find the average rate of change ​

Find The Average Rate Of Change

Answers

Answer 1

Answer:

3rd option

Step-by-step explanation:

the average rate of change of f(x) in the closed interval [ a, b ] is

[tex]\frac{f(b)-f(a)}{b-a}[/tex]

here [ a, b ] = [ 1, 4 ] , then

f(b) = f(4) = 3³ + 2 = 27 + 2 = 29

f(a) = f(1) = [tex]3^{0}[/tex] + 2 = 1 + 2 = 3 , then

average rate of change = [tex]\frac{29-3}{4-1}[/tex] = [tex]\frac{26}{3}[/tex]


Related Questions

Find the value of x.

Answers

Answer:

x = 20°

Step-by-step explanation:

(4x-10)+x=90

4x-10+x=90

4x+x-10=90

5x-10=90

5x=100

x=20

Answer:

20

Step-by-step explanation:

Straight line angles:

     Angles on a straight line add up to 180°.

 90 + 4x - 10 + x = 180

 90 - 10 + 4x + x = 180

Combine like terms.

         80 + 5x     = 180

Subtract 80 from both sides,

                 5x    = 180 - 80

                    5x = 100

Divide both sides by 5

                      x = 100 ÷ 5

                      [tex]\sf \boxed{x = 20^\circ}[/tex]

Please help me I need this for exam tomorrow and can u please show the working

Answers

Answer:

46,57/4

Step-by-step explanation:

area = π.r^2 = π.(d^2)/4

d^2 = AB^2= 5,6^2+3,9^2 =46,57

----> area = π.46,57/4

Solve for x.
Use the quadratic formula.
2x² - 9x + 8 =0

Answers

Answer:

x = 9/4 + 1/4 √17 or x = 9/4 + −1/4 √17

/ = over

Step-by-step explanation:

a = 2, b=-9, c=8

x = −b±√b2−4ac/2a

x = −(−9)±√(−9)2−4(2)(8)/2(2)

x = 9±√17/4

x = 9/4 + 1/4 √17 or x = 9/4 + −1/4 √17

On a number line, 6.3 would be located ______. Choose all answers that make a true statement.



6.3
《--|----|----|----|----|----|----|----|----|----|--》

A. between 6.2 and 6.4
B. to the left of 6.42
C. to the right of 6.45
D. to the right of 6.5​

Answers

Answer:

A).

Step-by-step explanation:

The numbers should be in consecutive order e.g. - 6.2 6.3 6.4

6.3 will be between 6.2 and 6.4 because the number line has a difference of 0.2 per large space

Which of the following terms best describes a vertical line that the graph of a
function approaches but never intersects?

A Horizontal asymptote
B Proportion
C Vertical asymptote
D Inverse variation

Answers

The answer is (C) vertical asymptote.

georgia drew a scale model of one of the stepping stones in her garden. the two shapes are similar, and the ratio of the lengths of the sides is 4:1. if the length of side dc equals twelve inches, what is the length of side ut in the scale drawing?

Answers

The length of the UT is 3 inches if the ratio of the lengths of the sides is 4:1. if the length of side DC equals 12 inches,

What is a scale factor?

The ratio among comparable dimensions of an object and a model with that object is known as an exponent in algebra. The replica will be larger if the scale factor is a whole number. The duplicate will be lowered if the step size is a fraction.

We have:

Georgia drew a scale model of one of the stepping stones in her garden. the two shapes are similar, and the ratio of the lengths of the sides is 4:1.

The length DC = 12 inches

DC/UT = 4/1

12/UT = 4/1

UT = 12/4 = 3 inches

Thus, the length of the UT is 3 inches if the ratio of the lengths of the sides is 4:1. if the length of side DC equals 12 inches,

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Answer:

3 in.

Step-by-step explanation:

Keep it simple :)

Use trigonometric identities to verify each expression is equal.

c) csc^2(x)-2csc(x)cot(x)+cot^2(x) = tan^2(x/2)

d) [cos(x)cos(y)][tan(x)+tan(y)] = sin(x+y)

Answers

Part (c)

[tex]\text{LHS}=\csc^{2} x-2\csc x\cot x+\cot^{2} x\\\\=(\csc x-\cot x)^{2}\\\\=\left(\frac{1}{\sin x}-\frac{\cos x}{\sin x} \right)^{2}\\\\=\left(\frac{1-\cos x}{\sin x})^{2}\\\\=\tan^{2} \left(\frac{x}{2} \right)\\\\=\text{RHS}[/tex]

Part (d)

[tex]\text{LHS}=[\cos x \cos y][\tan x+\tan y]\\\\=[\cos x\cos y]\left[\frac{\sin x}{\cos x}+\frac{\sin y}{\cos y} \right]\\\\=\sin x \cos y+\sin y \cos x\\\\=\sin(x+y)\\\\=\text{RHS}[/tex]

a car travels along the highway to little rock a steady speed. when it begins it is 280 miles after 4 hours it 100

Answers

The function that describes the car's distance from little rocks would be option A; y = 45x + 280

What is a system of equations?

