Answer:
The sum of the first 35 terms of the arithmetic sequence when a = 5 and d = 4 is 2555.
Step-by-step explanation:
Given:
a = 5
d = 4
To Find :
The sum of first 35 terms of the arithmetic sequence = ?
Solution:
Step 1 : finding the 35th term
[tex]a_n = a_1 +(n-1)d[/tex]
[tex]a_35 = 5 +(35-1)4[/tex]
[tex]a_35 = 5 +(34)4[/tex]
[tex]a_35 = 5 +136[/tex]
[tex]a_35 = 141[/tex]
Step 2: Finding the sum of first 35 terms
[tex]S_n = \frac{n(a_1 +a_n)}{2}[/tex]
Substituting the values
[tex]S_n = \frac{35(5+141)}{2}[/tex]
[tex]S_n = \frac{35(146)}{2}[/tex]
[tex]S_n = \frac{35(146)}{2}[/tex]
[tex]S_n = \frac{5110)}{2}[/tex]
[tex]S_n = 2555[/tex]
The equation 5x - 7(x-1) = ax+b has exactly one solution.
Answer:
a = -2 and b = 7
Step-by-step explanation:
We need to solve for the value of "a" and "b".
We need to distribute and make the left side of the equation same form as the right side of the equation and match the coefficients, simple.
We will use the distributive property shown below to expand the left side and simplify.
Distributive Property: a(b-c) = ab - ac
Now, simplifying left hand side:
5x - 7(x - 1)
= 5x -7(x) -7(-1)
= 5x -7x +7
= -2x + 7
The right hand side is "ax + b".
If we match left-hand side and right-hand side, we see that:
a = -2
and
b = 7
THese are the only solution.
if w = -2 and V = -8 which of the following Expressions shown the values correctly substituted and for the valuables in the expression w^2 - v + 1
1. -2^2 - (-8) + 1
2. -2^2 - 8 + 1
3. (-2)^2 - (8) + 1
4. (-2)^2 - (-8) + 1
Answer:
D) (-2)^2-(-8)+1
Step-by-step explanation:
Answer: 4
Step-by-step explanation:
As the pastry chef in a restaurant, you have a recipe that uses 4 cups of flour to make 3 dozen cookies. You want to make 15 dozen cookies. How many cups of flour will you need
Answer:
you will need 4cups of flour
-9x-6y=15
9x-10y=145
Solve for x and y
Answer:
y = - 10 and x = 5
Step-by-step explanation:
[tex] - 9x - 6y = 15 \\ + 9x - 10y = + 145 \\ add \: the \: two \: equations \: together \\ 0 - 16y = 160 \\ y = \frac{160}{ - 16} \\ y = - 10 \\ substitute \: for \: y\: in \: any \: equation \\ - 9x - 6( - 10) = 15 \\ - 9x + 60 = 15 \\ - 9x = 15 - 60 \\ - 9x = - 45 \\ x = \frac{ - 45}{ - 9} \\ x = 5[/tex]
Answer:
y=-10
x-5
Step-by-step explanation:
A group of mountain climbers begin a expedition with 250 pounds of food. They plan to eat a total of 12 pounds of food per day . Write and solve a linear equation to find the number of days their food will last
Answer:
The equation representing total food consumption in [tex]x[/tex] days can be given as:
[tex]y=12x[/tex]
where [tex]y[/tex] represents total food taken which is =250 pounds and [tex]x[/tex] represnts the number of days the food will last.
The food will last for [tex]20\frac{5}{6}[/tex] days.
Step-by-step explanation:
Total pounds of food taken at the beginning = 250 pounds
Food consumed per day = 12 pounds
Let the total food at the beginning be = [tex]y[/tex] pounds
Let number of days the food will last be = [tex]x[/tex] days
Using unitary method to find the food consumed in [tex]x[/tex] days.
If in 1 day food consumed = 12 pounds
Then, in [tex]x[/tex] days food consumption = [tex]12\times x = 12x[/tex] pounds
So,the equation representing total food consumption in [tex]x[/tex] days can be given as:
[tex]y=12x[/tex]
Total food taken =250 pounds
Plugging in [tex]y=250[/tex] in the equation:
[tex]250=12x[/tex]
Solving for [tex]x[/tex]
Dividing both sides by 12.
[tex]\frac{250}{12}=\frac{12x}{12}[/tex]
[tex]\frac{250}{12}=x[/tex]
Simplifying fractions.
