An airport parking lot charges a basic fee of $2 plus $1 per half-hour parked. what is the total charge from parking in the lot for 72 hours? a. $144 b. $146 c. $74 d. $72 please select the best answer from the choices provided a b c d

[tex]\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}[/tex]

▪ [tex]\longrightarrow \sf{f(x) = |x + 4| + 2}[/tex]

You need to remember that the form of an Absolute Value Function is:

• For the vertex:

[tex]\small\longrightarrow \sf{H= \: \: x -coordinate}[/tex]

[tex]\small\longrightarrow \sf{K= y-coordinate}[/tex]

• For the definition:

If "a" is positive (+) , then the range of the function is:

[tex]\small\longrightarrow \sf{R:y \: \underline > \: k}[/tex]

If "a" is negative (-), the range of the function is:

[tex]\small\longrightarrow \sf{R: y \: \underline < \: k}[/tex]

In this case we can identify that:

[tex]\small\longrightarrow \sf{a = 1}[/tex]

[tex] \small\longrightarrow\sf{a = 2}[/tex]

[tex]\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}[/tex]

[tex] \large \bm{R: {f(x) \in ℝ | f(x) \underline > 2}}[/tex]

The roots of the given polynomials exists

[tex]$x=8+\sqrt{10},[/tex]  and [tex]$ x=8-\sqrt{10}[/tex]

For a quadratic equation of the form [tex]$a x^{2}+b x+c=0$[/tex] the solutions are

[tex]$x_{1,2}=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}[/tex]

Therefore by using the formula we have

[tex]$x^{2}-16 x+54=0[/tex]

Let, a = 1, b = -16 and c = 54

Substitute the values in the above equation, and we get

[tex]$x_{1,2}=\frac{-(-16) \pm \sqrt{(-16)^{2}-4 \cdot 1 \cdot 54}}{2 \cdot 1}$[/tex]

simplifying the equation, we get

[tex]$x_{1,2}=\frac{-(-16) \pm 2 \sqrt{10}}{2 \cdot 1}[/tex]

[tex]$x_{1}=\frac{-(-16)+2 \sqrt{10}}{2 \cdot 1}, x_{2}=\frac{-(-16)-2 \sqrt{10}}{2 \cdot 1}$[/tex]

[tex]$x=8+\sqrt{10}, x=8-\sqrt{10}[/tex]

Therefore, the roots of the given polynomials are

[tex]$x=8+\sqrt{10},[/tex]  and [tex]$ x=8-\sqrt{10}[/tex].

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Answer:

length is (-7,-1) and radius is 6

Step-by-step explanation:

We are given the expression of the equation of a circle that is

x2 + y2 + 14x + 2y + 14 = 0.

Using completing the squares:

x2 + y2 + 14x + 2y + 14 = 0(x+7)^2 + (y+1) ^2 = -14 + 49 + 1(x+7)^2 + (y+1) ^2 = 36 center thus is at (-7,-1) and the radius is equal to square root of 36 equal to 6.

Answer:

800÷100 = 8

65×8=520

[tex]\frac{520}{800}[/tex]

another way:

100%-65%=35%

35% = 0.35

800×0.35= 280

800-280=520

another way:

65% = 0.65

0.65×800=520

Hope it helped! :)

I'll assume the ODE is

[tex]y'' - 3y' + 2y = e^x + e^{2x} + e^{-x}[/tex]

Solve the homogeneous ODE,

[tex]y'' - 3y' + 2y = 0[/tex]

The characteristic equation

[tex]r^2 - 3r + 2 = (r - 1) (r - 2) = 0[/tex]

has roots at [tex]r=1[/tex] and [tex]r=2[/tex]. Then the characteristic solution is

[tex]y = C_1 e^x + C_2 e^{2x}[/tex]

For nonhomogeneous ODE (1),

[tex]y'' - 3y' + 2y = e^x[/tex]

consider the ansatz particular solution

[tex]y = axe^x \implies y' = a(x+1) e^x \implies y'' = a(x+2) e^x[/tex]

Substituting this into (1) gives

[tex]a(x+2) e^x - 3 a (x+1) e^x + 2ax e^x = e^x \implies a = -1[/tex]

For the nonhomogeneous ODE (2),

[tex]y'' - 3y' + 2y = e^{2x}[/tex]

take the ansatz

[tex]y = bxe^{2x} \implies y' = b(2x+1) e^{2x} \implies y'' = b(4x+4) e^{2x}[/tex]

Substitute (2) into the ODE to get

[tex]b(4x+4) e^{2x} - 3b(2x+1)e^{2x} + 2bxe^{2x} = e^{2x} \implies b=1[/tex]

Lastly, for the nonhomogeneous ODE (3)

[tex]y'' - 3y' + 2y = e^{-x}[/tex]

take the ansatz

[tex]y = ce^{-x} \implies y' = -ce^{-x} \implies y'' = ce^{-x}[/tex]

and solve for [tex]c[/tex].

