Tutor profile: Abigail R.
Find an equation of the line that passes through the point (3, 2) and has a slope of 4.
The easiest and quickest way to do this will be using point-slope form of a line. Point-slope form looks like this: y - y1 = m*(x - x1) wherein m represents slope and the line crosses through the point (x1 , y1). Now that we know this, let's plug in our numbers to find our line! y - 2 = 4 * ( x - 3 ) Let's simplify this to present our final answer by putting it in slope-intercept form (y = mx + b) y - 2 = 4x - 12 y = 4x - 10
Billy the squirrel climbs a tree. The tree is at at 80 degree angle with the ground. If you measure the distance he climbed along the tree, the total is 10 feet. Billy stops at this distance. What is the vertical distance Billy has attained in comparison to the ground?
With geometry it always helps to draw a sketch! First, draw a line to represent the tree. Take note of the 80 degree angle from the ground. Next, label the line you just drew with the total length (10 feet). This line now represents the total distance Billy traveled along the tree. At the top of this line, draw a line that goes straight down. This is the vertical distance to the ground. You may want to label the distance of the line with a variable. Let's call it h for height. It may also help you to draw in the ground. Once you are done, you should have a drawing that looks like a triangle. The distance Billy traveled should be the hypotenuse. Next, let's use our trig rules to figure out how high up Billy traveled (h): sin(80 degrees) = h/10 10* sin(80) = h h = 10 * 0.9848 Let's multiply and round: h = 9.85 So, our final answer will be 9.85 feet.
Alice has $50 to spend. While at the mall, she finds a store that is offering 25% off all purchases. Alice picks out several items of clothing to buy. The original prices of these items are $10 and $20. Without accounting for taxes, how much money will Alice have left once she buys these items?
First let's write out what we were given: - Alice starts with $50 - Everything in the store is 25% off - Alice buys three items and the original price of these items are $10 an $20 - We will NOT account for taxes Now let's think about what the question is asking: - how much money will she have left over? Now that we understand what is given and what we are being asked to solve for, let's begin! First, let's calculate the new price of each item once we have taken off the 25% discount. When we take off 25%, we know that the buyer will pay 100% - discount which is 75% of the original price. As such, we can multiply the original price by 0.75 to find the new sale price. Therefore: $10 ----> 0.75*10 = $7.50 $20 ----> 0.75*20 = $15 Next, let's set up an equation to relate how much she spent to how much is left. We will let the letter x represent the remaining money: 7.5 + 15 + x = 50 To solve for the equation, subtract the numerical values on the left side of the equation from 50 so that x is alone on the left side. You should get: x = 27.5. Your final answer should include the units dollars. So the answer is: Alice will have $27.50 remaining after the purchase