[tex]\frac{125}{6}=x[/tex]
Converting fraction to mixed number by writing quotient as whole number, remainder as numerator and divisor as denominator.
∴ [tex]x=20\frac{5}{6}[/tex] days.
Thus, the food will last for [tex]20\frac{5}{6}[/tex] days.
the square root of 52 is between which two consecutive intergers?
a) 26 and 27
b) 7 and 8
c) 25 and 26
d) 8 and 9
Answer: 7 and 8
Step-by-step explanation:
The square root of 7 is 49 and the square root of 8 is 64
52 is in between the 2 consecutive integers 7 and 8
Answer: b) 7 and 8
Step-by-step explanation:
The formula for calculating the square root of non perfect square is given as :
square root of non perfect square = square root of the nearest lower perfect square + (difference between the number and the perfect square)/ 2x the perfect square.
To find the square root of 52.
The nearest lower perfect square to 52 is 49 , applying the formula , we have:
[tex]\sqrt{52}[/tex] = [tex]\sqrt{49}[/tex] - [tex]\frac{52-49}{2\sqrt{49}}[/tex]
[tex]\sqrt{52}[/tex] = 7 + [tex]\frac{3}{2(7)}[/tex]
[tex]\sqrt{52}[/tex] = 7 + [tex]\frac{3}{14}[/tex]
This shows clearly that [tex]\sqrt{52}[/tex] is between the integer 7 and 8
One-third of the result of three times a number that is increased by 12.
Answer:
Step-by-step Let's break down the problem step by step.Let "a number" be represented by 'x'.Three times a number: 3 * xIncreased by 12: 3 * x + 12One-third of the result: (1/3) * (3 * x + 12)Now, let's simplify the expression:(1/3) * (3 * x + 12)The '3's cancel out:= (1/1) * (x + 12)= x + 12So, the expression "One-third of the result of three times a number that is increased by 12" is equivalent to "x + 12."
What is the value of e^ln7 x1
7e
7x
7
Answer:
7x
Step-by-step explanation:
Assuming your expression is :
[tex]e^{\ln 7x}[/tex]
Then we simplify as follows
[tex]e^{\ln 7x}=e^{\ln x+\ln 7}[/tex] since [tex]\ln A+\ln B=\ln AB[/tex]
[tex]\implies e^{\ln 7x}=e^{\ln x}\times e^{\ln 7}[/tex] since [tex]a^{m+n}=a^m\times a^n[/tex]
[tex]\implies e^{\ln 7x}=x\times7[/tex] since [tex]e^{\ln a}=a[/tex]
[tex]\implies e^{\ln 7x}=7x[/tex]
What is the area of the following circle?
Either enter an exact answer in terms of π (pi) or use 3.14 and enter your answer as a decimal.
Answer:
Area of the circle is following:
[tex]a = \pi \: r {}^{2} [/tex]
So there is radius=1
Putting it into formula:
[tex]a = \pi \: 1 {}^{2} \\ a = \pi \\ a = 3.14[/tex]
So the answer is
[tex]3.14 \: units {}^{2} [/tex]
Good luck!
Intelligent Muslim,
From Uzbekistan.
Petra was given 12 yards of fabric to make costumes for the school play if each costume requires 1 1/2 yards how many costumes can she make
Petra can make 8 costumes with 12 yards of fabric
Solution:Given that Petra was given 12 yards of fabric to make costumes for the school play
Each costume requires [tex]1\frac{1}{2}[/tex] yards
To find: number of costume Petra can make
The number of costume Petra can make is calculated by dividing the total fabric she has by fabric needed for one costume
[tex]\text {number of costume Petra can make }=\frac{\text {total fabric she has }}{\text {fabric needed for one costume }}[/tex]
Total fabric she has = 12 yards
Fabric needed for 1 costume = [tex]1\frac{1}{2} = \frac{2 \times 1 + 1}{2} = \frac{3}{2}[/tex] yards
Therefore,
[tex]\text {number of costume Petra can make }=\frac{12}{3 / 2}=\frac{12}{3} \times 2=8[/tex]
Thus petra can make 8 costumes with 12 yards of fabric
Alex will be x years old in 3 years how old his he now
Answer:
(x - 3)
Step-by-step explanation:
age in 3 years : x
age now = age in 3 years - 3 years = (x - 3)
Answer:
x-3
because...
we only have 3 so we have to find the value of x by subtracting 3 from it.
now = 3 year-3 which is equal to x-3
Mr. Snow bought 90 grams of Christmas candy for each of his 14 grandchildren. How many total kilograms of candy did he buy?
