Answer: Expressions A and C yield the same result.
Step-by-step explanation:
When simplifying, it turns out that only A and C reduce to 6x-4
Answer:
The photographer sold 72 small photos and 54 large photos.
Step-by-step explanation:
We can create a system of equations based on the details provided. Let X represent small photos and Z represent large photos.
It is given that the total number of photos sold is 126:
X + Z = 126
Additionally, she generated $2,250 from selling specific amounts of small and large photos, stated as:
$2,250 = $11X + $27Z
From the first equation, we know X=126-Z. Substituting this into the second equation gives:
2,250 = 11(126-Z) + 27Z
2,250 = 1,386 - 11Z + 27Z
2,250 - 1,386 = 16Z
864 = 16Z
Z = 864/16
Z = 54, which indicates the number of large photos sold. To find X:
X = 126 - Z
X = 126 - 54
X = 72, representing the small photos sold.
Let L represent the yards in a roll of lace ribbon and S represent the yards in a roll of satin ribbon. We can formulate two equations: 3L + 2S = 120 yards (Equation 1) and 2L + 4S = 160 yards (Equation 2). If we multiply Equation 1 by 2 and subtract Equation 2, we have: 6L + 4S = 240 yards (Equation 1) and 2L + 4S = 160 yards (Equation 2). Thus, 4L equals 80 yards, leading to L equating to 20 yards. For Equation 1, substituting gives 3(20 yards) + 2S = 120 yards, leading to 2S equal to 60 yards, so S equals 30 yards. Therefore, a roll of lace ribbon contains 20 yards, while a roll of satin ribbon has 30 yards.
Sample Response: Rotations fall under rigid transformations, meaning they keep the figure’s size, lengths, shapes, and angle measurements unchanged. Despite this, the orientation of the figure does change. Line segments that connect the center of rotation to points on both the original figure and its rotated image are congruent in length. However, corresponding edges between matching vertices do not run parallel to each other.