[tex]ce^{-x} + 3ce^{-x} + 2ce^{-x} = e^{-x} \implies c = \dfrac16[/tex]

Then the general solution to the ODE is

[tex]\boxed{y = C_1 e^x + C_2 e^{2x} - xe^x + xe^{2x} + \dfrac16 e^{-x}}[/tex]

Answer:

Decreasing at an increasing rate

Step-by-step explanation:

graph looks like an arch

right side is going down

right side is going down as x increases

Step-by-step explanation:

its 29 9x4=29 9+4=13 13+4=17

The answers to this question can be given as

This is the point of the function while is it shown on the graph where it is said to be at its highest point or it is at its highest vertex.

When you trace the graph, the highest point is at 2.25.

This is the point or the part of the function where it is at the vertex that is the lowest in the graph.

This is at -0.25

This is a function that can be said to be increasing from the behavior of this graph.

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Answer:

B. the second graph.

Step-by-step explanation:

Literally the photo is on the question.

Second graph represents (y-3)²/25 + (x+1)²/4 > 1 and y <= square root{x+5}+2. Therefore, the correct option is option B.

The study of graphs, that are mathematical constructions used to represent pairwise relationships between things, is known as graph theory in mathematics. In this sense, a network consists of vertices, also known as nodes or points, linked by edges, also known as links or lines.

Undirected graphs, in which edges connect two vertices symmetrically, are distinguished from directed graphs, in which edges connect two vertices asymmetrically. One of the main topics that are investigated in discrete mathematics is graphs. Second graph represents (y-3)²/25 + (x+1)²/4 > 1 and y <= square root{x+5}+2.

Therefore, the correct option is option B.

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4710

4709.94107458

The nearest whole number for 4709.94107458 is 4710 since the number 9 after the decimal is greater than 5. Therefore, if you add 1 to 9 before the decimal, you get 10.

Hope this helps :)

Answer:

Yes, this is a valid inference because she took a random sample of the neighborhood.

Step-by-step explanation:

As we can see, Sue's survey was perfectly random and without any prejudice.

18% of the families, according to her research, would volunteer at the shelter. According to her, 18% of the local households should be required to volunteer at the animal shelter.

Therefore, given that she chose a representative sample of the area, her conclusion is valid.

dis i know functiin of fx is ♾

Answer:

4th option

Step-by-step explanation:

the end behaviour is what happens when x gets larger and positive (right- hand end )or larger and negative ( left- hand end )

f(x) = [tex]\frac{1}{2}[/tex] x² ← is of even degree (2) and has a positive leading coefficient , then

• even degree and positive leading coefficient

f(x) → +∞ as x → + ∞ and

f(x) → + ∞ as x → - ∞

Answer:

  3.16

Step-by-step explanation:

An estimate is usually made to 1 or 2 significant digits. Here, we want an estimate accurate to hundredths, which will be 3 significant digits.

We can round the numbers to some reasonable values, then look at the effect of the rounding error.

  0.235 × 13.467 = (0.25 -0.015) × (13.5 -0.033)

  = 0.25(13.5) -0.25(0.033) -0.015(13.5) +0.015(0.033)

  = 3.375 -0.00825 -0.2025 + (something small)

  ≈ 3.375 -0.008 -0.203 = 3.375 -0.211 = 3.164

  0.235 × 13.467 ≈ 3.16

Note that the values we have can make use of mental math methods.

  0.25 = 1/4 = (1/2)(1/2)

  0.015 = 0.01(1 +1/2)

That is, dividing numbers by 2 mentally is usually not terribly difficult. (Here, it is made more difficult by the odd digits involved.)

  0.25 × 13.5 = (1/2)(13.5/2) = 1/2(6.75) = 3.375

  0.015 × 13.5 = 0.135 +0.135/2 = 0.135 +0.0675 = 0.2025

or, recognizing that 1.35 = 1.5 -.15, ...

