G2010 Algib Basic Skills

Each figure is created by adding an additional row of equilateral triangles to the previous figure. The first figure has 1 triangle, the second has 4 triangles, the third has 9 triangles, and so on. The number of triangles in each figure follows the pattern of square numbers. Therefore, the fifth figure will have 5^2 = 25 triangles. Since each triangle has a side length of 1, the perimeter of the fifth figure will be 25 * 1 = 25.

The sequence follows the pattern of the first letter of each month in the year. The sequence starts with J for January, followed by F for February, M for March, A for April, M for May, J for June, J for July, A for August, S for September. The next three letters in the sequence would be O for October, N for November, and D for December.

The given expression is a product of two binomials: (3x + 4) and (3x - 4). To simplify the expression, we can use the distributive property to multiply the terms within each binomial. The first terms give us 9x^2, the outer terms give us -12x, the inner terms give us +12x, and the last terms give us -16. Simplifying further, we combine like terms and get 9x^2 - 16.

The correct ratio of Bluumps to Spahzbhotts is 3 to 5. This can be determined by dividing the number of Bluumps (15) by the number of Spahzbhotts (25). Simplifying the ratio gives us 3 to 5.

The given example A x B x C = C x A x B demonstrates the Commutative Property of Multiplication. This property states that the order of multiplication does not affect the result. In other words, you can multiply a set of numbers in any order and still get the same answer. In this example, rearranging the order of the variables A, B, and C does not change the product, showing the commutative property.

The answer 5/8 is smaller than 66 2/3% because when we convert 66 2/3% to a fraction, it becomes 2/3. Comparing this with 5/8, we can see that 5/8 is smaller.

To "Factor a quadratic expression" means to rewrite it as a product of two linear expressions. This involves finding two binomials that, when multiplied together, give the original quadratic expression. By factoring the quadratic expression, we can often simplify and solve equations more easily.

The given expression is a quadratic expression in the form of ax^2 + bx + c. In order to factorize it, we need to find two binomials that when multiplied together, give us the original expression. In this case, we can see that the factors (x + 3) and (x + 4) when multiplied together, give us the expression x^2 + 7x + 12. Therefore, the correct factorized form of the expression is (x + 3)(x + 4).

If 6 people can sit at one table, and 10 people can sit at two tables, and 14 people can sit at three tables, then we can determine the pattern. The number of people that can sit at each additional table is increasing by 4. So, for 30 people, we can calculate the number of tables needed by subtracting 6 (the number of people that can sit at one table) from 30 and then dividing the result by 4. This gives us 6 tables. However, since the question asks for the number of tables needed, we need to add 1 more table to the result, giving us a total of 7 tables.

The given expression is a combination of like terms. By combining the terms with the same exponent of k, we can simplify the expression. The coefficients of the like terms are added or subtracted based on their signs. In this case, the simplified expression is 1k^2 - 6, where 1k^2 represents the term with the coefficient 1 and exponent 2 of k, and -6 represents the constant term.

The given number, 134.8 x 10^8, is already in scientific notation. Scientific notation is a way to express very large or very small numbers in a compact form. It consists of a number between 1 and 10, multiplied by a power of 10. In this case, the number 134.8 is multiplied by 10^8, which means it is equal to 134.8 multiplied by 10 raised to the power of 8. Therefore, no changes are needed and the given number is already in scientific notation.

The set { 9.0X10^5 ... 0.9x10^5 ... 9.0x10^3 } is in decreasing order because the numbers are arranged from largest to smallest. The first number, 9.0X10^5, is the largest, followed by 0.9x10^5, and finally 9.0x10^3, which is the smallest number in the set.

The set of coordinates { (0,-4) (0,8) (0,-33) } contains points that are ONLY on the y-axis because all the x-coordinates are zero, indicating that these points lie on the vertical line passing through the origin.

Based on the information given, we can calculate the expected number of LORAXES in the population. First, we find the number of DELLS in the population by multiplying the population size (230) by the percentage of DELLS (80%). This gives us 184 DELLS. Then, we find the number of MINEOS by multiplying the number of DELLS (184) by the percentage of MINEOS (30%). This gives us 55.2 MINEOS. Finally, we find the number of LORAXES by multiplying the number of MINEOS (55.2) by the percentage of LORAXES (60%). This gives us approximately 33.12 LORAXES. Since we cannot have a fraction of a person, we can expect about 32 to 35 people to be LORAXES in the population.

The vertex formula is used to find the maximum or minimum point of a quadratic equation. In this case, the vertex formula can be used to find the maximum height of the ball. By plugging the values into the vertex formula, we can determine the time at which the ball reaches its maximum height. Then, by plugging this time back into the "throw formula" (which represents the height of the ball at any given time), we can find the maximum height of the ball.

To solve the equation -11 = 2x - 5, we can start by isolating the variable term. Adding 5 to both sides of the equation, we get -11 + 5 = 2x - 5 + 5, which simplifies to -6 = 2x. Next, we can divide both sides of the equation by 2 to solve for x. Dividing -6 by 2, we get x = -3. Therefore, the correct answer is -3.

The given inequality is -3x - 1 ≤ 14. To solve this inequality, we need to isolate the variable x. By adding 1 to both sides, we get -3x ≤ 15. Then, dividing both sides by -3 (remember that when dividing by a negative number, the direction of the inequality sign flips), we have x ≥ -5. Therefore, the correct answer is "x is greater than or equal to -5."

