Answer:
all real numbers greater than or equal to -1
Step-by-step explanation:
In order to solve this problem we need to know the vertex and the direction its pointing.
First we expand,
x^2-6x+8
To find the x value of the vertex we use this formula (-b/2a).
-(-6)/2(1) = 3
Now we plug 3 in the equation to get the y value,
(3)^2 - 6(3) + 8 = 9 - 18 + 8 = -1
The vertex is (3,-1)
We know the graph points up because x^2 is positive
The vertex is the lowest point, so we now know that -1 is the starting range and if the graph is pointing up, that means all values greater than -1.
This leads to our answer all real numbers greater than or equal to -1.
-50 POINTS- (2/5) please no wrong answers for points. A) y = [tex]\frac{9}{2}[/tex] x + [tex]\frac{1}{2}[/tex] B) y = - [tex]\frac{1}{2} x + \frac{7}{2}[/tex] C) [tex]y = -4x +9[/tex] D) [tex]y=4x+15[/tex]
This problem is about creating a linear regression model.
First, we should take note of the points:
(-4,8)
(-2,4)
(-1,2)
(1,5)
(2,2)
(6,-5)
(7,6)
It's necessary to find a equation y = ax + b that brings us the least MSE (Mean Squared Error). You can calculate at hand, but I bet it is going to be tiresome.
So, basically intuitively you just need to choose a line that fits closer to the given points.
First: remember if y = ax+b, a is the slope which means if a > 0 the line is " / " and a < 0 the line is " \ ".
A) No, this equation is " / "
B) It could be this one.
C) It could be this one too.
D) Nope. " / "
B) a = -1/2
C) a = -4
You can draw those two lines and see that B) gets closer to the points.
Equation:
Y = -0.4957*X + 3.780
Answer: B)Answer:
[tex]\Large \boxed{y=-\frac{1}{2} x+\frac{7}{2} }[/tex]
Step-by-step explanation:
Using a graph,
we can see that the line y = -1/2x + 7/2 best fits for the data.
PLLLEEEASSSSEEEE ANSWER FAST
The shape is based only on squares, semicircles, and quarter circles. Find the area of each shaded part.
Answer:
36.48 cm²
Step-by-step Explanation:
If you take a careful look at the figure given, you'd realise that the area of the shaded portion is actually created by 2 overlapping quarter circle.
The area of the shaded portion = Area of Square - Area of Unshaded part
Area of square = s² = 8² = 64 cm²
Area of the Unshaded portion = 2(Area of Square - Area of Quarter Circle)
= 2(s² - ¼*πr²)
Where, radius (r) = s = 8 cm, take π as 3.14
Area of unshaded part = 2(8² - ¼*3.14*8²)
= 2(64 - ¼*3.14*64)
= 2(64 - 1*3.14*16)
= 2(64 - 50.24)
= 2(13.76)
Area of unshaded part = 27.52 cm²
Area of shaded part = Area of Square - Area of Unshaded part
Area of shaded part = 64 - 27.52 = 36.48 cm²
1. Determine whether the given procedure results in a binomial distribution. If not, state the reason why.
Rolling a single die 53 times, keeping track of the "fives" rolled.
A) Not binomial: there are too many trials.
B) Not binomial: there are more than two outcomes for each trial.
C) Not binomial: the trials are not independent.
D) Procedure results in a binomial distribution.
2. Determine whether the given procedure results in a binomial distribution. If not, state the reason why.
Spinning a roulette wheel 7 times, keeping track of the winning numbers.
A) Not binomial: there are more than two outcomes for each trial.
B) Procedure results in a binomial distribution.
C) Not binomial: there are too many trials.
D) Not binomial: the trials are not independent.
1. Not binomial: there are more than two outcomes for each trial.
Thus, option (B) is correct.
2. Procedure results in a binomial distribution.
Thus, option (B) is correct.
1. Not binomial: there are more than two outcomes for each trial.
In a binomial distribution, each trial can have only two outcomes (usually referred to as success and failure).
In this case, the procedure involves rolling a single die 53 times and keeping track of the "fives" rolled.
Since the outcome can be any number from 1 to 6 on each trial, it does not meet the criteria for a binomial distribution.
Thus, option (B) is correct.