Answer:
1.26 kg.
Step-by-step explanation:
We have been given that Mr. Snow bought 90 grams of Christmas candy for each of his 14 grandchildren. We are asked to find the amount of candy bought by Mr. Snow in kilograms.
First of all, we will find the amount of candy in grams by multiplying 90 grams by 14 as:
[tex]\text{Amount of candy bought in grams}=14\times 90[/tex]
[tex]\text{Amount of candy bought in grams}=1260[/tex]
We know that 1 kilogram is equal to 1000 grams. To convert 1260 grams into kg, we will divide 1260 by 1000 as:
[tex]\text{Amount of candy bought in kilograms}=\frac{1260}{1000}[/tex]
[tex]\text{Amount of candy bought in kilograms}=1.26[/tex]
Therefore, Mr. Snow bought 1.26 kilograms of candy.
what is this help me
Answer:
A
Step-by-step explanation:
Consider the values of y, that is
9, 36, 144, 576, 2304
Then the common ratio r is
r = 36 ÷ 9 = 144 ÷ 36 = 576 ÷ 144 = 2304 ÷ 576 = 4 → A
would it yes or no?
Answer:
Yes
Step-by-step explanation:
Given point to test : (5,10)
Give system of linear inequalities:
[tex]x>2[/tex]
[tex]y\geq3x-7[/tex]
To check if the point lies in the solution set for the given system of inequalities.
Solution:
In order to check if the point lies in the solution set for the given system of inequalities, we will plugin the given point in the inequalities and see if it is true or not.
For the given point [tex]x=5[/tex] [tex]y=10[/tex]
Testing the first inequality.
Plugging in [tex]x=5[/tex] in the inequality.
[tex]5>2[/tex]
The above inequality will always hold true and thus the given point will lie in the solution set of this inequality.
Testing the second inequality:
Plugging in [tex]x=5[/tex] and [tex]y=10[/tex] in the inequality.
[tex]10>3(5)-7[/tex]
Simplifying.
[tex]10>15-7[/tex]
[tex]10>8[/tex]
The above inequality will always hold true and thus the given point will lie in the solution set of this inequality also.
Thus, we can say that the point (5,10) will lie in the solution set of the given system of inequalities.
Answer:
Yes!
Step-by-step explanation:
5x=2x-42-3x
please help first person is the brainlist
Answer:
[tex]5x = - 42 - x[/tex]
[tex]6x = - 42[/tex]
[tex]x = - 7[/tex]
Select the statement that explains the error in the given statement.
Three points have to be collinear.
A .Three points have to be noncollinear.
B. Three points have to lie on an infinite number of planes. They do not have to be collinear.
C. Four points have to be collinear. Three points may be collinear or noncollinear. D. The three points could be the vertices of a triangle.
Answer:
D. The three points could be the vertices of a triangle.
Step-by-step explanation:
collinear points : points are said to be collinear if they lie on the same line.so, any three given points need not be collinear because, they can even be the vertices of a triangle.this is explained in the option D so, it is correct.option A is wrong because, those three points can be collinear also i.e if we put three points on a line, then they will be collinear.option B is wrong because, it is saying that they do not have to be collinear. but the fact is, they can be collinear.option C is wrong because, four points also need not be collinear. they can be vertices of a square!
Which BEST describes the system of equations?
y - 2x = 4
y + 2 = 2x
Consistent
Inconsistent
Consistent and Dependent
Consistent and independent
Answer:
Inconsistent
Step-by-step explanation:
Given system of equations.
A) [tex]y-2x=4[/tex]
B) [tex]y+2=2x[/tex]
We will solve the system of equations to check the solutions and tell whether the system is consistent or inconsistent
Rearranging equation A, to solve for [tex]y[/tex] in terms of [tex]x[/tex]
Adding both sides by [tex]2x[/tex]
[tex]y-2x+2x=4+2x[/tex]
[tex]y=4+2x[/tex]
Substituting value of [tex]y[/tex] we got from A into equation B.
[tex]4+2x+2=2x[/tex]
Simplifying.
[tex]2x+6=2x[/tex]
Subtracting both sides by [tex]2x[/tex]
[tex]2x-2x+6=2x-2x[/tex]
[tex]6=0[/tex]
This is never true. So, we can say the system of equation has no solutions as the equations of the lines given are parallel.
