If I can drive 4,800 miles in 48 hours and I am driving at constant speed, how many miles will I travel each hour?

Answer:

Part A)

[tex]f(1)=2, \; f^{-1}(1)=0, \; f^\prime(1)=1.4, \; (f^{-1})^\prime(1)=\frac{10}{7}[/tex]

Part B)

[tex]y=\frac{5}{14}x+\frac{4}{7}[/tex]

Step-by-step explanation:

Please refer to the table of values.

Part A)

A. 1)

We want to find f(1).

According to the table, when x=1, f(x)=2.

Hence, f(1)=2.

A. 2)

We want to find f⁻¹(1).

Notice that when x=0, f(x)=1.

So, f(0)=1.

Then by definition of inverses, f⁻¹(1)=0.

A. 3)

We want to find f’(1).

According to the table, when x=1, f’(x)=1.4.

Hence, f’(1)=1.4.

A. 4)

We will need to do some calculus.

Let g(x) equal to f⁻¹(x). Then by the definition of inverses:

[tex]f(g(x))=x[/tex]

Take the derivative of both sides with respect to x. On the left, this will require the chain rule. Therefore:

[tex]f^\prime(g(x))\cdot g^\prime(x)=1[/tex]

Solve for g’(x):

[tex]g^\prime(x)=\frac{1}{f^\prime(g(x))}[/tex]

Substituting back f⁻¹(x) for g(x) yields:

[tex](f^{-1})^\prime(x)=\frac{1}{f^\prime({f^{-1}(x)})}[/tex]

Therefore:

[tex](f^{-1})^\prime(1)=\frac{1}{f^\prime({f^{-1}(1)})}[/tex]

We already determined previously that f⁻¹(1) is 0. Therefore:

[tex](f^{-1})^\prime(1)=\frac{1}{f^\prime(0)}[/tex]

According to the table, f’(0) is 0.7. So:

[tex](f^{-1})^\prime(1)=\frac{1}{0.7}=\frac{10}{7}[/tex]

Hence, (f⁻¹)’(1)=10/7.

Part B)

We want to find the equation of the tangent line of y=f⁻¹(x) at x=4.

First, let’s determine the points. Since f(2)=4, this means that f⁻¹(4)=2.

Hence, our point is (4, 2).

We will now need to find our slope. This will be the derivative at x=4. Therefore:

[tex](f^{-1})^\prime(4)=\frac{1}{f^\prime({f^{-1}(4)})}[/tex]

We know that f⁻¹(4)=2. So:

[tex](f^{-1})^\prime(4)=\frac{1}{f^\prime(2)}[/tex]

Evaluate:

[tex](f^{-1})^\prime(4)=\frac{1}{f^\prime(2)}=\frac{1}{2.8}=\frac{10}{28}=\frac{5}{14}[/tex]

Now, we can use the point slope form. Our point is (4, 2) and our slope at that point is 5/14.

So:

[tex]y-2=\frac{5}{14}(x-4)[/tex]

Solve for y:

[tex]y-2=\frac{5}{14}x-\frac{20}{14}[/tex]

Adding 2 to both sides yields:

[tex]y=\frac{5}{14}x-\frac{20}{14}+\frac{28}{14}[/tex]

Hence, our equation is:

[tex]y=\frac{5}{14}x+\frac{4}{7}[/tex]

Answer:

Is there suppose to be a graph?

If not, if the original coordinates were (x,y) the new ones will be (y,x)

Step-by-step explanation:

The point C(x , y) is reflected through the line x = y, the coordinates of C is (y, x).

A reflection is "geometric transformation results in mirror image".

According to the question,

The point C(x, y) is reflected through the line X - Y = 0.

Formula to find new coordinates (x-x₁)/a =(y-y₁)/b= -2(ax₁+by₁+c)/(a² + b²)

The point (x, y) = (x₁, y₁) and from the line a = 1, b = - 1,c = 0.

(x-x₁)/1 = -2(x₁ - y₁)/2

x - x₁ +x₁ -y₁ =0

x = y₁.

similarly we get y = y₁

Hence, The point C(x , y) is reflected through the line x = y, the coordinates of C is (y, x).

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Answer:  

the first one and the last one

Step-by-step explanation:

Answer:

11,10.45

Step-by-step explanation:

4.4/8=0.55

6.05/0.55=11

11*0.55=0.45

Answer:

Read below

Step-by-step explanation:

I whole. 5. Elena bought 8 tokens for $4.40. At this rate: Next Page. Unit 3: Unit Rates and Percentages Lesson 10: What Are Percentages?

Answer:

74

Step-by-step explanation:

Answer:

I need the points, thanks!!!

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

We have the expression:

[tex]-4ab[/tex]

And we want to find its sign given that a>0 and b<0.

Notice that the expression is already negative since we have -4.

a>0 means that a is positive. Therefore, we can ignore it since it won’t do anything.

b<0 means that b is negative. Therefore, we will have two negatives being multiplied together. Hence, this will make a positive.

Therefore, the sign of our expression will be positive.

We can see this with an example. Let a=1 (1>0) and let b=-1 (-1<0). Then:

[tex]-4(1)(-1)=4[/tex]

So, the sign is positive.

Hence, the answer is A.

Answer:

The answer is A

Step-by-step explanation:

khan said so

Answer:

y = -1/2x + 2

Step-by-step explanation:

Topic: Graphs and Functions

If you would like to venture further into mathematics, you can check out my Instagram page (learntionary) where I post notes and mathematics tips. Thanks!

Answer:

y < - 2x + 1

Step-by-step explanation:

The relationship between lines KO and K’O’ is given as Line K'O' = 5*line KO

Transformation is the movement of a point from its initial point to a new location. Types of transformation are reflection, rotation, translation and dilation.

