The speed that describes how fast the car was traveling when the driver applied the brakes is 49 mph.
What was the speed?
The formula that is often used by police officers to determine the speed from a skid mark is this s = √21d.
So, in this case, the length or distance of the skid mark is 115 feet. We can substitute this value in the formula to get;
Speed of car = √21(115)
Speed of car = √2,415
Speed of car = 49.1426 approximately 49 mph.
So, the speed that describes how fast the car was traveling when the driver applied the brakes is 49 mph.
Complete Question:
A police officer investigating an accident finds a skid mark 115 feet long. Approximately how fast was the car traveling when the driver applied the brakes?
Determine which of the following graphs represent the equation below. Also determine the y-intercept of the graph.
Answer:
Option (a)
Step-by-step explanation:
The given equation is
y = 4 (2ˣ)
To find y-intercept, substitute x=0 in the equation.
y = 4 (2⁰) = 4 (1) =4
Hence y-intercept is 4.
Since y-intercept is 4, the equation should pass through the point (0,4).
The only graph passing through the point (0,4) is the graph in option (a).
Hence the answer is option (a).
Answer:
a
Step-by-step explanation:
A herd of dinosaurs made paintings in the sand with their claws. Each baby dinosaur made 1515 paintings and each adult dinosaur made 77 paintings. The entire herd made 208208 paintings in total, and there were 33 times as many baby dinosaurs as adult dinosaurs. How many baby dinosaurs and adult dinosaurs were there?
Answer:
4 adult dinosaurs and 12 baby dinosaurs.
Step-by-step explanation:
Let the number of adult dinosaurs be x.
Number of baby dinosaurs = 3x
Number of paintings made by each baby dinosaur = 15
Number of paintings made by each adult dinosaur = 7
Total number of paintings made by 3x baby dinosaurs = Number of baby dinosaurs * Number of paintings made by each baby dinosaur
= 3x * 15
= 45x
Total number of paintings made by x adult dinosaurs = Number of adult dinosaurs * Number of paintings made by each adult dinosaur
= x * 7
= 7x
Total number of paintings made by both baby and adult dinosaurs = 45x + 7x
= 52 x
Again the problem says that the total number of paintings made = 208
So, 52x = 208
Dividing both sides by 52
[tex]\frac{52x}{52}[/tex] = [tex]\frac{208}{52}[/tex]
Cancelling out the 52's from the top and bottom on the left
x = 4
So, number of adult dinosaurs = 4
Number of baby dinosaurs = 3x = 3*4 = 12
A system of equations based on the information given can be used to find the number of baby and adult dinosaurs. The two equations are 1515b + 77a = 208208 and b = 33a. Solve these to find the number of each type of dinosaur.
Explanation:This problem can be solved by setting up a system of equations. Let's denote the number of baby dinosaurs as 'b' and the number of adult dinosaurs as 'a'. Then, from the statement, we know two things:
'Each baby dinosaur made 1515 paintings and each adult dinosaur made 77 paintings. The entire herd made 208208 paintings in total, we can set up the equation as 1515b + 77a = 208208.'There were 33 times as many baby dinosaurs as adult dinosaurs', so this can be represented as b = 33a.By substituting the second equation into the first, we can determine the number of adult dinosaurs, and subsequently, the number of baby dinosaurs. Solving this would give us the solution needed.
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A 1200 sq ft house is advertised for sale at a price of 96000. What is the cost per square foot?
Answer:$80.00
Step-by-step explanation:
APEX
Paws at play made a total of $1,234 grooming 22 dogs. Paws at play charges $43 to groom each small dog and $75 for each large dog. Write a system of equations that can be used to determine the number of small and large dogs that were groomed
Step-by-step explanation:
We are asked to write a system of equations using our given information.
Let x be number of small dogs and y be number of large dogs.
We have been given that paws at play made a total of $1,234 grooming 22 dogs, which means that number of small dogs and large dogs is 22. We can represent this information as:
[tex]x+y=22...(1)[/tex]
We have been given that paws at play charges $43 to groom each small dog and $75 for each large dog. So the total grooming charges for grooming x small and y large dogs will be 43x+75y, that is equal to total charges for grooming $1234.
