Factor first: (sinx+1)(2sinx-1)=0
sinx+1=0 or 2sinx-1=0
sinx=-1 or sinx=1/2
0≤x≤360, so x=270, or x=30 or x=150
1) 3^6 * 3^5 = 3^11
2) 2^3 * 2^7 = 2^10
3)7^2*7^6 = 7^8
hope it helps
Step-by-step explanation:
xy + 10 = 0. => y = -10/x.
2x + 3y = 7. => 3y = -2x + 7, y = -2/3 x + 7/3.
When -10/x = -2/3 x + 7/3,
-10 = -2/3 x² + 7/3 x, 2/3 x² - 7/3 x - 10 = 0.
=> 2x² - 7x - 30 = 0
=> (2x + 5)(x - 6) = 0
=> x = -2.5 or x = 6.
dy/dx = d/dx [-10/x] = 10/x².
When x = -2.5, dy/dx = 10 / (-2.5)² = 1.6.
When x = 6, dy/dx = 10 / (6)² = 5/18.
Hence the gradients at the points are 1.6 and 5/18.
Hi, again!
First blank: multiplication property of equality
Both sides of the equation were multiplied by (1/2).
Second blank: m<E
Angle E is an inscribed angle intercepting arc FGD, so by the inscribed angle theorem, its measure is half the measure of the arc.
Third blank: m<G
Same explanation as the prior blank
Fourth blank: substitution property of equality
Since angle E is equal to half the measure of arc FGD, we can replace that term. Likewise with angle G.
Since we have the triangle, but don't know which side 4 is on, we have one where x is opposite a 50 degree angle (they are the same if across either 50 degree side) and another across the 80 degree one. In addition, it's really ratios and sin/cos/tan from there!