The product of the solutions to each problem can be found by solving each equation separately and then multiplying the solutions together. For the first equation, -x + 3 = 4, we can subtract 3 from both sides to get -x = 1, and then multiply both sides by -1 to get x = -1. For the second equation, -x + 2 = 6, we can subtract 2 from both sides to get -x = 4, and then multiply both sides by -1 to get x = -4. The product of -1 and -4 is 4, so the answer is 4.

The given quadratic trinomial has (x - 4) as a factor because when we factor out (x - 4) from x^2 + 2x - 24, we get (x - 4)(x + 6), which is the given quadratic trinomial.

To simplify the given expression, we need to follow the order of operations (PEMDAS/BODMAS). First, we simplify the parentheses: (8 - 3) = 5 and (9 + 3) = 12. Then, we perform the multiplication: 5 * 12 = 60. Finally, we subtract 7 from 4: 4 - 7 = -3. Adding these results together: 60 + (-3) = 57. Therefore, the correct answer is 57.

The equation P(1-.03)^5 represents the population of Pandas decreasing at a rate of 3% per year for five years. In this equation, P represents the initial population, (1-.03) represents the decrease in population each year (97% remaining), and the exponent 5 represents the number of years. By multiplying the initial population by the decrease factor raised to the power of the number of years, we can calculate the population after five years.

The probability of randomly choosing a blue sock can be calculated by dividing the number of blue socks by the total number of socks in the drawer. In this case, there are 3 blue socks out of a total of 15 socks. Therefore, the probability is 3/15, which simplifies to 1/5.

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Five-sixths of a million dollars is greater than seven-ninths of a million dollars because when comparing fractions, a larger denominator indicates smaller parts. Since six is larger than nine, five-sixths represents a larger portion of the whole than seven-ninths. Therefore, five-sixths of a million dollars is the greater amount.

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The height of the tree can be determined using the concept of similar triangles. The ratio of the length of the yardstick to its shadow is the same as the ratio of the height of the tree to its shadow. Therefore, the height of the tree can be calculated by setting up the proportion: 36 inches (yardstick) / 24 inches (yardstick shadow) = x feet (tree height) / 36 feet (tree shadow). Solving for x, we get x = (36 inches * 36 feet) / 24 inches = 54 feet. Therefore, the height of the tree is 54 feet.

The given expression is a combination of terms with variables h, v, and s. To simplify the expression, we can combine like terms. Combining the terms with h, we have 8h + 3h = 11h. Combining the terms with v, we have -9v + 12v = 3v. Finally, combining the terms with s, we have -7s. Therefore, the simplified expression is 11h + 3v - 7s.

When a fourth person who is 9 years old is added, the total age of the four people becomes 17 + 17 + 17 + 9 = 60 years. Since there are now four people, the new mean age is 60 divided by 4, which equals 15 years.

The given expression is a product of two binomials, (4m - 5b) and (4m + 5b). To distribute these binomials, we multiply each term of the first binomial by each term of the second binomial. Using the FOIL method, we get:

(4m - 5b)(4m + 5b) = 4m * 4m + 4m * 5b - 5b * 4m - 5b * 5b
= 16m^2 + 20mb - 20mb - 25b^2
= 16m^2 - 25b^2

Therefore, the correct answer is 16m^2 - 25b^2.

In order to find the time it takes for all three people to meet at the starting point again, we need to find the least common multiple (LCM) of their individual times. The LCM of 9, 6, and 4 is 36. Therefore, it will take 36 minutes for Aqua-man, Batman, and Catwoman to all meet at the starting point again.

The given expression 45 x 9 / 5 - 1 is not a prime answer because it involves multiplication, division, and subtraction operations, which are not considered prime numbers.

The correct answer is $180. This can be calculated by multiplying the number of hours worked (15) by the rate charged per hour ($12). 15 x $12 = $180.

There are 3 brackets with 4 teams in each bracket, so there are a total of 3 x 4 = 12 teams in the tournament. Each team has an average of 12 players, so there are a total of 12 x 12 = 144 players in the tournament.

The given expression involves a series of arithmetic operations. First, we divide 8 by 4, which gives us 2. Then, we multiply 0.5 by 14, resulting in 7. Next, we subtract 2 and 7 from 9, giving us 0. Finally, we subtract 1 from 0, resulting in -1. Therefore, the correct answer is 13.

The correct answer is 72 because when you multiply 9 by 8, you get the product of 72.

The given expression is -4(-12y - 8). To simplify this expression, we distribute -4 to both terms inside the parentheses. This gives us -4 * -12y which is 48y, and -4 * -8 which is 32. Therefore, the simplified expression is 48y + 32.

The correct answer is "The opposite of Six and Three is the Opposite of Three." This statement is correct because when we take the opposite of both Six and Three, we get -6 and -3 respectively. Therefore, the opposite of Six and Three is the opposite of Three.

By using the distributive property, we can simplify the given expression. First, we multiply 3b by both terms in the second parentheses to get 15b^2 + 6b. Then, we multiply -4 by both terms in the second parentheses to get -20b - 8. Combining these results, we have 15b^2 + 6b - 20b - 8. Simplifying further, we can combine like terms by subtracting 20b from 6b to get -14b. Thus, the simplified expression is 15b^2 - 14b - 8.

Option SS is the best choice if you send more than 190 text messages per month because the fixed cost of $20 is cheaper than the cost of sending more than 190 text messages using Option RR. With Option RR, the cost per text message increases after the first 80 messages, so if you send more than 190 text messages, the total cost will likely be higher than $20.

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