2. Procedure results in a binomial distribution.
In this case, the procedure involves spinning a roulette wheel 7 times and keeping track of the winning numbers. The outcome of each trial is either a win or a loss, which satisfies the requirement for a binomial distribution.
Thus, option (B) is correct.
Learn more about Binomial Distribution here:
https://brainly.com/question/29163389
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Use a t-test to test the claim about the population mean at the given level of significance using the given sample statistics. Assume the population is normally distributed.
Claim: μ ≥8 300, α = 0.10
Sample statistics: x = 8000, s = 440, n = 24
A. What are the null and alternative hypotheses?
B. What is the value of the standardized test statistic?
C. What is the p-value?
D. Decide whether to reject or fail to reject the null hypothesis.
Answer:
A
The null hypothesis is [tex]H_o : \mu \ge 8300[/tex]
The alternative hypothesis is [tex]H_a : \mu < 8300[/tex]
B
[tex]t = -3.34[/tex]
C
[tex]p-value = P(t< -3.34) = 0.00041889[/tex]
D
reject the null hypothesis
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 8300[/tex]
The sample mean is [tex]\ = x = 8000[/tex]
The standard deviation is [tex]s = 440[/tex]
The sample size is [tex]n = 24[/tex]
The level of significance is [tex]\alpha = 0.01[/tex]
The null hypothesis is [tex]H_o : \mu \ge 8300[/tex]
The alternative hypothesis is [tex]H_a : \mu < 8300[/tex]
The test statistic is mathematically evaluated as
[tex]t = \frac{\= x - \mu }{ \frac{s}{\sqrt{n} } }[/tex]
=> [tex]t = \frac{8000- 8300 }{ \frac{440}{\sqrt{24} } }[/tex]
=> [tex]t = -3.34[/tex]
The p-value is obtained from the z -table ( reference calculator dot net ) , the value is
[tex]p-value = P(t< -3.34) = 0.00041889[/tex]
Looking at the values of [tex]p-value and \ \alpha[/tex] we see that [tex]p-value < \alpha[/tex] Hence we reject the null hypothesis
in the diagram,QOS and ROU are straight lines.OT is the bisector of angle UOS. Angle POQ and angle QOR are complementary angles. Find the values of x and y.pleaseeee answer sooonnn
Answer:
x=50° and y=45°
Step-by-step explanation:
x=QU(90°)-QP(40°)
x=50°
y=SU(90°)/2
y=45°
Which quadratic equation would be used to solve for the unknown dimensions?
0 = 2w2
512 = w2
512 = 2w2
512 = 2l + 2w
Answer:
C
Step-by-step explanation:
Answer:
C: 512 = 2w2
Step-by-step explanation:
on edge
36x7 please EXPLAIN the process of the multiplication plse
36×7
=252
Explaination :
First Multiply 6 and 7 we get 42 !
Write 2 and 4 will be added to the product of 3×7
We get 21 and add 4 here
So we get 252
Answer:
[tex]36 \times 7 = 252[/tex]
Step-by-step explanation:
Firstly multiply 6 with 7 you have to write 2 and take 4 carry and then multiply 7 with 3 u get 21 now add the number u carry in 21 u get ur answer. 252.
Hope it helps u mate
Heidi bought a machine that throws tennis balls for her dog to fetch. The height of each ball thrown by the machine, in feet, is modeled by the function f(x) = –x2 + x + 2, where x represents time in seconds. How many seconds after the machine throws the ball does it hit the ground?
Answer:
2 seconds
Step-by-step explanation:
Given the equation:
[tex]f(x) = -x^2 + x + 2[/tex]
Where f(x) represents the height of each ball thrown by machine.
and x represents the time in seconds.
To find:
The number of seconds after which the machine throws the balls hits the ground = ?
Solution:
In other words, we have to find the value of [tex]x[/tex] after which the [tex]f(x) = 0[/tex]
(Because when the ball hits the ground, the height becomes 0).
Let us put [tex]f(x) = 0[/tex] and solve for [tex]x[/tex]
[tex]f(x) = -x^2 + x + 2 =0\\\Rightarrow -x^2 + x + 2 =0\\\Rightarrow x^2 - x - 2 =0\\\Rightarrow x^2 - 2x+x - 2 =0\\\Rightarrow x(x - 2)+1(x - 2) =0\\\Rightarrow (x+1)(x - 2) =0\\\Rightarrow x =-1, 2[/tex]
[tex]x=-1[/tex] sec is not a valid answer because time can not be negative.
