The algebraic equation for small and large marbles are y=5x and z=3x+2. The number of small marbles is 310.The number of small marbles is 310.The number of large marbles is 188.
<u>Step-by-step explanation:</u>
From the given information, Amy has three sizes of marbles.
Let x represents the medium marbles, y as small marbles and z as large marbles.
The number of small marbles she has is 5 times more than medium marbles. Then the algebraic equation for small marbles:
⇒ y = 5x.
The number of large marbles she has is two more than three times. Then the algebraic equation for large marbles:
⇒ z=3x+2.
And the sum of three marbles is 560.
∴x+y+z=560.
To find each number of marbles, substitute the algebraic equation of y and z in the above equation.
⇒x+5x+3x+2=560.
9x+2=560.
9x= 560-2.
9x=558.
x= 62.
∴The number of medium marbles is 62.
The number of small marbles y = 5x.
⇒y= 5(62)
y= 310.
∴The number of small marbles is 310.
The number of large marbles z = 3x+2.
⇒z= 3(62)+2
z= 186+2.
z=188.
∴The number of large marbles is 188.
Answer is A
Hope this helps
I think it’s irrational, because the 5 is repeating
This is a simple percentage question. 6/100 * 1000 = 60 people have forgotten
Octagon, stop sign.
Eight isoscles triangles. It looks like we're told the side is 9.9 and the height to the side (also called the apothem) is 12.
So each isosceles triangle has area (1/2)(9.9)(12) and we have eight of them,
area = 8(1/2)(9.9)(12) = 475.2
Answer: 475.2
Usually we wouldn't be told 9.9 -- this is the baby version. We know each of those isoscles triangles has unique angle 360/8=45 degrees, so the apothem and half the side of the octagon are a right triangle with acute angle 22.5 degrees.
The area of the right triangle with long leg 12, short leg x,
tan 22.5 = x/12 or
x = 12 tan 22.5
Twice that is what we're told is 9.9; let's check:
2x = 24 tan 22.5 = 9.941125496954282
The area of the little right triangle is
(1/2) 12 × 12 tan 22.5
and there are 16 of these
16 (1/2) 12 × 12 tan 22.5 ≈ 477.174
