A baggage check service charges $4 for the first hour and $1 for each additional hour or fraction of an hour. Which point is NOT included in the graph of this step function?

A. (6.9, 10)
B. (6.1, 10)
C. (6.0, 10)
D. (5.9, 9)

a) The smallest zero of f is -7 with multiplicity 2.

   The largest zero of f is 1 with multiplicity 1.  (Choice B.)

(b) The graph touches the x-axis at x = -7 and crosses at x = 1. (Choice C)

(c) The maximum number of turning points on the graph is 2.  

(d) The power function that the graph of f resembles for large values of |x| is y = 2x^3.

(a)  To find each real zero and its multiplicity:

set f(x) equal to zero and solve for x:

2(x - 1)(x + 7)^2 = 0

Setting each factor equal to zero separately:

x - 1 = 0 => x = 1 (with multiplicity 1)

x + 7 = 0 => x = -7 (with multiplicity 2)

Therefore, the real zeros and their multiplicities are:

x = 1 (multiplicity 1)

x = -7 (multiplicity 2)

(b) To determine whether the graph crosses or touches the x-axis at each x-intercept, examine the sign changes around those points.

At x = 1, the multiplicity is 1, indicating that the graph crosses the x-axis.

At x = -7, the multiplicity is 2, indicating that the graph touches the x-axis.

(c) The maximum number of turning points on the graph is 2 because the maximum number of turning points on the graph is equal to the degree of the polynomial minus 1

(d) The power function that the graph of f resembles for large values of |x| is y = 2x³because the leading term of f(x) = 2(x - 1)(x + 7)^2 is 2x^3. As x approaches positive or negative infinity, the dominant term is 2x^3, which is a power function with an odd degree.

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Answer:

x = -2

Step-by-step explanation:

3/2 (x-5) - 3/2 = 9x/2

3x/2 - 15/2 - 3/2 = 9x/2 ... alldenominator

are 2 so we can multiply all term by 2

2(3x/2 - 15/2 - 3/2 = 9x/2)

3x - 15 - 3 = 9x ... simplify it

3x - 12 = 9x

-12 = 9x - 3x ... take 3x to the left

-12 = 6x ... simplify

6x/6 = -12/6 ... dividing both side by 6

x = -2 ... simplify and solve x

Answer:

100-20=80

80+ 6.75 = 86.75

139/100 X 86.75 = 120.5825

$120.58

The formula A = | ax (by - cy) + bx (cy - ay) + cx (ay - by) | / 2 is used to find the area of a parallelogram whose vertices are given. The vertices are (-2, 0), (0, 3), (1, 3), and (-1, 0). The area of the parallelogram is 11/2 square units.

To find the area of a parallelogram whose vertices are given, we use the formula

A = | ax (by - cy) + bx (cy - ay) + cx (ay - by) | / 2 .

Here, ax and ay are the x and y coordinates of vertex A, bx and by are the x and y coordinates of vertex B, and cx and cy are the x and y coordinates of vertex C. Given the vertices are (-2, 0), (0, 3), (1, 3), and (-1, 0).We will use the above formula to find the area of the parallelogram.

Area = |(-2(3)-0(1)+1(0)) + (0(0)-3(-1)+(-1)(-2))|/2

=|(-6+0+0)+ (0+3+2)|/2

=11/2 square units.

Hence, the area of the parallelogram whose vertices are (-2, 0), (0, 3), (1, 3), and (-1, 0) is 11/2 square units.

Therefore, the answer is: The area of the parallelogram whose vertices are (-2, 0), (0, 3), (1, 3), and (-1, 0) is 11/2 square units.

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The landscaper will have 183 feet of rope left over after completing the seven pieces.

The landscaper wants to cut a 2418-foot rope into pieces for fences. The length of each fence must be 315 feet. We can figure out how many pieces the landscaper can make by dividing the total length of the rope by the length of each piece.

7.68 (rounded down to the nearest whole number) is 2418 feet divided by 315 feet.

Consequently, the exterior decorator can make 7 pieces from the rope.

We subtract the total length of the pieces from the original length of the rope to determine how much rope is left over.

2418 feet divided by 7 pieces equals 183 feet.

Therefore, the landscaper will have 183 feet of rope left over after completing the seven pieces.

The landscaper will need this information to effectively plan their work. They can use the seven pieces to make fences that are 315 feet long. They also have 183 feet of rope left over, which could be put to use for smaller projects or put aside for other uses. Arranging and understanding the accessible assets are significant for any gardener to do their work productively and successfully.

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To solve this problem both units must have the same units.

So, let's convert quarts to gallons

1 quart ----------------------- 0.25 gallon

34 quarts -------------------- x

x = (34 x 0.25) / 1

x = 8.5 gallons

8.5 gallons or 34 quarts > 8 gallons

the rate of change of the radius at the instant the volume equals 36π cm³ is 7 / (36π) cm/sec.

