Answer: 14x56=784
Step-by-step explanation:
Let's start with y = 4x + b (since 4 is the slope);
We need to find what number should be put instead of b;
Then, let's see what needs to be done;
Plug in the y and x values from the coordinate (22,12) into y=4x+b;
12 = 4(22) + b
Solve;
12 = 88 + b
12 - 88 = b
b = -76
Remember the equation y = 4x + b? Put the -76 instead of b:
y = 4x + -76
or: y = 4x - 76
That is the equation.
To make it standard form, put x and y both in the left side, with x first then y:
-4x + y = -76
^^Answer!
Proving a relation for all natural numbers involves proving it for n = 1 and showing that it holds for n + 1 if it is assumed that it is true for any n.
The relation 2+4+6+...+2n = n^2+n has to be proved.
If n = 1, the right hand side is equal to 2*1 = 2 and the left hand side is equal to 1^1 + 1 = 1 + 1 = 2
Assume that the relation holds for any value of n.
2 + 4 + 6 + ... + 2n + 2(n+1) = n^2 + n + 2(n + 1)
= n^2 + n + 2n + 2
= n^2 + 2n + 1 + n + 1
= (n + 1)^2 + (n + 1)
This shows that the given relation is true for n = 1 and if it is assumed to be true for n it is also true for n + 1.
<span>By mathematical induction the relation is true for any value of n.</span>
Answer:
$40 per week
Step-by-step explanation:
Step one:
Given data
the initial amount is = $100
the total amount= $500
let the number of weeks be x
Step two:
The expression for the scenario is
From the expression above, the rate of the change is $40 per week.
this means that in every week the account will be increased by $40
Answer:
frequency= 165Hz
period= 
Step-by-step explanation:
1. To calculate the frequency using the formula:
f = v/λ
where,
f=frequency (what the question asked)
v=speed of wave (given in the question=330m/s)
λ=wavelength (given in the question=2m)
SO,
= 165Hz
2. To calculate the period use the formula:
since 
therefore, 
where,
f= frequency (what we solved above=165Hz)
T= period (what the question asked)
SO,
