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Questions and Answers
Find the next two elements of the sequence 1, 6, 13, 24, 37, ...
Find the next two elements of the sequence 1, 6, 13, 24, 37, ...
44, 55
Factor completely: 25a^2 - 9b^2
Factor completely: 25a^2 - 9b^2
(5a + 3b)(5a - 3b)
Simplify: 3^n + 3^n + 3^n
Simplify: 3^n + 3^n + 3^n
3^(n + 1)
Write in lowest terms without zero or negative exponents: (a^3b + 1b^2 + 2)/(a^3p - 1b^2)
Write in lowest terms without zero or negative exponents: (a^3b + 1b^2 + 2)/(a^3p - 1b^2)
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Reduce to lowest terms: ((2a + 7)(a + 3))/((2a + 7)(a + 3))
Reduce to lowest terms: ((2a + 7)(a + 3))/((2a + 7)(a + 3))
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Perform the indicated operation and simplify: (x^3/(x^2 - 4x + 3)) - ((x^2 + 2x - 15)/(x^2 + 5x))
Perform the indicated operation and simplify: (x^3/(x^2 - 4x + 3)) - ((x^2 + 2x - 15)/(x^2 + 5x))
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Solve the equation for F: C = 5/9(F - 32)
Solve the equation for F: C = 5/9(F - 32)
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Factor completely: x^3 + 64y^3
Factor completely: x^3 + 64y^3
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Write in lowest terms without zero or negative exponents: (x^3y^2/z^7)^(-1/3)
Write in lowest terms without zero or negative exponents: (x^3y^2/z^7)^(-1/3)
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What is the perimeter of a square if its area is 16x^2 + 56x + 49, where x > 0?
What is the perimeter of a square if its area is 16x^2 + 56x + 49, where x > 0?
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As part of a school's coastal cleanup drive, a trip to visit its marine station has been organized. Eight teachers and staff, together with 210 students, signed up for the trip to pick up garbage that has been washed up on shore. How many buses are needed for the trip, if each bus can accommodate 40 people?
As part of a school's coastal cleanup drive, a trip to visit its marine station has been organized. Eight teachers and staff, together with 210 students, signed up for the trip to pick up garbage that has been washed up on shore. How many buses are needed for the trip, if each bus can accommodate 40 people?
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How many solutions does the system of equations have? {5x - 4y = 20, 4x - 5y = 1}
How many solutions does the system of equations have? {5x - 4y = 20, 4x - 5y = 1}
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If f(x) = |x|, what is f(a) if a < 0?
If f(x) = |x|, what is f(a) if a < 0?
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Perform the indicated operations and simplify: (4/(1+y) + (6y/(y-1) + 3/(y-1))
Perform the indicated operations and simplify: (4/(1+y) + (6y/(y-1) + 3/(y-1))
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Factor completely: ay^3 - 2ay^2 - 9ay + 18a
Factor completely: ay^3 - 2ay^2 - 9ay + 18a
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Solve the equation: (3x + 2)/(x + 2) - 3x = 2 - (2x - 3)/(x - 5)
Solve the equation: (3x + 2)/(x + 2) - 3x = 2 - (2x - 3)/(x - 5)
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Solve the inequality: 3x + 6 < 5x - 12
Solve the inequality: 3x + 6 < 5x - 12
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Let m be an integer. Give the contrapositive of the statement "If m^2 is even then m is even."
Let m be an integer. Give the contrapositive of the statement "If m^2 is even then m is even."
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The denominator of a fraction is 3 less than twice the numerator. If 2 is added to the numerator and subtracted from the denominator, the resulting fraction is equal to 2. Find the original fraction.
The denominator of a fraction is 3 less than twice the numerator. If 2 is added to the numerator and subtracted from the denominator, the resulting fraction is equal to 2. Find the original fraction.
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What is the domain of the function g(x) = √(√(4 - x^2))?
What is the domain of the function g(x) = √(√(4 - x^2))?
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If f(x) = 1/(x - 1) and g(x) = 1 + 1/x, what is f(g(2))?
If f(x) = 1/(x - 1) and g(x) = 1 + 1/x, what is f(g(2))?
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What is the slope of the line through the points (-7, 3) and (-1, 1)?
What is the slope of the line through the points (-7, 3) and (-1, 1)?
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In ΔPQR, m∠Q = 49° and m∠R = 77°. Arrange the sides of the triangle in order of increasing length.
In ΔPQR, m∠Q = 49° and m∠R = 77°. Arrange the sides of the triangle in order of increasing length.
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Solve the equation for b: (a/b) = (az/(x + y))
Solve the equation for b: (a/b) = (az/(x + y))
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Simplify the complex fraction: 1/(1 + 1/x)
Simplify the complex fraction: 1/(1 + 1/x)
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A line with slope 2/3 passes through the point (8, -5). Write an equation of the line in slope-intercept form.
A line with slope 2/3 passes through the point (8, -5). Write an equation of the line in slope-intercept form.
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What are the domain and range of the function h(x) = 3/(x - 2), whose graph has no y-intercept?
What are the domain and range of the function h(x) = 3/(x - 2), whose graph has no y-intercept?