The volume V of a sphere with radius r is given by the formula V = (4/3)πr³. We are given that the rate of change of the volume is 7 cm³/sec. Differentiating the volume formula with respect to time, we get dV/dt =(4/3)π(3r²)(dr/dt), where dr/dt represents the rate of change of the radius with respect to time.

We are looking for the rate of change of the radius, dr/dt, when the volume equals 36π cm³. Substituting the values into the equation, we have: 7 = (4/3)π(3r²)(dr/dt)

7 = 4πr²(dr/dt) To find dr/dt, we rearrange the equation: (dr/dt) = 7 / (4πr²) Now, we can substitute the volume V = 36π cm³ and solve for the radius r: 36π = (4/3)πr³

36 = (4/3)r³

27 = r³

r = 3  Substituting r = 3 into the equation for dr/dt, we get: (dr/dt) = 7 / (4π(3)²)

(dr/dt) = 7 / (4π(9))

(dr/dt) = 7 / (36π)

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Liberal arts math is a broad category that includes a variety of mathematical topics designed to give students a well-rounded understanding of mathematics and its applications.

Some common topics in liberal arts math courses may include logic, probability, statistics, geometry, and algebra. These subjects help to develop critical thinking and problem-solving skills that are useful in various aspects of life. If you have a specific question or concept you'd like help with, feel free to ask, and I'll do my best to assist you.

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Answer: b) 2 units left, 4 units up, reflect across y-axis

Step-by-step explanation:

The easiest way to do this is to graph the black triangle using the the given options to see which one lands on the red triangle.

The second option is the one that works.

The naive forecast for day 6 is 94.

The naive forecast for the nth period is calculated as follows.

Forecast period Yn=Yn−1​

Period Sales Naive Forecasts

1         90                   -

2         97                  90

3         92                  97

4         90                  92

5         94                  90

6                            94

Hence, the naive forecast for day 6 is 94.

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Answer:

The first and third options are parallel.

Step-by-step explanation:

They both have a slope of 2.

Pls mark brainliest. Thanks!

Answer:

Answer A: y = 2x + 3 and B: y = 2x -12

Step-by-step explanation:

Because of the fact that parallel lines have the same slope A and B have to be parallel to each other because their slopes are both 2.

Answer:

24.8cm

Step-by-step explanation:

To find the perimeter of the compound shape we first jave to find distance DE. For this we can use pythagoras theorem which states that the square of the longest side of a RIGHT-ANGLED TRIANGLE (which is opposite the right angle) is equal to the sum of the squares of the two adjuscent sides.

USING TRIANGLE EFD

ED² = EF²+FD² (Pythagoras theorem)

ED² = 6²+5²

ED²=61

find the square root of both sides to find distance ED

\( \sqrt{ {ed}^{2} } = \sqrt{61} \)

ED= 7.8 cm

Add up all the distances on the exterior edges of the shape to find the perimeter.

6cm+3cm+5cm+3cm+7.8cm=24.8cm

Answer:

An example is 6/10

Step-by-step explanation:

We can multiply the numerator and denominator by the same number to get an equivalent fraction. I multiplied by 2. 3 times 2 = 6. 5 times 2 = 10. Therefore, it is 6/10.

I hope this helped and please mark me as brainliest!

The area of the sector in radians is calculated as: B. 8π units squared.

The area of a sector where the central angle of the sector that is shaded in a circle is given in radians is calculated using the formula that is expressed as:

Area of sector = (1/2) × r²θ; where we have:

θ = the angle subtended at the center/central angle measure in radians

r = the radius of the circle

Given the following:

The shaded area is half of the circle. Its measure would be 180 degrees which when expressed in radians would be π.

Central angle measure in radians (θ) = π

Radius (r) = 4 units

Plug in the values into the area of sector formula

Area of sector = (1/2) × r²θ = (1/2) × (4²)(π)

Area of sector = (1/2) × (16)(π)

Area of sector = (1 × 16 × π)(2)

Area of sector = (16π)(2)

Area of sector = 8π units squared

In conclusion, the area of the shaded sector in the image given below is calculated as: B. 8π units squared.

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Answer:

$20 was the original price. 16÷20= .8=80%

Answer:

The original price is 100%. and 80%

Step-by-step explanation:

The original price is 100%. and 80%=$15. ⇒1%=$1580=$0.1875. ⇒100%=$0.1875×100=$18.75.

Answer:

\( \boxed{Measure \: of \: third \: angle = 87\degree} \)

Step-by-step explanation:

The sum of angles of a triangle equals the straight angle (180°, π radians, two right angles, or a half-turn).

Let measure of the third angle be 'x'

\( = > 67 \degree + 26\degree + x\degree = 180\degree \\ \\ = > 93\degree + x\degree = 180\degree \\ \\ = > x\degree = 180\degree - 93\degree \\ \\ = > x\degree = 87\degree\)

Step-by-step explanation:

Sum interior measure of triangle = 180°

Sum interior measure = (n-2)180

Where n is the no. of sides

Sum interior measure = (n-2)180

=(3-2)180

=180°

61+42+x =180

103+x =180

x = 180-103

x = 77°

Good Luck

Answer:

put 244 add 7e8ue

Step-by-step explanation:

i53838 divede 73838

The average rate of change of f(x) on the interval 5≤ x ≤ 7.

