Please help my question is in the attachment!

The rate of change of the function over the interval [ 4, 8 ] will be 6.

The rate of change function represents the rate at which one quantity changes in relation to another. Simply put, the rate of change is the difference between the amount of change in one item and the comparable amount of change in another.

Given function:-

The formula for calculating the rate of change will be given as:-

[tex]ROC = \dfrac{F(x_2)-F(x_1)}{x_2-x_1}[/tex]

We have x₁ = 4 and x₂ = 8 given in the question

F(x₂) =  x²₂ - 6x₂ + 10 = (8)² - ( 6 x 8 ) + 10 =

F(x₂) = 64 - 48 + 10

F(x₂) = 26

F(x₁) =  x²₁ - 6x₁ + 10 = (4)² - ( 6 x 4 ) + 10 =

F(x₁) = 16 - 24 + 10

F(x₁) = 2

[tex]ROC = \dfrac{F(x_2)-F(x_1)}{x_2-x_1}[/tex]

[tex]ROC = \dfrac{26 -2}{8-4}=\dfrac{24}{4}=6[/tex]

Therefore the rate of change of the function over the interval [ 4, 8 ] will be 6.

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Answer:

$980

Step-by-step explanation:

Given the cost of gasoline = $2.80/mile

Total Distance = 175miles x 2 (Back and forth)

= 350 miles

Total Cost = Cost of gasoline x Total Distance =

= $2.80 x 350

= $980

The total cost of the trip from Seattle to Portland and back cost in dollars will be;

⇒ $250

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The driving distance from Seattle to Portland is 175 miles.

Your car gets 25 miles per gallon and the cost of gasoline is $2.80 per gallon.

Now,

Since, The driving distance from Seattle to Portland is 175 miles.

Hence, The total distance from Seattle to Portland and back = 175 + 175

                                                                                            = 350 miles

And, Your car gets 25 miles per gallon and the cost of gasoline is $2.80 per gallon.

Hence, The cost of gallon = 350/25 x $2.50

                                        = 100 x $2.50

                                        = $250

Thus, The total cost of the trip from Seattle to Portland and back cost in dollars will be;

⇒ $250

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Answer:

First Inverse function= f^-1(x)=x/3-5/3

Second Inverse function=f^-1(x)=x/3-5/3

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

We need to isolate the variable, aka make y on one side. So, if we divide 8 on both sides, it will be

y8=40

y8/8=40/8

y=5

Answer:

(6,2)

Step-by-step explanation:

When solving a system of simultaneous equations, we want to see where the graphs intersect.

2x+5y =22 is the red line

x+y = 8 is the green line

They intersect at a point

The point is x=6   y=2

(6,2)

Answer:

here you go

Step-by-step explanation:

no of times he failed = -3

points he losed = -3 x 4 = -12

no of times he need to hit the target to get 48 points = 6x

equation

-12 + 6x = 48

6x = 60

x = 10

no of points he  will  gain = 10 x 6 = 60

Based on the amount saved per week and the down payment of the property, the number of months it will take to save the amount is 46 months.

First, find out the amount saved per month:

= (30% x 2,051) x 2 payments a month

= $1,230.60

The downpayment is:

= 281,700 x 20%

= $56,340

The closing cost is:

= 1.15 x 56,230

= $843.45

The number of months till the amount is saved is:

= (56,340 + 843.45) / 1,230.60

= 46 months

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Answer:

First find the x and y intercepts. Recall that intercepts intersect the x and y axis of a graph, therefore either the x or y value of a coordinate point must be 0 in order for it to be an intercept.

After you find the intercept, plot the them on the cartesian coordinate system and draw a straight line (it’s a linear equation) going through the two intercepts.

Side note: Not sure how credentials work on Quora yet. I meant to say I am a student

The equation of the lines can be plotted on the graph after calculating the coordinates on each line.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

We have two linear equation:

x = 4y  

x + y = 7.0

To plot the linear equation first we will find the few coordinates to plot on the coordinate plane.

