Answer:
the two roots are x = 1 and x = 4
Step-by-step explanation:
Data provided in the question:
(x³ − 64) (x⁵ − 1) = 0.
Now,
for the above relation to be true the following condition must be followed:
Either (x³ − 64) = 0 ............(1)
or
(x⁵ − 1) = 0 ..........(2)
Therefore,
considering the first equation, we have
(x³ − 64) = 0
adding 64 both sides, we get
x³ − 64 + 64 = 0 + 64
or
x³ = 64
taking the cube root both the sides, we have
∛x³ = ∛64
or
x = ∛(4 × 4 × 4)
or
x = 4
similarly considering the equation (2) , we have
(x⁵ − 1) = 0
adding the number 1 both the sides, we get
x⁵ − 1 + 1 = 0 + 1
or
x⁵ = 1
taking the fifth root both the sides, we get
![\sqrt[5]{x^5}=\sqrt[5]{1}](https://tex.z-dn.net/?f=%5Csqrt%5B5%5D%7Bx%5E5%7D%3D%5Csqrt%5B5%5D%7B1%7D)
also,
1 can be written as 1⁵
therefore,
![\sqrt[5]{x^5}=\sqrt[5]{1^5}](https://tex.z-dn.net/?f=%5Csqrt%5B5%5D%7Bx%5E5%7D%3D%5Csqrt%5B5%5D%7B1%5E5%7D)
or
x = 1
Hence,
the two roots are x = 1 and x = 4
You should use Order of Operations or PEDMAS for this (Parenthesis, Exponents, Division and Multiplication in the order they appear, Addition and Subtraction in the order they appear). So we do the 2+12 because that is in parentheses first which gives 14-3+6. Next we do 14-3 because there are no exponents and no division or multiplication, which gives 11+6. This yields your answer, 17.
7 with 13 over 125 this is the mixed number form.
Answer:
38.5 cm^2
Step-by-step explanation:
Area(shaded) = Area(large semicircle) - area(2 small equal semicircles)
= Area (large semicircle) - area (small circle)
= π(7)² x 1/2 - π(7/2)²
22/7 x 7 x 7 x 1/2 - 22/7 x 7/2 x 7/2
= 77 - 38.5
= 38.5 cm^2
Answer:
<u>Jack has at least 15 marbles: 12 red, 2 blue and 1 yellow.</u>
Step-by-step explanation:
1. Let's review the information given to us to solve the problem correctly:
Number of red marbles = 10 more than blue marbles
Number of yellow marbles fewer than blue marbles
2. How many of each color marble could Jack have?
r = Number of red marbles
b = Number of blue marbles
y = Number of yellow marbles
r = b + 10
y < b
If y = 1, then b ≥ 2, and r = b + 10,
fulfilling the three conditions, we have:
<u>y = 1, b = 2, and r = 12</u>
