Answer:
[tex]\boxed{x^2=-8y}[/tex]
Step-by-step explanation:
[tex](a,b)\ is \ the\ focus\\y=k\ is \ the\ directrice\\\\Formula\ to\ use:\ y=\dfrac{(x-a)^2}{2(b-k)} +\dfrac{b+k}{2} \\\\Here: \ a=0,\ b=-2, \ k=2\\\\y=\dfrac{(x-0)^2}{2(-2-2)} +\dfrac{-2+2}{2} \\\\so\ y=-\dfrac{x^2}{8} \\\\or\ x^2=-8y[/tex]
The equation which represents the parabola is x^2 = 8y, the correct option is C.
What is vertex form of a quadratic equation?
If a quadratic equation is written in the form
y=a(x-h)^2 + k
then it is called to be in vertex form. It is called so because when you plot this equation's graph, you will see vertex point(peak point) is on (h,k)
First of all, i used this vertex formula thing since it is visible that there are quadratic functions. Otherwise, you had to use calculus to get critical points, then second derivative of functions to find the character of critical points as minima or maxima or saddle etc to get the location of vertex point.
This point (h,k) is called the vertex of the parabola that quadratic equation represents.
We are given that;
Focus of parabola= (0,–2)
Now,
The vertex is halfway between the focus and the directrix on a line perpendicular to them. Since the focus is at (0,-2) and the directrix is y = 2, we can find that:
The vertex is at (0,0), because it has an x-coordinate of 0 (same as the focus) and a y-coordinate of 0 (the average of -2 and 2).
p is equal to 2, because it is half of the distance between -2 and 2.
Now we can plug in these values into the formula:
(x - 0)^2 = 4(2)(y - 0)
Simplifying, we get:
x^2 = 8y
Therefore, the equation of the parabola will be x^2 = 8y.
Learn more about vertex form of a quadratic equation here:
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Use linear combination to solve for x and y.
2x+4y=-4
3x+5y=-3
Dautienbanchuyenvexophuongtrinhthu1saudothevaophuontrinhthu2,thuchiencacbuoc
chuyenvedoidaularaketquanhe
Samantha found a great deal on sweatshirts at the mall and bought 5 sweatshirts at the
Super Duper sale price. Allison went the next day, but the sale was over, so she only bought
2 sweatshirts and paid $30 more per sweatshirt than Samantha. If the total cost of all 7
sweatshirts was $340, how much did one sweatshirt cost at the Super Duper sale price?
Answer:
$40
Step-by-step explanation:
You have two sweatshirts that cost $30 more the day after.
First, you do [tex]340 -(2*30)[/tex]
Second, you divide what you got above ($280), by 7 and voila, you have $40 per sweatshirt.
Mr Brown spends 65% of his monthly income and saves the rest. After being promoted, his salary increases by 40% and his expenses increase by 20%. Find the percentage change in his savings.
Answer:
There is a percentage increase of 77.1% in savings
Step-by-step explanation:
The answer can be determined by assigning a value to the income of Mr Brown.
Let Mr. Brown's initial income = 100
Percentage spent = 65%
Amount spent = 100 x 0.65 = 65
Percentage he saves = 100 - 65% = 35%
Amount he saves = 100 x 0.35 = 35
Salary after increase = 1.40 x 100 = 140
Increase in expenses = 1.2 x 65 = 78
Amount saved after increase in income = 140 - 78 = 62
Percentage increase = (new amount saved / previous amount saved) - 1
Percentage increase = (62 / 35) - 1 = 0.771 = 77.1%
56 out of the 56 employees at the sports shop are part-time employees. What percentage of the employees at the sports shop work part-time?
Answer:
100%
Step-by-step explanation:
Since 56/56 employees at the sports shop work part time, that means 100% of them do, or all of them.
