Answer: ~54.54 units squared, or 25*pi - 24
Step-by-step explanation:
To find this, we need to find both the area of the triangle and circle, and then subtract the area of the triangle from the area of the circle.
Area of triangle: ![A = (bh)/2](https://tex.z-dn.net/?f=A%20%3D%20%28bh%29%2F2)
Area of circle: ![A = \pi r^2](https://tex.z-dn.net/?f=A%20%3D%20%5Cpi%20r%5E2)
To find the radius, we first need to find the hypotenuse of the triangle, which happens to be the diameter of the circle.
Pythagorean Theorem:
, where a and b are sides and c is the hypotenuse.
6^2 + 8^2 = c^2
36 + 64 = 100, c = 10
Knowing that the diameter is 10, we also know that the radius is 5.
Area of the circle with a radius of 5 is 25*pi, or 78.54~
Area of the triangle with side lengths of 6 and 8 is 24.
78.54 - 24 = 54.54 units squared.
One way is to make it into slope intercept form which is
y=mx+b
m=slope
b=y intercept or where the line will go though the y axis
treat the equal to or greater than sign as equals for now
5x-y=5
subtract y from both sides
5x=5+y
subtract 5
5x-5=y
put the sign back in
5x-5 ≥ y
reverse
y ≤ 5x-5
one way is to subsitute values and get values out so
if x=1 then
y≤5(1)-5
y≤0
(x,y)
(1,0)
(2,5)
(3,10)
(4,15)
(0,-5)
plot the points
then the ≤ sign
since ther is an underline, that means that the points are included so draw a solid line through the points
then figure out which side to shade on
the easy way is, is the point (0,0) a solution?
subsitute
0 ≤ 5(0)-5
0 ≤ -5
false so we shade the section that does not include the point (0,0) in it
the graph would look like this attachment
Bobby has the most pencils. You have to convert all of the fractions so they have the same number in the denominator. To do this you have to find the lowest common multiple (LCM) for this question, all of the denominators have the number 24 in common. If you divide 24 by 6 you get 4 then you have to multiply 4 by the numerator to make sure that the fraction is being fully converted. You will get (8/24). Apply this to all three fractions and you will get (8/24), (16/24), (12/24). 16 is the largest number therefore bobby would have the most pencils. To check this you can simplify all of the fractions back down. Do 8/24 and you will get .33333. If you do 2/6 then you get .33333, they are the same number which means you converted correctly and you have the right answer. Hope this helps!
Answer:
x2 + x - 20
Step-by-step explanation:
multiply the two : x(x+5) - 4 (x+5)