A firefighter determines that 350 feet of hose is needed to reach a particular building. If the hoses are 60 feet in length, what is the minimum number of lengths of hose needed?

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:

(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:

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:

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:

n=48

Step-by-step explanation:

n  

_ = 1 6

3

Multiply each side by 3

n/3 * 3 = 16*3

n = 48

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

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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