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

Point 1:

(x, y) = (0, 280)

Since we are told the car's initial position is 280 miles in the time 0 h

Point 2:

(x, y) = (4, 100)

Since we are told the car's final position is 100 miles after 4h.

Let's find the Slope :

m = 45

Now, the equation of the line is:

y = mx + b

y = 45x + 280

Then, The function that describes the car's distance from little rocks would be option A; y = 45x + 280

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For f(x)=3x+1 and g(x)=x²-6, find (f-g)(x)

Answers

Answer:

-x² + 3x + 7

Step-by-step explanation:

(f-g)(x) = f(x) - g(x) = (3x+1)-(x²-6) = -x² + 3x + 7

The value of (f - g)(x) is -x² + 3x + 7.

What is Function?

The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

Here, the given functions are;

   f(x) = 3x + 1

   g(x) = x² - 6

Now,

 (f - g)(x) = f(x) - g(x)

              = (3x + 1) - (x² - 6)

              = 3x + 1 - x² + 6

(f - g)(x)  = -x² + 3x + 7

Thus, the value of (f - g)(x) is -x² + 3x + 7.

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Solve 1 2 1 2x = x2 − 7x 10 4x by rewriting the equation as a proportion. which proportion is equivalent to the original equation?

Answers

The proportion that is equivalent to the original equation is [tex]\frac{x+1}{2x} =\frac{x^2-7x+10}{4x}[/tex]

Rational expressions

Given the following expression

[tex]\frac{1}{2} + \frac{1}{2x} =\frac{x^2-7x+10}{4x}[/tex]

In order to find the equivalent proportion, we will find the LCM of the right side expression to have:

[tex]\frac{1}{2} + \frac{1}{2x} =\frac{x^2-7x+10}{4x}\\\frac{x+1}{2x} =\frac{x^2-7x+10}{4x}[/tex]

Hence the proportion that is equivalent to the original equation is [tex]\frac{x+1}{2x} =\frac{x^2-7x+10}{4x}[/tex]

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Answer: For the next part

✔ x = 1 and x = 8

✔ x = 0

the nth term of the sequence is 3n + 2. Find the first three terms of the sequence

Answers

Answer:

5, 8, 11, ...

Step-by-step explanation:

f(n)=3n+2

the first three terms will be f(1), f(2), and f(3).

f(1)=3(1)+2=5

f(2)=3(2)+2=8

f(3)=3(3)+2=11

Hope this helps!

If not, I am sorry.

Section B, Q5
please answer, it is urgent

Answers

The answers are in the picture below.

Solve for 'x' in the following equation, explaining each step.

3^ (-3x+7) = 3^ (7x-13)

Answers

Answer:

x = 2

Step-by-step explanation:

In order to have the two sides of the equation be equal, the exponents must equal.

-3x + 7 = 7x - 13

Add 3x to both sides.

7 = 10x - 13

Add 13 to both sides.

20 = 10x

Divide by 10.

2 = x

Check:

3^(-3•2+7)=3^(7•2-13)

3^1 = 3^1

3 = 3

8.
36.2
22.3
- 30-
33
Find the value of x.
(Round answer to the nearest tenth when necessary)
44.6
33.2

Answers

Answer:

36.2

Step-by-step explanation:

Assuming that the dotted line is a perpendicular bisector, we can say that it splits the side that is 30 units long into 2 sets of 15 units. Then, we can use the pythaogrean theorem to solve (Leg A is 33 and Leg B: 15). a^2+b^2=c^2

33^2+15^2=c^2

1089+225=c^2

1314=c^2

Square root of 1314 = square root of c^2

36.2 aapproximately c

If Bob sells each fish at a profit of $1.25, how much money will he have after selling all 24 fish? Show your calculation.

Best answer receives brainliest

Answers

Answer:  $30

Step-by-step explanation:

So if Bob sells his fish at a profit of $1.25 and he has 24 fish to sell then 1.25*24= 30

(I'm assuming what you mean by "how much money he will have" is profit)

Answer:

The answer is $30. remove the decimal from the price and multiply it by the amount of fish. then when you finish multiplying add the decimal back in.