So, the answer is after 2 seconds, the ball hits the ground.
Given f(x) = –2x+5 find f'(x).
a f'(x)=- 5x+1.5
b.
x 5
2 2
f'(x) =
C. f'(x) = 2x-5
d.
x 5
2 2
f'(x) -- +
R
Please select the best answer from the choices provided
B.
ОООО
D
Answer: D
Step-by-step explanation:
To find the inverse function, you switch y with x and x with y. Then you solve for y.
y=-2x+5 [replace y with x and x with y]
x=-2y+5 [subtract both sides by 5]
x-5=-2y [divide both sides by -2]
(x-5)/-2=y
Now that we have our inverse function, we can rewrite it so that it matches the answer choice. D matches our answer choice the best.
Tia uses 3/4 cup of pumpkin to make 1 1/4 pounds of dog treats. How much pumpkin does Tia use to make 1 pound of treats?
Answer:
4/5 cups to make 1 pound of dog treats
Step-by-step explanation:
3/4 cups : 1 1/4 pounds
x cups : 1 pound
Cross multiply
3/4 * 1 = 1 1/4 * x
x = 3/4 / 1 1/4
= 3/4 / 5/4
= 3/4 * 4/5
= 3/5 cups
Is math a feature of the universe or a feature of human creation?
Answer:
a feature of the universe
Step-by-step explanation:
Math is a feature of the universe because what we call math is just a way of explaining how things work.
Examine the diagram. Triangle M P L. Angle P is 90 degrees and angle L is (4 x + 6) degrees. The exterior angle to angle M is 136 degrees. What is the value of x?
Answer:
x = [tex]10^{0}[/tex]
Step-by-step explanation:
From Δ MPL given that; <P = [tex]90^{0}[/tex], exterior angle to M = [tex]136^{0}[/tex] and <L = [tex](4x+6)^{0}[/tex].
In the triangle, the exterior angle is equal to the sum of the two adjacent interior angles. So that;
[tex]136^{0}[/tex] = [tex]90^{0}[/tex] + [tex](4x+6)^{0}[/tex]
= [tex]90^{0}[/tex] + 4[tex]x^{0}[/tex] + [tex]6^{0}[/tex]
[tex]136^{0}[/tex] = [tex]96^{0}[/tex] + [tex]x^{0}[/tex]
⇒ 4[tex]x^{0}[/tex] = [tex]136^{0}[/tex] - [tex]96^{0}[/tex]
4[tex]x^{0}[/tex] = [tex]40^{0}[/tex]
Divided both sides by 4 to have;
[tex]x^{0}[/tex] = [tex]10^{0}[/tex]
The value of x is [tex]10^{0}[/tex].
Answer:
The correct answer is in fact 10 degrees.
Step-by-step explanation:
I hope this helps!
Have a great day! :)
If you want to turn a ball into a giant water balloon, how many cubic feet of lake water can you fill it with if the radius of this balloon is 1.5 feet?
Answer:
14.13 cubic feet of lake water can fill the given balloon.
Step-by-step explanation:
concept used:
volume of sphere = 4/3 [tex]\pi r^3[/tex]
where r is the radius of sphere
we take [tex]\pi[/tex] = 3.14
_____________________________________
shape of balloon can be taken as spherical.
Amount water filled in the balloon will be equal to capacity of balloon which is equal to volume of spherical balloon.
Given radius of balloon = 1.5 feet
Thus, volume of balloon = 4/3 [tex]\pi[/tex] 1.5^3 = 4/3*3.14*1.5^3
volume of balloon = 42.39/3 = 14.13 cubic feet
Thus, 14.13 cubic feet of lake water can fill the given balloon.
Musah stands at the centre of a rectangular field. He first takes 50 steps north, then 25 steps
west and finally 50 steps on a bearing of 3150
.
i. Sketch Musah’s movement [Mark 4]
ii. How far west is Musah’s final point from the centre?
Answer:
Inokkohgy8uokokj76899
PLEASE ANSWER!!! Brainliest to whoever answers at first!Order the following expressions by their values from least to greatest.
Answer:
-j, 0, j-k
Step-by-step explanation:
j is a positive number, so -j will be less than 0.
j is a number greater than k, so j - k will be greater than 0.
