Answer:
12) y=3x-15
14) y=-1/2x
16) y=13x-105
Step-by-step explanation:
Parallel lines always have the same slopes but different y-intercepts. So, we can make the equation (b is y-intercept of new equation):
12) y=3x+b
14) y=-1/2x+b
16) y=13x+b
now, we can plug in each of the coordinates given to these equations.
12) (4,-3): 4 is x, -3 is y.
-3=3(4)+b
simplify: b= -15
14) (-4,2): -4 is x, 2 is y
2=-1/2(-4)+b
simplify: b=0
16) (9,12): 9 is x, 12 is y
12=13(9)+b
simplify: b=-105
Now, plug in those numbers to your equation for b value.
12) y=3x-15
14) y=-1/2x
16) y=13x-105
*for 14 we don't need to write anything after -1/2x because b=0*
Answer:
E) 613.9 m2
Step-by-step explanation:
sum of measures of interior angles of a polygon of n sides:
(n - 2)180
For a pentagon:
(5 - 2)180 = 3(180) = 540
measure of one interior angle of a regular pentagon:
540/5 = 108
Draw a segment from the center of the pentagon to the top vertex. Now you have a right triangle.
The triangle has a 90 deg angle where the segment in the figure meets the side of the pentagon. Let half of the side of the pentagon be x. x is a side of the right triangle.
For the 54 deg angle in the triangle, 13 m is the opposite leg, and x is the adjacent leg.
tan A = opp/adj
tan 54 = 13/x
x = 13 m/tan 54 = 9.445 m
x is half of the side of the pentagon.
2x is the side of the pentagon.
2x = 2(9.445 m) = 18.89 m
The given 13 m segment is the apothem of the pentagon.
A = nsa/2
where n = number of sides, s = length of 1 side, a = length of apothem
A = (5)(18.89 m)(13 m)/2
A = 613.9 m^2
Answer: E) 613.9 m2
Answer:
a. From x = -2 to x = 0, the average rate of change for both functions is negative
d. The quadratic function, y = x², has an x-intercept at the origin
Step-by-step explanation:
From x = -2 to x = 0, the rate of change is negative because both functions are going in a downward slope. The quadratic function y = x² touches the x-axis right at (0, 0), meaning it has an x-intercept at the origin.
The second answer is incorrect because y = x² does not intersect the other parabola at (2, 3). The third is incorrect because y = x² + 3 does not even touch the x-axis. The fifth is incorrect because the rate of change is negative, not positive. Finally, the sixth is incorrect because y = x² + 3 does not intersect the other parabola at (2, 7). Hope this helps! Feel free to ask any questions!
