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:
x=2.25
Step-by-step explanation:
4x=3 x 3
The pie must stay for 60 - x more minutes must the pie bake
<h3>For how many more minutes must the pie bake?</h3>
Let the amount of time spent in the oven be x
So, we have
Total amount of time = 60 minutes
This means that
Remaining time + Amount of time spent = 60
This gives
Remaining time + x = 60
Evaluate
Remaining time = 60 - x
Hence, the pie must stay for 60 - x more minutes must the pie bake
Read more about equations at:
brainly.com/question/2972832
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Answer:
A = 219
C = 362
Step-by-step explanation:
Given,
581 = C + A
and
$1090.50 = 1.5C + 2.5A
solve 1st for A
A =581 - C
substute into 2nd
1090.50 = 1.5C + 2.5(581 - C)
solve for C
1090.50 = 1.5C + 1452.50 - 2.5C
1090.50 = -C + 1452.50
1090.50 - 1452.50 = -C
-362 = -C
C = 362
then
581 = C + A
581 = 362 + A
219 = A
A = 219
If all were children, revenue would be 700*$7 = $4900. Revenue is actually $6400 -4900 = $1500 more than that. Each adult admission that replaces a child's admission adds $10 -7 = $3 to the revenue, so there must have been
$1500/$3 = 500 . . . . adult admissions
There were 200 children at the show.
There were 500 adults at ths show.
