Use this Distant vs time graph to answer the questions:

1. What measurement is represented on the x-axis and what unit is it measured in?

2. What measurement is represented on the y-axis and what unit is it measured in?

3. Hours 0-4 (Section A) the person is traveling away from their starting location. How far do they travel in those 4 hours? Remember to include units.

4. What is their rate of change (speed) in Section A? Remember to include units.

5. What is happening in Section B (Hours 4-6)?

6. What is the rate of change (speed) in Section B? Remember to include units

7. How far did this person travel in Section C (Hours 6-7)? Remember to include units.

8. What is their rate of change (speed) in Section D (Hours 7-10)? Remember to include units.

9. During which section was the person moving at the highest speed? What was their speed? Defend your answer.

10. During which section did the person travel the farthest? How far did they travel?

11. BONUS: Write a short (paragraph) scenario that tells the story about where the data on the graph came from. You can be as creative as you want!

1. (a) The answer to the given part is 12.56

(b)the answer to the given part 50.24

(c) the answer to the given part153.86

2. (a)the answer to the given part ₋1

(b)the answer to the given part 2

(c) the answer to the given part4

3. (a)the answer to the given part 12

(b) the answer to the given part5

(c) the answer to the given part1

Given,

1. A(r) = πr²

a. A(2) = π(2)²

= π4

= 3.14 ₓ 4

= 12.56

b. A(4)

A(r) = πr²

= π(4)²

= π16

= 50.24

c. A(7)

A(r) = πr²

= π(7)²

=  π(49)

= 153.86

2. s(t) = t² ₋ 2t ₊ 1

a. S(0) = 0² ₋ 2(0) ₋ 1

= ₋1

b. S(3) = 3² ₋ 2(3) ₋ 1

= 9 ₋ 6 ₋ 1

= 2

c. S(₋1) = (₋1)² ₋ 2(₋1) ₊ 1

= 1 ₊ 2 ₊ 1

= 4

3. (a) f(₋3) which means x ≤ ₋1

therefore, f(₋3) = 4 ₋ 3x

= 4 ₋ 3(₋3)

= 4 ₊ 9

= 12

(b) f(0) which means ₋1<x<1

therefore, value of f(0) = 5.

(c) f(2) which means x≥ 1

therefore, value of f(2) = x² ₋ 3

= 2² ₋ 3

= 4 ₋ 3

= 1

hence, we get the desired results.

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The expression that represents the power of a product property is a^m * a^n = a^(m + n)

This power of a product property states that when two powers that have the same base are multiplied, the exponents of the bases are added

The statement is given as

The power of a product property

The definition above implies that the representation of the power of a product property is

x^m * x^n = x^(m + n)

Using the above as a guide, we have

a^m * a^n = a^(m + n) -- option (d)

Hence, the expression that represents the power of a product property is a^m * a^n = a^(m + n)

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   The simplification of the given expression can be expressed as: 8√2m⁷n⁹

Simplification is defined as a final operation that shows the result of a reduction of a number or set without altering its value.

 In other words, when we simplify we express the same value in a shorter or summarized form.

  The algebraic expression that we must simplify to its minimum expression is:

4√32 m⁷n⁹,  we can see that it is an expression that has two variables

we reduce the value of the square root

√32 = √4x4x2 = √4²x2 = 4√2

4(4√2)m⁷n⁹  Variables are irreducible

8√2m⁷n⁹

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Answer: 210,000

Step-by-step explanation:

there are 120 seconds in 2 minutes.

125 times 120= 15,000

15,000 times 2= 30,000

so it spins 30,00 times in a day.

30,000 times 7=210,000

so it spins 210,000 times in a week.

The percent increase and decrease between the given starting and ending quantities above are as follows:

In Mathematics, there are two main types of percentage and these include the following:

Mathematically, percentage increase can be calculated by using this formula:

Percentage increase/decrease = [Final value - Initial value]/Initial value × 100

Substituting the given parameters into the formula, we have;

Percentage increase = [10 - 3]/3 × 100

Percentage increase = 7/3 × 100

Percentage increase = 233.3%.

Percentage increase = [20 - 9]/9 × 100

Percentage increase = 11/9 × 100

Percentage increase = 122.2%.

Percentage decrease = [100 - 85]/9 × 100

Percentage decrease = 15/85 × 100

Percentage decrease = 17.7%.

Percentage decrease = [45 - 20]/20 × 100

Percentage decrease = 25/20 × 100

Percentage decrease = 125%.

Percentage increase = 30/30 × 100

Percentage increase = 100%.

