1. Mandy kept track of the trade-in value of a collector’s coin for several months through February of this year. She determined the line of best fit for the data was y = 4x + 12, where y is the trade-in value, in dollars, x months after February of this year. According to the equation, when will the trade-in value of the coin be $44?
a) December of the same year
b) October of the same year
c) April of the following year
d) June of the following year
2. Two sides of a triangle have lengths of 8 inches and 12 inches. Which could be the length of the third side?
a)2 in.
b)4 in.
c)16 in.
d)20 in.
3.Dino used three pieces of string to make a model of a triangle in art class. The lengths of two of the pieces of string were 3 inches and 8 inches. Which could be the length in inches of the third piece of string Dino used?
a)2
b)7
c)5
d)3
4. A figure is dilated with the center at the origin and a scale factor of 1/4. Which statement is true?
a)The coordinates are decreased by 4.
b)The coordinates are increased by 4.
c)The coordinates are multiplied by 4.
d)The coordinates are divided by 4.
5. Shara's new lawn sprinkler watered a circular area with three times the radius of the old sprinkler. How many times greater was the area watered by the new sprinkler than the area watered by the old sprinkler?
a)3
b)6
c)9
d)36
6.How many x-intercepts does the graph of the equation below have ?
y = 2x^2 - x - 3
a)3
b)2
c)1
d)0
1. To find when the trade-in value of the coin will be $44, we can substitute 44 for y in the equation y = 4x + 12 and solve for x.
44 = 4x + 12
Subtracting 12 from both sides:
32 = 4x
Dividing both sides by 4:
8 = x
Therefore, the trade-in value of the coin will be $44 in 8 months after February of this year. This would be in October of the same year.
So the answer is b) October of the same year.
2. According to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
For our given triangle with side lengths of 8 inches and 12 inches, let's consider the third side:
a) 2 inches - 8 + 2 < 12, so this is not possible.
b) 4 inches - 8 + 4 = 12, so this is possible.
c) 16 inches - 8 + 16 > 12, so this is possible.
d) 20 inches - 8 + 20 > 12, so this is possible.
Therefore, the possible lengths for the third side of the triangle are:
b) 4 inches, c) 16 inches, and d) 20 inches.
3. Using the triangle inequality theorem again, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
For our given triangle with side lengths of 3 inches and 8 inches, let's consider the third side:
a) 2 inches - 3 + 2 < 8, so this is not possible.
b) 7 inches - 3 + 7 > 8, so this is possible.
c) 5 inches - 3 + 5 > 8, so this is possible.
d) 3 inches - 3 + 3 < 8, so this is not possible.
Therefore, the possible lengths for the third piece of string used by Dino are:
b) 7 inches and c) 5 inches.
4. When a figure is dilated with a scale factor of 1/4 centered at the origin, the coordinates of the figure are multiplied by the scale factor.
Therefore, the correct statement is:
c) The coordinates are multiplied by 4.
5. The area of a circle is given by A = πr^2, where r is the radius of the circle.
If the new sprinkler has a circular area with three times the radius of the old sprinkler, then the area of the new sprinkler is (3r)^2 = 9r^2.
Comparing this to the old sprinkler's area:
9r^2 / (πr^2) = 9
Therefore, the area watered by the new sprinkler is 9 times greater than the area watered by the old sprinkler.
So the answer is c) 9.
6. To find the x-intercepts of the graph of the equation y = 2x^2 - x - 3, we set y equal to 0 and solve for x.
0 = 2x^2 - x - 3
We can either factor this quadratic equation or use the quadratic formula to find the solutions.
Factoring:
0 = (2x + 1)(x - 3)
Setting each factor equal to zero:
2x + 1 = 0 --> x = -1/2
x - 3 = 0 --> x = 3
Therefore, the graph of the equation has 2 x-intercepts.
So the answer is b) 2.
1. To find out when the trade-in value of the coin will be $44, we can substitute the value of y into the equation y = 4x + 12 and solve for x.
4x + 12 = 44
Subtract 12 from both sides:
4x = 32
Divide both sides by 4:
x = 8
Since x represents the number of months after February, the trade-in value of the coin will be $44 in October of the same year. Therefore, the answer is (b) October of the same year.
2. According to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
In this case, the two given sides have lengths of 8 inches and 12 inches.
So, for the length of the third side to be possible, it should satisfy the condition:
8 + 12 > x
20 > x
Therefore, the possible lengths for the third side should be greater than 20 inches.
Among the given options, only option (c) 16 inches satisfies this condition. So, the answer is (c) 16 in.
3. Again, using the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
In this case, the two given lengths are 3 inches and 8 inches.
So, for the length of the third side to be possible, it should satisfy the condition:
3 + 8 > x
11 > x
Therefore, the possible lengths for the third side should be greater than 11 inches.
Among the given options, option (b) 7 inches satisfies this condition. So, the answer is (b) 7.
4. When a figure is dilated with the center at the origin and a scale factor of 1/4, the coordinates of the points are multiplied by the scale factor.
So, the correct answer is (c) The coordinates are multiplied by 4.
5. The area of a circle is proportional to the square of its radius.
If the new sprinkler has three times the radius of the old sprinkler, the area of the new sprinkler will be (3^2) = 9 times greater than the area of the old sprinkler.
Therefore, the answer is (c) 9.
6. To find the x-intercepts of the equation y = 2x^2 - x - 3, we can set y equal to zero and solve for x.
0 = 2x^2 - x - 3
This equation can be factored or solved using the quadratic formula.
Using factoring, we can rewrite the equation as:
0 = (2x + 1)(x - 3)
Setting each factor equal to zero gives us two possible values for x:
2x + 1 = 0 -> 2x = -1 -> x = -1/2
x - 3 = 0 -> x = 3
Therefore, the equation has two x-intercepts, and the answer is (b) 2.
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