Write the integer that best describes the scenario. 35 feet below sea level
The key thing that we have to notice with a problem like this is the word "below". We also have to understand that sea level is representative of the number 0. Zero is the threshold between positive numbers and negative numbers. Anything above sea level would be considered a positive elevation. Anything below sea level would be considered a negative elevation. The problem says 35 feet BELOW sea level. This means that we are going to have a negative elevation. How negative? 35 feet. The answer is -35 feet.
Simplify: 3^-2 * 2^2 * 4^0
When looking at this problem the first thing we want to note is the exponents. In this case we see we have -2, 2 and 0 as exponents on 3, 2, and 4 respectively. We also must know that any number raised to the 0 power is 1. We also must know that in order to turn an exponent positive we must take its reciprocal. 3^-2 * 2^2 * 4^0 turns into the following 2^2 * 4^0 ___________ 3^2 Let's expand the problem 2 * 2 * 1 (Remember any number raised to the 0 power is 1) ________ 3 * 3 4 _ 9 The answer to 3^-2 * 2^2 * 4^0 is 4 _ 9.
Robin cross-stitches bookmarks and wall hangings. A bookmark takes her 1 1/2 days, and a wall hanging takes her 4 days. Robin recently spent 18 days cross stitching 7 items. Solve the system of equations to find the number of bookmarks, b, and the number of wall hangings, w, that Robin cross-stitched.
In order to solve this problem we know that we are going to need to solve a system of liner equations. Essentially, we will need to find the point at which the lines of the two equations cross. First we must write out our equations. The first equation we get is: b + w = 7 because we know that she created 7 total items so the number of bookmarks, b, plus the number of wall hangings, w, must equal 7. Our second equation is 1 1/2b + 4w = 18 because it takes her 1 1/2 days to make a bookmark and 4 days to make a wall hanging. When we multiply the 1 1/2 (the amount of time needed to create a bookmark) times the number of bookmarks and add it to 4 (the amount of time needed to make a wall hanging) times the number of wall hangings we will get the number of days she spent which in this case is 18. Now that we have our two equations we can either use the substitution method or the elimination method. Substitution method: Step 1: Solve for one of the variables in the equation. b + w = 7 b - b + w = 7 - b (Subtract b from both sides) w = 7 - b Step 2: Place the value of the variable you solved for into the other equation and solve for the variable. 1 1/2b + 4w = 18 1 1/2b + 4(7 - b) = 18 (Use the distributive property) 1 1/2b + 28 - 4b = 18 (Combine like terms) - 2.5b + 28 = 18 (Subtract 28 from both sides) -2.5b + 28 - 28 = 18 - 28 -2.5b = -10 (Divide by -2.5 on both sides) -2.5/-2.5b = -10/-2.5 b = 4 Step 3: Plug the value of the variable that you solved for into either equation (choose the easier one) b + w = 7 (Input value) 4 + w = 7 (Solve for w) 4 - 4 + w = 7 - 4 w = 3 Robin made 4 bookmarks and 3 wall hangings in 18 days. Elimination method: b + w = 7 1 1/2b + 4w = 18 Step 1: Decide which variable you'd like to eliminate and use multiplication to match the coefficients. I'm eliminating w, so I need the coefficients to match which in this case is 4. I need to multiply the top equation by 4. b + w = 7 4(b + w = 7) 4b + 4w = 28 Step 2: Eliminate the variable by combining the equations using addition or subtraction (in this case it'd be subtraction) and solve for the variable. 4b + 4w = 28 - 1 1/2b + 4w = 18 __________________ 2.5b + 0w = 10 2.5b = 10 (Divide by 2.5 on both sides) 2.5/2.5b = 10/2.5 b = 4 Step 3: Use the value you found to solve for the other variable. b + w = 7 4 + w = 7 4 - 4 + w = 7 - 4 w = 3 Robin made 4 bookmarks and 3 wall hangings in 18 days.