Convert f(x) = 5x(x – 6) to standard form
1 answer:
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Answer:
Step-by-step explanation:
Answer:
- The scale factor is one-half
- The perimeter of the model is the product of the scale factor and the perimeter of the original rectangle
-The area of the reduced figure is (1/2)^2 = 1/4 times the area of the original figure
Step-by-step explanation:
The ratio of the length of the original rectangle to that of the reduced rectangle is 6 to 3, or a factor of 1/2. The ratio of the width of the original rectangle to that of the reduced rectangle is 2 to 1, or, again, a factor of 1/2. So, because this ratio of 1/2 is constant, we know the total scale factor is 1/2, making B correct.
The perimeter of a rectangle is: , where l is the length and w is the width. The perimeter of the reduced figure is: P = 2 * 3 + 2 * 1 = 6 + 2 = 8 units. The perimeter of the original figure is: P = 2 * 6 + 2 * 2 = 12 + 4 = 16 units.
Notice that 16 * (1/2) = 8, which means that the perimeter of the scale-factored, reduced rectangle is "the product of the scale factor (which is 1/2) and the perimeter of the original rectangle (which is 16)". So, C is correct.
The area of a rectangle is: , where l is the length and w is the width. The area of the reduced figure is: A = 3 * 1 = 3 units squared. The area of the original figure is: A = 6 * 2 = 12 units squared.
Notice that 12 * (1/4) = 3, which means that E is correct, but D is wrong.
Hope this helps!
Step-by-step explanation:
The question above is answered below.
Consecutive numbers are set of numbers that follow one another in ascending or descending order, e.g. 1, 2, 3, 4, 5....
The sum of three consecutive numbers = 72
Let the unknown consecutive numbers be represented by x+1, x+2 and x+3 such that:
Remove the brackets
Collect like terms and simplify
Make 3x subject of formula by subtracting 6 from both sides
To obtain the value of x, divide through by the coefficient of x, which is 3. Hence;
Since x = 22,
The smallest of these numbers is 23.
Check,
23 + 24 + 25 = 72