Any system of equation with no solutions is termed as inconsistent.
Answer:
D) Consistent and Independent
Step-by-step explanation:
I did it on USA test prep.
The ages of three friends are consecutive integers. If the sum of the three
friends' ages is 45, which equation below can be used to determine the age, x,
of the youngest friend?
Answer:
Step-by-step explanation:
Let the consecutive integers be (x - 1), x, (x + x)
x - 1 + x + x + 1 = 45
3x = 45 ---------> this is the equation
x = 45/3
x = 15
The ages are 14,15,16
Answer:
Step-by-step explanation:
consecutive integers means 1 right after the other....with x being the youngest, then x + 1 being the second friend, and x + 2 being the third friend.
so ur equation would be : x + x + 1 + x + 2 = 45......but since I cant see ur answer choices, it could also be : 3x + 3 = 45
Which number(s) from the set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, if any, will solve this equation? I PROMISE TO MARK BARINLEST + EXTRA POINTS!!!!!!!!!!!!
2x + 3 = 5x - 3
Answer:
2
Step-by-step explanation:2x + 3 = 5x - 3
Move x to one side:
[tex]2x-2x+3=5x-2x-3\\3=3x-3[/tex]
Remove the -3:
[tex]3x-3(+3)=(3+3)[/tex]
[tex]3x=6[/tex]
Remove the 6 to get x by itself:
[tex]\frac{3x}{3} =\frac{6}{3} \\x=2[/tex]
The number 2 from the number set would solve the equation.
Checking the Answer:2(2) + 3 = 5(2) - 3
4 + 3 = 10 - 3
7 = 7
The statement is true.
An equation is formed of two equal expressions. The number(s) from the set that will satisfy the given equation is 2.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
The given equation can be simplified as shown below,
2x + 3 = 5x - 3
Subtract 2x from both sides of the equation,
2x + 3 - 2x = 5x - 3 - 2x
3 = 5x - 3 - 2x
Add 3 on both sides of the equation,
3 + 3 = 5x - 3 - 2x + 3
6 = 3x
3x = 6
Divide both the sides of the equation by 3,
3x/3 = 6/3
x = 2
Hence, the number(s) from the set that will satisfy the given equation is 2.
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Write point-slope form of the equation that represents the line that passes through the point (−3, 9) and has a slope of 5.
Answer:
y-9=5(x+3)
Step-by-step explanation:
y-y1=m(x-x1)
y-9=5(x-(-3))
y-9=5(x+3)
Two cars leave towns
400
kilometers apart at the same time and travel toward each other. One car's rate is
12
kilometers per hour less than the other's. If they meet in
2
hours, what is the rate of the slower car?
The speed of slower car is 94 kilometers per hour.
Step-by-step explanation:
Given,
Total distance covered by both cars = 400 km
Time period = 2 hours
Let,
Speed of one car = x
Speed of slower car = x-12
Combined speed = [tex]x+(x-12)=x+x-12=2x-12[/tex]
Distance = Speed*Time
[tex]400=(2x-12)*2\\400=4x-24\\400+24=4x\\424=4x\\4x=424[/tex]
Dividing both sides by 4
[tex]\frac{4x}{4}=\frac{424}{4}\\x=106[/tex]
Speed of slower car = x-12 = 106-12 = 94 km/h
The speed of slower car is 94 kilometers per hour.
Keywords: distance, speed, time
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[tex]2x + 5y = 25 \\ 3x - 2y = 9[/tex]
A) How to solve it by elimination method.
B) by substitution method
C) graphical method
I will show you A and B, and give you a hint how to do C, since brainly doesn't provide C option.
A.
The elimination method is how I would solve this system
[tex]
\begin{cases}
2x+5y=25 \\
3x-2y=9
\end{cases}
[/tex]
We start by multiplying the first equation by 3 and second by -2 to obtain
[tex]
\begin{cases}
6x+15y=75 \\
-6x+4y=-18
\end{cases}
[/tex]
Now add the two equations and thus eliminate the x-terms to obtain
[tex]19y=57\Longrightarrow y=\dfrac{57}{19}=3[/tex]
Then we insert the y into either of the original equations and solve for x
[tex]
2x+5\cdot3=25 \\
2x=25-15 \\
2x=10 \\
x=5
[/tex]
And we have the solution at [tex]P(5,3)[/tex].
B.
We pick one equation and express x
[tex]
2x+5y=25 \\
2x=25-5y \\
x=\dfrac{25-5y}{2}
[/tex]
Then we replace the x in other equation with expression we just calculated and solve for y
[tex]
3\cdot\dfrac{25-5y}{2}-2y=9 \\
\dfrac{75-15y}{2}-2y=9 \\
\dfrac{75-15y-4y}{2}=9 \\
75-19y=18 \\
-19y=-57 \\
y=3
[/tex]
Now we put y in either of the original equations to get x
[tex]
2x+5\cdot3=25 \\
2x=25-15 \\
2x=10 \\
x=5 \\
[/tex]
And again we get the solution [tex]P(5,3)[/tex].
C.
To find solution graphically, you need to put both lines in general form [tex]f(x)=mx+n[/tex] where [tex]f(x)=y[/tex]
[tex]
\begin{cases}
2x+5y=25\Longrightarrow y=\frac{25-2x}{5}=-\frac{2}{5}x+5 \\
3x-2y=9\Longrightarrow y=-\frac{9-3x}{2}=-\frac{3}{2}x-\frac{9}{2}
\end{cases}
[/tex]
Then plot the lines on the graph. The solution will be point [tex]P(5,3)[/tex] where lines intersect, because we can represent lines as sets of points ordered pairs. Consider our two lines represented as two functions g and f where
[tex]
f(x)=-\frac{2}{5}x+5 \\
g(x)=-\frac{3}{2}x-\frac{9}{2}
[/tex]
Graphs (sets) of these two functions are defined as (assuming [tex]f,g:D_f,D_g\to T_f,T_g=\mathbb{R}\to\mathbb{R}[/tex] since not specified):
[tex]
\displaystyle
G_f=\{(x,f(x)):x\in D_f\wedge f(x)\in T_f\} \\
G_g=\{(x,g(x)):x\in D_g\wedge g(x)\in T_g\}
[/tex]
Where D is definition zone (set of all x defined for function f or g) and T transformation zone (set of all f(x) or g(x)). Note that in our case [tex]D_f,T_f=D_g,T_g[/tex] because [tex]D_f,T_f,D_g,T_g=\mathbb{R}[/tex]
The solution is is intersection of these two sets
[tex]G_f\cap G_g=(5,3)[/tex]
Hope this helps.
an object of mass 300kg is observed to accelerate at the rate of 4 m/s^2. Caculate the force required to produce this acceleration
Answer:
1200 N
Step-by-step explanation:
Newton's second law:
F = ma
F = (300 kg) (4 m/s²)
F = 1200 N
-4 ^ 3 * 2 / 8 * 20 + 125
The measurement of the side of a RV is 469 inches the actual length is 480 inches what is the percent error
Answer:
Step-by-step explanation:
error in measurement = 480 - 469 = 11 inches
Percent error = error *100/actual length
= 11 * 100 /480 = 2.9%
A city allocates 31.84% of its budget for schools. If the schools receive $17,467,472 this year, what is the city’s total budget to nearest dollar?
Answer:
The city’s total budget is [tex]\$54,860,151[/tex]
Step-by-step explanation:
we know that
31.84% of the city's total budget represent $17,467,472
so
using proportion
Find out what is the city’s total budget (100% percentage)
[tex]\frac{\$17,467,472}{31.84\%}=\frac{x}{100\%}\\\\x=\$17,467,472(100)/31.84\\\\x=\$54,860,151[/tex]
A birdhouse has a shadow that is 12 feet long.
Jin is 5 feet tall, and he is standing next to the birdhouse.
Jin has a shadow that is 3 feet long. What is the height of the birdhouse in feet ?
Answer: 5 feet tall
Step-by-step explanation:
because he is beside the bird house he is 5 feet tall
The birdhouse's height is 20 feet, calculated using the proportion: [tex]\( \frac{h}{12} = \frac{5}{3} \).[/tex]
We can solve this problem using proportions.
Let [tex]\( h \)[/tex] be the height of the birdhouse.
According to the given information, the ratio of Jin's height to his shadow length is the same as the ratio of the birdhouse's height to its shadow length:
[tex]\[ \frac{h}{12} = \frac{5}{3} \][/tex]
Now, cross-multiply to solve for [tex]\( h \):[/tex]
[tex]\[ 3h = 5 \times 12 \][/tex]
[tex]\[ 3h = 60 \][/tex]
[tex]\[ h = \frac{60}{3} \][/tex]
[tex]\[ h = 20 \][/tex]
So, the height of the birdhouse is 20 feet.
