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
Answer:
12
Step-by-step explanation:
A 2 - sided counter ; (red, yellow)
A spinner (1,2,3,4,5,6)
Number of trials = 80
P(red and number > 3) :
P(red) = 1/2 ;
P(number >3) : numbers greater Than 3 = (4, 5, 6)
Hence, P(number <3) = 3 /6 = 1/2
Theoretical probability = 1/2 *1/2 = 1/4
Expected number of outcomes :
1/4 * number of trials
1/4 * 80 = 20
Experimental outcome :
Relative frequency = number of outcomes / number of trials
Relative frequency = 2/5
Hence,
2/5 = number of outcomes / 80
Cross multiply :
160 = number of outcomes * 5
Number of outcomes = 160 /5 = 32
Actual outcomes = 32
Difference between actual and expected :
32 - 20 = 12
Answer:
<h3>If the taste tester takes 10 minutes to eat a cheeseburger, then it would take him is
minutes
Eating round the clock, it would take him is
</h3>
Step-by-step explanation:
Given that "In order to develop a more appealing cheeseburger, a franchise used taste tests with 13 different buns, 5 different cheeses, 2 type of lettuce, and 3 types of tomatoes"
From the given we can write
13 buns
8 cheese
4 lettuces
3 tomatoes
∴ There would be different cheeseburger combinations is given by
Given that if the taste tester takes 10 minutes to eat a cheeseburger, then it would take him
minutes
Eating round the clock, it would take him
hours
The first question answer is 21*10^7
The second question answer is 5*10^2
Only the first one works
y = 3(-1)-2 = -5
y = -(0) -6 = -6 not -2
This is a substitution problem...