We can represent this information as:
[tex]43x+75y=1234...(2)[/tex]
Therefore, our desired system of equations is:
[tex]x+y=22...(1)[/tex]
[tex]43x+75y=1234...(2)[/tex]
select the two binomials that are factors of this trinomial x^2+10x+16
A: x+8
B: x+6
C: x+2
D: X-2
Answer:
The correct options are A: x+8 and C: x+2.
Step-by-step explanation:
We are given the following expression and we are to factorize it:
[tex]x^2+10x+16[/tex]
We are to find such factors that when multiplied they give a result of 16 (1 x 16 = 16) and when added they give a result of 10.
The two such factors of 16 are positive 2 and positive 8.
Factorizing the given expression to get:
[tex]x^2+10+16\\\\x^2+2x+8x+16\\\\x(x+2)+8(x+2)\\\\(x+2)(x+8)[/tex]
Therefore, the two binomial factors of the given expression [tex]x^2+10x+16[/tex] are (x+8) and (x+2).
Answer: x+6 x+2
tell me if I’m wrong because I put x+8 and x+2 and got it wrong it told me it was x+6 and x+2
Jayda is cutting a roll of biscuit dough into slices that are 3/4 inches thick if the roll is 10 1/2 inches long how many slices can he cut?
Answer:
Jayda can cut 14 slices of dough that are 3/4 inches thick.
Step-by-step explanation:
In order to solve this problem, we need to take the total amount of dough at 10 1/2 inches and divide it by the thickness of one slide, 3/4 inches, to find the number of slices that can be made from the total amount. You can solve this two different ways. You can either convert your fractions to decimals so that 10 1/2 becomes 10.5 and 3/4 become 0.75 and then divide 10.5/0.75 to get 14. However, you can also keep them as fractions converting 10 1/2 to 21/2 and dividing by 3/4. When we divide with fractions with keep-change-flip, or keep the first fraction-change the sign to multiplication-flip the second fraction. So, we multiply 21/2 x 4/3 and get 84/6, or 14.
H values from the specified set make up the solution set of the inequality? 5w–10>20 ; {5,6,7,8} Select each correct answer. A.5 B.6 C.7 D.8 plz help
Answer: (C) 7 and (D) 8
Step-by-step explanation:
5w - 10 > 20
+10 +10
5w > 30
÷5 ÷5
w > 6
Anything GREATER than 6 will work.
Suppose a normal distribution has a mean of 98 and a standard deviation of 6. What is P(x< or = to 110)
Answer:
97.8%
Step-by-step explanation:
110 is 2 standard deviations above the mean (6+6 = 12)
12+98 = 110
Looking at the standard deviation curve
P(x< or = to 110) = 1 - P(x>110)
We can find the probability that x>100 by adding anything above 2 standard deviations above the curve.
P(x>110) = 2.1+.1 = 2.2%
P(x< or = to 110) = 1 - P(x>110)
= 1- 2.2%
= 1- .022
= .978
= 97.8 %
Answer:
0.975
Step-by-step explanation:
A P E X
which type of correlation is suggested by the scatter plot
Answer:
Negative Correlation
Step-by-step explanation:
As you can see in the image I added, a negative correlation happens when the variables move in opposite directions, in other words, one variable increases as the other decreases. We can see this correlation represented by a value of -1 slope.
I hope you find this information useful and interesting! Good luck!
Answer: That's negative.
Step-by-step explanation: hope this helps.
in 2004, there were approximately 7100 cinema sites. In 2000, there were 8300.
Write an equation describing this relationship.
The relationship between the year and the number of cinema sites can be expressed with the linear equation y = -300x + 608300, where y is the number of cinema sites and x is the year. This equation was derived by calculating the slope and y-intercept using the points provided.
Explanation:The subject of the question falls into the domain of mathematics, specifically algebra. We are given two points on a line where the x-axis is the year and the y-axis represents the number of cinema sites. The two points are (2000, 8300) and (2004, 7100).
First, we need to calculate the slope, m: m = (y2 - y1) / (x2 - x1) = (7100 - 8300) / (2004 - 2000) = -1200 / 4 = -300.
The slope, -300, is the rate of change suggesting the number of cinemas decreases by 300 each year.
The equation of the line, or the linear equation, will be in the form y = mx + b. We now need to find the y-intercept (b) by substituting one of our points into the equation and solving for b.
If we use the point (2000, 8300): 8300 = -300*2000 + b. Solving for b gives b = 8300 + 600000 = 608300.
