Math Flashcards

If 4x + 3x − 2(x + 5) = −9, then x = ?

Answer: 1/5

To solve the equation, first distribute the -2: 4x + 3x - 2x - 10 = -9. Combine the x terms: 5x - 10 = -9. Add 10 to both sides: 5x = 1. Finally, divide by 5 to find x: x = 1/5.

What is 181.5% of 18?

Answer: 32.67

To find a percentage of a number, convert the percentage to a decimal by dividing by 100. So, 181.5% becomes 1.815. Then, multiply this decimal by the given number: 1.815 * 18 = 32.67.

In a coordinate plane, triangle ABC has coordinates: (−2,7), (−3,6), and (4,5). If triangle ABC is reflected over the y-axis, what are the coordinates of the new image?

Answer: (2,7), (3,6), (−4,5)

When a point (x, y) is reflected over the y-axis, its x-coordinate changes sign, while its y-coordinate remains the same. Applying this rule to each vertex: (-2, 7) becomes (2, 7); (-3, 6) becomes (3, 6); and (4, 5) becomes (-4, 5).

David purchased new shoes that were on sale for $45.44. The original price was $60.59. What percentage discount was the sale price?

Answer: 25%

First, calculate the discount amount by subtracting the sale price from the original price: $60.59 - $45.44 = $15.15. Then, divide the discount amount by the original price to find the decimal percentage: $15.15 / $60.59 ≈ 0.25. Multiply by 100 to convert to a percentage: 0.25 * 100 = 25%.

ABC is a triangle with coordinates (3, 1), (6, 1), and (1, 3). It is translated to points A′(−3, 3), B′( 0, 3), and C′(−5, 5). Find the rule for the translation.

Answer: 6 units left and 2 units up

The correct answer is 6 units left and 2 units up. The rule of translation is the rule, which when applied to the first set of points, yields the second set of points. The difference between the x values of the non-translated and translated points is: (x2 − x1) = (−3 − 3) = (0 − 6) = (−5 − 1) = −6 This corresponds to a shift of 6 units to the left. Likewise, for the y values: (y2 − y1) = (3 − 1) = (3 − 1) = (5 − 3) = 2

(2x^2 + x - 6)/(x + 2) = ?

Answer: (2x - 3)

Begin by factoring the numerator. Assume that (the denominator) is one of the factors for a quick start to the process. At this point, you should have the following: 2x² + x - 6 = (x + 2) (2x - ?). The first term of the second set of parentheses must be 2x because 2x² ÷ x = 2x. The sign of the second set must be negative because a positive times a negative equals a negative, and the original problem has -6 as the final term in the numerator. To determine what replaces the “?” above, determine what number multiplied by 2 equals 6. The answer is 3. Now you have fully factored the numerator:2x² + x - 6 = (x + 2) (2x - 3). Rewrite the original problem, substituting the factored numerator for the original numerator and solve: (2x² + x - 6) / (x + 2) = ((x + 2) (2x - 3)) / (x + 2) = 2x - 3

Given the equation, 3/(y - 5) = 15/(y + 4) what is the value of y?

Answer: 54

Rearranging the equation gives 3(y + 4) = 15(y - 5), which is equivalent to 15y - 3y = 12 + 75, or 12y = 87, and solving for y, y = 87/12 = 29/4

Which of the following expressions is a factor of the polynomial x² - 4x - 21

Answer: (x - 7)

The polynomial can be factored as (x - 7) (x + 3). Thus, (x - 7) is a factor of the given polynomial.

What are the zeros of a quadratic expression, represented by the factors, (x + 5)and (x - 6)

Answer: x = -5 and x = 6

The zeros of an expression are the points at which the corresponding y-values are 0. Thus, the zeros of the expression, represented by the given factors, will occur at the x-values that have corresponding y-values of 0. Setting each factor equal to 0 gives x + 5 = 0 and x - 6 = 0. Solving for x gives x = -5 and x = 6. Thus, the zeros of the expression are x = -5 and x = 6.

