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
Answer:
x = 30
m<Y = 60
m<Z = 60
m<X = 60
Step-by-step explanation:
All of this should add up to 180 so...
2x + 2x + 3x - 30 = 180 (collect like terms)
7x - 30 = 180 (add 30 on both sides)
7x = 210 (divide by 7 on both sides)
x = 30
PLUG IN
2(30) = 60
3(30) - 30
90 - 30 = 60
m<Y = 60
m<Z = 60
m<X = 60
equilateral triangle
Hope this helps ya! Keep smiling!
315/356 = about 0.88 or 88%. <span>
64/144= about .044 or 44%
</span><span>They will not have equal opportunity to get the math class they requested, if both percents were equal, it would be fair. For honors students, 88% of them will get the class they requested, but for non honors students it's 44%.</span>
The sale price was 30% off the original price, which means it was on sale for 70% of the original cost ( 100% - 30% = 70%)
To find the original cost, divide the sale price by the percent of the original cost:
21 / 0.70 = 30
The original price was $30
check:
30 x 0.3 = 9 ( amount of discount)
30 - 9 = 21 ( sale price)