Step-by-step explanation:

     125

×    24

  --------

    500

+ 2500

-----------

  30.00

The graph of y=x^2-4x by drawing the line y=x-4

Answers

Answer:

the graph of y=x^2-4x is parabola as shown in the image

Step-by-step explanation:

The graph of [tex]y = x^{2} -4x[/tex] by drawing the line y=x-4

so this gives us that the line  y=x-4 satisfies the equation  [tex]y = x^{2} -4x[/tex]

To get points put y = x - 4 in the equation  [tex]y = x^{2} -4x[/tex]

so we get x -4 = x( x- 4)

x =1 and x - 4 = 0

from here we get x = 1,4

now put these values in y = x -4

From here we get y = -3,0

so the points are (1 , -3) and ( 4 , 0)

Plot these on graph and we get the straight line .

For equation  [tex]y = x^{2} -4x[/tex]

As we know it is of type of parabola with shifted centre.

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What are the coordinates for point b?


a. (7, 0)
b. (0, 7)
c. (0, 8)
d. (1, 7)

Answers

The coordinates for point B are (a) (7,0)

Complete Question

Point B is located 7 units right of the origin. What are the coordinates for point b?

How to determine the coordinates?

The origin is located as:

(0,0)

From the question, we understand that:

B ⇒ 7 unit right of origin

This means that:

B = (0 + 7, 0)

Evaluate the sum

B = (7,0)

Hence, the coordinates for point B are (a) (7,0)

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Answer:a

Step-by-step explanation:

Trapezoid GHJK was rotated 180° about the origin to determine the location of G'H'J'K', as shown on the graph. What are the coordinates of pre-image point H?
(2, 3)
(–2, 3)
(3, 2)
(3, –2)

Answers

The coordinates of pre-image point H is (3, 2) option third (3, 2) is correct.

What is geometric transformation?

It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have a trapezoid GHJK that was rotated 180° about the origin.

The rule for 180-degree rotation about the origin:

(x, y) → (-x , -y)

From the graph:

Coordinate of H' is (-3, -2)

(-3, -2) → (3, 2)

Thus, the coordinates of pre-image point H is (3, 2) option third (3, 2) is correct.

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if a/b and c/d are rational expressions, then: a/b / c/d = a*b/c*d

Answers

if a/b and c/d are rational expressions,a/b / c/d = a*b/c*d is false.

What is the definition of a fraction number?

A fraction number is a number that represents a portion of a larger number, where the larger number might be any integer. It has the shape of a numerator and a denominator.

The given rational expression is;

a/b and c/d

Given relation;

[tex]\rm \frac{\frac{a}{b}}{\frac{c}{d}}\\\\ \frac{a d}{bc}[/tex]

When two fractions are divided the number got reversed and multiplied by the fraction.

Hence the given calculation is false.

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Answer: false

Step-by-step explanation: .

On January 1, 2023, One of Mr. Cutter’s chickens flies away and lands on a Hawaiian Island. She
immediately begins laying and hatching eggs. The chicken population on the island begins to
triple every year. Write and graph a function that represents this situation. How many chickens
will be on the island on January 1, 2033?

Answers

Answer:

Step-by-step explanation:

Do you have any options or a graph?

Suppose y varies inversely with x, and y = a when x = a 2. What inverse variation equation relates x and y ?
a.
y = a2xa2x
b.
y = a 3x
c.
y = a3xa3x
d.
y = ax

Answers

The variation equation is xy = a^3

How to determine the equation?

An inverse variation is represented as:

xy = k

Where k is the constant of variation

When y = a and x =a^2, we have:

k = a * a^2

Evaluate

k = a^3

Substitute k = a^3 in xy = k

xy = a^3

Hence, the equation is xy = a^3

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Let a population consist of the values ​cigarettes, ​cigarettes, and cigarettes smoked in a day. Show that when samples of size 2 are randomly selected with​ replacement, the samples have mean absolute deviations that do not center about the value of the mean absolute deviation of the population. What does this indicate about a sample mean absolute deviation being used as an estimator of the mean absolute deviation of a​ population?.

Answers

Based on the given mean absolute deviations, the sample mean absolute deviation will be 2 and the population mean absolute deviation will be 3.8.

What is the sample mean absolute deviation?

This can be found as:

= Sum of sample mean absolute deviation / Number

= (0 + 0.5 + 4.5 + 0.5 + 0 + 4 + 4.5 + 4 + 0) / 9

= 2

What is the population mean absolute deviation:

First find the population mean:

= (10 + 11 + 19) / 3

= 13.3

Population mean absolute deviation:
= 1/3 x ( (10 - 13.67) + (11 - 13.3) + (19 - 13.3))

= 3.8

We can therefore see that the sample mean deviations is a biased estimate of the population mean absolute deviation.

