...6 and 10 are roots, so x – 6 and x – 10 are factors.
y = a(x – 6)(x – 10).....plug in the point (8, 2) and solve for a:
2 = a(8 – 6)(8 – 10)
2 = –4a
a = –1/2
...y = (–1/2)(x – 6)(x – 10)
...y = (–1/2)(x² – 16x + 60)
...y = (–x²/2) + 8x – 30 <<<------Answer, or:
...y = (–1/2)(x – 8)² + 2 <<<------Answer
The figure consists of a rectangle and a circle.
first lets find the sides of the triangle
sides of the triangle are 4+4=8 and 3+1=4
therefore area of the rectangle is 8*4=32
now area of semicircle =πr^2/2 = π2^2/2=2π=6.3
we have to add the area of rectangle with the area of semicircle
this is because it the given figure no part of area of circle and rectangle are in common.
therefore total area of given figure = 32+6.3=38.3
The explicit rule will be an = 1/3 + (n - 1)
<h3>An explicit formula for a sequence</h3>
Given the following information
a2 = a1 + 1
a2 = 4/3
For the third term
a3 = a2 + 1
a3 = 4/3 + 1
a3 = 7/3
The resulting seqence is 1/3, 4/3, 7/3
The sequence is an arithmetic sequence
a = 1/3
d = 1
The explicit rule will be an = 1/3 + (n - 1)
Learn more on explicit rule here: brainly.com/question/2059043
Answer:
Step-by-step explanation:
<u>Given points:</u>
The perpendicular bisector passes through the midpoint.
<u>Finding the coordinates of the midpoint first:</u>
- x = (-2 + 6)/2 = 2, y = (-2 + 0)/2 = -1
<u>Next finding the slope of AB:</u>
- m = (0 - (-2))/(6 - (-2)) = 2/8 = 1/4
The perpendicular lines have negative-reciprocal slopes.
<u>The line will have a slope of -4 and pass through the point (2, -1)</u>
- y - (-1) = -4(x - 2)
- y + 1 = -4(x - 2) - point-slope form
- y = -4x + 7 - slope-intercept form
