Answer:
That their milkshakes need more caramel or less ice cream.
Step-by-step explanation:
We can see that Ari's numbers for a perfect milkshake gives us a caramel to ice cream ratio of 333 / 555 = 0,6.
But the Freeze Zone uses a caramel to ice cream ratio of 666 / 888 which is equal to 0,75.
Their milkshakes have less caramel and more ice cream than Ari's perfect milkshake so Ari will think that Freeze Zone's milkshakes are not sweet enough.
I hope this answer 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
The two fractions that added together give you a sum of -7/24 are 1/24+-8/24= -7/24
Answer: 20.71 m
Step-by-step explanation:
Given
the length of the poles are 25m and 35 m
The length of the cable is 23 m
Suppose the distance between them is x
From the figure, apply Pythagoras theorem
Distance between Poles is 20.71 m
<u><em>Answer:</em></u>
AC = 10sin(40°)
<u><em>Explanation:</em></u>
The diagram representing the question is shown in the attached image
Since the given triangle is a right-angled triangle, we can apply the special trig functions
<u>These functions are as follows:</u>
sin(θ) = opposite / hypotenuse
cos(θ) = adjacent / hypotenuse
tan(θ) = opposite / adjacent
<u>Now, in the given diagram:</u>
θ = 40°
AC is the side opposite to θ
AB = 10 in is the hypotenuse
<u>Based on these givens</u>, we will use the sin(θ) function
<u>Therefore:</u>