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Can someone help me out with this problem

Answers

From the given options the options B and C are correct for the given equation.

we have given the equation,

70=10+12r

We have to determine the correct option

What is the equation?

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign.

Therefore from the given options the options B and C are correct for the given equation.

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21 added to a number is the same as 37

Answers

Answer:

Step-by-step explanation:

Hi, let me help you out.

First I'm going to turn the verbal phrase into an algebraic phrase...

21+n=37. here n is the unknown number

Next, I believe you need to find what n equals.

This can be done by subtracting 21 from both sides.

n=37-21

n=16

Thus the number we need is 16.

_________________

Hope I helped. Best wishes.

point-slope equation for perpendicular lines y=-2x-7 that passes through (-2,-3)

Answers

Answer: below! ^^

Step-by-step explanation:

Hii, do you need an answer to your question? Let me help you out! (;

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Part 1 ⚜

Perpendicular lines have slopes that are opposite inverses of each other.

The slope (m) of the line that is perpendicular to y=-2x-7 is [tex]\sf -\cfrac{1}{2}[/tex].

Part 2 ⚜

⚜ Point slope formula

[tex]\boldsymbol{y-y1=m(x-x1)}[/tex]

⚜Stick in the known values

[tex]\boldsymbol{y-(-3)=-\cfrac{1}{2}(x-(-2)}[/tex]

⚜ Simplify

[tex]\boldsymbol{y+3=-\cfrac{1}{2}(x+2)}[/tex]

Voila! There's our answer, cheers! (:

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Hope I helped! Best wishes!

Reach far. Aim high. Dream big.

[tex]\underbrace[/tex]

List the angles in triangle JKL in order from largest to smallest.

Answers

Answer:

answer is B

Step-by-step explanation:

We know,

Opposite of a big arm has a big angle....the same way you can find the next two....

as 18>16>14

Kelly wants to buy a dress that costs $40.00. She has a coupon for 25% off, and
there is a 10% sales tax
How much will she pay altogether?
44 QUES
25% of $40.00 is $
Select
After using the coupon, the sale price is $
Select...
The 10% tax on the sale price is $
Select
The final price is $
Select

Answers

A percentage is a way to describe a part of a whole. The amount that Kelly will pay for the dress is $33.

What are Percentages?

A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

Given Kelly wants to buy a dress that costs $40.00. She has a coupon for 25% off, and there is a 10% sales tax. Therefore, the amount she will pay is,

25% of $40.00 is,

0.25 × $40 = $10

After using the coupon, the sale price is,

$40 - $10 = $30

The 10% tax on the sale price is,

0.10 × $30 = $3

The final price is $

$30 + $3 = $33

Hence, the amount that Kelly will pay for the dress is $33.

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1. Given the points A (2, 14) and B (17, -6).

(a) Find the distance of the line AB.

(b) Find the midpoint of the line AB.

(c) Find the gradient of the line AB.

(d) Find the equation of the line AB.

(e) Find the equation of the line parallel to AB passing through the point (3,5).

(f) Find the equation of the line perpendicular to AB passing through point (4,-2).

(g) Draw the above 3 lines on a graph.

Answers

Answer:

Step-by-step explanation:

Write 3x^2+12x+20 in the form a(x+b)^2+c

Answers

The equation is written as 3(x+12)²+20.The formula for ax² + bx + c is (Ax + B)² + C.

What is the equation?

A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.

3x^2+12x+20

The equation is compared the equation with,ax²+bx+c

After comparing the equation we get;

a=3

b=12

c=20

The equation is written in the form as;

⇒a(x+b)^2+c

⇒3(x+12)²+20

The formula for ax² + bx + c is (Ax + B)² + C.

Hence the equation is written as 3(x+12)²+20.

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HELP ME!! FIND X AND Y.

Answers

Answer:

x = 26

y = 72°

Step-by-step explanation:

Finding x:Alternates angles are equal.

(4x - 16)° = (3x + 10)°

Subtract 3x to both sides

4x - 3x - 16 = 10

x - 16 = 10

Add 16 to both sides

x = 10 + 16

x = 26

Finding y:Angles on a straight lines add up to 180 degrees.

(4x - 16)° + y° = 180°

4x - 16 + y = 180

4(26) - 16 + y = 180

104 - 16 + y = 180

88 + y = 180

Subtract 88 to both sides

y = 180 - 88

y = 72°

[tex]\rule[225]{225}{2}[/tex]

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