In which situation below would you want to use the Explicit Formula instead of the Recursive Formula?

a. Find the 100th term when the first term is -3 and the common difference is 4.
b. Find the 3rd term when the first term is 2 and the common difference is 5.
c. Find the 7th term when the first term is -1 and the common difference is 10.
d. Find the 5th term when the first term is 7 and the common difference is -2.

Answer:

i'm assuming you want to solve for t?

t=(2√3+3)/6

Answer:

f(2) = -6

f inverse of 1/2 is 17/2

Step-by-step explanation:

We are given a function [tex]\displaystyle \large{f(x) = \frac{6}{2x-5}}[/tex]

To solve for part (a), we have to substitute x = 2 in f(x).

[tex]\displaystyle \large{f(2)=\frac{6}{2(2)-5} \\\displaystyle \large{f(2)=\frac{6}{4-5}=\frac{6}{-1}=-6[/tex]

Therefore, f(2) is -6.

Now we solve for part (b), we see the notation which is a minor different similar to f(x). We see that there is exponent of -1 between f and 1/2. The part (b) indicates that the function is an inverse of f(x).

[tex]\displaystyle \large{y=f^{-1}(x) \longrightarrow x=f(y)}[/tex]

To solve for part (b), first we solve for x in the function. Let f(x) = y.

[tex]\displaystyle \large{y=\frac{6}{2x-5}}[/tex]

Multiply both sides by 2x-5.

[tex]\displaystyle \large{y(2x-5)=\frac{6}{2x-5}(2x-5)}\\\displaystyle \large{y(2x-5)=6}[/tex]

Divide both sides by y-term.

[tex]\displaystyle \large{\frac{y(2x-5)}{y}=\frac{6}{y}}\\\displaystyle \large{2x-5=\frac{6}{y}}\\\displaystyle \large{2x=\frac{6}{y}+5}\\\displaystyle \large{x=\frac{6}{2y}+\frac{5}{2}}\\\displaystyle \large{x=\frac{3}{y}+\frac{5}{2}}[/tex]

Then swap x and y which we receive [tex]\displaystyle \large{y=\frac{3}{x}+\frac{5}{2}}[/tex]

Therefore, [tex]\displaystyle \large{f(x)=\frac{6}{2x-5} \longrightarrow f^{-1}(x)=\frac{3}{x}+\frac{5}{2}}[/tex]

Thus, [tex]\displaystyle \large{f^{-1}(\frac{1}{2})=\frac{3}{\frac{1}{2}}+\frac{5}{2}}\\\displaystyle \large{f^{-1}(\frac{1}{2})=6+\frac{5}{2}}\\\displaystyle \large{f^{-1}(\frac{1}{2})=\frac{17}{2}}[/tex]

____________________

Let me know if you have any questions in comment.

Answer:

easy

Step-by-step explanation:

Its very easy for any human to be able to see and compare data as when they are right next to eachother, so you can easily prove a good strong point

Answer: 40 HOURS

Step-by-step explanation:

If the students complete 30% of the project in 12 hours,

that means:

12 h................................30%

? h...................................100%

(12*100)/30= 40H

THE STUDENTS NEED 40H TO COMPLETE THE PROJECT

It will take 40 hours for the group to finish the project.

If the students complete 30% of the project in 12 hours,

that means:

⇒ 12 h = 30%

⇒ ? h = 100%

By using percentage theory:

Percentage formula = (Value/Total value) × 100.

⇒ (12*100)/30= 40H

The answer is 40 hours.

To determine the percentage, we have to divide the value by the total value and then multiply the resultant by 100. Percentage formula = (Value/Total value) × 100.

