Answer:
The price for 3.75 pounds of cherries is $17.775.
Step-by-step explanation:
The price las week was $ 4.99 and it got a discount of 15% for this week, this means that the price for this week is 100% of the one prior minus 15%, therefore it is 85% of the last price. We need to calculate the price per pound with this discount as shown below:
[tex]\text{this week} = \text{last week}*\frac{95}{100}\\\\\text{this week} = 4.99*0.95 = 4.74 \text{ per pound}\\[/tex]
Since the price is $4.74 per pound and we want to buy 3.75 pounds, then the total amount we need to pay is:
[tex]\text{total amount} = 3.75*4.74 = 17.775[/tex]
The price for 3.75 pounds of cherries is $17.775.
Suppose that a large mixing tank initially holds 400 gallons of water in which 70 pounds of salt have been dissolved. Pure water is pumped into the tank at a rate of 4 gal/min, and when the solution is well stirred, it is then pumped out at the same rate. Determine a differential equation for the amount of salt A(t) in the tank at time t > 0. What is A(0)
Answer:
[tex]\dfrac{dA}{dt}+ \dfrac{A}{100}=0[/tex]
A(0) = 70 (i.e the pounds of salt dissolved into the tank)
Step-by-step explanation:
Given that:
a large mixing tank initially holds 400 gallons of water in which 70 pounds of salt have been dissolved.
The rate at which pure water is pumped into the tank is 4 gal/min
After stirring; the pure water is then pumped out at the same rate.
The objective is to determine the differential equation for the amount of salt A(t) in the tank at time t > 0. What is A(0)
Taking the differential of:
[tex]\dfrac{dA}{dt}=R_{in}-R_{out}[/tex] ---- (1)
where ;
[tex]R_{in[/tex] = 0
[tex]R_{out} =\dfrac{A(t)}{400}*4[/tex]
[tex]R_{out} =\dfrac{A}{100}[/tex]
replacing them into (1) ; we have:
[tex]\dfrac{dA}{dt}=0 - \dfrac{A}{100}[/tex]
[tex]\dfrac{dA}{dt}=- \dfrac{A}{100}[/tex]
[tex]\dfrac{dA}{dt}+ \dfrac{A}{100}=0[/tex]
A(0) = 70 (i.e the pounds of salt dissolved into the tank)
The differential equation for the amount of salt A(t) in the tank at time t > 0 is [tex]\frac{dA}{dt} + \frac{A}{100} = 0[/tex]
A (0)= 70
Given that,
Suppose that a large mixing tank initially holds 400 gallons of water in which 70 pounds of salt have been dissolved. Pure water is pumped into the tank at a rate of 4 gal/minThe Calculation is as follows:[tex]dA\div dt=R_{in}-R_{out}[/tex]
Rin=0
[tex]R_{out}=A(t)\div 400 \times (4)\\\\ =A\div 100[/tex]
so,
[tex]dA\div dt=R_{in}-R_{out}\\\\dA\div dt=0- A\div 100[/tex]
So,
[tex]dA\div dt +A\div 100=0[/tex]
A(0)=70
Find out more information about the Water here:brainly.com/question/4381433?referrer=searchResults
Coaching companies claim that their courses can raise the SAT scores of high school students. But students who retake the SAT without paying for coaching also usually raise their scores. A random sample of students who took the SAT twice found 427 who were coached and 2733 who were uncoached. Starting with their verbal scores on the first and second tries, we have these summary statistics: Try 1 Try 2 Gain n \overline x s \overline x s \overline x sCoached 427 500 92 529 97 29 59Uncoached 2733 506 101 527 101 21 52Use Table C to estimate a 90% confidence interval for the mean gain of all students who are coached.toat 90% confidence.Now test the hypothesis that the score gain for coached students is greater than the score gain for uncoached students. Let \mu_1 be the score gain for all coached students. Let \mu_2 be the score gain for uncoached students.(a) Give the alternative hypothesis: \mu_1 - \mu_20.(b) Give the t test statistic:(c) Give the appropriate critical value for \alpha =5%: .
