The equation of a line is y = mx + b where m is the slope and b is the y-intercept. The derivative of f at x=A is the slope of the tangent line: f '(A) = 2.2 = m. So the equation of the tangent line so far is
y = 2.2x + b. To find b, you need to plug in the x and y-values...

For a trapezoid, AREA = (1/2)(base1 + base2)*height. Let x = the length of the shorter base (base1):
The larger base (base2) is three times as long as the shorter base: base2 = 3x
The height is 2 inches linger than the shorter base: height = x + 2
The AREA = 70 in2
...

Let x = the weight of the peanuts that the biker added to the 11 pounds of raisins. The weight of the final mixture of raisins and peanuts is 11 + x.
11*($2.30) + x*($4.50) = (11+x)*($3.29)
25.30 + 4.5x = 36.19 + 3.29x
Solve...

Do you mean 27% OF 6,200,672,930,123?
(6,200,672,930,123)*(0.27) = 1,674,181,691,133.21
which is the same as 1.67718169113321*1012 = 1.67718169113321*E12

8-1/3 = 1/81/3 = 1/(23)1/3 = 1/2 (since 23 = 2*2*2 = 8)
so log(8-1/3) = log(1/2)

let h = the height of the tree and d = days:
h(t) = (2.5 cm)*d + 5 cm
65 = 2.5*d + 5
60 = 2.5d
24 = d

N = N0(1/2)t
Where:
N = the number of coins left after "t" tosses
N0 = the initial or starting number of coins
t = tosses
What is the average half-life of 25 coins? 50 coins? 1 million coins?
N =...

Think of the bus and car as 1/2 km apart. If both the bus and car are going 55 kph, the gap never closes. But the bus closes that 1/2 km in one minute or 1/60 of an hour. Speed is distance divided by time, so to close the 1/2 km gap in 1/60 hour, the bus was going (1/2)/(1/60)...

x-intercept = (4,0)
y-intercept = (0,9)
y = mx+b
where:
m = the slope
b = the y-intercept = 9 (given in the problem statement)
Use the slope formula to find the slope given the two points (4,0) and (0,9):
...

There are 16 ounces in 1 pound. So for the ribeye, 1 pound 4 ounces = 1
4/16 pounds = 1.25 pounds. The unit rate (cost per pound) is:
Unit Rate Ribeye = $4.99/1.25 lbs = $3.99 per pound (rounded to
nearest cent)
For...

Let x be the smallest of the three numbers. Since the numbers are consecutive, the other two numbers are x+1 and x+2. The sum of the three numbers is 96:
x + (x+1) + (x+2) = 96
3x + 3 = 96
Solve for x.

This is an exponential growth:
Output = (Output0)*(1 + r)t
Where:
OUTPUT is the output of the factory = 2*OUTPUT0 at t=2
OUTPUT0 is the initial factory output at t = 0
r is the growth rate expressed as a decimal = unknown...

Use the formula for the impulse, a force applied for a given amount of time:
F*Δt = m*Δv
where:
F = the force = 600 N
Δt = the time the force is applied to the ball (aka foot is in contact w/ball) = unknown
m = mass of the ball = 430 g = 0.43 kg (watch...

Let's break the problem up into three segments
segment 1 is distance traveled while the train is accelerating at 1 m/s2
segment 2 is the distance traveled at constant speed - given as 2100 m
segment 3 is the distance traveled while decelerating at 2 m/s2
In segment...

Let x be the unknown negative number.
The square of the negative number: x2
is =
60 more than 4 times the negative number: 4x + 60
x2 = 4x + 60
x2 - 4x - 60 = 0
Factors to:
...

As you point out, d(tan-1t)/dt = 1/(1+t2). But here, you have tan-1(1/t). So you need to use the
chain rule (not the product rule):
df(u)/dt = df(u)/du * du/dt
Let u = 1/t:
d(tan-1u)/dt = d(tan-1u)/du *...

(78+84+x)/3 = 81 Solve for x
(78+84+y)/3 = 87 Solve for y
Your next test must have a score from x to y (x ≤ score ≤y).

f(x) = 7x2 + 6
f(1+√2) = 7(1+√2)2 + 6
= 7(1 + 2√2 + 2) + 6
= 7(3 + 2√2) + 6
= 21 + 14√2 + 6
...

V = pi*r2*h
V/(pi*h) = r2
√(V/pi*h) = r
Normally when you take a square root, you get two answers: ±√. Since we can't have a negative radius, we just take the principle root (positive) as the answer.

(2/3)*Cost = $18
Multiply both sides of the equation by 3/2:
Cost = $18*(3/2) = _____