Therefore, the equation describing the relationship between the year and the number of cinema sites is y = -300x + 608300.
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Carmen enters a painting in an art contest. The contest rules say that all paintings must be rectangular, with an area no greater that 3,003.04 cm2. Carmen painting is 16 cm wode. What is the greatest lenth the painting can have and still have an area within the contest rules?
Answer:
187.69 cm
Step-by-step explanation:
We have that the maximum area allowed for the painting = 3003.04 [tex]cm^{2}[/tex].
Also, the width of Carmen's painting = 16 cm.
It is required to maximum length of Carmen's painting that will be eligible to take part in the competition.
Let the maximum length of the painting = L cm.
Since, Area of a rectangle = length of the rectangle × width of the rectangle.
i.e. 3003.04 = L × 16
i.e. [tex]L=\frac{3003.04}{16}[/tex]
i.e. L = 187.69 cm
Hence, the length of the painting should not exceed 187.69 cm in order to be eligible to participate in the competition.
(-2/3, sqrt5/3) is a point on a unit circle. Find the cosine, cosecant, and sine of the angle.
Look at the picture.
[tex]\csc\theta=\dfrac{1}{\sin\theta}=\dfrac{1}{\frac{y}{r}}=\dfrac{r}{y}[/tex]
We have the right triangle x, y and r. From the Pythagorean theorem we have:
[tex]r^2=x^2+y^2\to r=\sqrt{x^2+y^2}[/tex]
We have the point
[tex]\left(-\dfrac{2}{3};\ \dfrac{\sqrt5}{3}\right)[/tex]
Substitute:
[tex]r=\sqrt{\left(-\dfrac{2}{3}\right)^2+\left(\dfrac{\sqrt5}{3}\right)^2}\\\\r=\sqrt{\dfrac{4}{9}+\dfrac{5}{9}}\\\\r=\sqrt{\dfrac{9}{9}}\\\\r=1[/tex]
[tex]\csc\theta=\dfrac{1}{\frac{\sqrt5}{3}}=\dfrac{3}{\sqrt5}=\dfrac{3\cdot\sqrt5}{\sqrt5\cdot\sqrt5}=\boxed{\dfrac{3\sqrt5}{5}}[/tex]
The cosine of the angle is -2/3, the sine is √5/3, and the cosecant, being the reciprocal of the sine, is √5/5 after rationalization.
The point (-2/3,√5/3) on a unit circle represents the cosine and sine of a specific angle. Here, the x-coordinate is the cosine of the angle, and the y-coordinate is the sine of the angle.
Therefore, the cosine of the angle is -2/3, and the sine is √5/3.
To find the cosecant of the angle, we take the reciprocal of the sine, which gives us 3/√5 or √5/5 after rationalizing the denominator.
If l and m are parallel, which pairs of angles are congruent? SELECT ALL THAT APPLY
1 and 3
2 and 4
6 and 7
3 and 6
Answer:
(<1 and <3) (<2 and <4) (<3 and <6)
Step-by-step explanation:
1 and 3 are corresponding equal angles
If one and three are equal, so are 2 and 4 since they are supplementary to equal angles.
6 and 7 are supplementary but not equal.
3 and 6 are equal angles because they are alternate interior angles.
Eric made two investments: Investment Q Q has a value of $ 5 0 0 $500 at the end of the first year and increases by $ 4 5 $45 per year. Investment R R has a value of $ 4 0 0 $400 at the end of the first year and increases by 1 0 % 10% per year. Eric checks the value of his investments once a year, at the end of the year. What is the first year in which Eric sees that investment R R's value exceeded investment Q Q's value?
Answer: After 8 year from the first year Eric will see that investment R's value exceeded investment Q's value.
Step-by-step explanation:
Let after x year from the first year Eric sees that investment R's value exceeded investment Q's value.
Investment Q has a value of $ 500 at the end of the first year and increases by $ 45 per year.
Thus, after x year from the first year the total amount of Investment Q,
500 + 45 x
Similarly, after x year from the first year the total amount of Investment R,
⇒ [tex]400(1+\frac{10}{100} )^x = 400(1.1)^x[/tex]
Thus, [tex]500 + 45 x = 400(1.1)^x[/tex]
By plotting the equations in the graph,
We get, x = -6.178 or 8.069
But year can not be negative,
Therefore, x = 8.069
Thus, Approx after 8 year from the first year Eric will see that investment R's value exceeded investment Q's value.
Answer: it’s 10 I’m 100% sure
Jaz was 43 inches tall. 18 months later she was 52 inches tall. Find the constant rate of change for Jaz's height.
The price of a pair of jeans was $45 after a 50% markup. What was the price of the jeans before the markup?
Answer:
$30
Step-by-step explanation:
Mark up is the profit on cost. if the pair of jeans was $45 after a 50% markup
Let the price of the jeans before the markup be p then;
p + 50%p = 45
1.5p =45
p = 45/1.5
p = 30
The price before mark up was $30, while the mark up or profit is $15. This shows 50% of the price before mark up.
HELP PLEASE!! which of the following represents a function?
please explain too i don’t understand this.
Answer:
I think it's c.
Step-by-step explanation:
A graph usually stands as a representation for functions.
5a + 5b + 5c + 5d
Which expression is another way to write the expression shown here?
A) 5abcd
B) 5a + bcd
C) 5(a + b + c + d)
D) (5a)(5b)(5c)(5d) what the answer
The correct way to rewrite the expression 5a + 5b + 5c + 5d using the distributive property is option C) 5(a + b + c + d).
The expression given is 5a + 5b + 5c + 5d. This is a sum where each term is multiplied by 5. According to the distributive property, also known as the distributive law of multiplication, a common factor can be factored out of a sum. The distributive property is represented as (A + B)C = AC + BC. In this case, the common factor is 5, and the sum of the variables a, b, c, and d is grouped, giving us 5(a + b + c + d).
So, the correct representation of the expression is 5(a + b + c + d), which corresponds to option C).
Solve by elimination
2x-y=0
3x-2y=-3
To solve a system of equations by elimination, make the coefficients of one variable equal. Subtract one equation from the other to solve for one variable, then substitute this solution into one of the original equations to solve for the other variable. In this case, the solution to the given system of equations is x = 3, y = 6.
Explanation:In mathematics, specifically in algebra, the method of elimination is used to solve a system of simultaneous equations. Your equations are:
2x -y = 03x - 2y = -3To solve this system by elimination, we need to make the coefficients of y in both equations equal by multiplying if necessary. We can obtain this by multiplying the first equation by 2:
4x - 2y = 0
3x - 2y = -3
Next, we subtract one equation from the other to eliminate y:
4x - 3x = 0 - (-3) => x = 3
To find y, substitute x = 3 into the first equation:
2*3 - y = 0 => y = 2*3 = 6
So, the solution to the system of equations is x = 3, y = 6.
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What is the inverse of f(x)=(x-5)^2 for x greater or equal to 5 where function g is the inverse of function f
The inverse function of f(x) = (x - 5)² for x greater or equal to 5 is g(x) = sqrt(x) + 5.
Explanation:The function f(x) = (x - 5)² for x greater or equal to 5 has a specific inverse function denoted as g(x). To find the inverse of a function, one typical solution is to replace f(x) with y, swap x and y, and solve for y. Here, it means writing y = (x - 5)², changing it to x = (y - 5)², and solving for y.
The solved y function is g(x) = √(x) + 5 (where sqrt indicates a square root), ensuring the range for x is greater than or equal to 5 to adhere to the original function constraints.
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Please help me out!!!!!!!
Answer: 1%
Explanation:
Add up the frequencies in the bottom row: 350+200+245+125+66+10+4 = 1000
There are 1000 families total. Of this total, 10+4 = 14 families have more than six people. I added up the frequency counts for "7 people" and "8 people" to get 14.
Divide 14 over 1000 and we get 14/1000 = 0.014 = 1.4% which rounds to 1%
BRAINLIEST!!HELPPP!!
Answer:
the answer if am not wrong would be C.n+5
Step-by-step explanation:
An airplane with a speed of 160 knots is headed east while a 24-knot wind is blowing from 240°. Explain how you would use the result of finding the ground speed to find the course of the airplane.
Question: Explain how you would use the result of finding the ground speed to find the course of the airplane.
Answer: 181.2
Explanation: vertical speed of 20.78 knots
new course is (-148 , 20.78) = inverse tan ( 20.78 / -148) = 172° or 8° N of East at 149.45 knots
New speed (- 148)² + ( 20.28)² = 149.45 knots round and you get 181.2
question answered by
(jacemorris04)
The ground speed of the airplane is 181.18 knots (approx).