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Answer:

ray DB I think good luck brother

All the zeros of each function y=3x³-7x²-14 x+24 are

X₁ = -2, X₂≈ 1.33333, X₃ = 3

Polynomial roots are the answers to any polynomial for which we need to determine the value of the unknowable variable. Knowing the roots will allow us to evaluate the polynomial's value to zero. A polynomial of degree "n" in variable x is an expression with the following formula: anxn + an-1xn-1 +...... + a1x + a0.

The greatest power of a variable in a polynomial is referred to as the polynomial's degree.

A monomial is a polynomial with a single term. A monomial is referred to as a polynomial of zero degrees if it simply has a constant term.

According to the given data,

y=3x³-7x² -14x + 24

Substitute y = 0

0=3x³-7x²- 14x + 24

Move the expression to the left

0-3x³+7x² +14x-24=0

Remove 0

Rewrite

- 3(x³+8) +7x(x+2)=0

Factor the expression

-3(x+2) x(x²-2x + 4) +7x(x+2)=0

Remove the parentheses

-(x+2)x(3x²-6x+12-7x) = 0

Collect like terms

-(x+2)x (3x²-13x+12) 13x+12=0

Rewrite the expression

(x+2)x(3x-4)x(x-3)=0

Separate into possible cases

x+2=0

3x-4=0

X 3=0

Solve the equations

x = -2

X=4/3

X = 3

The equation has 3 solutions

Solution

X₁ = -2  , X₂=4/3 , X₃ = 3

Alternative Form

X₁ = -2, X₂= 1.33333, x₃ = 3

Hence ,all the zeros of each function y=3x³-7x²-14 x+24 are

X₁ = -2, X₂≈ 1.33333, X₃ = 3

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Step-by-step explanation:

The perimeter of a trapezoid is All the sides combined. We already know two of the sides. You can simplify the square roots to be 2[tex]\sqrt{2}[/tex]+6+x. We know that two sides (or the ones we don't know) are equal, and we see an altitude. This shows that we can make a right triangle be a^2+b^2=c^2. Once we substitute everything, we find [tex]2\sqrt{2}[/tex]^2(or 8)+x^2+c^2. This means that we now need to find x. Also, sorry, but I don't know what to do after this so I hope you can solve it from here. The things you need to find out are c^2 and x.

Answer:

6

Step-by-step explanation:

You have to divide 24 by four.

Answer:

D. y = 8x

Step-by-step explanation:

[tex]\mathrm{y(out put) = x(in put) \times 8}[/tex]

Answer: Exercise 8 module 3 Describe the graph of the Celsius - Fahrenheit relationship is    F =  8C + 3  and     C = (F-3) / 8

Step-by-step explanation:

Celsius and Fahrenheit are two scales used to measure temperature. The temperature in the centigrade scale will be expressed in degrees Celsius. The temperature in the Fahrenheit scale will be expressed in degrees Fahrenheit. The relation between Celsius and Fahrenheit is proportional. Both have a different freezing point of water and both follow the varied unit difference between each scale.

Celsius to Fahrenheit

The conversion from Celsius to Fahrenheit can be mathematically expressed as-

                            F = [ (9/5) x C ] + 32

Where,

F is the temperature in Fahrenheit.

C is the temperature on the Centigrade scale.

Fahrenheit to Celsius

The conversion from Fahrenheit to Celsius can be mathematically expressed as-

                          C = (5/9) [ (F-32) ]

Where,

F is the temperature in Fahrenheit.

C is the temperature on the Centigrade scale.

Units of Celsius and Fahrenheit :

The units of temperature scale are useful in differentiating temperatures from one scale to another.

The temperature on the Celsius scale is denoted by °C

The temperature on the Fahrenheit scale is denoted by °F

Using linear function concepts, the graph of the Celsius-Fahrenheit relationship is linear with an intercept of 3 and slope of 8 module.

A linear function is modeled by:

                    y = mx + b

where,    m is the slope

so, we can write,

                    F =  8C + 3

we can also express the Celsius in terms of Fahrenheit :

                     8C = F - 3

                      C = (F-3) / 8

Therefore,

Exercise 8 module 3 Describe the graph of the Celsius - Fahrenheit relationship is    F =  8C + 3  and    C = (F-3) / 8.

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If  certain refrigerator requires 170 watts of electricity when it is running. It typically runs about 20 minutes per hour. The amount it cost to run this refrigerator for one year if the cost per kWh is $0.11 is:  $53.856.