For the equation of line:

x = 4y

x 0 1 2 3 -1 -2 -3

y 0 4 8 12 -4 -8 -12

For the equation of line:

x + y = 7.0

x 0 1 2 3 -1 -2 -3

y 7 6 5 4 8 9 10

Thus, the equation of the lines can be plotted on the graph after calculating the coordinates on each line.

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Answer:

{x∈R | [tex]\frac{2x}{3\pi } +\frac{1}{2}[/tex], x∉Z}

Step-by-step explanation:

Given the function y=3tan(2/3x)

We know that tangent is a function that's continuous within it's domain but not continuous on all real numbers

Also, the roots of y=3tan(2/3x) is [tex]3\pi n/2[/tex] where n is an integer

Note that the domain of the function cannot be within [tex]3\pi n/2[/tex]

Therefore, {x∈R | [tex]\frac{2x}{3\pi } +\frac{1}{2}[/tex], x∉Z}

If the standard deviation for a set of data is 9.5. The margin of error is: 19.5.

Using this formula

Margin of error=Standard deviation×Mean

Let plug in the formula

Margin of error=205 × 9.5%

Margin of error = 19.475

Margin of error = 19.5 (Approximately)

Therefore If the standard deviation for a set of data is 9.5. The margin of error is: 19.5.

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Answer:

–6x + 15 < 10 – 5x

An open circle is at 5 and a bold line starts at 5 and is pointing to the right.

Step-by-step explanation:

When you break down -6x + 15 < 10 - 5x, you get x > 5.

Because x is GREATER than 5, when making a number line, there is an open circle on 5 and a bold line pointing to the right.

Answer:

-59

Step-by-step explanation:

x = -2

4(-2)³ - 6(-2)² + (-2) - 1

= -32 - 24 - 2 - 1

= - 59

Option B. x-8 = 40-2x is the correct equation for the opposite angle theorem.

According to the Opposite angles theorem,

Vertical angles theorem or vertically opposite angles theorem states that two opposite vertical angles formed when two lines intersect each other are always equal (congruent) to each other.

[tex]= > x-8=40-2x[/tex] ( : Because opposite vertex angles are equal)

So option B is correct in the given question

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Answer:

D.) 3y-15 =85+

Step-by-step explanation:

simply put, opposite angles theorem is where the angles are on the opposite side so the parallelogram in the photo shows that 3y-15 is on the opposite angle as 85+y (I also got this one right lol)

Answer:

a ) cylinder

b) triangular pyramid

Answer:

g-1(x)=5×-9, (g-1g) (1)=1, h-1(3)= -

Step-by-step explanation:

The probability P(-0.5 ≤ z ≤ 0.5) is the greatest for a standard normal distribution, and the value of P(-0.5 ≤ z ≤ 0.5) is 38.2% option second is correct.

It's the probability curve of a continuous distribution that's most likely symmetric around the mean. On the Z curve, at Z=0, the chance is 50-50. A bell-shaped curve is another name for it.

We have a statement:

Which of the following probabilities is the greatest for a standard normal distribution:

The options are:

P(-1.5 ≤ z ≤ -0.5)

P(-0.5 ≤ z ≤ 0.5)

P(0.5 ≤ z ≤ 1.5)

P(1.5 ≤ z ≤ 2.5)

As we know from the normal distribution curve we can find the probability between the range given. At Z=0, the chance is 50-50.

From the Z-curve:

P(-1.5 ≤ z ≤ -0.5)  = 9.2% + 15% = 24.2%

P(-0.5 ≤ z ≤ 0.5) = 19.1% + 19.1% = 38.2%

P(0.5 ≤ z ≤ 1.5) = 15% + 9.2% = 24.2%

P(1.5 ≤ z ≤ 2.5) = 4.4% + 1.7% = 6.1%

Thus, the probability P(-0.5 ≤ z ≤ 0.5) is the greatest for a standard normal distribution, and the value of P(-0.5 ≤ z ≤ 0.5) is 38.2% option second is correct.