Learn more about percentage here: brainly.com/question/843074

#SPJ2

[tex]\left(-\dfrac 16 \right)^2 +\dfrac 58 \left(-\dfrac 19} \right)\\\\\\=\dfrac 1{36} -\dfrac{5}{72}\\\\\\=\dfrac 2{72} - \dfrac{5}{72}\\\\\\=-\dfrac 3{72}\\\\\\=-\dfrac 1{24}[/tex]

Answer:

Step-by-step explanation:

(-1/6)^2 + 5/8(-1/9)= -0.0416

Thus the answer is -1/24

Answer:

x=19

Step-by-step explanation:

The 2 angles are same side interior angles, so together they add to 180 degrees. So you can make this equation:

6x + 4 + 4x - 14 = 180

10x - 10 = 180 (Combine like terms)

10x = 190 (add 10 to each side)

x = 19 (divide both sides by 10)

Answer:

The increase as a percentage was 11.1%.

Step-by-step explanation:

The increase is $10.  The ratio of this increase to the original $90 is

$10

------- = 1/9

$90

Multiplying this by 100%, we get 11.1%.

The increase as a percentage was 11.1%.

Answer:

-26

Step-by-step explanation:

well add the negative numbers first so you get

-17-18=(-35)

then you add 9 so its (-35)+9=26

Answer:

Step-by-step explanation:

-17 + 9 +(-18) = -8 -18 = -26 final answer

Answer:

A (2,-1)

B (-3,-2)

C (-2,1)

Step-by-step explanation:

A (-2,-1), B (3, - 2), and C (2,1)

Image of triangle ABC reflexión over the y: opposite of the x-coordinates. The y coordinates stay the same.

A’ (2,-1), B’ (-3, -2), and C’ (-2,1)

Answer:

Solution given:

slope(m)=4

passes through (x',y')=(-2,5)

we have

equation of a line is:

y-y'=m(x-x')

substituting value we get

y-5=4(x-(-2))

y-5=4(x+2)

y-5=4x+8

y=4x+8+5

y=4x+13 is a required equation of a line.

Answer:

9%

Step-by-step explanation:

Set up a ratio:

[tex]\frac{33}{100}[/tex] = [tex]\frac{35.97}{x}[/tex]

Cross multiply: 33x = 35.97 * 100

33x = 3597

Divide by 33: x = 109

That means the tax is 9%.

The answer is A. y=2x+1

A is the only equation in which the numbers are not naturally written,but there is another numbering being either taken or added to the situation (+1). B and D both are divided which is linear, and C is multiplying which is also linear. This only leaves us with A.

Hope this helps. & don't forget to drink water <3

Answer 48

Step-by-step explanation:

The two-digit number that satisfies the given condition will be 48.

In a positional numeral system, a numerical digit is a single sign that can be used singly or in combination to represent numbers.

For example 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 are digits.

Suppose the two-digit number is xy.

Sum x + y = 12

By multiplying by 3,

3(10x + y) = 144

10x + y = 48

Put y = 12 - x

10x + 12 - x = 48

9x = 36

x = 4

And, y = 12 - 4 = 8 so the number will be 48.

Hence "The two-digit number that satisfies the given condition will be 48".

To learn more about digits,

https://brainly.com/question/10913044

#SPJ2

ANSWER

-3 -2, 0, .5, 1, 100 for domain

0, 1.8, 10, 19, 77, 100 For Range

Step-by-step explanation:

Domain is all the x values from least to greatest, and range is all the y vlues from least to greatet

Answer:

The answer would be 27 students

Step-by-step explanation:

4=boys

5=girls

4 x 3 = 12

5 x 13 = 15

12+ 15 = 27

Answer:

Yes

Step-by-step explanation:

None of the X values are the same number.

Answer:

aq lang to Yung d na binalikan Yung iniwan na parang basura

Answer: a I think

Step-by-step explanation:

Answer:

R - (-6,10)

Flip the x-value when reflecting over y axis, and flip y-value when reflecting over x-axis

Answer:

6

Step-by-step explanation:

Answer: As you can see when you list out the factors of each number, 2 is the greatest number that 24 and 62 divides into.

Step-by-step explanation:

Answer:

500000N=2m

x. =6m

cross multiply, it'll be

6×50000÷2

=150,000N