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]
Learn more about conic sections here: https://brainly.com/question/12854078
Answer:
I took the quiz.
Step-by-step explanation:
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Pat a
mber
4. In a hockey league, 87 players play on seven
different teams. Each team has at least 12
players. What is the maximum number of players
on any one team?
Answers
Answer:
15
Step-by-step explanation:
since there is 7 teams and 12 can be the minimum we can do 7 x 12=84
this means that 3 people could possibly be on one single team.
the maximum number is 12+3=15
HELLO PLEASE GIVE ME THE RIGHT ANSWER ASAP THANK YOU !
Answers
[tex]\large\underline{\sf{Solution-}}[/tex]
[tex]\textsf{Given expression;}\\[/tex]
[tex] \rm{23 = \frac{7}{9}(6x - 36) + 9 } \\ [/tex]
[tex] \rm{\longmapsto} \: 23 = \frac{(42x - 256)}{9} + 9 \\ [/tex]
[tex] \rm{\longmapsto} \: 23 = \frac{(42x - 256 + 81)}{9} \\ [/tex]
[tex] \rm{\longmapsto} \: 23 = \frac{(42x - 175)}{9} \\ [/tex]
[tex] \rm{\longmapsto} \: \frac{23}{1} = \frac{(42x - 175)}{9} \\ [/tex]
[tex]\textsf{By doing cross multiplication, we get}\\[/tex]
[tex] \rm{\longmapsto}23(9) = 1(42x - 175) \\ [/tex]
[tex] \rm{\longmapsto}207 =42x - 175\\ [/tex]
[tex]\rm{\longmapsto} \: 42x = - 175 - 207 \\ [/tex]
[tex]\rm{\longmapsto} \: 42x = - 379 \\ [/tex]
[tex]\rm \therefore \: x = - \frac{375}{42} \\ [/tex]
[tex]\textsf{Hence, the value of x will be -375/42 respectively.}\\[/tex]
[tex]\textbf{Read more:}[/tex]
[tex]\textsf{Similar Questions}[/tex]
Solve the expression and find the value of x. [tex] \frac{x…
https://brainly.com/question/25420312
14. At a local fruit stand, Luisa spends $5.25 for 2 pounds of strawberries. At this rate, how much can she expect to pay for 3.5 pounds of strawberries? (round to the nearest hundredt
h) Proportion Answer
Answers
please helpppppppppoppo
Answers
Step-by-step explanation:
360_90_110=1602a+3a=160a=32°Find the lowest common multiple (LCM) of 18 and 21.
Answers
LMC (18,21) = 126
ok done. Thank to me :>
1) An airplane is at 10,000 feet above the ground. It needs to fly higher to reach the regular flying height. It increases its height at a constant rate of 2,000 feet per minute. How high will the plane be in 10 minutes?
Answers
Answer:
20000
Step-by-step explanation:
Answer: 30,000 feet
Step-by-step explanation: We start with the 10,000 feet original height. From there, we can take 2,000 feet per minute and multiply it by 10 minutes. That gets us 20,000 feet. Add 20,000 to our original 10,000 and we get 30,000.
please help
y∝1/√x If y=5
when x=36 find,
x when y=3
Answers
Answer:
x = 100.
Step-by-step explanation:
y ∝ 1/√x
y = k /√x where k is a constant.
When x = 36 y = 5 so we have:
5 = k / √36
5 = k / 6
k = 30
So we have the relation:
y = 30 /√x
When y = 3
3 = 30/ √x
√x = 30/3 = 10
x= 100.
Will mark brainiest if right Is this function linear or nonlinear?
y=3x−5
Answers
Answer: This function is linear because it forms a straight line when graphed.
Would appreciate brainly <3
Which graph is right?
Answers
Answer:The first option is correct
Step-by-step explanation:
Answer:
3rd option
Step-by-step explanation:
3rd option because m is bigger than or equal -2 which means that it is going to be from [-2,infinity[
no need to explain just tell the answer
Answers
Answer: z = 18
Step-by-step explanation:
180 = 90 + (3z+4) + (2z-4)
z = 18
Which circle has a radius that measures 10 units?
10
D
20
F
10
OG
20
Answers
Hope this helps :))
Option B is correct, the circle with center F and diameter 20 units is the circle which has a radius of 10 units.
What is Circle?A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.
Radius of a circle is the distance from the center of the circle to any point on it's circumference.
The distance across a circle through the centre is called the diameter.
Diameter = 2 × radius
In the given figures, option B has a diameter of 20
so radius = diameter /2
=20/2
=10 units
Hence, option B is correct, the circle with center F and diameter 20 units is the circle which has a radius of 10 units.
To learn more on Circles click:
https://brainly.com/question/11833983
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solve |8y+4|=2|y-1|
please show the work!