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Answer:

B) P (-0.5 <= z <= 0.5)

Step-by-step explanation:

Answer:

B. △RTS

Step-by-step explanation:

△MON ≅ △RTS

Answer:

Answer:

460

Step-by-step explanation:

4 tens is equivalent to 40, so 500-40 is = to 460.

Hope this helps! :D

hi brainly user! ૮₍ ˃ ⤙ ˂ ₎ა

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[tex]\large \bold {ANSWER}[/tex]

[tex]\large \bold {SOLUTION}[/tex]

5 hundreds is 5 multiplied by 100, so it equals 500. 4 tens is 4 times 10, so 40.

So 5 hundreds minus 4 tens is 460.

Answer:

11/2

Step-by-step explanation:

Multiply by 2/2 to remove the decimal.

Answer:

D.

because 2 times 120 reduced.

Answer:

the equivalent fractions for 2/5 are:

(2/5) × (2/2) = (2 × 2) / (5 × 2) = 4/10

(2/5) × (3/3) = (2 × 3) / (5× 3) = 6/15

(2/5) × (4/4) = (2 × 4) / (5 × 4) = 8/20

Answer:

4/10, 6/15, 8/20, etc.

Step-by-step explanation:

I hope you got some idea

Answer:

[tex]h(x)=\frac{1}{2}x -\frac{1}{2} .[/tex]

Step-by-step explanation:

if the initial function is f(x)=2x+1, then

x=2*h(x)+1;

2h(x)=x-1;

[tex]h(x)=\frac{x}{2} -\frac{1}{2}.[/tex]

PS. change design according the local requirements.

Answer:

[tex]y^{-1} =\frac{1}{2} x-\frac{1}{2}[/tex]

Step-by-step explanation:

To find the inverse, you want to swap the inputs with the outputs, which is why you have the swapped domain and range between a function and its range.

So, given f(x)=2x+1, its inverse would give,

x=2y+1.

Solve for y,

2y=x-1 -> y=(x-1)/2 -> y=[tex]\frac{1}{2} x-\frac{1}{2}[/tex]

Therefore, [tex]y^{-1} =\frac{1}{2} x-\frac{1}{2}[/tex]

Answer:

The Mean and Standard deviation for the given data would be as follows:

μ =79.7

б =7.81

Step-by-step explanation:

Mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.

Standard deviation is the square root of the arithmetic mean of the squares of deviations of the items from their mean values.

Frequency Distribution

Given that,

Temperature       Lower Limit           Upper Limit             Days([tex]f_{i}[/tex])

50-59                       50                           59                          2

60-69                       60                           69                         313

70-79                         70                           79                          1419

80-89                        80                          89                          1503

90-99                        90                          99                           319

100-109                    100                         109                            9  

Average([tex]x_{i\\}[/tex])    

[tex]\frac{50+59}{2} = 54.5\\ \\\frac{60+69}{2} = 64.5\\ \\\frac{70+79}{2} = 74.5\\\\\frac{80+89}{2} = 84.5\\ \\\frac{90+99}{2} = 94.5\\ \\\frac{100+109}{2} = 104.5[/tex]

As we know,

Mean (μ) =∑ [tex](x_{i}f_{i})[/tex]/∑[tex]f_{i}[/tex]

= { (54.5 * 2) + (64.5 * 313) +(74.5 * 1419)+(84.5*1503)+(94.5*319) + (104.5*9)/ (2+313+1419+1503+319)

∵ μ = 79.7

As we know,

Standard Deviation:-

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

by putting the values, we get

∵ б = 7.81

Hence, μ = 79.7 and б=7.81  are the correct answers.

