The key to starting this one is recognizing that you can factor the difference of two squares. Taking the first part of the relationship: a+b = a^2 - b^2 (you goofed on the sign here!) You can factor the difference of two squares, so: a+b...
The key to starting this one is recognizing that you can factor the difference of two squares. Taking the first part of the relationship: a+b = a^2 - b^2 (you goofed on the sign here!) You can factor the difference of two squares, so: a+b...
The end of the question is missing. I'm assuming that it ask how many people earned more than $60,000. We know how many people were surveyed: 1200. 2 1/2% of those people earn more than $60,000. The question is, "How many people is that?" Stated differently,...
Shivam, I don't have time to write it all out right now, but here's how you need to approach the problem. You have to solve absolute value equations in two parts. When (x-3) ≥ 0 you get one line. That's when x ≥ 3. For x ≥...
We're looking for grandfather's age at death. We'll call it A. He married grandmother after 1/3 of his life. That would be A/3 years. Their first daughter was born 4 years later. That would be at A/3 + 4. I'm assuming that mother is that first...
Courtney, Here's the trick that lets you solve this type of problem. s is the boat's speed in still water. The speed relative to the shore is s-3 going upstream and s+3 going down stream. The time t is the same for 140 miles in one direction and 100 miles...
Here's a possibility: y=1 + [99 / (1 + x2)] The x2 term cannot be negative, so the "+1" in the denominator eliminates the singularity issue. This function can never exceed 100 and it cannot reach 1. Don't know if the lower...
This will be a system of equations problem. Here's the piece that may not be obvious: Both runners went the same distance because they started at the same place and ran to the end of the trail. Let the distance be d. Let the time for the first runner be t. The...
Here's the trick: You can write an equation for the length of the carpet in terms of the width. If the width is w, then the length l = w + 26. The perimeter is 2 * w + 2 * l, and we can substitute (w+26) for l. 2w + 2(w+26) = P = 204 2w +2w + 52 =...
You can add/subtract a multiple of one equation to/from another. This will let you eliminate a variable. (1) x + 4y = 8 (2) 5x + 6y = 12 For this problem, we can multiply the first equation by 5: (1) 5*(x+4y) = 5 * 8 (1) 5x + 20y =...
Look at the atomic number of the element copper (Cu). That is the number of protons in the nucleus (as well as the number of electrons). Copper is 29. The elementary charge per proton (or electron) is 1.602x10^-19 coulomb. This is a positive charge for protons and...
It looks like two brothers each have an account. One is adding money monthly and the other is making withdrawals. If that is the case, you left an "m" out of the equation. Also, is the starting value of one account really a negative number? First I'll assume...
To answer the question you asked, the equation is 5.5x+32=57 If you want to know what x is: 5.5x = 57-32 =25 x = 25/5.5 x = 4.5454...
Susannah, Yes, the function is linear. How can you tell? It's because the term with x in it is just x. If it had a term with x2 or x3, it would curve instead of being a straight line (linear). The equation is actually already in slope intercept form...
Average speed is just the total distance traveled divided by the total time. You already have the total time. It's 100 + 100 = 200 seconds. Calculate the two distances, add them together, then divide by 200: D1 = 100 * 5 = 500 m D2 = 100...
Another way to get the answer is to put the equation in slope-intercept form: y = mx + b 3x+2y=9 2y = -3x + 9 y = (-3/2)x + 9/2 The slope (-3/2) tells you how much y changes for each unit change in x. If x...
Don't let the minus sign confuse you. Just multiply both sides of the equation by -9: I'll include extra parentheses for more clarity. a / (-9) = 2 (a) * (-9) / (-9) = 2 * (-9) a * 1 = -18 a = -18 &nbs...
Mathematically, the answer is definitely "yes"! A line with positive slope rises from left to right, negative slope falls from left to right. When they intersect the x-axis and you measure the angle of the intercept from left to right, two lines with the same...
Barbara, Simple interest uses the formula: I = prt where p = the initial principal, r = the interest rate per unit time t = time in the units used to express the interest rate. Your time unit is "year", and the interest rate is annual interest (per...
Tami, 12=4(b-2) Expand the right side using the distributive rule: 12=4b - 4*2 12=4b - 8 Add 8 to both sides: 12+8 = 4b - 8 + 8 20 = 4b Divide both sides by 4: 20/4 = 4b / 4 5 = b All you need to know is the distributive rule...
I can't be sure what form the answer is expected to have. You could divide the numerator and denominator by -4x2: -20x6 - 24x4 - 12x2 5x4 + 6x2 + 3 ----------------------- = --------------- -4x4 ...