The choices b and c are equivalent to 
.
Step-by-step explanation:
Step 1:
First, we need to bring the fraction to its simplest form. To do so, we divide the numerator and the denominator by the greatest factor.
The greatest factor for 4 and 6 is 2. So we divide it by 2.
So 
.
Step 2:
Similarly, we need to do the same for all the given four options.
a. 
, the greatest factor for 2 and 4 is 2. So we divide the fraction by 2.
So 
.
b. 
, the greatest common factor for 8 and 12 is 4. So we divide the fraction by 4.
So 
.
For options c and d, 1 is the greatest factor so they cannot be simplified. They remain as they are.
Step 3:
So options b and c are equal to the simplification of i.e. 
.
Answer:
$1,700.
Step-by-step explanation:
Since Cándido normally pays $ 875 for bodily injury and property damage insurance, and his insurance company increases premiums by 150% for 1 accident, 200% for 2-3 accidents, and 250% for 4 accidents, to find his premium for the year after he has three accidents to the nearest dollar, the following calculation must be performed:
875 x 200 / 100 = X
875 x 2 = X
1,700 = X
Therefore, his premium for the year after he has three accidents is $1,700.
Answer:
the volume of the solid is 
Step-by-step explanation:
Given the data in the question;
y = x and y = x²
so
x = x²
x - x² = 0
Radius will be; r = ( x - x² )/2
Area of the circular disk πr² = π[ ( x - x² )/2 ]²
A = 
( x - x² )²
So, our volume will be;
V = ₀∫¹ A(x) dx
we substitute
= ₀∫¹ ( x - x² )² dx
{ lets expand; ( x - x² )² = x(x-x²) -x²(x-x²) = x² - x³ - x³ + x⁴ = x² + x⁴ - 2x³ }
so we have;
= ₀∫¹ ( x² + x⁴ - 2x³ ) dx
= 
+ 
- 
![]^1_0](https://tex.z-dn.net/?f=%5D%5E1_0)
= [ 
+ 
- ]
= [ 
]
V =
Therefore, the volume of the solid is
Answer:5p^3-2p^2-7p+1
Step-by-step explanation:
-3p^3+5p+(-2p^2)+(-4)-12p+5-(-8p^3)
open brackets
-3p^3+5p-2p^2-4-12p+5+8p^3
Collect like terms
-3p^3+8p^3-2p^2+5p-12p-4+5
5p^3-2p^2-7p+1