Rent received from a tenant was debited to the rent receivable account and credited to the case book. What type of error has been made? A commission B compensating C complete reversal D principle
Answer: C complete reversal
Step-by-step explanation:
When there is a complete reversal error which is also known as an " error of complete reversal entry", the debit entry is switched with the credit entry. This is one of the more difficult errors to pick up because the Trial balance remains balanced when this happens as the debits and the credits would still be equal.
When rent is received from a tenant. The correct entries are to debit it to cash which is an asset and so will be debited when it increases.
Then credit it to Rent Receivable because this is a revenue account and these are credited when they increase.
The entries were therefore reversed.
A ball is thrown off the roof of the school. Its path can be described by the equation: h(t) = -2t^2 + 8t + 10, where h is height in meters after t seconds.
a) How tall is the building?
Answer:
10 meters
Step-by-step explanation:
The given function [tex]h(t)=-2t^2+8t+10[/tex] represents the height, [tex]h[/tex], in meters, [tex]t[/tex] seconds after the ball is thrown.
Since the ball is thrown off the roof, then ball's height will be equal to the roof's height before being thrown (0 seconds). Therefore, substitute [tex]t=0[/tex] into the given function [tex]h(t)=-2t^2+8t+10[/tex]:
[tex]h(0)=-2(0^2)+8(0)+10,\\h(0)=0+0+10,\\h(0)=\boxed{10\text{ meters}}[/tex]
Therefore, the building is 10 meters tall.
help asap answer ----------------
Answer:
[tex]f^-^1(f(3.14))=3.14[/tex]
[tex]f(f(-7))=5[/tex]
Step-by-step explanation:
Hi there!
[tex]f^-^1(f(x))=x[/tex]
Therefore, [tex]f^-^1(f(3.14))=3.14[/tex]
[tex]f(f(-7))[/tex]
The table tells us that f(-7) is equal to -12.
[tex]f(-12)[/tex]
The table also tells us that f(-12) is equal to 5.
[tex]5[/tex]
I hope this helps!
The function f(x) = –x2 – 4x + 5 is shown on the graph. On a coordinate plane, a parabola opens down. It goes through (negative 5, 0), has a vertex at (negative 2, 9), and goes through (1, 0). Which statement about the function is true? The domain of the function is all real numbers less than or equal to −2. The domain of the function is all real numbers less than or equal to 9. The range of the function is all real numbers less than or equal to −2. The range of the function is all real numbers less than or equal to 9.
Answer:
"The range of the function is all real numbers less than or equal to 9."
Step-by-step explanation:
For this question the domain is (-∞,∞)
The range is all numbers less than 9 (the y-coordinate of the vertex)
The reason the numbers are less than 9 is because the graph is concave down (aka it looks like a frowny face)
Therefore the answer is "The range of the function is all real numbers less than or equal to 9."
what is the solution to the system of equation below y=2/5x-3 and X=_10
Answer:
read explanation
Step-by-step explanation:
since y=2/5x-3 we substitute x=10 in making it y=2/5*10-3
following PAMDAS we do multiplication first so 2/5*10=4.
so y=4-3 and then we subtract and get y=1. Hope this helps:> if you need more explanation message me. If not give this a heart for helping. Good luck.
Hey can someone help me
Which of the following statement is false?
a. all real numbers are complex numbers.
b. all irrational numbers are real numbers.
c. all complex numbers are pure imaginary numbers.
d. all whole numbers are rational numbers
Answer:
c not all complex are imaginary
but all imaginary are complex
please brainlist
Answer:
C is False
Step-by-step explanation:
A complex number is represented by
[tex]z = a + bi[/tex]
A imaginary number is represented by
[tex]z = bi[/tex]
A complex number could include a real number so it cant be a pure imaginary number so C is False.
Suppose a normal distribution has a mean of 98 and a standard deviation of 6. What is P(x < 104)?
A. 0.16
B. 0.975
C. 0.84
D. 0.025
Answer:
Step-by-step explanation:
If the mean is 98, then 104 is only standard deviation away. If we are looking for the values less than this, we have the areas under the normal curve of 34%, 34%, 13.5%, 2.35%, .15% which add to 84%, or as a decimal, .84, choice C.
The z-score of the normal distribution P ( x ≤ 104 ) = 0.84
What is a z-score?The relationship between a value and the mean of a set of values is expressed numerically by a Z-score. The Z-score is computed using the standard deviations from the mean. A Z-score of zero indicates that the data point's score and the mean score are identical.
The Z-score is calculated using the formula:
z = (x - μ)/σ
where z: standard score
x: observed value
μ: mean of the sample
σ: standard deviation of the sample
Given data ,
Let the z-score of the distribution be z
And , the mean be μ = 98
And , the standard deviation be σ = 6
where z = (x - μ)/σ
So , P ( x ≤ 104 ) = [ P ( x - 98/6 ) ≤ 104 - 98 / 6 ) ]
On further simplification , we get
P ( x ≤ 104 ) = P ( x ≤ 1 )
Using a standard normal distribution table or calculator, we can find that the probability of a z-score less than 1 is approximately 0.8413. Therefore, the probability of x being less than 104 is approximately:
P(x < 104) = P(z < 1) ≈ 0.8413
So there is approximately an 84.13% chance that a value selected at random from this normal distribution will be less than 104
Hence , the probability is 0.84
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What is the multiplicative rate of change of the
exponential function shown on the graph?
81
2,
4
0
16
1
A
12
4
AN
8
1.
NI
-2.
2
-1.
9
x
(0,1)
1
-3 -2
-1
N
3
Answer:
The answer for thue would happened to be 2
-1.
Answer:
9/2
Step-by-step explanation:
Quadrilateral MNTU below is a parallelogram. If m2 M = 4x + 6 and m2N = 2x + 30, what is the value of x?
Answer:
x=12
Step-by-step explanation:
im not 100% but i think you would get the answer by setting the equations equal to one another.
4x+6=2x+30
2x=24
x=12
Help Now Please!!!
Find The Volume Of This Cylinder
Answer:
502.4 m³.
Step-by-step explanation:
Formula: πr²h
4² = 16 x 10 = 160
160 x 3.14 (about π) ≈ 502.4 m³.
Hope this helps.
If there is something wrong, please let me know.
Answer:
160[tex]\pi[/tex] or
500[tex]m^{3}[/tex]
Step-by-step explanation:
[tex]\pi[/tex] x [tex]4^{2}[/tex] x 10 = 160[tex]\pi[/tex] or 500[tex]m^{3}[/tex]
can someone help with this, and explain it as well
Answer:
WRS and VRT are vertical angles
Step-by-step explanation:
Vertical angles are formed by the same lines and share a vertex
WRS and VRT are vertical angles
Simplify the following:
1) √12 =
Answer:
2[tex]\sqrt{3}[/tex]
Step-by-step explanation:
Using the rule of radicals
[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex] , then
[tex]\sqrt{12}[/tex]
= [tex]\sqrt{4(3)}[/tex]
= [tex]\sqrt{4}[/tex] × [tex]\sqrt{3}[/tex]
= 2[tex]\sqrt{3}[/tex]
Plssss help thank youuu
didn't pay attention and now im stuck :/
Answer:
A (First One)
Step-by-step explanation:
Side AC Is Congruent By Side DF
Side CB Is Congruent By Side FE
Side AB Is Congruent By Side DE
(There's no angles shown so it can't be the second option.)
The diagram has lines on the sides, if it we're SAS then the triangle would have an angle.
Answer:
ΔABC≅ΔDEF by SSS Postulate
Step-by-step explanation:
Hi there!