Factor the equation :

Answer: 3x² (4x - 1) (x-2)

Begin by looking for anything that is common to all three terms. You should notice that each of the coefficients is divisible by three and that each of the x-terms has a power of 2 or more. Factor out a 3 from each term and you have 3(4x⁴ - 9x³ + 2x²). Next, factor out x2 from each term and you are left with 3x²(4x² - 9x + 2). The portion inside the parentheses can be further factored as follows: 3x²(4x² - 9x + 2) = 3x²(4x - 1) (x - 2) This step may take a bit of trial and error, but you should be able to find it without too much trouble. Look at the answer choices to get a hint. If a combination you are considering is not a choice, then it is not the correct answer. If you are having trouble factoring the problem, you can always work backwards. Look at the answer choices and multiply them out to see which one gives the original problem as its answer. This method is more time consuming, but it will yield a correct answer if you get stumped.

10 workers can make all the furniture for 5 days. If each worker makes as quickly as the others then how much of the furniture could 7 workers make in 5 days?

Answer: 7/10

10 workers can make a furniture in 5 days. Each worker makes 1/10 of the furniture in 5 days. In 5 days 7 worker would make 7 × 1/10 of the furniture. In 5 days 7 worker would make 7/10 of the furniture.

In the metric system of units: 1 meter = 100 centimeters and 1 meter:1 foot = 3.25:1

Answer: 6.4615

3.25 feet = 1 meter 1 foot = 1÷3.25 meters 21 feet = 21×1÷3.25 = 6.4615 meters

What is the x value such that y =30 - 5x and y = 0?

Answer: 6

y =30-5x and y = 0 Hence 30 - 5x = 0 Hence 30 = 5x, divide both sides to 5. x = 6

Put these four fractions in order from smallest to largest: 1/4, 2/3, 4/7, 1/2

Answer: 1/4, 1/2, 4/7, 2/3

If 1/4, 2/3, 4/7, 1/2 are converted to decimals we get 0.25, 0.6666...., 0.571....., 0.5 then the correct order is obvious or If 1/4, 2/3, 4/7, 1/2 are converted to fractions with a common denominator 21/84, 56/84, 48/84, 42/84 then the correct order is obvious.

On a number line what is the distance between -3/7 and -2/3 ?

Answer: 5/21

The distance between numbers can be found by using absolute values (|a| or abs(a)). The distance between these numbers is abs(-3/7 − -2/3 ) = abs(-(3/7 -2/3)) = abs(3/7 -2/3) = abs(9/21 - 14/21) = abs(-5/21 ) =5/21

In the diagram below, which line has a positive slope?

Answer: AC

The coordinates of A are (1,2), the coordinates of B are (3,2). The slope of AB is (2-2)/( 3-1) = 0 The coordinates of A are (1,2), the coordinates of D are (-2,4). The slope of AD is (4-2)/( -2-1) = -4/3 The coordinates of A are (1,2), the coordinates of C are (2,4). The slope of AB is (4-2)/( 2-1) = 2 The coordinates of D are (-2,4), the coordinates of B are (3,2). The slope of DB is (2-4)/( 3− -2) = -4/5

One third of the candidates for a scholarship were 25 years old or younger. Two sevenths of the candidates were at least 50 years old. If 84 people applied for the scholarship, how many were between 25 and 50?

Answer: 32

One third of 84 is 84 × 1/3 = 84÷3 = 28. 28 people 25 years old or younger applied for the scholarship. Two seventh of 84 is 84 × 2/7= 2×84÷7 = 24. 24 people who were at least 50 years old applied for the scholarship. 84 - 28 - 24 = 32. 32 people applied for the scholarship who were between 25 and 50.

Which of the following is a factor of 450 and multiple of 25?

Answer: 75

It can be confirmed by division that (a), (b) and (c) are factors of 450, while 100 is not. The multiples of 25 are 25, 50, 75,.... 75 is both a factor of 450 and multiple of 25

The formula h -15 = 3.2t gives the height h in inches of a plant t weeks after planting. How high was the initial height of the shrub?

Answer: 3.2 inches

h =15 + 3.2t gives the height of a shrub in inches after t weeks. When planting occurs the height is 15 + 3.2× 0 = 15 inches. After one week the height is 15 + 3.2× 1 = 18.2 inches The rate at which the height increases is 18.2 - 15 = 3.2 inches

A graph of the temperature T (degrees Fahrenheit) in a refrigerator t hours after midday. What is the equation of the axis of symmetry of this graph?

Answer: t = 0

It is clear from the diagram that the T -axis is the mirror line or axis of symmetry of this diagram. The equation of the T- axis is t = 0. The equation of the axis of symmetry of this graph is t = 0