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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.