From least to greatest, the order is ...
-j, 0, j-k
Answer:
Step-by-step explanation:
If cot Theta = Two-thirds, what is the value of csc Theta? StartFraction StartRoot 13 EndRoot Over 3 EndFraction Three-halves StartFraction StartRoot 13 EndRoot Over 2 EndFraction Eleven-thirds
Answer:
csctheta= [tex]\frac{\sqrt{13} }{3}[/tex]
Step-by-step explanation:
answer is provided on top
The value of the [tex]\rm cosec \theta = \frac{\sqrt{13} }{3}[/tex]. Cosec is found as the ratio of the hypotenuse and the perpendicular.
What is trigonometry?The field of mathematics is concerned with the relationships between triangles' sides and angles, as well as the related functions of any angle
The given data in the problem is;
[tex]\rm cot \theta = \frac{2}{3}[/tex]
The [tex]cot \theta[/tex] is found as;
[tex]\rm cot \theta = \frac{B}{P} \\\\ \rm cot \theta = \frac{2}{3} \\\\ B=2 \\\\ P=3 \\\\[/tex]
From the phythogorous theorem;
[tex]\rm H=\sqrt{P^2+B^2} \\\\ \rm H=\sqrt{2^2+3^2} \\\\ H=\sqrt{13} \\\\[/tex]
The value of the cosec is found as;
[tex]\rm cosec \theta = \frac{H}{P} \\\ \rm cosec \theta = \frac{\sqrt{13} }{3}[/tex]
Hence the value of the [tex]\rm cosec \theta = \frac{\sqrt{13} }{3}[/tex].
To learn more about the trigonometry refer to the link;
https://brainly.com/question/26719838
What happens to the probability of making a Type II error, beta,as the level of significance, alpha,decreases? Why?
Answer:
Lowering the level of significance, α increases the probability of making a Type II error, β.
Step-by-step explanation:
Lowering the level of significance, α increases the probability of making a Type II error, β.
This is because the region of acceptance becomes bigger, and it makes it less likely for one to reject a null hypothesis, when it is false, the type II error.
Hi people, Please if someone can give me a hand, l already have done the first part of the exercise, but l cant make Angle CAB= X^0 c) calculate the lower bound for the value of tan X^0 there is the answer 1.02 (2dp) but l have no clue how to get it thanks i used Toa (Tan = Opp/ adj) but l couldnt find it thanks
Answer:
(c) 1.02
Step-by-step explanation:
(c) The tangent is the ratio of Opposite to Adjacent. Its lowest value will be found where Opposite is lowest, and Adjacent is highest:
min tan(A) = (min BC)/(max AB) = 75/73.5 ≈ 1.020408...(42-digit repeat)
What is the area of the house (including the drawing room, TV room, balcony, hallway, kitchen, and bedroom)?
Answer:
1256 i think
Step-by-step explanation:
Foram prescritos 500mg de dipirona para uma criança com febre.Na unidade tem disponivel ampola de 1g/2ml.Quantos g vão ser administrados no paciente
De acordo com a disponibilidade da unidade, há apenas a seguinte dosagem: 1g/2mL - ou seja, uma grama de dipirona a cada 2mL
O enunciado está meio mal formulado, pois é dito que foram prescritos 500mg de dipirona e é essa quantidade de farmaco que a criança tem que tomar. Deseja-se saber quantos mL deverao ser administrados.
Fazendo a classica regra de 3, podemos chegar no volume desejado:
(atentar que 500mg = 0,5g)
g mL
1 --------- 2
0,5 --------- X
1 . X = 0,5 . 2
X = 1mLthere was a total of 400 oranges and mangoes at a fruit stall.3/8 of these fruits were mangoes.each orange was priced at 40 cents,and each mango was priced at 60 cents.how much would mr.mead make if he sold 2/3 of the mangoes and 4/5 of the oranges?
Answer:
First find the number of Mango and oranges. 400 divided by 8 = 50. We use 8 because it is the whole part of the percentage. Since, there is 3/8 mangoes, multiply 50* 3= 150 mangoes and 50*5= 250 oranges.
2/3 of 150=100 mangoes. You would find this by dividing 150/3=50 then multiply by 2.