We are given 2 triangles
And we want to prove them congruent
You may notice that AC and FD have the same tick markings, AB and ED have the same tick markings, and CB and FE have the same tick markings
This means that those sides are congruent
In other words,
AC≅FD
AB≅DE
CB≅FE
If we have 3 pairs of congruent sides, that is enough for one concurrency postulate called side-side-side (SSS), which states that if 3 sides of a triangle are congruent to 3 sides in another triangle, then those triangles are congruent
So the triangles are congruent, but we need to put their vertices in the correct order
So if we make the name of the first triangle ABC, then we need to find the corresponding vertices in the second triangle
So let's find those vertices
D is corresponding to A, as they are both in between line segments that have 1 and 2 tick markings on them
E is corresponding to B, as they are both between line segments that have 2 and 3 tick markings on them
And finally, F is corresponding to C, as they are both between line segments that have 1 and 3 tick markings on them
So the name of the second triangle is DEF
ΔABC≅ΔDEF by SSS Posulate
Hope this helps!
Suppose a triangle has two sides of length 3 and 4 and that the angle
between these two sides is 60°. What is the length of the third side of the
triangle?
A. /13
B. 3
C. 4/3
D. /3
Pls help ASAP
Answer:b /13
Step-by-step explanation:
Please help me out!!!!!
Answer:
From the figure, we´ll use the ratio of sin74
sin74=x/16
x=16/sin74
x=16.64
OAmalOHopeO
Can someone help me please like please I need to turn it in like in 10 minutes
If triangle BCD was reflected over the x-axis, what would be the coordinates of the new triangle's vertices?
A. (-1, 0), (-1, -2), (-4, 1)
B. (-1, 0), (-1, 2), (-4, 1)
C. (-1, 0), (-1, 2), (4, -1)
D. (1, 0), (-1, 2), (-4, 1)
on time 4 learning
Answer:
b the answer is B because
During a sale, Cindy found boxes of dog biscuits on sale for $0.69 that had previously cost $2.23. What percentage is the discount?
Answer:
The dog biscuits are approximately 69% off.
Step-by-step explanation:
(1 - 0.69/2.23) * 100
(223/223 - 69/223) * 100
154/223 * 100 = 69%
Use the drawing tools to form the correct answer on the graph.
Every day the ocean has two low tides and two high tides. Function grepresents the height, in feet, of the water level in a cove relative to the
average sea level. Let trepresent the number of hours elapsed since the water height was equal to the average sea level after a low tide.
g(t) = 4sin(t)
Plot the points where g(t) is equal to the average sea level.
Answer:
The sinusoidal function that represent the height of the water level, is presented as follows;
[tex]g(t) = 4 \cdot sin \left(\dfrac{\pi}{6} \cdot t \right)[/tex]
Where;
t = The number of hours since the water height was the average sea level height
The graph of g(t) showing the points where g(t) = The average see level, created with MS Excel is attached
Step-by-step explanation:
Answer:
put a dot on points
(0,0)
(0,6)
(0,12)
Step-by-step explanation:
yea...we most def ain't learn this in class
Answer:
F. 300,000
Step-by-step explanation:
logically, it is decreasing by 1.
Can someone please help me with this??
Answer:
Use photo math
Step-by-step explanation:
its easier
Find x. PLEASE HELP ASAP
Answer:x=35.6
Step-by-step explanation:
look at the left triangle. I hope you're familiar with SOH, CAH and TOA.
sin 60°=O/(11√7)
so O= (11√7)sin 60°
now look at the triangle on the right.
cos 45=adjacent/x
cos 45=[(11√7)sin60°]/x
therefore, using ur calculator, you'll get x= [(11√7)sin60°]/cos 45
x=35.64407384
Rosa worked 28 hours this week and was paid $7 per hour. What were her tot earnings for the week?
Answer:
$196.
Step-by-step explanation:
Multiply the hours (h) by amount per hour (a) (h*a), 28*7 and you will get her total earnings, $196.
Answer:
$196
Step-by-step explanation:
28 hours and $7 per hour so you do 28x7 which equals 196.
please help me with this problem !
