
Means 60 % data = 0.6 below this
from z table , z score for this = 0.253
z score = ( Value - Mean ) / SD
=> 0.253 = ( Value - 28 ) /5.4
=> 1.3662 = Value - 28
=> Value = 29.3662
=> Value = 29.4
29.4 minutes represents the 60th percentile
100 points if u get this right ty bye now!
Answer:
4 mi²
Step-by-step explanation:
Area of Square: Length x Length
=> Area of Square: 2 x 2
=> Area of Square: 4 mi²
Therefore, the area of the square is 4 mi².
Hoped this helped
Answer:
4 mi²
Step-by-step explanation:
Area of Square: Length x Length
=> Area of Square: 2 x 2
=> Area of Square: 4 mi²
Therefore, the area of the square is 4 mi².
Roxana makes bracelets and necklaces and sells them at the farmers’ market. She sells the bracelets for $12 each and the necklaces for $18 each. At the market next weekend she will have room to display no more than 40 pieces, and she needs to sell at least $500 worth in order to earn a profit. (Thank you so much for anyone who answers it
Answer:
She could out 20 necklaces and 20 bracelets on display and she would make $600.
Step-by-step explanation:
$18 necklaces x 20= $360
$12 bracelets x 20 = $240
totalling $600
Can someone please solve question 8
Answer:
22.84
Step-by-step explanation:
What is the common difference for this arithmetic sequence 45,40,35,30,25,
Answer:
-5
Step-by-step explanation:
Which of the following is a run on sentence
Answer:
B.
Step-by-step explanation:
There is no pause and the use of a connection word (and) makes the sentence seem longer. Hope this helps :) brainliest?? <3
Jack estimates that a piece of wood measures 4.5 cm. If it actually measures 4.72 cm, what is the percent error of Jack’s estimate? (Show all of your work)
Answer:
ion
Step-by-step explanation:srry
Can I get some help on this I have so many assignments to do and I just want to go to sleep
train tickets cost $48 for adults and $32 for children there are 27 adults and 55 children on the train how much did the passengers pay to ride the train
An Apple Watch was marked down 1/9 of the original price. If the sales price was $224 what is the original price?
Answer:
ok so that means that the new price is 8/9th of the original one so we divide 224 by 8/9=252
Hope This Helps!!!
Marked down 1/9 means it sold for 8/9 of the original price.
Divide the sale price by 8/9:
224 / 8/9 = 224 x 9/8 = (224 x 9)/8 = 2016/8 = 252
The original price was $252