Answer:
Step-by-step explanation:
The question is incomplete. The complete question is
Coaching companies claim that their courses can raise the SAT scores of high school students. But students who retake the SAT without paying for coaching also usually raise their scores. A random sample of students who took the SAT twice found 427 who were coached and 2733 who were uncoached. Starting with their verbal scores on the first and second tries, we have these summary statistics:
Try 1 Try 2 Gain
n x s x s x s
Coached 427 500 92 529 97 29 59
Uncoached 2733 506 101 527 101 21 52
Use Table C to estimate a 90% confidence interval for the mean gain of all students who are coached.
at 90% confidence.
Now test the hypothesis that the score gain for coached students is greater than the score gain for uncoached students. Let μ1 be the score gain for all coached students. Let μ2 be the score gain for uncoached students.
(a) Give the alternative hypothesis:
μ1 - μ2.
(b) Give the t test statistic:
(c) Give the appropriate critical value for \alpha =5%:
Solution:
The formula for determining the confidence interval for the difference of two population means is expressed as
Confidence interval = (x1 - x2) ± z√(s²/n1 + s2²/n2)
Where
x1 = sample mean score gain for all coached students
x2 = sample mean score gain for all uncoached students
s1 = sample standard deviation score gain of coached students
s2 = sample standard deviation score gain of uncoached students
For a 90% confidence interval, the z score is 1.645
From the information given,
x1 = 29
s1 = 59
n1 = 427
x2 = 21
s2 = 52
n2 = 2733
x1 - x2 = 29 - 21 = 8
z√(s1²/n1 + s2²/n2) = 1.645√(59²/427 + 52²/2733) = 4.97
90% Confidence interval = 8 ± 4.97
a) The population standard deviations are not known. it is a two-tailed test. The random variable is μ1 - μ2 = difference in the score gain for coached and uncoached students.
We would set up the hypothesis.
The null hypothesis is
H0 : μ1 = μ2 H0 : μ1 - μ2 = 0
The alternative hypothesis is
H1 : μ1 > μ2 H1 : μ1 - μ2 > 0
This is a right tailed test.
b) Since sample standard deviation is known, we would determine the test statistic by using the t test. The formula is
(x1 - x2)/√(s1²/n1 + s2²/n2)
t = (29 - 21)/√(59²/427 + 52²/2733)
t = 2.65
The formula for determining the degree of freedom is
df = [s1²/n1 + s2²/n2]²/(1/n1 - 1)(s1²/n1)² + (1/n2 - 1)(s2²/n2)²
df = [59²/427 + 52²/2733]²/[(1/427 - 1)(59²/427)² + (1/2733 - 1)(52²/2733)²] = 9.14/0.1564
df = 58
c) from the t distribution table, the critical value is 1.67
In order to reject the null hypothesis, the test statistic must be smaller than - 1.67 or greater than 1.67
Since - 2.65 < - 1.67 and 2.65 < 1.67, we would reject the null hypothesis.
Therefore, at 5% significance level, we can conclude that the score gain for coached students is greater than the score gain for uncoached students.
What is the total surface area of the square pyramid below?
14 cm
10 cm
10 cm
Answers:
100 cm
200 cm
250 cm
Answer: A = 93.8 cm so if you round up it's about 100 cm
Step-by-step explanation:
Area means you have to multiply all measurements by each other in any order of course because it doesn't matter in this case.
14 * 10 * 10 = 1400
Now you can/should divide the answer which is (1400) by how many measurements you have times the sides it has, sides - which is 5 , measurements - which is 3, so it would look like this:
1400 / 15 = 93.8
which expression gives the distance between the points (2,5)and (-4,8)
Answer:
[tex]3\sqrt{5}[/tex]
Step-by-step explanation:
Use the distance formula:
[tex]\sqrt{(8-5)^2+(-4-2)^2}=\sqrt{9+36}=3\sqrt{5}[/tex]
Answer: [tex]\sqrt{45} =3\sqrt{5}[/tex]
Step-by-step explanation:
To find the distance between 2 points use this formula:
[tex]\sqrt{(x1-x2) ^{2} +(y1-y2)^{2} }[/tex]
rad[(2+4)^2+(5-8)^2)]
=rad[36+9]
=rad45
=3rad5
Given the following exponential function, identify whether the change represents
growth or decay, and determine the percentage rate of increase or decrease.
y = 940(1.89)
Answer: The change represents growth with 89% of growth rate.
