You have to cross multiply
7x3=21
21 divided by 6 = 3.5 or 3 1/2
Width of the rectangle is 2 units
Step-by-step explanation:
- Step 1: Let the width of the rectangle be x. Then the length = 8 +
. Find dimensions of the rectangle if its area = 18 sq. units
Area of the rectangle = length × width
18 = x (8 +
)
36 = x(16 + x) (Cross multiplying 2)
36 = 16x + x²
x² + 16x - 36 = 0
x² + 18x - 2x - 36 = 0 (Using Product Sum rule to factorize)
x(x + 18) - 2(x + 18) = 0
(x + 18)(x - 2) = 0
x = -18, 2 (negative value is neglected)
x = 2 units
Distance from home to store = 4 * 0.5 = 2 miles.
Time taken to return home = (2/12) * 60 =10 minutes.
Total distance traveled = 2 * 2 = 4 miles.
Total time taken = 30 + 10 = 40 minutes.
Average speed for entire trip = total distance / total time in hours.
After staring at this for a few seconds, I think the equation
![-5\sqrt{10}\cdot\sqrt{15}=[1]\sqrt{[2]}](https://tex.z-dn.net/?f=-5%5Csqrt%7B10%7D%5Ccdot%5Csqrt%7B15%7D%3D%5B1%5D%5Csqrt%7B%5B2%5D%7D)
is asking you to simplify the left hand side so that it has a form matching the right hand side, and [1] and [2] are placeholders. My guess is that they're supposed to be integers.
Notice that
![\sqrt{10}=\sqrt{5\cdot2}=\sqrt5\cdot\sqrt2](https://tex.z-dn.net/?f=%5Csqrt%7B10%7D%3D%5Csqrt%7B5%5Ccdot2%7D%3D%5Csqrt5%5Ccdot%5Csqrt2)
![\sqrt{15}=\sqrt{5\cdot3}=\sqrt5\cdot\sqrt3](https://tex.z-dn.net/?f=%5Csqrt%7B15%7D%3D%5Csqrt%7B5%5Ccdot3%7D%3D%5Csqrt5%5Ccdot%5Csqrt3)
![\implies\sqrt{10}\cdot\sqrt{15}=(\sqrt5)^2\cdot\sqrt2\cdot\sqrt3=5\sqrt{2\cdot3}=5\sqrt6](https://tex.z-dn.net/?f=%5Cimplies%5Csqrt%7B10%7D%5Ccdot%5Csqrt%7B15%7D%3D%28%5Csqrt5%29%5E2%5Ccdot%5Csqrt2%5Ccdot%5Csqrt3%3D5%5Csqrt%7B2%5Ccdot3%7D%3D5%5Csqrt6)
Then multiplying by -5, we have
![-5\sqrt{10}\cdot\sqrt{15}=-25\sqrt6](https://tex.z-dn.net/?f=-5%5Csqrt%7B10%7D%5Ccdot%5Csqrt%7B15%7D%3D-25%5Csqrt6)
so I believe [1] = -25, and [2] = 6.