A ball is dropped from a certain height. The function below represents the height f(n), in feet, to which the ball bounces at the nth bounce: f(n) = 9(0.7)n What does the number 9 in the function represent?

Answer:

20

Step-by-step explanation:

Use the distance equation to find the length of each side:

d = √((x₂ − x₁)² + (y₂ − y₁)²)

where (x₁, y₁) and (x₂, y₂) are the points (the order doesn't matter).

AB:

d = √((-2 − (-2))² + (-2 − 4)²)

d = 6

BC:

d = √((4 − (-2))² + (-2 − (-2))²)

d = 6

AC:

d = √((-2 − 4)² + (4 − (-2))²)

d = 6√2

So the perimeter is:

AB + BC + AC

6 + 6 + 6√2

≈ 20

The nonempty set with no accumulation points and no isolated points cannot exist. An example of a nonempty set with no interior points and no isolated points is the set of all rational numbers within the interval (0, 1). A nonempty set with no boundary points and no isolated points also cannot exist.

(a) A nonempty set with no accumulation points and no isolated points cannot exist. An accumulation point in a set is a value that every open interval contains a point from the set different than itself. An isolated point is a point that has an open interval containing only itself. Every point in a nonempty set must be either an accumulated point or an isolated point.

(b) An example of a nonempty set with no interior points and no isolated points is the set of all rational numbers within the interval (0, 1). An interior point is a point where an open interval around the point lies completely within the set, which doesn't exist for this set. Also, this set does not contain any isolated points because between any two rational numbers, there always exists another rational number.

(c) A nonempty set with no boundary points and no isolated points cannot exist. A boundary point is a point that every neighborhood contains at least one point from the set and its complement. If a set does not have any boundary points, it means it cannot be separated from its complement, so it must be an empty set.

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Answer:

  $0.65

Step-by-step explanation:

When d increases by 1, A(d) increases by 0.65 dollars.

Thomas gets paid $0.65 for every mile of travel.

Answer:

Answer choice C

Step-by-step explanation:

When the values of x are greater than 2, the solution works. When the values oclf x are less than 3, the solution also works. :)

Answer:

C

Step-by-step explanation:

Inequalities of the form | x | > a have solutions of the form

x < - a OR x > a, thus

2x + 1 < - 5 OR 2x + 1 > 5 ( subtract 1 from both sides of both )

2x < - 6 OR 2x > 4 ( divide both sides of both by 2)

x < - 3 OR x > 2

Solution set is

{ x | x > 2 or x < - 3 } → C

Answer:

(1,4)

Step-by-step explanation:

Let's this of [tex]y=\sqrt{x}[/tex] which is it's parent function.

How do we get to [tex]y=-\sqrt{x-1}+4[/tex] from there?

It has been reflected about the a-axis because of the - in front of the square root.

It has been shifted right 1 unit because of the -(1) in the square root.

It has been moved up 4 units because of the +4 outside the square root.

In general:

[tex]y=a(x-h)^2+k[/tex] has the following transformations from the parent:

Moved right h units if h is positive.

Moved left h units if h is negative.

Moved up k units if k is positive.

Moved down k units if k is negative.

If [tex]a[/tex] is positive, it has not been reflected.

If [tex]a[/tex] is negative, it has been reflected about the x-axis.

[tex]a[/tex] also tells us about the stretching factor.

The parent function has a starting point at (0,0).  Where does this point move on the new graph?

It new graphed was the parent function but reflected over x-axis and shifted right 1 unit and moved up 4 units.

So the new starting point is (0+1,0+4)=(1,4).

Answer:

Step-by-step explanation:

You must specify the domain of the function.

We know: There is no square root of the negative number.

Therefore

x - 1 ≥ 0        add 1 to both sides

x ≥ 1

The first argument for which the function exists is the number 1.

We will calculate the function value for x = 1.

Put x = 1 to the equation of the function:

[tex]y=-\sqrt{1-1}+4=-\sqrt0+4=0+4=4[/tex]

Therefore the starting point of the graph of given function is (1, 4).

Answer:

Step-by-step explanation:

1. A graphing calculator or any of several solvers available on the internet can tell you the reduced row-echelon form of the augmented matrix ...

[tex]\left[\begin{array}{ccc|c}2&-2&-1&6\\-1&1&3&-3\\3&-3&2&9\end{array}\right][/tex]

is the matrix ...

[tex]\left[\begin{array}{ccc|c}1&-1&0&3\\0&0&1&0\\0&0&0&0\end{array}\right][/tex]

The first row can be interpreted as the equation ...

  x -y = 3

  x -3 = y . . . . . add y-3

The second row can be interpreted as the equation ...

  z = 0

Then the solution set is ...

