Angle 5x+7 is equal to the the sum of its remote interior angles, which we are given as x+15 and 6x-26. Therefore, 5x+7=x+15+6x-26. We will combine like terms to get 5x+7=7x-11. Move the 7x over to the other side by subtraction and the 7 to the other side by subtraction to get -2x = -18. That leaves us with an x value of 9. There you go!
Answer:
S1) False. 2³ is 2 × 2 × 2 which is <u>8, not 6.</u>
S2) False. ( 2x / 3y ^ (2) ) ^ (3) =
( (2x) ^ (3) / ( (3y) ^ (2) ) ^ (3) ) = (2)³ × (x)³ / (3)³ × (y²)³ = 8 × x³ / 27 × y<u>⁶</u> = 8x³ / 27y<u>⁶</u><u>.</u>
<u>i.e </u><u>(</u><u>a^</u><u>b</u><u>)</u><u>^</u><u>c</u><u> </u><u>=</u><u> </u><u>a^</u><u>(</u><u>b </u><u>×</u><u> </u><u>c)</u><u>.</u>
S3) True.
S4) True.
S5) False. x^(-3) = 1 / x^(3) ≠ 1 / 3x
Answer:
731 of the projects received a ribbon.
Step-by-step explanation:
850 x 0.86 = 731
Hope this helps!
![\bf 2sin(x)cos(x)=sin(x)\sqrt{2}\implies 2sin(x)cos(x)-sin(x)\sqrt{2}=0 \\\\\\ sin(x)~[2cos(x)-\sqrt{2}]=0\\\\ -------------------------------\\\\ sin(x)=0\implies \measuredangle x=0~~,~~\pi \\\\ -------------------------------\\\\ 2cos(x)-\sqrt{2}=0\implies 2cos(x)=\sqrt{2}\implies cos(x)=\cfrac{\sqrt{2}}{2} \\\\\\ \measuredangle x=\frac{\pi }{4}~~,~~\frac{7\pi }{4}](https://tex.z-dn.net/?f=%5Cbf%202sin%28x%29cos%28x%29%3Dsin%28x%29%5Csqrt%7B2%7D%5Cimplies%202sin%28x%29cos%28x%29-sin%28x%29%5Csqrt%7B2%7D%3D0%0A%5C%5C%5C%5C%5C%5C%0Asin%28x%29~%5B2cos%28x%29-%5Csqrt%7B2%7D%5D%3D0%5C%5C%5C%5C%0A-------------------------------%5C%5C%5C%5C%0Asin%28x%29%3D0%5Cimplies%20%5Cmeasuredangle%20x%3D0~~%2C~~%5Cpi%20%5C%5C%5C%5C%0A-------------------------------%5C%5C%5C%5C%0A2cos%28x%29-%5Csqrt%7B2%7D%3D0%5Cimplies%202cos%28x%29%3D%5Csqrt%7B2%7D%5Cimplies%20cos%28x%29%3D%5Ccfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%0A%5C%5C%5C%5C%5C%5C%0A%5Cmeasuredangle%20x%3D%5Cfrac%7B%5Cpi%20%7D%7B4%7D~~%2C~~%5Cfrac%7B7%5Cpi%20%7D%7B4%7D)
now, we're not including the III and II quadrants, where the cosine has an angle of the same value, but is negative, because the exercise seems to be excluding the negative values of √(2).
Answer/Step-by-step Explanation:
==>Given:
Ratio of cost of 1m polyester fabric to 1m of cotton fabric = 2:7
I.e. if 1m of polyester fabric = £2, then 1m of cotton fabric = £7.
==>Required:
a. Cost of polyester fabric for the following lengths:
i) 6m ii) 8m iii) 9m
Thus, having known that cost of 1m polyester fabric = £2, therefore,
i) 6m polyester fabric = 6×2 = £12
ii) 8m polyester fabric = 8×2 = £16
iii) 9m polyester fabric = 9×2 = £18
b. Cost 8 cotton fabric for the following lengths:
i) 2m ii) 6m iii) 8m iv) 9m
Thus, since 1m of cotton fabric = £7, therefore,
i) 2m cotton fabric = 2×7 = £14
ii) 6m cotton fabric = 6×7 = £42
iii) 8m cotton fabric = 8×7 = £56
iv) 9m cotton fabric = 9×7 = £63