Reflection happens when it is reflected over a line as we see in a mirror. But here the two triangles are not looking as images on  a line.  Hence no reflection

Rotation is keeping the same shape but rotating through a certain angle.

Translation is not right because there is no vertical or horizontal shift to get new triangle.

Dilation is the increase or decrease in size of a figure by a scale factor.

The larger figure was dilated using a scale factor of 5

hence

Line K'O' = 5 * line KO

The relationship between lines KO and K’O’ is given as Line K'O' = 5 * line KO

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Answer: 8

32 divided by 4 equals 8

Step-by-step explanation:

Answer:

$10.67

Step-by-step explanation:

$32 divided by 3 is about $10.67, in it's simplest form.

I hope this helped, please mark Brainliest, thank you!! :)

Answer:

f(7)=13

g(-9)=86

Step-by-step explanation:

f(7)=2*7-1=14-1=13

g(-9)=(-9)^2+5=81+5=86

a) because the denominators are the same add the numerators:

1 1/5 + 3 2/5 = 4 3/5

b) rewrite the fractions to have a common denominator:

1/2 = 3/6

1/3 = 2/6

Now subtract:

4 3/6 - 1 2/6 = 3 1/6

Answer:

6/5+30/5

=6/5+6

=36/5

b)9/2+4/3

=26/6

=13/3

Step-by-step explanation:

Answer:

m=-1/2

Step-by-step explanation:

m=-4-1/0- -10

m=-1/2

Answer:

4-12x

Step-by-step explanation:

-6(-2/3)= 12/3=4

Answer:

(-5, 17)

General Formulas and Concepts:

Pre-Algebra

Algebra I

Step-by-step explanation:

Step 1: Define systems

5x + 3y = 26

-2y = 6x - 4

Step 2: Rewrite systems

5x + 3y = 26

y = 2 - 3x

Step 3: Solve for x

Step 4: Solve for y

And we have our final answer!

Answer:

$5.99 per can of gas

Step-by-step explanation:

$23.96 divided by 4 = $5.99

This means that each can of gas is $5.99.

Answer:

$95.84

Step-by-step explanation:

Each can of Fuel is $23.96 and you want to find out How much she payed for 4. So all you have to do is multiply the given cost($23.96) by the amount of fuel cans(4). 23.96 times 4 give you the answer $95.84.

Answer:

7.2

Step-by-step explanation:

Mean is when you add all the numbers together and divide them by the number of values there are in total.

There are 10 numbers, so find the sum of all the numbers and divide by 10.

[tex]\frac{12+8+14+5+1+3+0+8+10+11}{10}[/tex] = 72/10 = 7.2

Answer:that is an s

Step-by-step explanation:

si quema cuh

Answer:

she has 4.5

and she should´ve got bacon egg and cheese than that burger

Answer:

11

Step-by-step explanation:

55 divide 5 = 11

11 + 3 = 15

5 × 11 = 55

Step-by-step explanation:

An integer is 3 less than 5 times another. If the product of the two integers is 36, then the integers are: 3 and 12. Solution: x * (5x 3) 36; 5x2 - 3x = 36; 5x2 -3x 36 = 0; (5x + 12)(x - 3) = 0; x = -12/5 or x =3.

Answer: the value of the diversity index D is Zero (0)

Step-by-step explanation:

Just as the meaning of diversity index is boldly explained in the question, it is the probability that randomly selected organism from a population are from a different species.

Now if the organisms are all from the same species in a population  then it is impossible to select two organisms from different species.

That is, we can never select two organisms that are not from the same species.

Hence, we cant fulfil or meet the definition of diversity index .

Therefore in this situation the value of our diversity index D will be exactly zero, D = 0.

Answer:

Quadrant 2

Step-by-step explanation:

Answer:

37%

$4trillion

$12000

Step-by-step explanation:

Answer:

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

Step-by-step explanation:

a) (x2 - 4)/(x + 2)

We can simply use factorization to solve the given question.

Here the first term will be numerator and second term will be denominator.

We will factorize the numerator.

So,

[tex]\frac{x^2-4}{x+2}[/tex]

Using formula, [tex]a^2+b^2 = (a+b)(a-b)[/tex]

[tex]\frac{x^2-4}{x+2}\\= \frac{(x^2)-(2)^2}{x+2}\\=\frac{(x+2)(x-2)}{x+2}\\= x-2[/tex]

b) (4x2 - 1) / (2x + 1)​

We can simply use factorization to solve the given question.

Here the first term will be numerator and second term will be denominator.

We will factorize the numerator.

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

Using formula, [tex]a^2+b^2 = (a+b)(a-b)[/tex]

[tex]= \frac{(2x)^2-(1)^2}{2x+1}\\=\frac{(2x+1)(2x-1)}{2x+1}\\= 2x-1[/tex]

Hence,

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

Answer:

they are parallel

Step-by-step explanation:

they have the same slope

The lines represents the parallel line.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

y=5/4x +1 and y=5/4x-7

4y= 5x+ 4 and 4y= 5x-7

Now, [tex]a_1[/tex]= 4, [tex]b_1[/tex]= 5,  [tex]c_1[/tex]= 4

[tex]a_2[/tex]= 4, [tex]b_2[/tex]= 5,  [tex]c_2[/tex]= -7

Now, on comparing the ratio we have

[tex]a_1[/tex]/[tex]a_2[/tex] =  [tex]b_1[/tex]/ [tex]b_2[/tex] ≠  [tex]c_1[/tex]/ [tex]c_2[/tex]

Hence, the lines represents the parallel line.

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