Step-by-step explanation:
The exponential function is given by :-
[tex]f(x)= Ab^x[/tex]... (i)
Where , A = initial value , b= multiplicative factor and x= time period
We call 'b' growth factor when b>1, we can write b= 1+r , where r is the rate of growth.We call 'b' decay factor when b<1 , we can write b= 1-r , where r is the rate of decay.The given function : [tex]y = 940(1.89)^x[/tex].
By comparing this to (i) , we get
b= 1.89 > 1 , thus it represent the growth.
Also,
[tex]b= 1+r\Rightarrow\ 1.89 = 1+r\\\\\Rightarrow\ r=1.89-1=0.89[/tex]
i.e. Percentage rate of growth = 0.89 x 100 = 89%.
Which of the following graphs Represents the equation above -3x+ 2 y=
How much of other chemicals must be evaporated from 400 grams of a hand sanitizer that is 24% alcohol to strengthen it to a hand sanitizer that is 30% alcohol? Correct your answer to the nearest whole number
Answer:
Mass of other chemicals to be evaporated is 24 grams.
Step-by-step explanation:
The initial mass of the hand sanitizer = 400 grams, and has an alcohol content of 24%.
mass of its alcohol content = [tex]\frac{24}{100}[/tex] × 400
= 96 grams
mass of non-alcoholic content = 400 - 96
= 304 grams
If the percentage of alcohol is increased to 30%, then;
mass of its alcohol content = [tex]\frac{30}{100}[/tex] × 400
= 120 grams
The mass of other chemicals to be evaporated = 120 - 90
= 24 grams
What must be a factor of the polynomial function f(x) graft on the coordinate plane below
X - 6
x - 3
x + 1
x +6
Answer:
Option D.
Step-by-step explanation:
The given graph represents the function f(x).
If graph of a function f(x) intersect x axis at x=c, then (x-c) is a factor of f(x).
From the given graph it is clear that the graph of f(x) intersect x axis at x=-6,-3,0. It means factors of given function are
[tex](x-(-6))=(x+6)[/tex]
[tex](x-(-3))=(x+3)[/tex]
[tex](x-0)=x[/tex]
It means (x+6), (x+3) and x are factors of given function.
Therefore, option D is correct.
Answer:
The answer is (x+6)
Step-by-step explanation:
Just took the test
Hope this helps
Complete the statements about the cone.
The height is
units.
The radius is
units.
The volume is
ut cubic units.
Answer:
Step-by-step explanation:
The height is 6 units.
The radius is 8 units.
The volume is 128 π cubic units.
What is the value of x if f(x) = 76
Answer:
The roots (zeros) are the x values where the graph intersects the x-axis. To find the roots (zeros), replace f(x) with 0 and solve for x
No solution
The decimal $0.76$ is equal to the fraction $\frac{4b+19}{6b+11}$, where $b$ is a positive integer. What is the value of $b$?
Answer:
The value of b is 19.
Step-by-step explanation:
With what the problem states, we have that:
[tex]\frac{4b + 19}{6b + 11} = 0.76[/tex]
Doing cross multiplication
[tex]4b + 19 = 0.76(6b + 11)[/tex]
[tex]4b + 19 = 4.56b + 8.36[/tex]
[tex]4.56b - 4n = 19 - 8.36[/tex]
[tex]0.56b = 10.64[/tex]
[tex]b = \frac{10.64}{0.56}[/tex]
[tex]b = 19[/tex]
The value of b is 19.
Among 343 women surveyed, 15 worked the graveyard shift. Among 294 men surveyed, 27 worked the graveyard shift. The samples are independent and were gathered using simple random sampling. Use the critical value method and a 1% significance level to test the claim that the proportion of women working the graveyard shift is less than the proportion of men working the graveyard shift. What is the critical value (rounded to the nearest hundredth)
Answer:
There is enough evidence to support the claim that the proportion of women working the graveyard shift is less than the proportion of men working the graveyard shift (z=-2.44).
