Basic Math Questions and Answers

Select the correct answer. What is the simplest form of4m-17/m^2-16 + 3m-11/m^2-16, assuming no denominator equals zero? A. 7/m+4 B. 7m/m+4 C. 7/m-4 D. 7m-6/m^2-16

In a reflection along the x-axis a given coordinate (2, -1) transforms itself into which of the following? (2,1) (-2,1) (-2, 0) (0, 1)

Which expression is equivalent to the given expression? (3m²n)³/mn^4 A. 9m^5/n B. 9m^4n C. 27m^4n D. m27m^5/n

A coffee shop begins the day with 75 bagels and sells an average of 10 bagels each hour. Function bmodels the bagel inventory, (*), x hours after opening. b(x) = 75 - 10x If the coffee shop wants to make a graph of function b, which values of x should it include on the graph to include the relevant domain within the context? A. 0≤ x ≤ 7.5 B. 0≤ x ≤ 75 C -∞ ≤x ≤ ∞ D. 0≤x ≤ ∞

Samantha is a waitress and earns a weekly paycheck of $350 plus any tips she earns throughout the week. One week, Samantha noticed that she earned about $12 in tips each hour. Let x represent the number of hours Samantha works during a week where her average hourly earnings is $22.

Marci earns $8 an hour. Write an equation that shows the direct proportionality between hours (h) and money earned (m). A. 8h=m C. 8mh B. 8m = h D. none of the above

The equation t = -1/1.008 ln(12.3/W - 0.5) is a mathematical model for the relationship between the weight W (in grams) of an individual leaf of a wheat plant and the number of days t since the leaf unfolded from the stalk of the plant. The weight of a certain leaf is 13.1 grams. According to this model, how many days ago did the leaf unfold? (Round to the nearest tenth of a day.) 0.4 days 1.5 days 1.4 days 0.8 days 0.5 days

Which of the following represents x = 1/3y written in general form? 3x - y = 0 x- 1/3y=0 1/3x-y=0

If you rolled a die, what is the probability that you would roll a 4 or a 5?

Grace is traveling to an island for vacation. She drives from home at a constant rate for the first 154 miles, then takes a ferry to travel the last 35 miles from the coast to the island. The ferry travels at a constant rate that is half the rate at which Grace drives. Given that the entire trip takes 4 hours, complete the statement below. Grace drives at a rate of miles per hour.

Let u = i +6j and v=-4i +4j. Decompose u into two vectors u₁ and u₂, where u₁ is parallel to v and u₂ is orthogonal to v. Write your answers in the form ai+bj.

Solve |2x + 2| = 10. A. x = 4 and x = 6 B. x = 4 and x = -6 C. x = 4 and x = -4 D. x = -4 and x = -6

Write a direct proportion equation that shows the price (y) for any number of posters (x) that are $2.50 each. A. y = kx B. 2.50x=y C. $2.50 = yx D. 2.50y = x

Which of these is a factor in this expression? 6z^4 - 4+9 (y³+6) A. (y³ + 6) B. 9 (y³ + 6) C. -4+9 (y³ + 6) D. 6z^4-4

Solve 4|x + 5| = 16. A. x= -1 and x = 9 B. x = -1 and x = − 9 C. x= 1 and x = -9 D.x= 1 and x = -1

Theo's kitchen is 192 square feet. A blueprint of his kitchen is created with the scale 1 inch: 4 feet. What is the area of the kitchen on the blueprint?

Which of the following is a name for an isometry that moves or maps every point of the plane the same distance and direction? Select all that apply. flip glide rotation slide translation

Solve |6x + 3| = 27. A. x = -4 and x = -5 B. x = -4 and x = 5 C. x = 4 and x = -5 D. x = 4 and a = - 4

Solve 9 ax + 10ax = 11ax + 32 for x. Assume a 0. A. x = 4a B. x = 8a C. x = 4/a D. x = 1/8a

Mia has 50 feet of fencing to make a rectangular kennel for her dog. She decides to use a part of her house as one side of the kennel. She needs a minimum enclosed area of 300 square feet. Of the inequalities listed, which forms of the inequality represent this situation? -2/² +50/-300 ≥ 0 (/-15)(/-10) ≥ 0 /(50-20/) ≥ 300 (/-15)(/-10) ≤ 0 /(2/-50) ≥ 300 -2/² + 50/- 300 ≤ 0

For a candy-making competition, Tanya made 3 kinds of candies. She made 3 times as many orange candies as pineapple candies. She made 30 more lemon candies than pineapple candies. The ratio of orange candies to lemon candies was 2 to 1. Which equation could be used to find the number of pineapple candies Tanya made for the competition? 3n+ 2n = 30 3n/n+30 = 2 2.3n = 1.(n + 30) n+30/3n = 2

Which value of r indicates a stronger correlation: r=0.837 or r= -0.921? Explain your reasoning. Choose the correct answer below. A. r=0.837 represents a stronger correlation because | -0.921|> |0.837|. B. r= -0.921 represents a stronger correlation because | -0.921|> |0.837|. C. r=0.837 represents a stronger correlation because 0.837> - 0.921. D. r= -0.921 represents a stronger correlation because 0.837> -0.921.

Click on the graphic to select the figure that would make the following "a reflection in line k."

