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A relatively simple Algebra I practice exam. Based on a 9th grade level.
Questions and Answers
1.
Put the following information in point-slope form.m= 2, (1,2)
A.
Y=2x+2
B.
Y=2x+0
C.
2x+y=2
Correct Answer B. Y=2x+0
Explanation The given information states that the slope of the line is 2 and it passes through the point (1,2). The point-slope form of a linear equation is y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope. Plugging in the values, we get y - 2 = 2(x - 1). Simplifying this equation gives y = 2x + 0. This is the equation of the line in point-slope form.
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2.
State the domain and the range of the relation. Then tell weather or not it is a function.{(-3, 0) (3,0) (5, -3) (0,3) (3, 3) (3,7)}
Explanation The given relation consists of multiple ordered pairs, where each input (x-value) is paired with a corresponding output (y-value). The domain of the relation is the set of all distinct x-values, which in this case are -3, 3, 5, and 0. The range of the relation is the set of all distinct y-values, which are 0, -3, 3, and 7. However, since there are repeated x-values paired with different y-values (-3 and 3), the relation is not a function.
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3.
Find the slope between the two given points. (-5, 3) and (-2, 9)
A.
-12/3
B.
18
C.
22
D.
-4
Correct Answer D. -4
Explanation The slope between two points can be found using the formula (change in y)/(change in x). In this case, the change in y is 9 - 3 = 6 and the change in x is -2 - (-5) = 3. Therefore, the slope is 6/3 = 2. However, the given answer is -4, which is incorrect.
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4.
Find the value of x so that the line that passes through the points (-8, 4) and (x, 9) has slope m= 2/5.
Correct Answer x= 9/2
Explanation To find the value of x, we can use the formula for calculating the slope of a line, which is (y2 - y1) / (x2 - x1). Given that the slope is 2/5 and one point on the line is (-8, 4), we can substitute these values into the formula. Solving for x, we get x = 9/2. Therefore, the value of x that satisfies the given conditions is 9/2.
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5.
What is the standard form of an equation of the line that passes through the points (3,0) and (6, -8)?
A.
8x+3y=24
B.
Y= -8/3x+8
C.
3x+8y=64
Correct Answer A. 8x+3y=24
Explanation The standard form of an equation of a line is Ax + By = C, where A, B, and C are constants. To find the equation of a line passing through two points, we can use the formula (y - y1) = m(x - x1), where m is the slope of the line and (x1, y1) are the coordinates of one of the points.
Using the points (3,0) and (6,-8), we can calculate the slope as m = (-8 - 0) / (6 - 3) = -8/3.
Substituting the slope and one of the points into the formula, we get (y - 0) = (-8/3)(x - 3), which simplifies to y = -8/3x + 8.
To convert this to standard form, we multiply through by 3 to eliminate the fraction, resulting in 3y = -8x + 24. Rearranging the terms, we get 8x + 3y = 24, which matches the given answer.
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6.
If you are using linear interpolation, then you are estimating a data point ____________.
Correct Answer between the given data points
Explanation Linear interpolation is a method used to estimate a data point between two given data points. By using this technique, we can approximate the value of the missing data point based on the linear relationship between the two known data points. Therefore, the correct answer is that when using linear interpolation, we are estimating a data point between the given data points.
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7.
Solve. (absolute value of y-2) < 3
A.
Y-1
B.
Y
Correct Answer A. Y-1
Explanation The correct answer is y-1. To solve the inequality (absolute value of y-2) < 3, we can split it into two cases: when y-2 is positive and when y-2 is negative.
When y-2 is positive, the inequality becomes y-2 < 3, which simplifies to y < 5.
When y-2 is negative, the inequality becomes -(y-2) < 3, which simplifies to -y+2 < 3. Solving for y, we get y > -1.
Combining both cases, we find that the solution is -1 < y < 5. However, the question only asks for the value of y-1, so the correct answer is y-1.
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8.
Solve. 4r-5>7 or 4r-5<-9
A.
R>3 or r
B.
R-1
C.
R>3 or r>-1
D.
R>3 and r>-1
Correct Answer C. R>3 or r>-1
Explanation The correct answer is r>3 or r>-1. The given inequality can be solved by solving each inequality separately and then combining the results using the "or" operator. For the first inequality, 4r-5>7, we can add 5 to both sides and divide by 4 to get r>3. For the second inequality, 4r-5-1. Therefore, the solution is r>3 or r>-1.
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9.
Find two consecutive integers whose sum is 35.
A.
None
B.
6,7
C.