  (x, y, z) = (x, x -3, 0) . . . . matches selection B

__

2. The second equation is 2 times the first equation, so the system of equations is dependent. There are infinite solutions.

Answer:

n=48

Step-by-step explanation:

n  

_ = 1 6

3

Multiply each side by 3

n/3 * 3 = 16*3

n = 48

Answer:

81

Step-by-step explanation:

g(x) = x^4                     put f(x) in for x in g(x)

g(f(x)) = (f(x))^4             Substitute the value for f(x) which is (-2x - 5) put - 4 in for the x in f(x)

g(f(x) = (-2x - 5)^4

g(f(x)) = (- 2*(- 4) - 5)^4  Combine

g(f(x)) = (8 - 5)^4             Subtract

g(-4) = (3)^4                    Raise 3 to the 4th power

g(-4) = 81                        Answer.  

Answer:

  6 lengths

Step-by-step explanation:

You essentially want the smallest integer solution to ...

  60x ≥ 350

  x ≥ 350/60

  x ≥ 5 5/6

The smallest integer solution to this is x = 6.

The minimum number of lengths of hose needed is 6.

_____

Informally, you know that dividing the required total length by the length of one hose will tell you the number of required hoses. You also know the ratio 350/60 is equivalent to 35/6 and that this will be between 5 and 6. (5·6 = 30; 6·6 = 36) The next higher integer value will be 6.

Answer:

  (1/2)(sin(105°) +sin(345°))

Step-by-step explanation:

The relevant identity is ...

  sin(α)cos(β) = (1/2)(sin(α+β) +sin(α-β))

This falls out directly from the sum and difference formulas for sine.

Here, you have α = 45° and β = 60°, so the relevant expression is ...

  sin(45°)cos(60°) = (1/2)(sin(45°+60°) +sin(45°-60°)) = (1/2(sin(105°) +sin(-15°))

Recognizing that -15° has the same trig function values that 345° has, this can be written ...

  sin(45°)cos(60°) = (1/2)(sin(105°) +sin(345°))

Given that angle A is 45 degrees and angle B is 60 degrees, we use the product-to-sum identity in Trigonometry to find sin(A)cos(B). The correct answer after simplifying the formula sin(A)cos(B) = ½ [sin(A + B) + sin(A - B)] is ½ [sin(105) + sin(345)].

In Mathematics, especially Trigonometry, there is a formula known as product-to-sum identities. One of the identities is Sin(A)Cos(B) = ½ [sin(A + B) + sin(A - B)].

Given that angle A is 45 degrees and angle B is 60 degrees, we will find sin(A)cos(B) by substituting A and B in the formula.

On substitution you get ½ [sin(45 + 60) + sin(45 - 60)], which simplifies to ½ [sin(105) + sin(-15)]. Note that sin(-15) is equivalent to sin(345) in the unit circle, therefore the expression further simplifies to ½ [sin(105) + sin(345)].

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a. If c is a constant then the sum of such constants is the same as multiplication of constants. Therefore [tex]\Sigma_{k=1}^{n}c=nc[/tex]

b. [tex]\Sigma_{k=1}^{n}k=1+2+3+\dots+\infty=\infty[/tex]

c. [tex]\Sigma_{k=1}^{n}k^2=1+4+9+\dots+\infty=\infty[/tex]

d. [tex]\Sigma_{k=1}^{n}k^3=1+8+27+\dots+\infty=\infty[/tex]

Hope this helps.

r3t40

Answer:

D. 10.6

Step-by-step explanation:

Using Pythagoras' theorem

hyp² = side ² + side²

hyp² = 7² + 8²

hyp² = 49 + 64

hyp² = 113

hyp = sqrt of 113

hyp = 10.6

PLEASE DO MARK ME AS BRAINLIEST IF MY ANSWER IS HELPFUL ;)

The correct answer is option d. 10.6.

Given:

The hypotenuse is AC. Therefore, we use the formula:

AC² = AB² + BC²

Substituting the given values:

AC² = 7² + 8²
AC² = 49 + 64
AC² = 113

Now, take the square root of both sides to find AC:

AC = √113 ≈ 10.6

Thus, the missing length AC is approximately 10.6.

The correct answer is d. 10.6.

Complete question: Find the missing length on the triangle.  AB = 7, BC = 8 ∠B = 90°. Round your answer to the nearest tenth if necessary

a. 15

b. 113

c. 12

d. 10.6