Looks more like Trig than Algebra II
They want us to apply the sum angle formula to 
5π/6 is 150°; I find it easier to think in degrees.
When the tangent of x is 3/4 that's a right triangle with opposite 3, adjacent 4 so hypotenuse 5. So a sine of 3/5 and a cosine of 4/5, both positive because we're told x is in the first quadrant.
The sine sum angle formula is
We know sin 150° = sin 30° = 1/2 and cos 150° = - cos 30° = -√3/2
Third choice
Answer: the slope is -1/15 and it means that the distance from home decreases 1/15 units per minute of walk, which indicates the your are going home.
Explanation:
The equation d = 4 - (1/5)t has these features:
- it is a linear (first degree) equation/
- d is the dependent variable, distance from home.
- t is the independent variable, minutes of walk
- 4 is the constant term and it is the value of d when t = 0, which means that it is the vertical axis intercept and represents the initial distance from home.
- - ( 1/15) is the coefficient of the independent variable, it is the slope of the equation, and means the rate of change of the distance per minute of walk.
- this slope, since it is negative, means that the distance decreases as times goes on. It means that each minute of walk the distance decreases 1/15 unit.
- you can find when the distance is zero, by doing the variable d = 0:
d = 0 = 4 - (1/15)t ⇒ t = 4×15 = 60 min.
The given equation, d = 4 - (1/5)t is a linear equation, whose y-intercept form is y = mx + b.
- m is the slope, therefore it is - 1/15.
- 4 is the y-intercept, therefore it is 4.
The domain of the function is the interval [0, 60], meaning that those are the minutes of the walk.
The range of the function is the interval [4, 0] meaning that the distance goes from 4 to 0 units.
You have plenty information to do the graph:
- label the horizontal axis t in minutes
- do marks at 0, 5, 10, 15, 20, 25, .... up to 60 on the horizontal axis
- lable the vertical axis d
- do marks at 4, 3, 2, 1, on the vertical axis
- draw the points (0, 4) and (60,0)
- draw a segment joining those two points.
You can see the graph in the image attached.
So,
Josh has 110 comic books total, and 82 of them feature superheroes. To find the percentage, just divide 82 by 110.
To convert to a percent, just move the decimal place two places to the left and add a percent sign.
Rounding, we get:
75%
So about 75% of Josh's comic books feature superheroes.
7x + 15x + 27 = 247
22x = 247 -27
22x =225
X= 10.22