  0.015 × 13.5 = (0.01)(1.5) × (10)(1.5-.15) = 1.5²×(.1 -.01) = .225 -.0225

__

Additional comment

A calculator gives the actual product as 3.164745, so our estimate is accurate to hundredths.

Considering the relation built the presence of point M on line LN, the numerical length of LN is of 9 units.

Point M splits line LN into two parts, LM and MN, hence the total length is given by:

LN = LM + MN.

From the given data, we have that:

Hence we first solve for x.

LN = LM + MN.

2x - 5 = 3 + x - 1

x = 7.

Hence the total length is:

LN = 2x - 5 = 2 x 7 - 5 = 14 - 5 = 9 units.

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Answer:

The bottom graph.

Step-by-step explanation:

The asymptote ( in between the 2 curves) on the bottom graph is  at x = 1, because when x = 1 the denominator = 0.

The functions f(x) and g(x) are different functions

The function f(x) is a cubic function, while the function g(x) is a logarithmic function.

The common feature in both functions is their range

According to the statement

we have given that the some functions and we have to justify these functions.

The functions are given as:

f(x) = x³ + x² - 2x + 3 and g(x) = log(x) + 2

This means that the function f(x) is a cubic function, while the function g(x) is a logarithmic function.

The common key features of the functions

To do this, we plot the graphs of both functions

From the attached graph, we have the following features:

Function f(x)

Domain: -∞ < x < ∞

Range: -∞ < y < ∞

y - intercept = 3

x - intercepts = -2.37

Function g(x)

Domain: x > 0

Range: -∞ < y < ∞

y - intercept = None

x - intercepts = 0.01

By comparing the key features above, we can conclude that the common features in both functions is their range.

The functions f(x) and g(x) are different functions

The function f(x) is a cubic function, while the function g(x) is a logarithmic function.

The common feature in both functions is their range

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The value of M is:

M = ± (1 / 2) · √[(k² + 5)² /(4 · k²) - 5] ∓ (1 / 2) · √[(k² / 100) · (25 / k² + 5)² - 5] + √3, for k ≠ 0.

In this question we have a product of two nonzero real numbers equal to 5, whose mathematical form is:

p · q = 5, where p = 2 · x + √(4 · x² + 5) = k and q = 2 · y + √(4 · y² + 5) = 5 / k

Then, we proceed to find the solutions for x and y in terms of k:

2 · x + √(4 · x² + 5) = k

2 · x = k - √(4 · x² + 5)

4 · x² = k² - 2 · k · √(4 · x² + 5) + 4 · x² + 5

2 · k · √(4 · x² + 5) = k² + 5

4 · k² · (4 · x² + 5) = (k² + 5)²

4 · x² + 5 = (k² + 5)² /(4 · k²)

4 · x² = (k² + 5)² /(4 · k²) - 5

x = ± (1 / 2) · √[(k² + 5)² /(4 · k²) - 5], for k ≠ 0.

2 · y = 5 / k - √(4 · y² + 5)

4 · y² = 25 / k² - (10 / k) · √(4 · y² + 5) + 4 · y² + 5

(10 / k) · √(4 · y² + 5) = 25 / k² + 5

(100 / k²) · (4 · y² + 5) = (25 / k² + 5)²

4 · y² + 5 = (k² / 100) · (25 / k² + 5)²

4 · y² = (k² / 100) · (25 / k² + 5)² - 5

y = ∓ (1 / 2) · √[(k² / 100) · (25 / k² + 5)² - 5], for k ≠ 0.

Therefore, the value of M is:

M = ± (1 / 2) · √[(k² + 5)² /(4 · k²) - 5] ∓ (1 / 2) · √[(k² / 100) · (25 / k² + 5)² - 5] + √3, for k ≠ 0.

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The mean of the set is : 16

The Slandered deviation of set : 5.8689389538863

Moderation is the quality of falling at or close to a medium point, whether it is in terms of location, period of time, quantity, or rate. 2 is the arithmetic mean. 3 denotes a plural noun: a tool for achieving one's goals. Attempt to locate it using all available techniques.

The average (mean) is equal to the sum of all the data values divided by the count of values in the data set.

An indicator of how much a group of numbers vary or are dispersed is the standard deviation. When the standard deviation is low, the values tend to fall within a narrow range of the set's mean, but when it is large, the values tend to deviate from that mean more.

