Step-by-step explanation:
Move expression to the left side and change its sign
5
y
−
3
+
10
y
2
−
y
−
6
−
y
y
+
2
=
0
Write
−
y
as a sum or difference
5
y
−
3
+
10
y
2
+
2
y
−
3
y
−
6
−
y
y
+
2
=
0
Factor out
y
and
−
3
from the expression
5
y
−
3
+
10
y
(
y
+
2
)
−
3
(
y
+
2
)
−
y
y
+
2
=
0
Factor out
y
+
2
from the expression
5
y
−
3
+
10
(
y
+
2
)
(
y
−
3
)
−
y
y
+
2
=
0
Write all numerators above the least common denominator
5
(
y
+
2
)
+
10
−
y
(
y
−
3
)
(
y
+
2
)
(
y
−
3
)
=
0
Distribute
5
and
−
y
through the parenthesis
5
y
+
10
+
10
−
y
2
+
3
y
(
y
+
2
)
(
y
−
3
)
=
0
Collect the like terms
8
y
+
20
−
y
2
(
y
+
2
)
(
y
−
3
)
=
0
Use the commutative property to reorder the terms
−
y
2
+
8
y
+
20
(
y
+
2
)
(
y
−
3
)
=
0
Write
8
y
as a sum or difference
−
y
2
+
10
y
−
2
y
+
20
(
y
+
2
)
(
y
−
3
)
=
0
Factor out
−
y
and
−
2
from the expression
−
y
(
y
−
10
)
−
2
(
y
−
10
)
(
y
+
2
)
(
y
−
3
)
=
0
Factor out
−
(
y
−
10
)
from the expression
−
(
y
−
10
)
(
y
+
2
)
(
y
+
2
)
(
y
−
3
)
=
0
Reduce the fraction with
y
+
2
−
y
−
10
y
−
3
=
0
Determine the sign of the fraction
−
y
−
10
y
−
3
=
0
Simplify
10
−
y
y
−
3
=
0
When the quotient of expressions equals
0
, the numerator has to be
0
10
−
y
=
0
Move the constant,
10
, to the right side and change its sign
−
y
=
−
10
Change the signs on both sides of the equation
y
=
10
Check if the solution is in the defined range
y
=
10
,
y
≠
3
,
y
≠
−
2
∴
y
=
10
Answer: The ball hits the ground at 5 s
Step-by-step explanation:
The question seems incomplete and there is not enough data. However, we can work with the following function to understand this problem:
(1)
Where 
models the height of the ball in meters and 
the time.
Now, let's find the time when the ball Sara kicked hits the ground (this is when 
):
(2)
Rearranging the equation:
(3)
Dividing both sides of the equation by 
:
(4)
This quadratic equation can be written in the form 
, and can be solved with the following formula:
(5)
Where:
Substituting the known values:
(6)
Solving we have the following result:
This means the ball hit the ground 5 seconds after it was kicked by Sara.
Answer: The answer is A.
Step-by-step explanation:
The formula for the area of circles:
A = πr^2
Plug in the radius
A = π8^2
A = π64
A = 201.06192983/ 201 (rounded)
Answer:
Step-by-step explanation:
Sara's base pay is $80
(a) The 9t represents the additional amount of money that she earns if she gives instruction for t hours. 9 stands for $9 per hour
b)The term in the expression is t which stands for the number of hours that she instructs. The coefficient is 9 which stands for the hourly rate
c) The expression for 7 hours would be
We will substitute t into 80 + 9t. It becomes
80 + 9×7
d) in all, she will earn
80 + 9×7 = $143