What is the formula to find ground speed of airplane ?
The formula of ground speed of a airplane is given below,
[tex]v_{g} =\sqrt{}[/tex][tex](v_{a} ^{2}+v_{w} ^{2}-2v_{a} v_{w}cos\alpha)[/tex]
where, [tex]v_{g}[/tex] = Ground speed of airplane
[tex]v_{a}[/tex] = Speed of the airplane relative to the air
[tex]v_{w}[/tex] = Wind speed
[tex]\alpha[/tex] = Internal angle
How to find the ground speed of given airplane ?Given, [tex]v_{a}[/tex] = 160 knots, [tex]v_{w}[/tex] = 24 knots
Here, the angles increase clockwise and east is 90° heading.
The airplane is flying a heading of 90° at 160 knots speed & wind is blowing from 240° at 24 knots speed.
So, the internal angle[tex](\alpha)[/tex] = 240°-90° = 150°
∴ Ground speed, [tex]v_{g} =\sqrt{}[/tex][tex](v_{a} ^{2}+v_{w} ^{2}-2v_{a} v_{w}cos\alpha)[/tex]
⇒ [tex]v_{g}[/tex] [tex]=\sqrt{}[/tex][tex](160^{2}+24^{2}-2*160*24*cos(150))[/tex]
⇒ [tex]v_{g}[/tex] = 181.18 knots (approx)
Hence the ground speed of airplane is 181,18 knots (approx).
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Taylor has $97.23 and her checking account she uses debit card to spend 29 .74 and then deposits 118.08 into her accounts what is Taylor's new balance
Answer:
Taylor's new balance is $ 185.57 .
Step-by-step explanation:
As given
Taylor has $97.23 and her checking account.
she uses debit card to spend $29 .74 .
Than
Balance in the account after uses debit card = $97.23 - $29.74
= $ 67.49
As given
Then deposits $118.08 into her accounts.
Total balance of the account = $118.08 + $67.49
= $ 185.57
Therefore Taylor's new balance is $ 185.57 .
Answer:
$185.57
Step-by-step explanation:
Mr robbins earns a commission on each airfare he books. At the end of the day,he had booked $208.60 worth if airfare and earned $31.29. Approximately what is Mr. Robins commision rate.
Answer:
Mr. Robins commision rate is 15%.
Step-by-step explanation:
Formula
[tex]Percentage = \frac{Part\ value\times 100}{Total\ value}[/tex]
As given
Mr robbins earns a commission on each airfare he books.
At the end of the day,he had booked $208.60 worth if airfare and earned $31.29.
Here
Part value = $31.29
Total value = $208.60
Put in the formula
[tex]Percentage = \frac{31.29\times 100}{208.60}[/tex]
[tex]Percentage = \frac{312900}{20860}[/tex]
Percentage = 15%
Therefore the Mr. Robins commision rate is 15%.
Carlotta drove 72.6 miles on Monday. She drove 84.18 miles on Tuesday. Which gives the best estimate for how many more miles Carlotta drove on Tuesday?
A)84 – 73 = 11 miles
B)73 – 84 = 11 miles
C)85 – 72 = 13 miles
D)84 – 71 = 13 miles
Answer:
A)84 – 73 = 11 miles
Step-by-step explanation:
On Tuesday she drove 84 miles (rounding to the nearest mile)
On Monday she drove 73 miles (rounding to the nearest mile)
Tuesday's mileage - Mondays miles = difference in miles
84-73 = 11 miles
Answer: A. 84 – 73 = 11 mi
Brandy is trying to factor the quadratic $3x^2 - x - 10.$ She starts by assuming that the quadratic factors as \[3x^2 - x - 10 = (x + B)(3x + D),\]for some integers $B$ and $D.$ After some work, Brandy successfully factors the quadratic. Find the ordered pair $(B,D).$
Answer:
(B , D) = (-2,5)
Step-by-step explanation:
The given quadratic expression is
[tex]3x^{2} -x-10[/tex]
compare the given expression with [tex]ax^{2} +bx+c[/tex]
so we have [tex]a = 3 , b = -1 ,c = -10[/tex]
now [tex]ac=3 (-10)=- 30[/tex] and [tex]b= -1[/tex]
we need to find two numbers such that their product is -30 and sum is -1
-6 and 5 are such numbers
so we have
[tex]3x^{2} -6x+5x-10[/tex]
grouping first two terms and last two terms
[tex](3x^{2} -6x)+(5x-10)[/tex]
factor out 3x from first two terms and 5 from last two terms
[tex]3x(x-2) +5(x-2)[/tex]
[tex](x-2)(3x+5)[/tex] ( factor out (x-2))
[tex](x+(-2))(3x+5)[/tex]
hence B =-2 and D= 5
(B,D)= (-2,5)
A triangle has two side of length 10 and 14 what value could the length of the third side be check all that apply
A) 26
B) 16
C) 10
D) 8
E) 5
F) 2
If a, b and c are the lengths of the sides of a triangle then
if a ≤ b ≤ c, then a + b > c.
A) 10, 14, 26
10 + 14 = 24 < 26 INCORRECT :(
B) 10, 14, 16
10 + 14 = 24 > 16 CORRECT :)
C) 10, 10, 14
10 + 10 = 20 > 14 CORRECT :)
D) 8, 10, 14
8 + 10 = 18 > 14 CORRECT :)
E) 5, 10, 14
5 + 10 = 15 > 14 CORRECT :)
F) 2, 10, 14
2 + 10 = 12 < 14 INCORRECT :(
Answer: B) 16, C) 10, D) 8, E) 5Options B, C, D and E are correct answers.
Given that, a triangle has two sides of lengths 10 and 14.
We need to find what value could the length of the third side be and check all that apply.
What is the triangle inequality theorem?Triangle inequality, in Euclidean geometry, theorem that the sum of any two sides of a triangle is greater than or equal to the third side; in symbols, a + b ≥ c. In essence, the theorem states that the shortest distance between two points is a straight line.
Now, from the given options:
A) 10, 14, 26
10 + 14 = 24 < 26 the triangle can not be formed
B) 10, 14, 16
10 + 14 = 24 > 16 the triangle can be formed
C) 10, 10, 14
10 + 10 = 20 > 14 the triangle can be formed
D) 8, 10, 14
8 + 10 = 18 > 14 the triangle can be formed
E) 5, 10, 14
5 + 10 = 15 > 14 the triangle can be formed
F) 2, 10, 14
2 + 10 = 12 < 14 the triangle can not be formed
Therefore, options B, C, D and E are correct answers.
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Janie receives an allowance of \$3$3 per week. In addition, she can earn \$2$2 for each chore she does. This week, she wants to earn enough money to buy a CD for \$13$13. Janie can do fractions of chores. Write an inequality to determine the number of chores, cc, Janie must do this week to earn enough money to buy a CD.
Answer:
Number of chores done by Janie are 5.
Step-by-step explanation:
Janie's allowance per week is $3.
For each chore she earns $2.
Now we assume that number of chores in a week she does = c
Then total earning from chore = $2 × c
So for the purchase of CD total earning this week inequality will be
⇒ 3 + 2c [tex]\geq[/tex]13
⇒ 2c [tex]\geq[/tex] 13-3
⇒ c [tex]\geq[/tex] 10÷2
⇒ c [tex]\geq[/tex] 5
Find the first six terms of the sequence.
a1 = -2, an = 3 • an-1
-6, -18, -54, -162, -486, -1458
-2, -6, -18, -54, -162, -486
-2, -6, -3, 0, 3, 6
0, 3, -6, -3, 0, 3
[tex]a_1=-2\\\\a_n=3\cdot a_{n-1}\\-----------------------------------\\a_1=-2\\\\a_2=3\cdot a_{2-1}=3\cdot a_1\to a_2=3(-2)=-6\\\\a_3=3\cdot a_{3-1}=3\cdot a_2\to a_3=3(-6)=-18\\\\a_4=3\cdot a_{4-1}=3\cdot a_3\to a_4=3(-18)=-54\\\\a_5=3\cdot a_{5-1}=3\cdot a_4\to a_5=3(-54)=-162\\\\a_6=3\cdot a_{6-1}=3\cdot a_5\to a_6=3(-162)=-486\\\\Answer:\ \boxed{-2,\ -6,\ -18,\ -54,\ -162,\ -486}[/tex]