The perimeter of the larger rectangle will be 3.5 times the perimeter of the smaller one.
The area of the larger rectangle will be 3.52 times larger than the area of the smaller rectangle.
The volume of the larger rectangle will be 3.53 times the volume of the smaller...

x = 2y= 3z= 12. So:
x = 12
2y = 12 so y = 6
3z = 12 so z = 4
Now you know the values of x, y, and z, so plug them into the given perimeter equation to get the answer.
Perimeter = 2x + 3y + 4z = ______?

Ah, when you factor the -3 out of -15x-18, it becomes -3(5x+6). Remember taking -3 out of -18, you get (-3)·(+6) = -18.

(-4)2 = 16
but
-42 = -(42) = -(16) = -16

(2x2·x4)3
(2x2+4)3 {[Add exponents with the same base]
(2x6)3
23·(x6)3 [Cube both the 2 and the x6]
8x6·3 [Multiply exponents when you raise a power to...

The two angles add up to 90°, so:
2x + 1 + 6x + 1 = 90
Solve for x. Once you have x:
m∠wxz = 2x+1 = ______?

A(t) = A0(1-r)t
A(t) = Area at time t
A0 = starting area = 2100 km2
r = decay rate = 7.25% = 0.0725
t = years = 9
A = A0(1-r)t
A(t) = 2100(1-0.0725)9
A(t) = 2100(0.9275)9
Can you finish from here?

The sum of x and -5: x + (-5) = x - 5
is -1: = -1
x - 5 = -1
Solve for x

The arc length, s, is given by:
s = r·θ
where s is the arc length = one nautical mile, r is the radius = 3960 miles, and θ is the central angle in radians. First, convert 1/60 degree to radians. One degree = pi/180 radians, so:
1/60 deg. =...

I'm going to use x vice theta because it's easier to type. You will need to use the following identities"
cos2(x) + sin2(x) = 1
sec(x) = 1/cos(x)
cot(x) = cos(x)/sin(x)
sin(x) = -3/5
cos2(x) + sin2(x) = 1
cos2(x) = 1 - sin2(x)
cos2(x)...

Remember that y = f(x), so which ordered pair in f has an x = 2? Answer: (2,3). So f(2) = y = 3.
f(5) = 0 (ordered pair 5,0))
g(-2) = 0 (ordered pair (-2,0))
f(5) + g(-2) = 0 + 0 = 0
BTW, it's pi, not pie. ...

If you haven't gotten to L'Hopital's Rule yet, the numerator and denominator can be factored and simplified:
lim x→3 (x-3)2(x-7)/(x-3)2(x+2) = lim x→3 (x-7)/(x+2) = (3-7)/(3+2) = -4/5

Let x = the number of students in the 10 am class. The 8 am class has 80 more students, so it has x+80 students
x+80 + x = 410
Solve for x.

sec2x - 1 = sec2x·sin2x
Now sec2x = 1/cos2x, Substituting:
(1/cos2x) - 1 = sin2x/cos2x
Multiply both sides by cos2x:
1 - cos2x = sin2x
1 = cos2x + sin2x
Which...

32log3(5)
= 3log3(5^2) [Log Property: b·log(a) = log(ab)]
= 3log3(25)
= 25 [Log Identity: aloga(x) = x]

FV = PV·(1 + r/n)nt
FV = Future Value = $12,000
PV = Present Value - unknown
r = rate expressed as a decimal = 3% = 0.03
n = number of compoundings per year = 4
t = years = 7
FV = PV·(1 + r/n)nt
$12,000 = PV·(1 + 0.03/4)4·7
$12,000 = PV·(1.0075)28
$12,000/(1...

V(t) = (21/5)t + 70
100 = (21/5)t + 70
30 = (21/5)t
30·5/21 = t
150/21 = 50/7 ≈ 7.14 sec = t

Profit = Revenue - Costs
P(x) = R(x) - C(x)
P(x) = -0.25x2 + 49x - (-0.11x2 + 11x + 800)
P(x) = -0.25x2 + 49x + 0.11x2 - 11x - 800
P(x) = -0.25x2 + 0.11x2 + 49x - 11x - 800
P(x) = -0.14x2 + 38x - 800

y = c + b·loga(x)
First, plug in (1,1) for the x and y values:
y = c + b·loga(x)
1 = c + b·loga(1)
Since loga(1) = 0 for any base, we get 1 = c. Now plug in the second point, (5,7):
...

G(x) = (-1/4)F(x+3) + 2/3
The graph of G(x) is the graph of F(x) translated 3 units to the left, 2/3 of a unit up, vertically stretched (compressed by 1/4) and inverted (the - sign in front of the 1/4).