(- 2, - 3) is a solution to the given system of equations.
Answer: Option D
<u>Step-by-step explanation:</u>
Given equation are not presented in proper format. So, let assume the given system of are as below,
2 x - y = -1
2 x -4 y = 8
Now, subtract the second equation from the first, we get
(2 x - y) -(2 x - 4 y) = -1 -8
3 y = -9
y = -3 (obtained this when divide by 3)
Substituting y = - 3 into the first equation, we get
2 x - (-3) = - 1
2 x = - 1 + 3
x = - 2 (obtained when divide by 2)
Now, the answer is (x, y) = (- 2, - 3)
Answer:
Part 1
Multiply both sides by 2π
2πf = √(g/L)
Square both sides
4π²f²= g/L
Invert both sides
1/(4π²f²) = L/g
Multiply both side by g
g/(4π²f²) = L
We usually write an equation with the subject (L) n the left
L = g/(4π²f²)
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Part 2
Using the above equation with the given values:
L = g/(4π²f²)
. .= 9.8 / (4π² x 1.6²)
. .= 0.097m (= 9.7cm)
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By the way, where it says
“f=1.6 then there are 2 beats a second, or 192 beats per minute (bpm).”
this should say
“f=1.6 then there are 3.2 beats a second, or 192 beats per minute (bpm)”
Step-by-step explanation:
Let the length of the 1st line segment = x
then the length of the second line segment = 4x + 5
The difference in their lengths = 35
so 4x + 5 - x = 35 ... [longer - shorter = 35]
3x = 30
x = 10
so the shorter (1st) line segment is 10 cm long
and the longer (2nd) line segment is 4 * 10 + 5 = 45 cm long
Answer: Ix - 5I ≥ 5.
Step-by-step explanation:
We want the set:
[0, 10]
to be the solution of:
Ix - bI ≤ c
So we need to find the values of c and b.
The first step is to find the middle point in our segment.
We can do that by adding the extremes and dividing it by 2.
M = (10 + 0)/2 = 5
And we also want to find half of the difference between the extremes, this is:
D = (10 - 0)/2 = 5.
Now, this set will be the set of solutions of:
Ix - MI ≥ D
Then in our case, we have:
Ix - 5I ≥ 5.
so we have that b = 5, and c = 5.