Average x = 16

Count n = 9

Sum     Sum =144

Average = Sum / Count

= 144 / 9

= 16

Standard Deviation, σ: 5.8689389538863

Count, N = 9

Sum, Σx: = 144

Mean, μ:  = 16

Variance, σ²: = 34.444444444444

Calculating slandered devotion:

[tex]\sigma=\sqrt{\frac{1}{N} \sum_{i=1}^{N}\left(x_{i}-\mu\right)^{2}}[/tex]

[tex]\sigma^{2}=\frac{\sum\left(x_{i}-\mu\right)^{2}}{N}[/tex]

[tex]=\frac{(16-16)^{2}+\ldots+(24-16)^{2}}{9}[/tex]

= 310/9

=  34.444444444444

σ =  √34.444444444444

σ =   5.8689389538863

The mean of the set is : 16

The Standard deviation of set : 5.8689389538863

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A pendulum that swings fully once in 1.9 seconds has a length of 2.93 feet.

A basic pendulum is a machine in which the point mass is hung from a fixed support by a light, inextensible string.

Length of pendulum is defined as the distance between the point of suspension to the center of the bob and is denoted by " 1 ".

Given the equation:

[tex]$$T=2 \Pi \sqrt{\frac{L}{32}}$$[/tex]

where L is the length in feet and T is the time in seconds.

Given that T = 1.9sec,

Hence:

[tex]$$T=2 \Pi \sqrt{\frac{L}{32}}$$[/tex]

L = 2.93 feet

A pendulum that swings fully once in 1.9 sec has a length of 2.93 feet.

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Answer:

2

-2

Step-by-step explanation:

Use the second equation for x = -4.

f(-4) = 2

Use the third equation for x = 3.

f(x) = -x + 1 = -3 + 1 = -2

Answer:

Step-by-step explanation:

Comment

There are a number of ways of doing this problem. I don't know which method you are intended to use. One sure way in this case is graphing the equation, I have done this for you. See below. The maximum volume occurs where x = 2

The graph shows that there is a peak at x = 2. That is where the maximum volume is,

Answer

x = 2

Answer:

(2,4)

Step-by-step explanation:

1. Add the 2 x-values together, then divide. The resulting number is the x-value of the midpoint. -4+8=4 and 4/2=2, so the x-value is 2

2. Do the above steps (add & divide) for the two y-values. 6+2=8 and 8/2=4, so the y-value is 4

3. put the two values together in a coordinate pair & you have your midpoint! so if x=2 and y=4, then the midpoint is (2,4)

hope this helps :)

Answer:

[tex]h^7-6[/tex]

Step-by-step explanation:

1) Regroup terms.

[tex]h^4h^3-6[/tex]

2) Use Product Rule: [tex]x^ax^b=x^{a+b}[/tex].

[tex]h^{4+3}-6[/tex]

3) Simplify 4 + 3 to 7.

[tex]h^7-6[/tex]

Answer:

"a[b(b + 6) +7(a²-2)]" (the third one)

Step-by-step explanation:

Step-by-step explanation:

Yes, an positive average rate of change means that our endpoint of the interval is greater than the initial point of our interval. By definition, a function, f is increasing over an interval [a,b], if f(b)> f(a)

Yes, a positive average rate of change means that our endpoint of the interval is greater than the initial point of our interval.

It is the average amount by which the function changed per unit throughout that time period. It is calculated using the slope of the line linking the interval's ends on the graph of the function.

Yes, a positive average rate of change indicates that the endpoint of our period is higher than the interval's starting point. A function f is rising over the range [a,b] by definition if f(b)> f. (a)

Therefore, the positive average rate of change over an interval must be increasing over that interval.

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Based on Alonso's budget, he can get 3.7 bags of avocados and the cost of 3 bags of avacodes or 9 avacadoes is $15.

21 = 2.50 + 5x

21 - 2.50 = 5x

18.50 = 5x

x = 18.50 / 5

x = 3.7 bags of avocados

To get 3 bags of avocados or 9 avocados

= $5 × 3

= $15

Therefore, Alonso can get 3.7 bags of avocados and the cost of 3 bags of avacodes or 9 avacadoes is $15.

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Answer:

127

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Answer:

Cosa/2-tana+sina

Step-by-step explanation:

Cosatana