A car purchased for $25,000 depreciates annually at a rate of 11%. The value of the car t years after its purchase is given by the expression 25,000(0.89). Which expression represents the quarterly depreciated value at the rate at which the car is depreciating? A. 25,000(0.89^4 )^4t B. 25,000(0.89^4)^1/4 t C. 25,000(0.89^1/4)^1/4 t D. 25,000(0.89^1/4)^4t

Evaluate 4(x − 3) + 5x − x² for x = 2. A. 2 B. 11 C. 16 D. -2

Consider this equation. 10x +25/3x + 12=5x/x+4 How many valid solutions does the equation have? The equation has valid solution(s).

A map that was created using a scale of 1 inch : 3 miles shows a lake with an area of 4.5 square inches. What is the actual area of the lake?

Jason hired a luxury car service. The service charges a fixed rate of $4.92, regardless of the number of miles traveled, plus an additional $3.79 per mile. If Jason wants to spend no more than $4.20 per mile, what is the minimum number of miles he should travel? 12 1 6 0

A rotation is an isometry that moves a plane across a line of symmetry moves a plane in a straight line motion moves a plane as a nor image moves a plane about a fixed point

Consider this product. x^2-3x-10/x^2-6x+5 . x-2/x-5 The simplest form of this product has a numerator of and a denominator of The expression has an excluded value of x =

Finance. Suppose that $4,100 is invested at 3.2% annual interest rate, compounded monthly. How much money will be in the account in (A) 10 months? (B) 20 years? (A) Amount after 10 months: $ (Round to the nearest cent.)

A transformation T: (x,y) → (x + 3, y + 1). The image of B(4, 1) under this transformation is (7.2) (1, 0) (-1,0)

Solve |x+6 |- 7 = 8. A. x = -9 and x = -21 B. x = 9 and x = − 21 C.x = 9 and x = -9 D. x = -9 and x = 21

Select the correct answer. When two pumps are used, they can fill a tank in 60 minutes. When the first pump is used alone, the tank will be filled in 150 minutes. When x represents the time it takes the second pump to fill the tank when used alone, the situation is represented by this equation: 1/150 + 1/x = 1/60 How long would it take the second pump, working alone, to fill the tank? A 75 minutes B. 90 minutes C 100 minutes D. 120 minutes

If no denominator equals zero, which expression is equivalent to x^2+10x+25/x+5 - x^2-6/x-5? A. 2x^2-19/x-5 B. 2x^2-19/x^2-25 C. 19/x-5 D. -19/x-5

Paper lanterns are $3.50 each. Write a direct proportion equation using p for paper lanterns and c for total cost. A. 3.50c = p B. 3.5pc C. 3.50+p=c D. 3.50p = c

Jack invested $2,900 in an account paying an interest rate of 8 1/8% compounded annually. Anthony invested $2,900 in an account paying an interest rate of 8 1/2% compounded continuously. After 10 years, how much more money would Anthony have in his account than Jack, to the nearest dollar?

What is the solution to this equation? 8x-5(x-3) = 18 A. x = 7 B. x = 5 C. x = 11 D. x = 1

Friends compared the number of pets they had at home. Their results are below: 2,3,1, 0, 0, 4, 2, 2 What is the mean number of pets in their homes? A. 14 B. 2.33 C. 1.75 D. 2

Instead of walking on the sidewalk around the perimeter, students take a diagonal shortcut from corner to corner across a rectangular vacant lot that measures 82 ft. by 195 ft. To the nearest foot, how much distance do they save? 130 ft. 99 ft. 17 ft. 212 ft. 65 ft.

Sean and Colleen are raking leaves in their yard. Working together, they can clear the yard of leaves in 24 minutes. Working alone, it would take Sean 20 minutes longer to clear the yard than it would take Colleen working alone. When c is the number of minutes it would take Colleen to finish the job when working alone, the situation is modeled by this rational equation: 1/c + 1/c+20 = 1/24 How long would it take Colleen alone to clear the yard of leaves? A 12 minutes B. 14 minutes C. 28 minutes D. 40 minutes

Solve |x + 5| = -7. A. No solution B. x = 2 and x = −12 C. x = −2 and x = − 12 D. x = − 2 and x = 12

Solve |x + 4| = -7. A. No solution B. x = -3 and x = −11 C. x = 3 and x = -11 D. x = -3 and x = 11

Solve |3x + 3 |= 27. A. x = 8 and x = −8 B. x= -8 and x = 10 C. x = 8 and x = −10 D. x = −8 and x = -10

Which list of ordered pairs represents solutions to x + y = 2? (-4, 6), (0, 2), (4,2) (-4, 6), (0, 2), (4, -2) (-4,-6), (0, 2), (4,2)

A parent volunteer group is raising money by making custom hats to sell at school activities. They plan to sell the hats for $11. Each hat costs $5 to make. They spent $50 for advertising. Use n to represent the number of hats they sell. Multiply this by the money they make for each hat, then subtract the advertising cost. Which expression represents the money that the group raises? A. (11-5) n - 50 B. 50 - (11-5) n c. 11-5n-50 D. 11n-5 -50

Consider this expression. 9 / 4x^2-12x + 7x / x^2-9 The least common denominator of the two rational terms is

Solve the formula d = rt for t. A. t= d-r B. t = d/r C. t = r/d D. t = dr

The Sanchez family wants to go on a vacation in September and they begin saving in December. The Sanchez family expects the vacation to cost $1,700. Each month they will deposit 5% more than the previous month. In December, they deposit $100. How much will the Sanchez family have saved for their vacation after 9 months? Round the answer to the nearest hundredth. *

Which series of transformations will always carry an image onto the original figure? reflection over the y-axis followed by reflection over the x-axis rotation by 180° about the origin reflection over the x-axis followed by reflection over the y-axis rotation by 360° about the origin