4/5 of 250= 200 oranges. You would find this by dividing 250/5=50 then multiply by 4.
$.40*100= $40.00 mangoes
$.60*200= $120.00 oranges
Mr. Mead would make $160.00
Step-by-step explanation:
Find the sum of (5x3 + 3x2 - 5x + 4) and (8x3 -5x2 + 8x + 9)
Answer:
(5x³+3x²-5x+4) + (8x³-5x²+8x+9)
= 5x³+3x²-5x+4 +8x³-5x²+8x+9
= 5x³+8x³+3x²-5x²-5x+8x+4+9
= 13x³-2x²+3x+13
Hope this helps
if u have question let me know in comments ^_^
Given that a is a multiple of 456, find the greatest common divisor of 3a^3+a^2+4a+57 and a.
Answer: 57
Step-by-step explanation:
Given: a is a multiple of 456
Let [tex]a = 456 x[/tex]
Then, expression [tex]3a^3+a^2+4a+57 =3(456x)^3+(456x)^2+4(456x)+57[/tex]
Since 456 = 57 x 8
Then, [tex]3(456x)^3+(456x)^2+4(456x)+57=3(57\times 8x)^3+(57\times 8x)^2+4(57\times 8x)+57[/tex]
[tex]=3(57)^3\times (8x)^3+(57)^2\times (8x)^2+4(57)\times (8x)+57[/tex]
Taking 57 out as common
[tex]=57[3(57)^2\times (8x)^3+(57)\times (8x)^2+4\times (8x)+1][/tex]
Now, the greatest common divisor of [tex]a = 456 x[/tex] and [tex]3a^3+a^2+4a+57=57[3(57)^2\times (8x)^3+(57)\times (8x)^2+4\times (8x)+1][/tex] is 57.
Hence, the greatest common divisor of 3a^3+a^2+4a+57 and a is 57.
Find n for the arithmetic sequence for which sn=345, u1=12 and d = 5 .
Answer:
n = 10
Step-by-step explanation:
The sum to n terms of an arithmetic sequence is
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]
where a₁ is the first term and d the common difference
Here a₁ = 12 and d = 5 and [tex]S_{n}[/tex] = 345, thus
[tex]\frac{n}{2}[/tex] [ (2 × 12) + 5(n - 1) ] = 345 ( multiply both sides by 2 )
n( 24 + 5n - 5) = 690 ← distribute and simplify left side
n(19 + 5n) = 690
19n + 5n² = 690 ( subtract 690 from both sides )
5n² + 19n - 690 = 0 ← in standard form
(5n + 69)(n - 10) = 0 ← in factored form
Equate each factor to zero and solve for n
5n + 69 = 0 ⇒ 5n = - 69 ⇒ n = - [tex]\frac{69}{5}[/tex]
n - 10 = 0 ⇒ n = 10
However, n > 0 , thus n = 10
(Score for Question 1: ____ of 5 points)
1. The equation of a circle is x2 + y2 - 4x + 2y - 11 = 0. What are the center and the radius of the circle?
Show your work
Answer:)
Answer:
The center of the circle:
(2, -1)
The radius of the circle:
r = 4
Step-by-step explanation:
The first step is to complete the square on both x and y:
x^2 + y^2 -4x + 2y - 11 = 0
x^2 -4x +y^2 +2y = 11
We determine c1 to complete the square on x:
c1 = (b/2)^2
c1 = (-4/2)^2 = 4
We then determine c2 to complete the square on y:
c2 = (2/2)^2 = 1
The equation of the circle is then re-written as:
x^2 -4x + 4 +y^2 +2y + 1 = 11 +4 +1
We then factorize the expressions in x and y separately:
(x-2)^2 + (y +1)^2 = 16
The center of the circle is thus:
(2, -1)
The radius is the square root of 16:
r = 4
Answer:
center : (2, -1)
radius : r = 4
Step-by-step explanation:
please help solving.
Answer:
right machine first, then left.6 into left machine, then rightStep-by-step explanation:
a) Putting 6 into the first (left) machine will give an output of ...
y = √(6 -5) = √1 = 1
Putting 1 into the second (right) machine will give an output of ...
y = 1² -6 = -5
This answers the second question, but not the first question.
__
If we put 6 into the right machine first, we get an output of ...
y = 6² -6 = 30
Putting 30 into the left machine, we get an output of ...
y = √(30 -5) = √25 = 5 . . . . . the desired output.
