Step-by-step explanation:
let's look at the full numbers under the square roots when bringing the external factors back in :
sqrt(9×9×2) - sqrt(3×3×7) + sqrt(8) - sqrt(28)
and let's present these numbers as the product of their basic prime factors
sqrt(3×3×3×3×2) - sqrt(3×3×7) + sqrt(2×2×2) - sqrt(2×2×7)
now we see that we have 2 pairs of square roots : 1 pair ends with a factor of 2, and one pair with a factor of 7.
let's combine these
sqrt (3×3×3×3×2) + sqrt(2×2×2) - sqrt(3×3×7) - sqrt (2×2×7)
and now we move the factors of 2 and 7 back out in front (of course, we need to apply the square root on these factors) :
9×sqrt(2) + 2×sqrt(2) - 3×sqrt(7) - 2×sqrt(7) =
= (9+2)×sqrt(2) - (3+2)×sqrt(7) = 11×sqrt(2) - 5×sqrt(7)
and that is the first answer option.
Answer:
Step-by-step explanation:
Let the number is x.
<u>2/3 of a number is 10:</u>
<u>0.15 times of the number is:</u>
Correct choice is d
Answer:
Step-by-step explanation:
11/5 is 2 1/5 reduced
Answer:
Answers in the pics
Step-by-step explanation:
If you have any questions about the way I solved it, don't hesitate to ask ÷)
Answer:
The new dimensions are 6 ft and 4 ft.
Step-by-step explanation:
Let x = side of original square.
The sides are increased by 3 ft and 1 ft, so the new side lengths of the rectangle are
x + 3 and x + 1
The area of the rectangle is length × width.
area = (x + 3)(x + 1)
area = x² + 4x + 3
The area is 24 ft².
x² + 4x + 3 = 24
x² + 4x - 21 = 0
(x + 7)(x - 3) = 0
x + 7 = 0 or x - 3 = 0
x = -7 or x = 3
x + 3 = 3 + 3 = 6
x + 1 = 3 + 1 = 4
The new dimensions are 6 ft and 4 ft.
