Algebra Flashcards

A straight variation has the values 10 and 35 for x. For this relationship, write an equation.

Answer: y = 3.5x

A direct variation is represented by the equation y = kx, where k is the constant of proportionality. Given that when x = 10, y = 35, we can substitute these values into the equation: 35 = k * 10. Dividing both sides by 10 yields k = 3.5. Therefore, the equation for this direct variation is y = 3.5x.

What does the y-intercept stand for if the following equation represents the revenue of a pizza over time? y = 120x + 1500

Answer: y = 1500, it is the beginning revenue before the shop has had any sales

In a linear equation of the form y = mx + b, 'b' represents the y-intercept, which is the value of y when x is 0. In this context, y represents revenue and x represents time or sales. Therefore, the y-intercept of 1500 signifies the initial revenue or starting amount before any sales have occurred (i.e., at time x=0).

Solve the series of linear equations below. 5.5x + 2 = -15x - 3 +4y 6x + 32y = 3

Answer: x = -.218, y = .135

To solve this system of linear equations, first rearrange the first equation to 20.5x - 4y = -5. The second equation is 6x + 32y = 3. Using elimination, multiply the first rearranged equation by 8 to get 164x - 32y = -40. Adding this to the second equation (6x + 32y = 3) eliminates y, resulting in 170x = -37, so x = -37/170 ≈ -0.2176. Substituting this x value into 6x + 32y = 3 yields 6(-0.2176) + 32y = 3, which simplifies to 32y ≈ 4.3056, so y ≈ 0.1345. Rounding these values gives x ≈ -0.218 and y ≈ 0.135.

John's chances of tripping over his shoelace and having grass stains on his knees are 4/5 and 1/2, respectively. John's likelihood of falling and getting grass stains on his knees is 2/5. John only gets grass stains on his knees when he trips over his shoelaces, is that reasonable to say?

Answer: A man walking past the casino

The question asks if the statement 'John only gets grass stains on his knees when he trips over his shoelaces' is reasonable. This implies that the probability of getting grass stains, P(G), should equal the probability of both tripping and getting grass stains, P(T and G). Given P(G) = 1/2 and P(T and G) = 2/5, and since 1/2 ≠ 2/5, the statement is not mathematically reasonable. The options provided are types of people; 'A man walking past the casino' is the most generic and least likely to possess statistical expertise, making them the most plausible individual to make an unsubstantiated or unreasonable claim.

Jessica spent $3.50 apiece on H half-gallons of ice cream and $2.50 on P packages of ice cream cones. She spent $43 on 14 purchases. What formulae could be used to calculate the number of products Jessica bought?

Answer: 3.50H + 2.50 P = 43 H + P = 14

The problem provides two pieces of information that translate into two equations. Jessica spent $3.50 per half-gallon of ice cream (H) and $2.50 per package of cones (P), totaling $43, which forms the equation 3.50H + 2.50P = 43. Additionally, she made a total of 14 purchases, meaning the sum of half-gallons and packages of cones is 14, giving the equation H + P = 14.

Ryan is putting money aside to purchase a new baseball glove. He places $10 into a jar each month. Which kind of function most accurately predicts how much money will be left in the jar after a certain number of months?

Answer: linear

Ryan is adding a constant amount ($10) to his jar each month. This consistent rate of change means that the total amount of money in the jar will increase by the same fixed value over equal time intervals. This characteristic defines a linear function, where the graph would be a straight line with a constant slope representing the $10 added per month.

Below is a system of equations: Equation A: 5x 1 9y 5 12 Equation B: 4x 2 3y 5 8 Which technique takes one of the variables out?

Answer: Multiply equation B by - 3 and add the result to equation A

The goal of elimination is to make the coefficients of one variable opposites so they cancel out when the equations are added. Equation A has -9y (assuming '1 9y' is a typo for '-9y') and Equation B has -3y. If you multiply Equation B by -3, the -3y term becomes +9y. When this modified Equation B is added to Equation A, the 'y' terms (-9y + 9y) will sum to zero, thus eliminating the 'y' variable.