The input must go into the right machine first, then its output goes into the left machine to get a final output of 5 from an input of 6.
__
b) The left machine cannot produce negative outputs, so achieving an output of -5 with the arrangement used in part A is not possible. (green curves in the attached graph)
However, as we have shown above, inputting 6 to the left machine first, following that by processing with the right machine, can produce an output of -5. (purple curve in the attached graph)
Musah stands at the center of a rectangular field. He first takes 50 steps north, then 25 steps west and finally 50 steps on a bearing of 315°. Sketch musah's movement. How far west is musah's final point from the center?
Answer: 4.17 steps
Step-by-step explanation:
Draw a point to use as the center and then sketch 50 units north (up) and 25 units west (left) and 315° which creates a right triangle that has an angle of 360° - 315° = 45°
Use Pythagorean Theorem to find the length of the hypotenuse.
50² + 25² = hypotenuse² --> hypotenuse = 55.9 units
Since Musah only walked 50 units along the hypotenuse, he is 5.9 units from the center.
Create another right triangle using the remaining 5.9 units as the hypotenuse. You can use 45°-45°-90° rules OR sin 45° to find the horizontal distance from the center to be 4.17.
see attachment for sketch
A mass of 5 kg stretches a spring 10 cm. The mass is acted on by an external force of 10sin( t ) N(newtons) and moves in a medium that imparts a viscous force of 2 N
when the speed of the mass is 4 cm/s. If the mass is set in motion from its equilibrium position with an initial velocity of 3 cm/s, formulate the initial value problem describing the motion of the mass.
A)Find the solution of the initial value problem in the above problem.
B)Plot the graph of the steady state solution
C)If the given external force is replaced by a force of 2 cos(ωt) of frequency ω , find the value of ω for which the amplitude of the forced response is maximum.
Answer:
A) C1 = 0.00187 m = 0.187 cm, C2 = 0.0062 m = 0.62 cm
B) A sample of how the graph looks like is attached below ( periodic sine wave )
C) w = [tex]\sqrt[4]{3}[/tex] is when the amplitude of the forced response is maximum
Step-by-step explanation:
Given data :
mass = 5kg
length of spring = 10 cm = 0.1 m
f(t) = 10sin(t) N
viscous force = 2 N
speed of mass = 4 cm/s = 0.04 m/s
initial velocity = 3 cm/s = 0.03 m/s
Formulating initial value problem
y = viscous force / speed = 2 N / 0.04 m/s = 50 N sec/m
spring constant = mg/ Length of spring = (5 * 9.8) / 0.1 = 490 N/m
f(t) = 10sin(t/2) N
using the initial conditions of u(0) = 0 m and u"(0) = 0.03 m/s to express the equation of motion
the equation of motion = 5u" + 50u' + 490u = 10sin(t/2)
A) finding the solution of the initial value
attached below is the solution and
B) attached is a periodic sine wave replica of how the grapgh of the steady state solution looks like
C attached below
Are you able to find tri-sector (equally divided by 3) rays for an arbitrary angle with straightedge-and-compass construction?
Answer:
Step-by-step explanation:
No, it is an ancient problem which has been proved to be impossible (in 1837), at least not for an arbitray angle.
However, we can trisect certain angles, such as 90 degrees, but rather than trisection, we are just constructing 30 degree angles.
For further reading, google "angle trisection"
X2 + (y - 1) 2 = 4 .............................
Answer:
Step-by-step explanation:
x²+(y-1)²=4
x²+y²+1-2y=4
x²+y²-2y=3
Answer:
[tex]x=\pm \sqrt{6-2y}[/tex]
[tex]$y=\frac{1}{2} (6-x^2)$[/tex]
Step-by-step explanation:
[tex]x^2+(y-1)\cdot 2 =4[/tex]
[tex]x^2+2y-2 =4[/tex]
[tex]x^2+2y =6[/tex]
I will solve it for [tex]x[/tex]
[tex]x^2 =6-2y[/tex]
[tex]x=\pm \sqrt{6-2y}[/tex]
Solving for [tex]y[/tex]
[tex]$y=3-\frac{x^2}{2} $[/tex]
[tex]$y=\frac{1}{2} (6-x^2)$[/tex]