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Shanna L.

Quantitative Associate, BS in Mechanical Engineering from Ivy League university

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Pre-Calculus

TutorMe

Question:

Find the x-intercept and the y-intercept of the following function: f(x) = 2*x^2 + 4x - 6

Shanna L.

Answer:

PART 1: Find the x-intercept Step 1: Set f(x)=0 since the x-intercept occurs when y=0. 0 = 2*x^2 + 4x - 6 Step 2: Divide both sides of the equation by 2 to simplify. Note: This step is optional, but will simplify the problem if you notice that all the numbers on the right side of the equal sign are multiples of 2. 0 / 2 = (2*x^2 + 4x - 6) / 2 0 = (2*x^2)/2 + (4x)/2 - 6/2 0 = x^2 + 2x - 3 Step 3: Factor the equation by finding factors that multiply to -3 and add to +2. Factors of -3: {1, -3} --> 1 + -3 = -2 {-1, 3} --> -1 + 3 = 2 Thus, the factor must be -1 and 3. 0 = (x - 1) (x + 3) Step 4: Set both factors to 0 and solve for x. x - 1 = 0 x = 1 x + 3 = 0 x = -3 The two x-intercepts are x = 1 and x = -3. PART 2: Find the y-intercept Step 1: Set x=0 since the y-intercept occurs when x=0. f(0) = 2*0^2 + 4*0 - 6 Step 2: Solve for f(0) f(0) = 0 + 0 - 6 f(0) = -6 The y-intercept is y = -6.

Pre-Algebra

TutorMe

Question:

On a hot summer day, Tom was driving home when he drove by two lemonade stands. Since he was so thirsty, he decided to stop and buy one cup for himself and two more cups for his friends. Stand 1 had the following deal: "Buy 2 cups, get 1 free." Each cup at stand 1 costs $0.80. At stand 2, each cup costs $0.60. Which stand should Tom go to if he wants to spend the least amount of money on 3 cups of lemonade? What if Tom were to buy 5 cups?

Shanna L.

Answer:

PART 1: Tom buying 3 cups of lemonade. Step 1: Determine how much it would cost to buy 3 cups of lemonade at stand 1. Since the deal is buy 2 get 1 free, the cost of 3 cups is the same as the cost of 2 cups, so the cost of 3 cups is the following: 2 * $0.80 + 1 * $0.00 = $1.60 It costs $1.60 to buy 3 cups at Stand 1 Step 2: Determine how much it would cost to buy 3 cups of lemonade at stand 2. 3 * $0.60 = $1.80 It costs $1.80 to buy 3 cups at Stand 2 Thus, if Tom were to buy 3 cups of lemonade, he should go to Stand 1. PART 2: Tom buying 5 cups of lemonade. Step 1: Determine how much it would cost to buy 5 cups of lemonade at stand 1. Since the deal is buy 2 get 1 free, the cost of 3 cups is the same as the cost of 2 cups. To buy two more cups, there is no deal, so the cost of 5 cups is the following: 2 * $0.80 + 1 * $0.00 + 2 * $0.80 = $3.20 It costs $3.20 to buy 5 cups at Stand 1 Step 2: Determine how much it would cost to buy 5 cups of lemonade at stand 2. 5 * $0.60 = $3.00 It costs $3.00 to buy 5 cups at Stand 2 Thus, if Tom were to buy 5 cups of lemonade, he should go to Stand 2.

Algebra

TutorMe

Question:

Solve the equation for x: 6 * (2x - 10) + 3x = 4 * (6 - x) - (x + 4)

Shanna L.

Answer:

Step 1: Distribute 6 * 2x - 6 * 10 + 3x = 4 * 6 - 4 * x - x - 4 12x - 60 + 3x = 24 - 4x - x - 4 Step 2: Combine like terms on either side of the equal side (12x + 3x) - 60 = (24 - 4) + (-4x - x) 15x - 60 = 20 - 5x Step 3: Move all terms with an x to the left side of the equal sign and combine like terms 15x - 60 + 5x = 20 - 5x + 5x 20x - 60 = 20 Step 4: Move all terms without an x to the right side of the equal sign 20x - 60 + 60 = 20 + 60 20x = 80 Step 5: Solve for x 20x / 20 = 80 / 20 x = 4

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