Given:

Electricity watts = 170 watts

Minutes run = 20 minutes

Cost per KWh =$0.11

Hence,

170 watts = 1.7×10^-1

20 min = 1/3 h

Now let calculate the cost of running the refrigerator for one year  

1.7×10^-1 × 1/3 × 24 ×360 × $0.11

= $53.856

Therefore If  certain refrigerator requires 170 watts of electricity when it is running. It typically runs about 20 minutes per hour. The amount it cost to run this refrigerator for one year if the cost per kWh is $0.11 is:  $53.856.

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Answer:

530-450=80

Answer = 80 feet

Answer: The answer is -28.

Step-by-step explanation: 2+4-52+2+5+7+4 = -28

Hope this helped :D

Answer:

The correct answer is -28

You need to make 3 batches if you want to get 6 dozen cookies.

Here we know that you need to make a total of 6 dozen cookies, and we know that each batch you make gives 2 dozen.

Then if you make b batches, the number of dozens of cookies that you get is given by the linear equation:

d = 2*b

So, if you want to get 6 dozens, you need to replace d by 6, we will get:

6 = 2*b

Solving that for b, we get:

6/2  =b = 3

You need to make 3 batches if you want to get 6 dozen cookies.

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Alice is wrong. Not all numbers that end with 7 is a prime numbers. an example is 57.

Prime numbers are numbers that are divisible by 1 and themselves alone. Examples are 2, 3, 7,17, and 11. However, 7  and 17 being prime numbers does not make any other number ending with 7 a whole number. E.g 57, a number that ends with 7 but it is not a prime number because it is divisible by 3.

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The correct answers are:

The range of packages shipped to  Rare Vinyl is greater than the range of packages shipped to  Rare Vinyl .

The distribution of packages shipped to both businesses are approximately symmetrical.

A line plot is a graph that is made up of a number line and check marks. A line plot is a graph that is used to show the frequency of data points in a data set using check marks above a number line.  The greater the frequency of the data point, the greater the number of marks above the number on the number line.

Range is used to measure the variation of a data set. It is the difference between the maximum number and the minimum number.

Range = maximum number - minimum number

Range of Rare Vinyl  = 13 - 8 = 5

Range of Aquarium World = 6 - 0 = 6

A line plot is symmetrical if the opposite sides of the line plot are identical in shape. It can be seen that opposite sides of both line plots are identical.

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If the scores on an exam follow an approximately normal distribution with a mean of 76.4 and a standard deviation of 6.1 points, then the minimum score needed to be in the top 7% is calculated to be 85.404.

This type of problem can be categorized as a normal distribution problem and can be solved with the help of z-score.

If we consider Z = standard score,

μ = mean

σ = standard deviation

Then the z-score to figure out the lowest score to be in the top 7% is given as,

Z = x - μ / σ

If the p-value is known, the z-score can be found with the help of the standard table.

As the minimum score to be in the top 7% is to be determined, p-value = 0.07

The z-score that corresponds to the p-value of 0.07 is 1.476 in the standard table.

Hence,

1.476 = x - 76.4 ÷ 6.1

1.476 × 6.1 = x - 76.4

1.476 × 6.1 + 76.4 = x

9.004 + 76.4 = x

x = 85.404

Therefore, 85.404 is the minimum score that is needed to be in the top 7%.

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Applying the quotient rule, the derivative of the function is given by:

[tex]f^{\prime}(x) = \frac{3(3x - 6)^2(3(2x - 2) - 2(3x - 6))}{(2x - 2)^4}[/tex]

Suppose a quotient function defined as follows:

f(x) = g(x)/h(x).

The derivative of the function is defined according to the following rule:

f'(x) = [g'(x)h(x) - h'(x)g(x)]/(h(x))²

For this problem, the function is given by:

f(x) = (3x-6)³ /(2x-2)³.

Hence the parameters are:

Applying the power rule and the chain rule, the derivatives of the functions are:

Hence the derivative of the function is:

[tex]f^{\prime}(x) = \frac{9(3x - 6)^2(2x - 2)^3 - 6(2x - 2)^2(3x - 6)^3}{(2x - 2)^6}[/tex]

[tex]f^{\prime}(x) = \frac{3(3x - 6)^2(2x - 2)^2(3(2x - 2) - 2(3x - 6))}{(2x - 2)^6}[/tex]

[tex]f^{\prime}(x) = \frac{3(3x - 6)^2(3(2x - 2) - 2(3x - 6))}{(2x - 2)^4}[/tex]

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Answer:

explain why a mission statement should not include monetary amount numbers percentages ratios or objectives

The constant of proportionality between y and x in the graph is 1.

From given graph we can see that

When x=2 then y=2

When x=4 then y=4

When x=6 then y=6

when x=10  then  y= 10

It means when x increases then y also increases .

It is in direct proportion.