15,17
Correct Answer A. None
Explanation None of the given options satisfies the condition of two consecutive integers whose sum is 35. The options 6,7 and 15,17 are not consecutive integers. Therefore, the correct answer is None.
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10.
Simplify. [(4y+2y)-(7y-y)]+8
Correct Answer 7y+1
Explanation The given expression can be simplified by combining like terms. First, we simplify the expression inside the parentheses by subtracting y from 7y, which gives us 6y. Then, we combine the terms outside the parentheses by adding 4y and 2y, which gives us 6y. Adding 6y and 6y gives us 12y. Finally, we add 12y to 8, which gives us 12y+8. Therefore, the simplified form of the expression is 12y+8.
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11.
What is the definition of parallel lines?
A.
1. the two slopes cannot equal each other. 2. the y-intercepts must equal each other.
B.
Everthing must equal -1
C.
Everything must equal 0
D.
1. the first slope must equal the second slope. 2. the y-intercepts cannot equal each other.
Correct Answer D. 1. the first slope must equal the second slope. 2. the y-intercepts cannot equal each other.
Explanation Parallel lines are defined as lines that are always the same distance apart and will never intersect. The first slope must equal the second slope because if the slopes are different, the lines will have different steepness and will eventually intersect. On the other hand, the y-intercepts cannot equal each other because if they do, the lines will coincide and will not be parallel. Therefore, the correct answer is that the first slope must equal the second slope and the y-intercepts cannot equal each other.
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12.
Given (1,1) and (-2, 3) state wich quadrant each belongs in.
Correct Answer (1,1) I
(-2,3) II
Explanation The point (1,1) is located in the first quadrant because both the x and y coordinates are positive. On the other hand, the point (-2,3) is located in the second quadrant because the x coordinate is negative and the y coordinate is positive.
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13.
Write the following out. 8.92635x10^{8}
Correct Answer 892635000
Explanation The given expression, 8.92635x108, represents a decimal number multiplied by 10 raised to the power of 8. This means that the decimal point is shifted 8 places to the right. When we perform this operation, we get the value 892635000, which is the same as the given answer.
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14.
Simplify.5x10^{-3}/2x10^{-4}
Correct Answer 25
Explanation The given expression is a division of two numbers in scientific notation. To simplify, we can divide the coefficients (5/2) and subtract the exponents (10^-3 / 10^-4). When we subtract the exponents, we get 10^-3-(-4) which simplifies to 10^-3+4 = 10^1. Therefore, the expression simplifies to (5/2) * 10^1 which is equal to 25.
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15.
True or false?Parallel lines have no solution because they never intersect.
Correct Answer True
Explanation Parallel lines are lines that never intersect, meaning they do not have a common point. Therefore, it is correct to say that parallel lines have no solution, as there is no solution to finding a point of intersection between them.
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16.
The corner of a rectangle is made up of two angles. The measure of one angle is 10 degrees more than three times the measure of the other. What are the measures of the two angles? (Hint: recall the degree measure of the corner of a rectangle.)
Correct Answer Corner x= 20 Corner y=70
Explanation The corner of a rectangle is formed by two adjacent sides. Let's assume that one angle is x degrees and the other angle is y degrees. According to the given information, the measure of one angle (x) is 10 degrees more than three times the measure of the other angle (y). Mathematically, this can be represented as x = 3y + 10.
Since the corner of a rectangle is a right angle, the sum of the two angles is 90 degrees. So, we can write another equation as x + y = 90.
Now, we have a system of two equations:
x = 3y + 10
x + y = 90
By solving these equations simultaneously, we find that x = 20 and y = 70. Therefore, the measures of the two angles are 20 degrees and 70 degrees.
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17.
A Culture of bacteria has 20 cells. Each cell divides to form 2 cells every half hour. How many cells are there after 4 hours?
Correct Answer 5,120
Explanation Starting with 20 cells, each cell divides into 2 cells every half hour. After 1 hour, there will be 40 cells. After 2 hours, there will be 80 cells. After 3 hours, there will be 160 cells. Finally, after 4 hours, there will be 320 cells. However, since each cell divides into 2 cells, this process can be represented as exponential growth. Using the formula 20 * 2^(hours/0.5), we can calculate that after 4 hours, there will be 5,120 cells.
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18.
What is the definition when multiplying radicals?
Correct Answer the square root of a times the square root of b equals the square root of ab
Explanation When multiplying radicals, the rule states that the square root of a multiplied by the square root of b is equal to the square root of ab. This means that when multiplying two radicals, you can simplify the expression by multiplying the numbers inside the radicals and taking the square root of the product.