Critical value (α=0.01) zc=-2.33.
Step-by-step explanation:
This is a hypothesis test for the difference between proportions.
The claim is that the proportion of women (subindex 1) working the graveyard shift is less than the proportion of men (subindex 2) working the graveyard shift.
Then, the null and alternative hypothesis are:
[tex]H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2< 0[/tex]
The significance level is 0.05.
The sample 1, of size n1=343 has a proportion of p1=0.0437.
[tex]p_1=X_1/n_1=15/343=0.0437[/tex]
The sample 2, of size n2=294 has a proportion of p2=0.0918.
[tex]p_2=X_2/n_2=27/294=0.0918[/tex]
The difference between proportions is (p1-p2)=-0.0481.
[tex]p_d=p_1-p_2=0.0437-0.0918=-0.0481[/tex]
The pooled proportion, needed to calculate the standard error, is:
[tex]p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{15+27}{343+294}=\dfrac{42}{637}=0.0659[/tex]
The estimated standard error of the difference between means is computed using the formula:
[tex]s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.0659*0.9341}{343}+\dfrac{0.0659*0.9341}{294}}\\\\\\s_{p1-p2}=\sqrt{0.0002+0.0002}=\sqrt{0.0004}=0.0197[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{-0.0481-0}{0.0197}=\dfrac{-0.0481}{0.0197}=-2.44[/tex]
For a significance level of 0.01 and a left-tailed test, the critical value of z is zc=-2.326.
If the test statistic is smaller than the critical value, the null hypothesis is rejected.
The test statistic z=-2.44 is smaller than the critical value zc=-2.326, so the null hypothesis is rejected.
There is enough evidence to support the claim that the proportion of women working the graveyard shift is less than the proportion of men working the graveyard shift.
Calculate the product of 8/15, 6/5, and 1/3.
B. 16:15
D. 16/75
A. 48
0115
Answer:
16/75, D
Step-by-step explanation:
6/5*1/3. We can cross simplify to make it 2/5*1/1. That is 2/5. Then, 2/5*8/15 is 16/75 which is answer choice D.
Please help! I'm stuck on this one :(
Answer:
[900, 1300]
Step-by-step explanation:
According to the empirical rule, 95% is within ±2 standard deviations.
1100 − 2(100) = 900
1100 + 2(100) = 1300
Plz help fast!!! will give brainiest to first correct answer For which distributions is the median the best measure of center? Select each correct answer.
Answer:
The top left picture and top right picture
Step-by-step explanation:
A cereal box has a volume of 450 cubic cm. The length and width are 43 cm and 12 cm. HOW can you find the height? PLEASE HELP ME!!
WILL GIVE BRAINLIEST!!!
Answer:
Step-by-step explanation:
Volume of a rectangular prism=length x width x height
450=43*12*x
x=0.87209cm
In a large class in statistics, the final examination grades have a mean of 67.4 and a standard deviation of 12. Assuming that the distribution of these grades is normal, the number of passes in a class of 180 is:_________ (if you get a number with decimals points, round up to the next whole number)
Answer:
The number of passes in a class of 180 is 75.
Step-by-step explanation:
The problem does not state, so I will suppose the passing grade is 70.
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question:
[tex]\mu = 67.4, \sigma = 12[/tex]
Proportion of students who passed:
This is 1 subtracted by the pvalue of Z when X = 70. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{70 - 67.4}{12}[/tex]
[tex]Z = 0.22[/tex]
[tex]Z = 0.22[/tex] has a pvalue of 0.5871.
1 - 0.5871 = 0.4129
Out of 180:
0.4129*180 = 74.32
Rounding up
The number of passes in a class of 180 is 75.
If x^6=20 and w^10=20, what is x^12 w^-10?