Direct proportion:y/x=k.

Where k=Proportionality constant

Using the formula

y/x=10/10=2/2=1

Hence, the value of proportionality constant=1

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The exponential function that models exponential growth is y = 5(3)ˣ.

The example of an exponential function that models exponential decay is y = 2(0.8)ˣ

Exponential growth is the process by which quantity increases over time. It happens whenever the instantaneous rate of change of a volume with respect to time has been proportional to the volume itself.

Consider exponential function; y = a(b)ˣ.

For the exponential growth a > 0 and b > 0.

Suppose a = 5 and b = 3.

Then, the function will become after substituting the both values.

y = 5(3)ˣ which is the exponential growth of the exponential function.

According to the law, exponential decay would be the decrease in a quantity (1) where is the exponential function and the initial value, for a parameter as well as constant (known as the decay constant).

Now, as per the question.

For the exponential decay a > 0 only.

Consider exponential function; y = a(b)ˣ.

Let, a = 2 and b = 0.8.

Then,

y = 2(0.8)ˣ

Therefore, the exponential function in the form of exponential decay is y = 2(0.8)ˣ.

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the term to term rule is that every next term becomes 2 times of the previous term and the 11th term is 5120 for the sequence 5, 10, 20, 40, 80.

We have a sequence:

5, 10, 20, 40, 80

We need to find the term to term rule of the sequence.

We get that:

10 / 5 = 2

20 / 10 = 2

40 / 20 = 2

80 / 20 = 2

Term to term rule is that every next term becomes 2 times of the previous term.

10th term = 2560

11th term = 2 × 2560

11th term = 5120

Therefore, we get that, the term to term rule is that every next term becomes 2 times of the previous term and the 11th term is 5120 for the sequence 5, 10, 20, 40, 80.

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The least amount of money she needs to deposit to avoid a fee is;  $16.62

We are given;

Amount Keisha has in her checking account = $585.43

Minimum balance to be maintained = $300

Check written = $302.05

Now, if x represents the variable, that would be used for the least amount of money she needs to deposit to avoid a fee, then the inequality is;  $585.43 - $302.05 + x ≥ $300

$283.38 + x ≥ $300

Subtract 283.38 from both sides to get;

x ≥ $16.62

Thus, the least amount of money she needs to deposit to avoid a fee is;  $16.62

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The function has a domain of x ≥5 and a range of y≤3

Given that

To find

So, according to the question

We have

A square root can only be calculated in values equal to or greater than zero, so keep that in mind.

So, if we want the domain to be x > 5, then we must have:

[tex]\sqrt{x-5}[/tex].

Now that we also want the range to be equal to or less than 3, we need a constant term with a value of 3 and a negative coefficient before the square root, which gives us:

y = - [tex]\sqrt{x-5}[/tex] +3

Answer:

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Answer:

C.

[tex]y = - \sqrt{x - 5 + 3} [/tex]

Answer:

Step-by-step explanation:

ik u already know this.. im still gonna answer for points.

In order to find how much is 1 bottle of shampoo you just divide the $20 by 8.

Just use a calculator and you will get $2.50

Answer:

The answer will be $2.50

Step-by-step explanation:

All you do is divide 20 by 8 and you will get 2.5 and if you need to check the answer you can multiply 2.5 by 8

Hope this helps and may God bless you<3

Answer:

163 degrees

Step-by-step explanation:

163 degrees is equal to y

Z = x

The measure of angle y is 163° and the measure of angle x and z is 17 degrees.

Given that:

Two lines are intersected with each other.

It is required to find the measure of angles x, y, and z.

The angles formed on the opposite side of the intersecting line are called vertical angles.

Also, by the Vertical Angles Theorem, the vertical angles formed are always equal.

Here, y is vertical to the given measure of 163°.

So, y = 163°.

Now, x and y are the angles formed along a line.

So, they are linear pair of angles.

Linear pair of angles are supplementary.

So, x + y = 180

x = 180 - 163

  = 17°

Also, x and z are vertical angles.

So, z = 17°

Hence, x = 17°, y = 163°, and z = 17°.

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Using proportions, Mrs. Terry total medical expenses are of $2,526.4.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.

For this problem, her expenses are divided as follows:

Hence her total medical expenses are given as follows:

2500 + 0.2 x 132 = $2,526.4.

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Answer:

3

Step-by-step explanation:

I can figure this out by counting, I just imagine its a rectangle, count the 6 squares, the cut it in half

Answer:

3

Step-by-step explanation:

Translate it 3 units left, then turn it 180 degrees starting from its right side to its left side. Now, the triangle is mirrored.