Answers
8y+4 = 2y-2
8y-2y+4 = -2
6y+4 = -2
6y = -2-4
6y = -6
y = -1
what is 4xy - 5y² - 3x² from 5x + 3y² - xy ?
Answers
[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]
The equivalent expression is ~
[tex] \boxed{ \sf8 {y}^{2} + 3 {x}^{2} + 5x - 5xy}[/tex]
[tex] \large \boxed{ \mathfrak{Step\:\: By\:\:Step\:\:Explanation}}[/tex]
Let's solve ~
[tex]5x² + 3 {y}^{2} - xy - (4xy - 5y {}^{2} - 3 {x}^{2} )[/tex][tex]5x² + 3 {y}^{2} - xy - 4xy +5 {y}^{2} + 3 {x}^{2} [/tex][tex]3 {y}^{2} + 5 {y}^{2} + 3 {x}^{2} + 5x² - xy - 4xy[/tex][tex]8 {y}^{2} + 8 {x}^{2} - 5xy[/tex]how many solutions does  3x+9=25x+14 have?
Answers
Answer:
one solution
Step-by-step explanation:
3x + 9 = 25x + 14
-3x -3x
9 = 22x + 14
-14 - 14
-5 = 22x
Craig wants to create a right triangle with side lengths 4 centimeters, 6 centimeters, and 8 centimeters. Is this possible? Why or why not?
Answers
Answer:
It's not possible
Step-by-step explanation:
In right triangle hipotenuse must be the longest side so it'll be 8 and legs will be 4 and 6.
So
[tex]4 {}^{2} + 6 {}^{2} [/tex]
Doesn't equal to
[tex]8 {}^{2} [/tex]
16+36=52 not 64
Which division problem is modeled
Answers
Answer:
The first one
Step-by-step explanation:
if you count, there are five full rows, and two extra, so 52/100. then you count the sections that the colored area is: 4. then count how many squares are in each colored section: 13.
The hypotenuse of a right triangle measures 19 cm and one of its legs measures 4 cm. Find the measure of the other leg. If necessary, round to the nearest tenth.
Answers
Answer:
18.9
Step-by-step explanation:
Please HELP!!!!PLSLSLSLSS
Answers
Answer: where is the question??
what do you need help with?
Expand & simplify 4 ( p + 3 ) + 4 ( p − 6 )
Answers
Answer:
8p -12Step-by-step explanation:
Expand & simplify 4 ( p + 3 ) + 4 ( p − 6 )
4(p + 3) +4(p - 6) =
4p + 12 + 4p - 24 =
8p -12
What is the value of this expression when c = 3 and d = 7? 15+c2⋅d−c3
Answers
Answer:
The value of this expression is 48
Step-by-step explanation:
15 + c2 * d - c3
c = 3
d = 7
Substitute the values of c and d
15 + (3)2 * 7 - (3)3
Multiply the parenthesis first
15 + 6 * 7 - 9
Now multiply 6 and 7
15 + 42 - 9
Now add 15 and 42
57 - 9
Now subtract
= 48
Answer:
48
Step-by-step explanation:
When you write out the problem it should look like this
15+c⋅2⋅d-c⋅3
or in other form
15+3⋅2⋅7-3⋅3
You can solve using PEMDAS
Paratheses
Exponents
Multiplication
Division
Addition
Subtraction
Just use those in order and you should find to answer.
-Rocketgamer360
write down three integers below 25 with the range of 10 and the mean of 13
Answers
Answer:
8, 13, 18
Step-by-step explanation:
Middle number is 13, there are only 3
Max is 10/2 more so 18
Min is 18-10
Complete the missing factors
6a^2 + 11b - 35b^2 = ( 3a _______)(2a______)
please help me, thank you.
Answers
That’s the answer
100 POINTS Suppose ܶTU is on a coordinate plane located at T(-6,-2) and U(2,-6) Under a dilation of scale factor 1/4, TU becomes T'U' with coordinates T'(-3/2,-1/2) and U'(1/2,-3/2) Where is the center of the dilation located ?
A(0,0)
B(2,2)
C(4,0)
D(4,4)
Answers
c because the center of dilation is the multiplicatory value of the original point
find the missing triangle measurements. I WILL GIVE BRAINLIEST! PLEASE
Answers
Answer:
ABC= 60
DCE= 65
DEF= 105
Step-by-step explanation:
Answer:
60°; 65°; 115°Step-by-step explanation:
ΔABC is equilateral since all sides marked as congruent. Therefore:
m∠ABC = 60°ΔCDE is isosceles since two sides marked as congruent:
m∠DCE = m∠DEC = 1/2(180° - 50°) = 1/2(130°) = 65°∠DEF forms a linear pair with ∠DEC, so they sum to 180°:
m∠DEF = 180° - 65° = 115°The FM radio station KAMB broadcast from an antennae atop a 150 meter tall radio tower at a frequency of 90 MHz with a total radiated power of 40 kilowatts. Neighbors have complained about problems they attribute to excessive radiation from the tower, but the city engineer who measured the radiation level near the base of the tower found it to be well below the accepted standard. You have been hired by the HOA to assess the engineer's report. You know a few things about electromagnetic radiation and therefore conclude that we must find the optimum place on the ground to measure the maximum radiation emitted from the antennae. From your extensive knowledge in physics, you know that the intensity of radiation, I, is given by the formula:
I=12/32π*Psin2(θ)/r^2
where P is the power output, r is the distance from the top of the tower to the point on the ground, and θ is the angle measured from the tower to r.