= {f(7) - f(5)} / 2

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

y = f(x)

f(x) at 5 =f(5)

f(x) at 7 = f(7)

The average rate of change of f(x) on the interval 5≤ x ≤ 7.

= {f(7) - f(5)}/ (7 -5)

= { f(7) - f(5) } / 2

Thus,

The average rate of change of f(x) on the interval 5≤ x ≤ 7.

= {f(7) - f(5)} / 2

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Answer:

Hi There! Here's your answer.

Answer:

Attached to this answer are some of the ways you could rewrite \(4*10^{-3}\)

The dependent variable in an experiment is the factor whose value is being measured or observed.

In an experiment, the dependent variable is the factor that is being observed or measured. It is the variable that responds to changes in the independent variable, which is the factor being manipulated or changed in the experiment. The dependent variable is often represented on the y-axis of a graph and is used to analyze and interpret the results of the experiment. For example, in an experiment testing the effect of fertilizer on plant growth, the dependent variable would be the plant growth, as it is being measured in response to the fertilizer treatment. The dependent variable is crucial in experimental design as it helps researchers determine the relationship between the independent variable and the observed outcome.

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The 24 walls must paint by each volunteer if the work is divided evenly and the club has 36 volunteers.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

We have:

As part of a community-service project, a local club has decided to paint 864 walls across town. The club has 36 volunteers.

Total number of volunteers = 36

Number of walls = 864

The number of walls each volunteer paint can be expressed as a fraction:

= 864/36

= 24

Thus, the 24 walls must paint by each volunteer if the work is divided evenly and the club has 36 volunteers.

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Based on the equation, in 10 years, the amount owed would be $37,226.90

The equation to represent the amount owed after x years is:

A = P(1 + r/n)^nt

where:

A is the amount owed after x years

P is the principal amount (initial loan amount)

r is the annual interest rate

n is the number of times per year that interest is compounded

t is the number of years

In this case, we have:

P = $10,000

r = 15% = 0.15

n = 12 (monthly compounding)

So, the equation becomes:

A = $10,000(1 + 0.15/12)^12t

The rate charged each month is:

r/n = 0.15/12 = 0.0125

In 10 years, the amount owed would be:

A = $10,000(1 + 0.0125)^120

= $37,226.90

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We can see in the solution below that the left-hand side is equal to the right-hand side, since the identity containing tan and cot have both simplified to the same expression, 2/cos ysin y = 2/cos xsin x. Therefore, we have verified the identity.

Simplifying left-hand side containing tan and cot:

2 tan x + 2 cot y/ tan x cot y
= 2(tan x + cot y)/ (tan x)(cot y)    
= 2(tan x/cot x + cot y/cot y)/ (tan x)(cot y)      
= 2[(tan x/cot x)(1/cos x) + 1/sin y]/ (sin x)(cos y)      
= 2[sin x/cos x + 1/sin y]/ (sin x)(cos y)    
= 2[(sin x/sin y)(1/cos y) + cos x/sin y]/ (sin x)(cos y)      (replace cos x with sin x/sin y and cot y with 1/tan y)
= 2[(sin x/sin y)(1/cos y) + (sin x/sin y)(cos y/sin y)]/ (sin x)(cos y)      
= 2/cos ysin y    

Simplifying right-hand side:

2 tan y + 2 cot x
= 2(tan y + cot x)    
= 2(cot x/cot x + tan y/cot x)  
= 2[(cos y/sin y)(1/sin x) + sin y/cos x]/ (sin x)(cos y)      (replace cot x with cos x/sin x )
= 2[(cos y/sin y)(1/sin x) + (cos y/sin y)(sin x/cos x)]/ (sin x)(cos y)    
= 2(cos y/sin x)/ (sin x)(cos y)      
= 2/cos xsin x    

Since,  both simplified to the same expression, hence identity is verified.

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Answer:

D. <15/√346>

Have a nice day! :)

Answer:

\( \sqrt{ - 147} = \sqrt{147} \times \sqrt{ - 1} = 7i \sqrt{3} \)

I hope I helped you ^_^

The answer ; √ –108 = √108 × √–1 = 6i √3

=====================================================

Explanation:

The value 12 is between the perfect squares 9 and 16

This means we can write the following inequality \(9 < 12 < 16\)

From here we apply the square root to all three sides and simplify like so

\(9 < 12 < 16\\\\\sqrt{9} < \sqrt{12} < \sqrt{16}\\\\3 < \sqrt{12} < 4\)

and we see that the square root of 12 is between 3 and 4.

Using a calculator would confirm this

\(\sqrt{12} \approx 3.464\)

Answer:

Step-by-step explanation:

Find the numbers closest to 12 on either side that are perfect squares:

1, 4, 9, 16, 25

12 is in between the numbers 9 and 16. The square root of 9 is 3 and the square root of 16 is 4. Therefore, the square root of 12 is in between 3 and 4.