A movie rental store charges a membership fee of $10.00 plus $1.50 per movie rented. What is a possible domain that shows the cost to a member of renting movies? A) The domain is all integers. B) The domain is all even integers. C) The domain is all integers 0 or greater. D) The domain is all integers 10 or greater.

Answers

Answer 1

Answer: For the question "A movie rental store charges a membership fee of $10.00 plus $1.50 per movie rented. What is a possible domain that shows the cost to a member of renting movies?" The correct answer is "The domain is all integers 0 or greater."This is because the equation that models the cost to a member of renting movies is given by y = 10 + 1.5x, where x is the number of movies rented.The domain of a function are the value the independent variable can take, in this case, the values x can take.Each member of the movie rental store has an option of renting from 0, 1, 2, 3, . . . number of movies.

Answer 2

Answer:

Answer:

B) The domain is all integers 0 or greater.

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Prove-: sin5A = 5cos^4 A sinA - 10cos^2 A sin^3 A + sin^5 A

Answers

$A=x\n\nsin5x=5cos^4xsinx-10cos^2xsin^3x+sin^5x\n\nL=sin(3x+2x)=sin3xcos2x+sin2xcos3x=(*)\n-------------------------------\nsin3x=sin(2x+x)=sin2xcosx+sinxcos2x\n=2sinxcosxcosx+sinx(cos^2x-sin^2x)\n=2sinxcos^2x+sinxcos^2x-sin^3x=3sinxcos^2x-sin^3x\n-------------------------------$

$sin3xcos2x=(3sinxcos^2x-sin^3x)(cos^2x-sin^2x)\n=3sinxcos^4x-3sin^3xcos^2x-sin^3xcos^2x+sin^5x\n=3sinxcos^4x-4sin^3xcos^2x+sin^5x\n-------------------------------$

$cos3x=cos(2x+x)=cos2xcosx-sin2xsinx\n=cosx(cos^2x-sin^2x)-2sinxcosxsinx\n=cos^3x-sin^2xcosx-2sin^2xcosx=cos^3x-3sin^2xcosx\n-------------------------------$

$sin2xcos3x=2sinxcosx(cos^3x-3sin^2xcosx)\n=2sinxcos^4x-6sin^3xcos^2x\n-------------------------------$

$(*)=3sinxcos^4x-4sin^3xcos^2x+sin^5x+2sinxcos^4x-6sin^3xcos^2x\n\n=5sinxcos^4x-10sin^3xcos^2x+sin^5x=R$

$=======================================\n\nsin(\alpha+\beta)=sin\alpha cos\beta+sin\beta cos\alpha\n\ncos(\alpha+\beta)=cos\alpha cos\beta-sin\alpha sin\beta\n\nsin2\alpha=2sin\alpha cos\alpha\n\ncos\alpha=cos^2\alpha-sin^2\alpha$

stephanie has the same number of dimes and nickels. she has $6.10 in all. what an equation that you could use to find the number of dimes and nickes

Answers

Equation: 5x + 10x = $6.10

A water balloon is tossed into the air with an upward velocity of 25 ft/s. Its height h(t) in ft after t seconds is given by the function h(t) = − 16t2 + 25t + 3. Show your work.After how many seconds will the balloon hit the ground? (hint: Use the quadratic formula)

What will the height be at t = 1 second
PLEASE HELP,,STUCK :(

Answers

1) $h (t) = -16t^2 + 25t + 3 \n \nh(t) = 0 \n \n 0 = -16t^2 + 25t + 3 \n \n quadratic \ formula \n \n a = -16 \ , \ b = 25 \ , c = 3 \n \n t = (-25 \pm √(25^2-4(-16)(3)) )/(2(-16)) \n \n (-25 \pm √(625+192) )/(-32) \n \n (-25 \pm √(817) )/(-32) \n \n (-25 \pm 28.5832)/(-32) \n \n t = (-25 - 28.5832)/(-32) \n \n t = (-25 + 28.5832)/(-32) \n \n (53.5832)/(32) \n \n (53.5832)/(32) \n \n 1.66447$

The water ballon will hit the ground after 1.66447 seconds.

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2) $t = 1 \n \n h(1) = -16(1)^2 + 25(1) + 3 \n \n -16 + 25 + 3 \n \n 12$

The height will be 12 feet if t = 1 second.

Final answer:

To find when the balloon hits the ground, set the height function equal to zero and solve using the quadratic formula. The balloon will hit the ground after approximately 1.924 seconds. To find the height at t = 1 second, substitute t = 1 into the height function to get a height of 12 feet.

Explanation:

To find when the water balloon hits the ground, we need to set the height function, h(t), equal to zero and solve for t. In this case, the height function is given by h(t) = -16t^2 + 25t + 3.

Setting h(t) equal to zero, we get:

-16t^2 + 25t + 3 = 0

Using the quadratic formula, t = (-b ± sqrt(b^2 - 4ac)) / (2a), where a = -16, b = 25, and c = 3, we can determine the value of t.

After substituting the values into the quadratic formula and solving for t, we find two values: t ≈ 0.051 seconds and t ≈ 1.924 seconds. Since we are looking for when the balloon hits the ground, we can ignore the first solution and conclude that the balloon will hit the ground after approximately 1.924 seconds.

To find the height at t = 1 second, we can substitute t = 1 into the height function. This gives us:

h(1) = -16(1)^2 + 25(1) + 3 = -16 + 25 + 3 = 12 feet.