Anthony's Responses in WyzAnt Answers

Is the value of x = 4/3?

If so, then substitute the (4/3) into the expression and evaluate.

18(4/3) - 3

18 times (4/3) minus 3

Order of operations: parentheses, exponents, multiplication/division, addition/subtraction

Multiplication/division before addition/subtraction.

So 18 times (4/3) means 18 times 4, divided by 3 which is

(72/3) - 3

24 - 3

21

This is a compound interest formula, where P = principal, r = rate, n = # compoundings per yr, t = time (in years).

P = 3000
r = 7% = 0.07
t = 6
n = 2 (semi-annually)

a) A = 3000(1 + 0.07/2)^(2*6) = $4,533.21

b) A = 3000(1 + 0.07/12)^(12*6) = $4,560.32 

Continuous compounding: A = Pe^(rt)

c) A = 3000(2.7183)^(0.07*6) = $4,565.90

d - 2(d - 3) + 5d ≥ 36

Solve using steps similar to ordinary equations:

d - 2d + 6 + 5d ≥ 36

4d + 6 ≥ 36

4d ≥ 30

d ≥ 30/4

d ≥ 15/2

So d must be a value that is greater than or equal to 15/2. 

            -5           0                      15/2
<--------|----------|-------------------•########################>

This is factorable by grouping. One thing to consider is that terms are commutative, meaning they can be rearranged. 

7m + 6mn + 3m² + 14n 

Rearrange terms and group 1st two and 2nd two==> (7m + 14n) + (6mn + 3m²)

From each group, factor out the GCF ==> 7(m + 2n) + 3m(2n + m)

Notice that the quantities in bold are identical (this let's you know you did the technique correctly). So now, the GCF of this new expression is the quantity (2n + m), so let's factor that out.

(2n + m)(7 + 3m) ==> note that if you distribute the bold quantity, you'd get the above expression again.

(1) 7y = x + 2
(2) 4x - 8y = 12

To solve this system, let's choose a variable from on of the equations to solve for (it doesn't matter which equation or which variable, so let's make it easy). I'll choose to solve for x in eqn 1.

x = 7y - 2

Now substitute for x in eqn 2

4x - 8y = 12

4(7y - 2) - 8y = 12

Notice that now we have an equation that's only in terms of one variable, y. Solve for y.

28y - 8 - 8y = 12
20y = 20
y = 1

Now that we have a value for y, substitute into any equation to find x (I'll use x = 7y - 2 since it was already solved for x)

x = 7y - 2
x = 7(1) - 2 = 5

So the point of intersection of these two lines is (5 , 1)