Write the numbers in order from greatest to least. 7.982, 7.981, 8.782, 8.981
Answer:
8.981, 8.782, 7.982, 7.981.Step-by-step explanation:
To order decimals is to subtract, line up, and comparing digits.
Comparing digits is a good way to order decimals for greatest to least.
(Most Understood.)
Comparing Decimals:
We could put numbers in any order to compare digits, but you should look closely:
Numbers can Trick You.Be wise, look closely.If the digit is 0 for a number, the other number is greater if it's not 0.Lastly, you (cannot) multiply, divide, add, or subtract.__________________________________________
First, we pick 2 numbers to compare, maybe 8.782 and 8.981.
We look at the digits for both numbers.
We see 8's, And 7 and 9, 9 is greater, so 8.981 is the greatest and 8.782 is the 2nd greatest.
8.981, 8.782, ?.???, ?.??? Is Our Order so far.Our last 2 numbers are 7.981 and 7.982,
We look at the digits for both numbers.
We see 7's, we see 9's, and we see 8's, but 1 and 2. 2 is greater so 7.982 is the 3rd greatest and 7.981 is the least.
Our order is: 8.981, 8.782, 7.982, 7.981.We checked it by comparing wisely. (√ Means Check)
Best of Luck to you.
If you have any questions, feel free to comment below.
-Also if anything is confusing!!
The numbers 8.981, 8.782, 7.982, and 7.981 are ordered from greatest to least. This is determined by comparing each digit from left to right, where 8.981 is the greatest and 7.981 is the least.
Explanation:The task that you are asked to do is to arrange the numbers from greatest to least. The numbers given are 7.982, 7.981, 8.782, and 8.981.
8.9818.7827.9827.981This order is determined by comparing the digits from left to right. The first digit is the most significant indicator of the size of the number. However, if the first digits are the same, then we consider the following digits and so on until we find one that differs. In our case, 8.981 has both the largest initial digit (8) and the largest subsequent digits (9 and 8 respectively) so it is the greatest. Similarly, 7.981 has the smallest digits and as a result, it's the least.
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m=7/4 (3,-4) point slope form
Answer:
y+4=7/4(x-3)
Step-by-step explanation:
y-y1=m(x-x1)
y-(-4)=7/4(x-3)
y+4=7/4(x-3)
three tanks are capable of holding 108 litres, 168 litres and 180 litres of milk. determine the capacity of the greatest vessel which can be used to fill each one of them an exact number of time.
A vessel of 7,560 liters
Step-by-step explanation:
This means finding the Least Common Multiple for;
108 168 180
We begin by finding the multiples of each number;
Multiples of 108:
108, 216, 324, 432, 540, 648, 756, 864, 972, 1080, 1188, 1296, 1404, 1512, 1620, 1728, 1836, 1944, 2052, 2160, 2268, 2376, 2484, 2592, 2700, 2808, 2916, 3024, 3132, 3240, 3348, 3456, 3564, 3672, 3780, 3888, 3996, 4104, 4212, 4320, 4428, 4536, 4644, 4752, 4860, 4968, 5076, 5184, 5292, 5400, 5508, 5616, 5724, 5832, 5940, 6048, 6156, 6264, 6372, 6480, 6588, 6696, 6804, 6912, 7020, 7128, 7236, 7344, 7452, 7560, 7668, 7776
Multiples of 168:
168, 336, 504, 672, 840, 1008, 1176, 1344, 1512, 1680, 1848, 2016, 2184, 2352, 2520, 2688, 2856, 3024, 3192, 3360, 3528, 3696, 3864, 4032, 4200, 4368, 4536, 4704, 4872, 5040, 5208, 5376, 5544, 5712, 5880, 6048, 6216, 6384, 6552, 6720, 6888, 7056, 7224, 7392, 7560, 7728, 7896
Multiples of 180:
180, 360, 540, 720, 900, 1080, 1260, 1440, 1620, 1800, 1980, 2160, 2340, 2520, 2700, 2880, 3060, 3240, 3420, 3600, 3780, 3960, 4140, 4320, 4500, 4680, 4860, 5040, 5220, 5400, 5580, 5760, 5940, 6120, 6300, 6480, 6660, 6840, 7020, 7200, 7380, 7560, 7740, 7920
The Least Common Multiple for the 3 number is;
= 7560
Therefore a vessel of 7,560 liters fills each one of them an exact number of times with no remainder.
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