Answer:
[tex]x^{12} =400[/tex]
[tex]w^{-10} =\frac{1}{20}[/tex]
Step-by-step explanation:
[tex]x^{6} =20[/tex]
[tex]x^{12} =(x^{6} )^{2} =20^{2} =400[/tex]
[tex]w^{10} =20[/tex]
[tex]w^{-10} =\frac{1}{w^{10} } =\frac{1}{20}[/tex]
[tex]x^{12} *w^{-10} =400*\frac{1}{20} =20[/tex]
Triangle ABC was dilated and translated to form similar triangle A'B'C'.
On a coordinate plane, 2 triangles are shown. Triangle A B C has points (0, 2), (2, 2), and (2, 0). Triangle A prime B prime C prime has points (negative 4, negative 1), (1, negative 1), and (1, negative 6).
What is the scale factor of the dilation?
One-fifth
Two-fifths
Five-halves
5
Answer:
Dilation is done by the scale factor of Five-halves.
Step-by-step explanation:
Please refer to the image attached,
The graph clearly shows the triangles [tex]\triangle[/tex]ABC and [tex]\triangle[/tex]A'B'C'.
Let us calculate the sides of triangles first then we will be able to find scale factor of dilation.
Using the distance formula:
Distance between 2 points [tex]P (x_1,y_1) \text{ and } Q (x_2,y_2)[/tex] is given by formula:
PQ = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Side AB is along x-axis, side AB =
[tex]\sqrt{(2-0)^2+(2-2)^2}\\\Rightarrow \sqrt{4}\\\Rightarrow 2\ units[/tex]
Similarly side, BC = 2 units
Now, in [tex]\triangle[/tex]A'B'C', A'B' can be calculated by distance formula:
[tex]\sqrt{(1+4)^2+(-1- (-1))^2}\\\Rightarrow \sqrt{25}\\\Rightarrow 5\ units[/tex]
B'C' = 5 units
The ratio of sides:
AB : A'B' = 2:5
[tex]\Rightarrow \dfrac{AB}{A'B'} = \dfrac{2}{5}\\\Rightarrow A'B' = \dfrac{5}{2} AB[/tex]
So, scaling factor is [tex]\dfrac{5}{2}[/tex] or 2.5.
OR
Scaling factor is Five-halves.
Answer:
The answer is C on Edge.
Step-by-step explanation:
Need helppppp asapppp
The answer is C. 65........
Answer:
25
Step-by-step explanation:
The angle of an arc is the same as the central angle. MarcCD is the same as the central angle COD which is given as 130o.
That means there are 50 degrees left for COA and DOA and because the chord and the diameter are equal, COA = DOA
That means that COA is 1/2 what is left over from 180 when 130 is subtracted from it.
1/2 * 50 = 25
The answer is A 25.
A data set includes the following test scores: 75, 82, 84, 62, 78. The score on a retake test is 96. It the retake score replaces the lowest test grade, how is the mean affected? A) The mean increases by 5. B) The mean increases by 6.8. C) The mean increases by 35. D) The mean does not change.
Answer:
B the mean increases by 6.8
Which of the following is a property of translations that is not also a property of other types of rigid motions? (1) they map line segments to other line segments of equal length (2) they map angles to other angles of the same size (3) they map lines to parallel lines (4) they map lines to perpendicular lines
Answer:
3 I think it's 3. sorry if I'm wrong
The correct answer is (3) they map lines to parallel lines
Transformation is the movement of a point from the initial location to a new location. Types of transformation is rotation, reflection, translation and dilation.
Translation is the movement of a point up, down, left or right in the coordinate plane.
Translation is a rigid transformation, that is, it preserves the size and shape of the figure. Reflection and rotation are also rigid transformation.
Translation maps lines to parallel lines whereas rotation does not since it changes the direction of the line.
Find out more at: https://brainly.com/question/11707700
The chart shows the number of students who participate
in various sports.
Sport
Number of
Students
Students can only play one sport at a time. What is the
ratio of students who cheer to students who participate
in a sport?
Step 1: Decide what comparison is being represented
You know the comparison is part-to-whole because the
question is asking you to compare some students to
the total number of students who participate in sports.
Flag Football
35
Tennis
27
The ratio of students who cheer to those who
participate in a sport is
to 164.
