Answer:
3m^2
Step-by-step explanation:
Find the prime factors of each term in order to find the greatest common factor (GCF).
3m^2 p.s. i love bob the tomato;)
Question:
You are making sandwiches for a large party. Each sandwich has two slices of bread, one slice of turkey, two slices of cheese, three slices of tomato and 5 slices of cucumber. How many sandwiches will you get from 10 slices of bread and 20 slices of cucumber? assuming you have plenty of everything
Answer:
4 sandwiches
Step-by-step explanation:
Given
1 Sandwich contains:
Required
Number of sandwiches from 10 slices of bread and 20 slices of cucumber?
Since we are to assume that every other thing is in abundance, we will only consider the unit amount of bread and cucumber
Express as ratio
When the ratio is multiplied by 5, the slice of cucumber (25) will exceed the available slices (20).
So, we multiply by 4
This implies that:
8 slices of bread and 20 slices of cucumber are used
Hence:
4 sandwiches can be made
Answer:
∠MDP = 90° = Right angle
∠MDP = 180° = Straight angle
∠ODM = 90° = Right angle
∠OND = Not an angle
∠NDO = 90° = Right angle
∠NDM = 180° = Straight angle
∠PMN = Not an angle
∠PDO = 180° = Straight angle
∠PDN = 90° = Right angle
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The sequence is an arithmetic sequence with
a₁ = -4
d = a₂ - a₁
d = -1 - (-4)
d = -1 + 4
d = 3
an = x
Sn = 437
General formula in arithmetic sequence
Formula to find nth term
an = a₁ + d(n - 1)
Formula to find sum of sequence (sn)
Sn = n/2 (a₁ + an)
We have to make an equation system based on the problem
plug the numbers into the formula
First equation
an = a₁ + d(n - 1)
x = -4 + 3(n - 1)
x = -4 + 3n - 3
x = 3n - 7
Second equation
Sn = n/2 (a₁ + an)
n/2 (a₁ + an) = 437
n/2 (-4 + x) = 437
n(x - 4) = 874
xn - 4n = 874
Solve the equation system by subtitution method
Subtitute x with 3n - 7 in the second equation
xn - 4n = 874
(3n - 7)n - 4n = 874
3n² - 7n - 4n = 874
3n² - 11n - 874 = 0
(3n + 46)(n - 19) = 0
n = -46/3 or n = 19
Because the number of terms shouldn't be negative, -46/3 isn't required, so the value of n is 19.
Solve for x, back to the first equatin
x = 3n - 7
x = 3(19) - 7
x = 57 - 7
x = 50
The solution is 50
