A rectangle has a perimeter of 28 units, an area of 48 square units, and sides that are either horizontal or vertical. If one ve
rtex is the point (−5, −7) and the origin is in the interior of the rectangle, find the vertex of the rectangle that is opposite (−5, −7).
1 answer:
Answer:
Opposite coordinate of (−5, −7) = (1,1)
Step-by-step explanation:
Let the sides of rectangle be a and b
Perimeter = 2 ( a+b ) = 28
a + b = 14
Area = ab = 48
The sides with sum 14 and product 48 is 8 and 6.
a = 8 and b = 6
Since origin is inside the circle, the side with 8 unit is parallel to y axis and side with 6 unit is parallel to x axis
Opposite coordinate of (−5, −7) = (−5+6, −7+8) =(1,1)
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Answer: x=0
Step-by-step explanation:
Multiply both sides of the equation by 35, the least common multiple of 5,7.
7×4x−5×3x=5×4x+5×5x
Multiply 7 and 4 to get 28.
28x−5×3x=5×4x+5×5x
Multiply −5 and 3 to get −15.
28x−15x=5×4x+5×5x
Combine 28x and −15x to get 13x.
13x=20x+25x
Combine 20x and 25x to get 45x.
13x=45x
Subtract 45x from both sides
13x−45x=0
Combine 13x and −45x to get −32x
−32x=0
Product of two numbers is equal to 0 if at least one of them is 0. Since −32 is not equal to 0, x must be equal to 0.
X=0