Find the distance R from the base of the tower to the optimum location for taking the radiation reading. (m)
What is the maximum radiation reading from the ground in kw/m^2
If the city code requires that electromagnetic radiation be under 200 microwatts per square meter, is this antenna operating within city code? Yes or No
Answers
Answer: 150 m, 5.305*10^-5 kW/m^2, No
Step-by-step explanation:
See attachment, hope this helps
Using the radiation intensity formula we will have to:
a) [tex]150 m[/tex]
b) [tex]5.305*10^{-5} kW/m^2[/tex]
c)No
From the data informed, we have:
[tex]h=150m\\P=40KW[/tex]
Using the given formula and performing some mathematical operations:
[tex]I=\frac{12Psin^2(\theta)}{32(\pi)r^2} \\I= \frac{12(40)(R/r)^2}{32(\pi)r^2} \\= \frac{15R^2}{r^2\pi } \\= \frac{15R^2}{(R^2+150^2)^2\pi} \\[/tex]
deriving the given equation, we will have:
[tex]=\frac{(R^2+150^2)^22R-R^2(2(R^2+150^2))2R}{(R^2+150^2)^2}[/tex]
So from this equation we have that the answer of the letter A corresponds:
[tex]R=150[/tex]
For letter B we will have to develop this equation:
[tex]I= 5.30X10^{-5}[/tex]
As for the letter C, when converting the value found, it should give 200 microwatts, which is false.
Learn more: brainly.com/question/10148635
-4 1/2 + 2 3/4
Guys help me Im having trouble on this EEEEEEEEEE
Answers
Julissa is printing out copies for a work training. It takes 4 minutes to print a color copy, and it takes 2 minutes to print a grayscale copy. She needs to print no fewer than 8 copies within 25 minutes.
Which system of inequalities represents the number of color copies, x, and grayscale copies, y, that Julissa can print to meet her goal?
Answers
Answer:
4x + 2y ≤ 25 , x + y ≥ 8 is the required system of inequalities to represent the given situation.
Step-by-step explanation:
Here, let the number of color copies = x
Now, the time taken to print each color copy = 4 minutes
⇒Time taken to print x color copies = x times ( Time taken by each copy)
= 4 (x) = 4x
and let the number gray scale copies = y
The time taken to print each gray scale copy = 2 minutes
⇒Time taken to print y gray scale copy = y times (Time taken by each copy)
= 2 (y) = 2y
Total copies printed = x + y
Maximum time taken to print x color copies and y grayscale copies
= 4x + 2y
So, according to the question:
4x + 2y ≤ 25 ( as maximum allotted time is 25 minutes)
and x + y ≥ 8 (as minimum number of copies is 8)
hence, the above system is the required system of inequalities to represent the given situation.
I hope this helps.
Write 0.012 as a fraction in simplest form.
Answers
Answer:
3/25Step-by-step explanation:
Remove The decimal,
= > 0.012 = 12/100
= > 3/25...ans
Hope it Helps you!!7/8 times 7/9 what is the answer
Answers
Find the slope of the line given the following points on the line:
(-6, 4) and 2, 7)
Answers
Answer:
3/8
Step-by-step explanation:
Answer:
[tex]\boxed{\sf Slope:3/8}[/tex]
Step-by-step explanation:
To determine the slope of a line given the coordinates of two points on the line, use the slope formula.
[tex]\boxed{\sf \sf{Slope\;(m)}=\frac{y_2-y_1}{x_2-x_1}}[/tex]
x1 and y1 are the coordinates of the first point. The second point's coordinates are x2, y2.
Points: [tex]\sf (-6, 4) \:and \:(2, 7)[/tex]
[tex]\longmapsto\sf \left(x_1,\:y_1\right):\left(-6,\:4\right)[/tex]
[tex]\longmapsto\sf \left(x_2,\:y_2\right)=\left(2,\:7\right)[/tex]
_______________
[tex]\leadsto\sf m=\cfrac{7-4}{2-\left(-6\right)}[/tex]
[tex]\leadsto\sf m=\cfrac{3}{8}[/tex]
_________________________________________