Dance
43
Basketball
33
Cheer
26
Answer:
the answer is 26
Step-by-step explanation:
The ratio of students who cheer to those who participate in a sport is 13/82.
What is Ratio?A ratio is a comparison between two amounts that is calculated by dividing one amount by the other. The quotient a/b is referred to as the ratio between a and b if a and b are two values of the same kind and with the same units, such that b is not equal to 0. Ratios are represented by the colon symbol (:). As a result, the ratio a/b has no units and is represented by the notation a: b.
Total students participated in sports
= 35 + 27 + 43 + 33 + 26
= 164
and, students who cheered = 26
So, the ratio of students who cheer to those who participate in a sport
= 26 / 164
= 13 / 82
Learn more about ratio here:
https://brainly.com/question/13419413
#SPJ7
Need to know if f(x)=x-4 and g(x)=3x+5, find (f+g) (x)
Answer:
4x+1
Step-by-step explanation:
f(x)=x-4 and g(x)=3x+5,
(f+g) (x) = x-4 +3x+5
Combine like terms
= 4x+1
You currently drive 300 miles per week in a car that gets 15 miles per gallon of gas. You are considering buying a new fuel-efficient car for $12,000 (after trade-in on your current car) that gets 50 miles per gallon. Insurance premiums for the new and old car are $800 and $600 per year, respectively. You anticipate spending $1200 per year on repairs for the old car and having no repairs on the new car. Assume gas costs $3.50 per gallon. Over a five-year period, is it less expensive to keep your old car or buy the new car?
Answer:
No, it is not less expensive to keep the old car as the price calculation is higher then the New Car
Purchasing new car is less expensive
Step-by-step explanation:
NEW CAR EXPENSES= $21,240
OLD CAR EXPENSES= $25,800
NB: Kindly check attached picture for calculations
Please answer this multiple choice question !! Will give brainliest !!
Answer: they deleted my answer but here is how to do it If that helps some
Step-by-step explanation:
way to solve a linear system algebraically is to use the substitution method. The substitution method functions by substituting the one y-value with the other. We're going to explain this by using an example.
y=2x+4
3x+y=9
We can substitute y in the second equation with the first equation since y = y.
3x+y=9
3x+(2x+4)=9
5x+4=9
5x=5
x=1
This value of x can then be used to find y by substituting 1 with x e.g. in the first equation
y=2x+4
y=2⋅1+4
y=6
The solution of the linear system is (1, 6).
You can use the substitution method even if both equations of the linear system are in standard form. Just begin by solving one of the equations for one of its variables.
Please help
Blake is going to invest in an account paying an interest rate of 1.5% compounded quarterly. How much would Blake need to invest, to the nearest dollar, for the value of the account to reach $910 in 10 years?
Answer:
A, of money in the account after 3 years subject to interest ... If you deposit P dollars at rate r, in decimal form, subject to compound interest paid
Step-by-step explanation:
(−98)+(−97)+(−96) + ⋯ +(−1)+0+1+2+ ⋯ +98+99+100
Answer:
199
Step-by-step explanation:
All of the terms of the sum cancel except the last two.
The total is 199.
round off the number 0.007326 correct to 3 significant figures 3 decimal places
Answer:0.007
Step-by-step explanation:
3x - 2y = 12
Find the x and y intercepts
Answer:
x-intercept: 4 y-intercept: - 6
Step-by-step explanation:
To find the y-intercept, we must first solve for y.
Isolate variable y on the left side of the equation by subtracting 3x from both sides.
- 2y = - 3x + 12
Now divide both sides by - 2 to find y.
y = 3/2x - 6
The y-intercept is - 6. (remember formula y = mx + b, where b is the y-intercept)
To find the x-intercept, we must solve for x.
Isolate variable x on the left side of the equation by adding 2y to both sides.
3x = 2y + 12
Now divide both sides by 3 to find x.
x = 2/3y + 4
The x-intercept is 4. (remember formula x = my + b, where b is the x-intercept)
Answer:
4 and - 6
Step-by-step explanation:
3x-2y=12
x= 0 ⇒ -2y=12 ⇒ y= -6y=0 ⇒ 3x= 12 ⇒ x= 4