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Answer:

[tex]7 469.8.56[/tex]

nossa nem sei como é bom saber se fala com a mãe e o pai do mundo e vc não tem mais nada pra comer e não tem como fazer a gente vai ficar muito tempo sem fazer a mãe dela não e vc como tá o trabalho rede de nada em casa e é só pra mim né não é fácil de fazer a mãe dela e a mãe dele tá bem né não é fácil de fazer o que vc quer que Deus quiser vai dar pra mim né e não tem como fazer d id da x não vou poder é o que eu te abençoe e ilumine e ilumine todos os dias entre?01029)

Answer:

180

Step-by-step explanation:

Answer:

180

Step-by-step explanation:

The triangle is not a right triangle. This is because the sum of the square of the two shorter lengths is not equal to the square of the longest length.

In order to determine if the triangle is a right triangle, Pythagoras theorem would be used.

The Pythagoras theorem: a² + b² = c²

where a = length

b = base

c = hypotenuse

12 ² + 24²

= 144 + 576 = 720

29² = 841

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The value of x for a height 1 foot below the starting point will be the negative 2.76.

The connection between the lengths and angles of a triangular shape is the subject of trigonometry.

A water ride with heights above and below the starting point can be modeled by the function is given below.

y = 3 sin⁡ (π / 2 (x + 3) − 2), Within the interval 0 < x < 5

We know that π / 2 = 90°

Then the value of x for a height 1 foot below the starting point will be

           1 = 3 sin⁡ (90 (x + 3) − 2)

        1/3 = sin⁡ (90 (x + 3) − 2)

   19.47 = 90 (x + 3) − 2

   21.47 = 90 (x + 3)

0.2385 = x + 3

          x = -2.76

Then the value of x will be the negative 2.76.

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Answer:

the technical number depends on what you are including to be algebraic identities.

There are multiple forms of most identities (pos. / neg.   and multiple ways of writing the same identity)

generally, you can consider there to be 10

Step-by-step explanation:

algebraic identity: an equality that holds true for any variable values

standard identities:

square of binomial:

(a+b)² = a² +2ab + b²

(a - b)² = a² - 2ab + b²

difference of squares:

(a + b)(a - b) = a² - b²

----

product of two binomials:

(x + a)(x + b) = x² + (a + b)x + ab

square of trinomial:

(x + y + z)² = x² + y² + z² + 2xy + 2yz + 2zx

(x - y - z)² = x² + y² + z² -2(xy + yz - zx)

cube of binomial:

(x + y)³ = x³ + y³ + 3xy (x + y)

(x - y)³ = x³ + y³ - 3xy (x - y)

(a - b)³ = a³ - 3a²b + 3ab² - b³

sum of cubes:

a³ + b³ = (a + b)(a² - ab + b²)

x³ + y³ = (x + y)(x² - xy + y²)

x³ + y³ = (x - y)(x² + xy + y²)

difference of cubes:

a³ - b³ = (a - b)(a² + ab + b²)

x³ - y³ = (x - y)³ + 3xy(x - y)

--

x³ + y³ + z³ - 3xyz = (x + y + z)(x² + y² + z² - xy - yz - zx)

                              = 1/2 (x + y + z) [(x -y)² + (y - z)² + (z - x)²]

(a + b + c)³ = a³ + b³ + c³ + 3(a + b)(b + c)(c + a)

--

and

if x + y + z = 0, then x³ + y³ + z³ = 3xyz

hope this helps!!

(this took me a while to write; there are also a few complicated identities also that I've left out)

[tex]( {a + b})^{2} = {a}^{2} + {b}^{2} + 2ab \\ \\ {(a - b)}^{2} = {a}^{2} + {b}^{2} - 2ab \\ \\ {a}^{2} - {b}^{2} = (a + b)(a - b) \\ \\ {a + b + c}^{2} = {a}^{2} + {b}^{2} + {c}^{2} + 2ab + 2bc + 2ca \\ \\ {a + b}^{3} = {a}^{3} + {b}^{3} + 3ab(a + b) \\ \\ {a - b}^{3} = {a}^{3} - {b}^{3} - 3ab(a - b) \\ \\ {a}^{3} + {b}^{3} + {c}^{3} - 3abc = (a + b + c)( {a}^{2} + {b}^{2} + {c}^{2} - ab - bc - ca).[/tex]