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
To find the volume of a dome, you would have to find the volume of the sphere, theoretically, and then divide it by two. To calculate the volume, we would use the formula 4/3
. The radius (r) in this case is half of the diameter which is 14. 4 x 3.14 (pi) = 12.56. 12.56 x 14 x 14 x 14 (2744) = 34464.64. If we divide this number by 3, we get 11488.2133. If we divide this by 2 (to get the dome), we get 5744.10656. Which would be 5744.1 rounded to the nearest tenth.
Hello from MrBillDoesMath!
Answer:
33769/181
Discussion:
Each term contains "x" so factoring it out gives
x( 1/4 + 1/14 + 1/17) = 71 (*)
Use common factor (17*14*4 = 952) as the denominator to combine terms:
1/4 = (17*14)/ 952 = 238/952
1/14 = (17*4)/952 = 68/952
1/17 = (14*4)/952 = 56/952
so 1/4 + 1/14 + 1/17 = (238 + 68 + 56)/ 952 = 362/952 = 181/476
Substituting in (*) gives
x ( 181/476) = 71 => multiply both sides by 476/181
x = (71 * 476)/181 => 71* 476 =33769
x = 33769/181
Thank you,
MrB
Answer:
40% . The single reduction together is 40%.
Step-by-step explanation:
Let the bicycle cost is x before reduced price.
First 25% is reduced and again 20% further reduced.
Let the single reduction is y% if the two reduction together are equal.
Solution,
Case .1
reduction cost
%
The cost of bicycle after reduction of 25% is
cost of reduction further reduction of 20% 
%
The new cost of bicycle is further reduction of 20% is
Case.2
if single reduction is done new cost of cycle is equal
%=
%
single reduction of a cycle is 40%
Assuming you want the slope, the answer is -2/-3.
X-change: -2
Y-change: -3
X-c/Y-c = -2/-3
If -2/-3 is not an answer, try 2/3 or .666 (infinite 6s).
