Answer:
103
Step-by-step explanation:
Answer:
Step-by-step explanation:
we are given
y varies directly as x
so, we can write equation as
where
k is constant of proportionality
We have
at x=-1 , y=6
so, we can use it to find k
so, we get
now, we can plug it back
now, we can plug x=5
and we get
2.6 rounds to 3, and 0.33 would round to 0.50. Adding 3 and 0.50 together would equal to 3.50. 59 and 3.50 are no where near to each other which concludes Minh is incorrect.
(Please mark me brainliest)
No because if it is the square root of 100, then it is rational, hope this helps
Answer:
- 4x² - 13x + 8 = 0
- 4x² - 11x + 5 = 0
- 16x² - 41x + 1 = 0
- x² + 5x + 4 = 0
- x² - 66x + 64 = 0
Step-by-step explanation:
<u>Given</u>
- α and β are roots of 4x²-5x-1=0
<u>Then the sum and product of the roots are:</u>
- α+b = -(-5)/4 = 5/4
- αβ = -1/4
(i) <u>Roots are α + 1 and β + 1, then we have:</u>
- (x - (α + 1))(x - (β + 1)) = 0
- (x - α - 1)(x - β - 1) = 0
- x² - (α+β+2)x + α+β+ αβ + 1 = 0
- x² - (5/4+2)x +5/4 - 1/4 + 1 = 0
- x² - 13/4x + 2= 0
- 4x² - 13x + 8 = 0
(ii) <u>Roots are 2 - α and 2 - β, then we have:</u>
- (x + α - 2)(x + β - 2) = 0
- x² + (a + β - 4)x - 2(α + β) + αβ + 4 = 0
- x² + (5/4 - 4)x - 2(5/4) - 1/4 + 4 = 0
- x² - 11/4x - 10/4 - 1/4 + 16/4 = 0
- x² - 11/4x + 5/4x = 0
- 4x² - 11x + 5 = 0
(iii) <u>Roots are α² and β², then:</u>
- (x - α²)(x-β²) = 0
- x² -(α²+β²)x + (αβ)² = 0
- x² - ((α+β)² - 2αβ)x + (-1/4)² = 0
- x² - ((5/4)² -2(-1/4))x + 1/16 = 0
- x² - ( 25/16 + 1/2)x + 1/16 = 0
- x² - 33/16x + 1/16 = 0
- 16x² - 33x + 1 = 0
(iv) <u>Roots are 1/α and 1/β, then:</u>
- (x - 1/α)(x - 1/β) = 0
- x² - (1/α+1/β)x + 1/αβ = 0
- x² - ((α+β)/αβ)x + 1/αβ = 0
- x² - (5/4)/(-1/4)x - 1/(-1/4) = 0
- x² + 5x + 4 = 0
(v) <u>Roots are 2/α² and 2/β², then:</u>
- (x - 2/α²)(x - 2/β²) = 0
- x² - (2/α² + 2/β²)x + 4/(αβ)² = 0
- x² - 2((α+β)² - 2αβ)/(αβ)²)x + 4/(αβ)² = 0
- x² - 2((5/4)² - 2(-1/4))/(-1/4)²x + 4/(-1/4)² = 0
- x² - 2(25/16 + 8/16)/(1/16)x + 4(16) = 0
- x² - 2(33)x + 64 = 0
- x² - 66x + 64 = 0
