Answer: John has 52 marbles in his collection
Step-by-step explanation:
Step 1
LET The number of marbles in John's collection can be represented by x. The and the number of marbles in Erica collection can be represented as =4x+ 10
The total number of marbles in both collections is 270 such that the expression to solve the equation will be
JOHN + ERICA = 270marbles
X + 4X+ 10= 270
Step 2--- solving
X + 4X+ 10= 270
5X+ 10= 270
5X= 270-10
5X= 260
X= 260/5
=52
John has 52 marbles in his collection
Erica has 4x + 10 = 4x 52 + 10=218 marbles
0 = -16t² + 36t + 4
0 = -8t² + 18t + 2 ← Complete the square to solve
-8(t² - 9t/2) = -2
8(t² - 9t/4 + 81/64) = 2 + 81/8
8(t - 9/8)² = 97/8
(t - 9/8)² = 97/64
t - (t = 0)
(h = 0) at:
<span>t = (9 + √97)/8 ≅ 2.356 seconds
</span>
The mechanical advantage of the block and tackle is that it is easier to lift a lock using multiple parts of the rope that go around the system of pulleys. If there are no friction, the mechanical advantage is exactly equal to the number of parts of the rope that are attached to the load.
Answer:
x =
25
/(1 − sin(y
)) and y ≠
π/2 +2πn
Step-by-step explanation:
Let's solve and simplify for x,
(x − 25
)/ x = sin(y)
Let's multiply both sides by x
((x − 25
)/x) *x= sin(y)*x
Then,
x − 25 = sin(y) * x
Let's add 25 to both sides
x − 25 + 25 = sin(y) * x + 25
If simplify again,
x = sin(y) * x + 25
Then we need subtract sin y x from both sides
x − sin(y) * x = sin (y)* x + 25 − sin (y)* x
It will equal:
x − sin (y)* x = 25
Factor x−sin(y) x: x(1−sin(y) ), then we get:
x (1 − sin(y)) = 25
Finally we need divide both sides by 1 − sin(y) ; y ≠π
/2
+ 2πn
And it will give us this equation:
x =
25
/(1 − sin(y
)) and y ≠
π/2 +2πn
