Rewrite the equation in vertex form: y=x^2-8x+13

Answers

Answer 1

Answer: $vertex\ form:y=a(x-p)^2+q\n\nwher\ p=(-b)/(2a)\ and\ q=f(p)\n\n\ny=x^2-8x+13\na=1;\ b=-8;\ c=13\n\np=(-(-8))/(2\cdot1)=(8)/(2)=4\n\nq=f(4)=4^2-8\cdot4+13=16-32+13=-3\n\nAnswer:y=(x-4)^2-3$

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Consider the sequence 51, 43, 35, 37, 19 which function describes the sequence.

Answers

The function f(n) = 8n - 5 + (-1)ⁿ × 3 indeed generates the given sequence 51, 43, 35, 37, 19.

The given sequence is 51, 43, 35, 37, 19. To identify the underlying function describing this sequence, let's analyze the pattern between the terms.

Subtraction: If we look at the differences between consecutive terms, we get the following sequence of differences: -8, -8, 2, -18.

Alternating Behavior: The differences between terms seem to alternate between subtracting 8 and adding 2.

Possible Linear Function: The alternating behavior suggests that this sequence might be generated by a linear function with some sort of periodic or alternating component.

Linear Function with Alternating Component: A possible function to describe this sequence could be:

f(n) = 8n - 5 + (-1)ⁿ × 3

Here, n represents the position in the sequence (starting from n = 1), and (-1)ⁿ introduces the alternating component. When n is even, (-1)ⁿ becomes 1, and when n is odd, (-1)ⁿ becomes -1.

Now, let's test this function with the given values:

- For n = 1: f(1) = 8(1) - 5 + (-1)¹ × 3 = 8 - 5 + (-1) × 3 = 3 - 3 = 0

- For n = 2: f(2) = 8(2) - 5 + (-1)² × 3 = 16 - 5 + 1 × 3 = 11 + 3 = 14

- For n = 3: f(3) = 8(3) - 5 + (-1)³ × 3 = 24 - 5 - 3 = 19 - 3 = 16

- For n = 4: f(4) = 8(4) - 5 + (-1)⁴ × 3 = 32 - 5 + 3 = 27 + 3 = 30

- For n = 5: f(5) = 8(5) - 5 + (-1)⁵ × 3 = 40 - 5 - 3 = 35 - 3 = 32

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jean needs to graph the function below y= 7x^2 + 8x - 6 How many time should the graph of this function intersect at the x-axis?

Answers

when it intersects the x axis, the y value is 0
0=7x^2+8x-6
2nd degree, therefor there are 2 solutions and also 2 intersections

answe is 2 times

A carton of paper is priced at $27.00 now. If the paper goes on sale for 25% off the current price, what will be the sale price of the carton?

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I think the answer would be $33.75.

Emmanuel wants to tile his rectangular floor. he has 2 kinds of tiles to choose from, one of which is larger than the other. a. What area will be covered by the 8" x 8" tile? 16 by 16 tile? b. if the rectangular floor has dimensions of 74" by 128", how many small square tiles are needed to cover it?

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$Area\ of\ rectangular\ floor:\n\n A_f=74*128=9472\n\n Area\ of\ small\ tile:\n\n A_s=8*8=64\ Small\ tile\ will\ cover\ 64''^2 \n\n Area\ of\ big\ tile:\n\n A_b=16*16=256\ Big\ tile\ will\ cover 256''^2\n\n A_f:A_s=9472:64=148\n\n A_f:A_b=9472:148=64\n\n\ To\ cover\ the \ floor\ 148\ small\ tiles\ are \ needed.$

A football is kicked toward the goal. The height of the ball is modeled by the function h(t) = -16t2 + 64t where t equals the time in seconds and h(x) represents the height of the ball at time t seconds. What is the axis of symmetry and what does it represent? t = 2; it takes 2 seconds to reach the maximum height and 2 seconds to fall back to the ground
t = 2; it takes 2 seconds to reach the maximum height and 4 seconds to fall back to the ground
t = 4; it takes 4 seconds to reach the maximum height and 4 seconds to fall back to the ground
t = 4; it takes 4 seconds to reach the maximum height and 8 seconds to fall back to the ground

Answers

h(t) = -16(t^2) + 64t

roots:

0 = -16t^2 + 64t
0 = t^2 - 4t
0 = t(t-4)
t=0 and t =4

The symmetry axis is at the middle of the two roots: t = (0+4)/2

That time (t=2) is what it takes the object to reach the maximum height.

Answer: t = 2; it takes 2 seconds to reach the maximum height and 4 seconds to fall back to the ground

Answer: B/ it takes 2 seconds to reach the maximum height and 4 seconds to fall back to the ground

Step-by-step explanation:

I NEED HELP ASAP (A new pizza shop opened up and started out$5,344.46 in the hole. Their first month being open they sold 61 pizzas ($3.06 profit each) and 89 sodas ($1.42 profit each). Thier bills for the first month were $1,208.01. How much money do they still need to make to break even?

Answers

Answer:

$894.97 is needed more to break even

Step-by-step explanation:

In this question, we want to know how much money the pizza shop need so that their profits will equal their expenses.

Let’s calculate their profit

This can be calculated from the pizza sales

That would be;

61(3.06) + 89(1.42) = $186.66 + $126.38 = $313.04

Now, given that their bills for the first month is $1,208.01, the amount still needed to break even would be the amount of their bills minus the profit made from selling soda and pizza

That would be 1,208.01 - 313.04 = $894.97

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