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. 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.
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
1. Y = 4x + 12 = $44.
4x = 44-12 = 32
X = 8 Months = Oct. of same yr.
2.C
3. 8 < x + 3
X > 8-3
X > 5.
7 > 5
Answer = b = 7.
1. To determine when the trade-in value of the coin will be $44, we can substitute y = 44 into 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
So, x is equal to 8 months after February. Since February is the starting month, we can count 8 months after to find the answer.
Now, let's determine the corresponding month:
February + 8 months = October
Therefore, the answer is b) October of the same year.
2. When a figure is dilated with a scale factor of 1/4 and the center of dilation is the origin, each coordinate is multiplied by the scale factor.
So, if the original coordinates of a point are (x, y), after the dilation, the new coordinates will be (1/4)x, (1/4)y.
Therefore, the answer is c) The coordinates are multiplied by 4.
3. In a triangle, the sum of the lengths of any two sides must be greater than the length of the remaining side.
Let's check which option satisfies this condition for the lengths of the three pieces of string:
a) 3 + 8 > 2 (False)
b) 3 + 8 > 7 (True)
c) 3 + 5 > 8 (True)
d) 3 + 3 > 8 (False)
From the options given, b) 7 and c) 5 satisfy the condition. Therefore, either 7 or 5 could be the length of the third piece of string Dino used.