We solve the equation, ( a + a + 1 )^2 = 112 + a^2 + ( a + 1 )^2;
Then, ( 2a + 1 )^2 = 112 + a^2 + a^2 + 2a +1;
4a^2 + 4a + 1 = 113 + 2a^2 + 2a;
Finally, 2a^2 + 2a - 112 = 0;
a^2 + a - 56 = 0;
We use <span>Quadratic Formula for this Quadratic Equation;
The solutions are a1 = 7 and a2 = -8;
But a is a natural number; so, a = 7;
The natural consecutive numbers are 7 and 8.</span>
There are two ways to do this.
The first is you plug in the x-value from the point in the table and see if that gives you the y-value from the same point.
For example, your first point is (5,49), so plug in x=5:
y = -5(5)+2 = -25+2 = -23
Since that's not the y-value in (5,49), then (5,49) is not a solution for the equation.
The other option is you plug in both the x-value and the y-value to see if you get a true statement. (A solution will make the equaiton a true statement.)
For example, the first point is (5,49), so you'd plug in x=5 and y=49:
49 = -5(5)+2
49 = -25 + 2
49 = -23
Since that's not true, (5,49) is not a solution.
You'll notice you're basically doing the same thing, it's just whether you plug in one value or both and that's your choice.
Answer:
$6.22
Step-by-step explanation:
Given;
Total number of coins N = 50
Number of pennies p = 14% of N = 0.14 × 50 = 7
Number of dimes d = 32% of N = 0.32×50 = 16
Number of nickels n = 4 + number of pennies = 4+p
n = 4+7 = 11
Number of quarters q;
N = p+d+n+q
q = N - (p+d+n)
q = 50-(7+16+11)
q = 16
1 Penny = 1 cent = $0.01
1 Nickel = 5 cent = $0.05
1 dime = 10 cents = $0.10
1 quarter = 25 cents = $0.25
Total amount in the bag is;
C = 0.01p + 0.05n + 0.10d +0.25q
Substituting the values;
C = 0.01(7) + 0.05(11) + 0.10(16) + 0.25(16)
C = $6.22
The bag contains $6.22
2.89 each person plus 7 for each meal total of 19.89
Answer:
2.56x10=25.6
Step-by-step explanation:
