Yoshi needs to find the inverse of f(x) = 5x – 2. What is the first step?

Answers

Answer 1

Answer:

Yoshi needs to find the inverse of f(x) = 5x – 2. The first step is to Switch x and y. The correct answer is option C.

In mathematics, an inverse function is a function that "undoes" the actions of another function. If a function f(x) maps an input x to an output y, the inverse function, denoted as f^(-1)(x) or sometimes written as f(x)^(-1), maps the output y back to the original input x. The correct answer is option C.

To find the inverse of a function, the first step is to switch the x and y variables. In this case, the function is f(x) = 5x - 2.

To find the inverse, we need to switch x and y, so the new function becomes x = 5y - 2.

It's important to note that not all functions have an inverse. A function must be one-to-one (each input maps to a unique output) for an inverse to exist. Additionally, the domain and range of a function and its inverse are swapped.

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Answer 2

Answer:

Answer:

D. Replace f(x) with y

Step-by-step explanation:

apex

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Solve for x Write both solutions, seperated by a comma 4x^2+5x+1=0

Answers

Answer:

-1/4 , -1

Step-by-step explanation:

I solved it using Factorization method and Quadratic Equation .

Factorization Method

$4x^2+5x+1=0\nWrite +5x- as- a -difference(write+5x-using- two- numbers -in-which-their-sum-is ; 5-and-their-product-is ; 4)\n4x^(2) +4x+1x+1=0\nFactorize-out-common-terms\n4x(x+1)+1(x+1)=0\nFactor-out-(x+1)\n(4x+1)(x+1)=0\n4x+1 =0 \nx+1=0\n4x=0-1\nx =0-1\n4x =-1\nx =-1\n4x=-(1)/(4) \n\nAnswer = -1/4 , -1$

Quadratic Equation

$4x^2+5x+1=0\na = 4\nb =5\nc = 1\n\nx =(-b\±√(b^2 -4ac) )/(2a) \n\nx = (-(5)\±√((5)^2-4(4)(1)) )/(2(4)) \n\nx = (-5\±√(25-16) )/(8) \n\nx = (-5\±√(9) )/(8) \n\nx = (-5\±3)/(8) \n\nx =(-5+3)/(8) \n\nx = (-5-3)/(8) \n\nx = (-2)/(8) \n\nx = (-8)/(8) \n\nx = -(1)/(4) \nx=-1$

Find the difference of 5.95 and 4.7

Answers

Answer:

1.25 is your answer.

Final answer:

To find the difference between 5.95 and 4.7, we subtract 4.7 from 5.95, following the rules of subtraction involving decimals, giving us the result of 1.25.

Explanation:

The question asks us to find the difference of 5.95 and 4.7. This can be easily done by using the subtraction operation. Here, since 5.95 is greater than 4.7, we subtract 4.7 from 5.95.

To solve this, follow these steps:

First, align the numbers by their decimal points: 5.95 - 4.7
Since you cannot subtract 7 from 5, you would need to borrow 1 from the number in the next decimal place to the left, i.e., 9.
Now subtract the numbers in each decimal and whole number place: (15 - 7) and (4 - 4).
After performing the subtraction, you get your answer, 1.25.

Therefore, the difference between 5.95 and 4.7 is 1.25.

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Find the greatest common factor of 108d^2 and 216d

Answers

Answer:

$\boxed{108d}$

Step-by-step explanation:

Part 1: Find GCF of variables

The equation gives d ² and d as variables. The GCF rules for variables are:

The variables must have the same base.
If one variable is raised to a power and the other is not, the GCF is the variable that does not have a power.
If one variable is raised to a power and the other is raised to a power of lesser value, the GCF is the variable with the lesser value power.

The GCF for the variables is d.

Part 2: Find GCF of bases (Method #1)

The equation gives 108 and 216 as coefficients. To check for a GCF, use prime factorization trees to find common factors in between the values.

Key: If a number is in bold, it is marked this way because it cannot be divided further AND is a prime number!

Prime Factorization of 108

108 ⇒ 54 & 2

54 ⇒ 27 & 2

27 ⇒ 9 & 3

9 ⇒ 3 & 3

Therefore, the prime factorization of 108 is 2 * 2 * 3 * 3 * 3, or simplified as 2² * 3³.

Prime Factorization of 216

216 ⇒ 108 & 2

108 ⇒ 54 & 2

54 ⇒ 27 & 2

27 ⇒ 9 & 3

9 ⇒ 3 & 3

Therefore, the prime factorization of 216 is 2 * 2 * 2 * 3 * 3 * 3, or simplified as 2³ * 3³.

After completing the prime factorization trees, check for the common factors in between the two values.

The prime factorization of 216 is 2³ * 3³ and the prime factorization of 108 is 2² * 3³. Follow the same rules for GCFs of variables listed above and declare that the common factor is the factor of 108.

Therefore, the greatest common factor (combining both the coefficient and the variable) is $\boxed{108d}$ .

Part 3: Find GCF of bases (Method #2)

This is the quicker method of the two. Simply divide the two coefficients and see if the result is 2. If so, the lesser number is immediately the coefficient.

$(216)/(108)=2$

Therefore, the coefficient of the GCF will be 108.

Then, follow the process described for variables to determine that the GCF of the variables is d.

Therefore, the GCF is $\boxed{108d}$ .

Answer:

Below

Step-by-step explanation:

If d is a positive number then the greatest common factor is 108d.

To get it isolate d and d^2 from the numbers.

108 divides 216. (216 = 2×108)

Then the greatest common factor of 216 and 108 is 108.

For d^2 and d we will follow the same strategy

d divides d^2 (d^2 = d*d)

Then the greatest common factor of them is d.

So the greatest common factor will be 108d if and only if d is positive. If not then 108 is the answer

An arithmetic series contains n terms. Show that if t1 = a−b and tn = a+b then the value of Sn is independent of b.[Arithmetic Sequences]

Answers

Answer:

Sn is independent of b

Step-by-step explanation:

t1=a-b

tn=a+b

we know that nth term of arithmetic series is an=a1+(n-1)d

a+b=a-b+(n-1)d

⇒2b=(n-1)d-----------equation 1

formula for sum of n terms of arithmetic series

Sn= $(n)/(2)$ (2a1+(n-1)d)

⇒Sn= $(n)/(2)$ (2(a-b)+2b) (since (n-1)d=2b from equation 1)

⇒Sn= $(n)/(2)$ (2a)

therefore we can see that Sn is independent of b

Help asap. yes i will give brainliest

Answers

Answer:

A = 1.5
B = -1/3
C = -4/3

Step-by-step explanation:

For A:

A is smack in the middle of 1 and 2, so it it 1 1/2 or 1.5 (same thing)

For B:

Each tick mark between the numbers represents 1/3
B is on the first tick mark between 0 and -1, so therefore it is -1/3

For C:

C is on the first tick mark between -1 and -2
That means C is -1 1/3
-1 1/3 = -4/3

I hope this helps!

Answer:

A ----> +1.5

B------> -0.33

C-------> -0.1322

Step-by-step explanation:

$A\ is\ +1.5\ as\ it\ is\ 1.5\ units\ upwards(positively)\ from\ 0.\nB\ is\ -(1)/(3)\ as\ it\ equates\ to\ -0.33\ which\ is\ between\ 0\ and\ -1.\nC\ is\ -(4)/(3)\ as\ it\ equates\ to\ -1.322\ which\ is\ between\ -1\ and\ -2.\n$

Can someone please help me –4x ≤ 36

Answers

Answer:

x > -9

Step-by-step explanation:

–4x ≤ 36

Divide by -4, remembering to flip the inequality

-4x/-4 > 36/-4

x > -9

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