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Write an equation of the line through the point (5, -3) and whose graph has no y-intercept.
Write an equation of the line through the point (5, -3) and whose graph has no y-intercept.
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Write an equation of the perpendicular bisector of the line segment joining (-5, -2) and (-9, 4).
Write an equation of the perpendicular bisector of the line segment joining (-5, -2) and (-9, 4).
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A rectangular lot has length in meters equal to 5 less than twice its width. One of the longer sides is against the wall so that only the three remaining sides needed fencing material. Find the dimensions of the lot if 39 meters of fencing material were used.
A rectangular lot has length in meters equal to 5 less than twice its width. One of the longer sides is against the wall so that only the three remaining sides needed fencing material. Find the dimensions of the lot if 39 meters of fencing material were used.
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The length of a large balikbayan box is 8 inches longer than its width, and its height is 1 inch shorter than its width. If the height of the box is x - 5, what is the volume of the box in terms of x?
The length of a large balikbayan box is 8 inches longer than its width, and its height is 1 inch shorter than its width. If the height of the box is x - 5, what is the volume of the box in terms of x?
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A man has x pesos. If he spends y centavos, how many pesos has he left?
A man has x pesos. If he spends y centavos, how many pesos has he left?
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Find the maximum value of x such that 13! is divisible by 2^x.
Find the maximum value of x such that 13! is divisible by 2^x.
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Claudine is participating in a cosplay contest. If she can choose from 5 different outfits, 4 wigs, and 8 props, how many different cosplay costumes can she make?
Claudine is participating in a cosplay contest. If she can choose from 5 different outfits, 4 wigs, and 8 props, how many different cosplay costumes can she make?
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Study Notes
Line and its properties
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Line l has x-intercept 4 and passes through the point (2, -5). What is the y-intercept of l?
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Write an equation of the line through the point (5, 3) and whose graph has no y-intercept.
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Write an equation of the perpendicular bisector of the line segment joining (-5, -2)
Rectangular Lot
- A rectangular lot has length in meters equal to 5 less than twice its width. One of the longer sides is against the wall so that only the three remaining sides needed fencing material. Find the dimensions of the lot if 39 meters of fencing material were used.
Large Box
- The length of a large balikbayan box is 8 inches longer than its width, and its height is 1 inch shorter than its width. If the height of the box is x, what is the volume of the box in terms of x?
Maximum Value
- Find the maximum value of x such that 13x is divisible by 2?
Different Outfits
- Claudine is participating in a cosplay contest. If she can choose from 5 different outfits, 4 wigs, and 8 props, how many different cosplay costumes can she make?
Linear System
- Find the solution set of the linear system:
- 2x + 3y = 5
- 3x + 2y = 14
Integer Sum and Difference
- Find two integers whose sum is 8 and whose difference is 12.
Triangles and Angles
- In the figure below, A, B, C, D are coplanar points with AB = AC and BD = CD. If m∠A = 40° and m∠D = 100°, what is m∠ACD?
Transversal Lines
- Lines L and M are cut by a transversal T. Find angles that will make line L || M. (2x + 7)° as shown in the figure above.
- 5x - 2)°
Area of Region
- Find the area of the region on the first quadrant of the xy-plane bounded by the x-axis, the y-axis and the line 4x + 3y = 24.
Taxi Fare Formula
- The Philippine transport agency LTFRB recently approved a new formula to compute taxi fares based on flagdown or fixed rate, total distance travelled, and total running time (computed whether the taxi is moving or stationary). For Metro Manila, the flagdown rate is Php 40, the taxi rate is Php 13.50 per km, and running time rate is Php 2 per min. Compute the taxi fare of a taxi trip in Metro Manila if the taxi was moving for 10 min and caught in a traffic jam for 20 min.
Mean of Numbers
- The mean of a set of 40 numbers is 60, and the mean of another set of 35 numbers is 30. What is the mean when the two sets are combined?
Typing Words
- Hannah typed her term paper at the rate of 36 words per min. After typing for 12 min, she had 648 words left to type. Let f(t) be the number of words Hannah would be left to type after typing for t min.
Senior Citizen Discount
- Senior citizens get a 20% discount for admission. Write a formula for a movie house priced at Php 250 per adult. If 1,000 tickets were sold and total receipts were Php 231,000, how many senior citizen tickets were sold?
Right Triangle Hypotenuse
- In right triangle ΔABC, the length of the hypotenuse AB is 15 cm. If m∠A =
Carpenter Job
- Von can do a carpentry job in 45 min while his brother JR can do the same job in 36 min. How long will it take them to finish the job if Von and JR work together?
Parallel Sides of Parallelogram
- The measures of two consecutive angles of a parallelogram are in the ratio 2:3. What are the measures of all angles of the parallelogram? Determine all possible relationships between the two angles.
Probability of Dice
- Two 6-sided dice are rolled simultaneously. If the dice are fair, what is the probability that the sum of the two numbers on the dice is divisible by 3?
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Description
This quiz covers various algebra topics including line properties, equations of lines, and geometric dimensions. Solve problems related to intercepts, rectangular dimensions, and volume calculations. Test your knowledge with practical applications of linear equations.
