What is the sum of the first thirteen terms in a geometric series with a1=−3 and r=4?

The function f(g) is 8/(8+9x) and the function g(f) is -8x/(x-9).

Functions are the fundamental part of the calculus in mathematics. 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.

The given functions are f(x)=x/(x-9) and g(x)= -8/x.

1) f(g)

Here, f(-8/x)= -8/x ÷ (-8/x -9)

= -8/x ÷ (-8-9x)/x

= -8/x × x/(-8-9x)

= 8/(8+9x)

2) g(f)

Now, -8/x/(x-9)

-8x/(x-9)

3) f(f)

Here, f(f) = x/(x-9) ÷ (x/(x-9) -9)

= x/(x-9) ÷ ((x-9x+81)/(x-9))

= x/(x-9) × (x-9)/(-8x+81)

= x/(-8x+81)

4) g(g)

Now, -8/(-8/x)

= 64/x

Therefore, the function f(g) is 8/(8+9x).

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Answer:

y = -3/4x + 52

y + 6 = -3/4(x-8)

Step-by-step explanation:

y = mx + c

as long as the number is -3/4x , it represents slope -3/

Answer:

B. y = -3/4x + 52, C. y + 6 = -3/4(x - 8), and F. 3x + 4y = 9

Step-by-step explanation:

A. -3x + 4y = -34

y = 3/4x - 17/2

Slope = 3/4

INCORRECT

B. y = -3/4x + 52

Slope = -3/4

CORRECT

C. y + 6 = -3/4(x - 8)

y = -3/4x

Slope = -3/4

CORRECT

D. 4x + 3y = -22

y = -4/3x - 22/3

Slope = -4/3

INCORRECT

E. 4x - 3y = 48

y = 4/3x - 16

Slope = 4/3

INCORRECT

F. 3x + 4y = 9

y = -3/4x + 9/4

Slope = -3/4

CORRECT

G. y - 6 = 3/4(x - 8)

y = 3/4x

Slope = 3/4

INCORRECT

will she have enough time for 12 slides?  we dunno, but we know it takes 1/6 hour to make one hmmm for 12 slides that'd be simply their product

[tex]\stackrel{slides}{12}\cdot \stackrel{\textit{it takes one}}{\cfrac{1}{6}}\implies \cfrac{12}{6}\implies 2~hours\qquad \textit{yeap, she has enough time}[/tex]

she even has an extra 30 minutes to check out what's for dinner.

Complete the table with values 3, 2, 24 and 10 respectively

The constant of proportionality is the ratio of the y value to the x value i.e.

constant of proportionality (k) = y/x

The table can be completed by determining the constant of proportionality. That is:

k = y/x

where y = hours and x = magnets

k = 4/12 = 1/3

when y = 1:

1/3 = 1/x

x = 3

when x = 6:

1/3 = y/6

y = 2

when y = 8:

1/3 = 8/x

x = 24

when x = 30:

1/3 = y/30

x = 10

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Answer: x=0

Step-by-step explanation:

2(2)=4

4+x=4

-4 on both sides

so x=0

Answer:

B) x = 0

Step-by-step explanation:

We will get our equation in here first. Our equation is:

2 * 2 + x = 4

We simplify the multiplication giving us:

4 + x = 4

Finally, we subtract 4 from both sides to find the value of x. We get:

x = 0.

So the correct answer is B) x = 0.

Hope this helped!

Answer:

8 hours

Step-by-step explanation:

21/3=7 and 56/7=8

Answer:

She worked for 8 hours

Step-by-step explanation:

She earned $21 for 3 hours 21 divided by 3 is 7 so $7 an hour. She made $56 so 56 divided by 7 = 8 hours

Answer:

8ft. 9in.

+13ft. 7in.

_________

22ft. 4in.

because 12 in.= 1 ft. so 9+7=16

16-12=4

so 12in.=1 ft. , as 12 in, got carried by 1ft.

Answer: 0.166666667 yards OR 0.1524 meters OR 0.5 feet

Step-by-step explanation:

1 / 6 = 0.166666667 yards

1 yard = 0.9144 meters

0.9144 / 6 = 0.1524 meters

1 yard = 3 feet

3 / 6 = 0.5 feet

The equation of the line passing through the points (-2,9) and (1,3) is

y = -2x + 11 where the slope is -2 and the y-intercept is +11

The equation of a line can be formed with the help of the slope of the line and a point on the line. The slope of the line is the inclination of the line with the positive x-axis and is expressed as a numeric integer, fraction, or the tangent of the angle it makes with the positive x-axis. The point refers to a point in the coordinate system with the x coordinate and the y coordinate.

m = (y2 - y1) / (x2 - x1)

y1 = 9

y2 = 3

x1 = -2

x2 = 1

m = (3 - 9) / (1 - (-2))

m = - 6 / 3

m = - 2

The equation of the line;

m = (y - y1) / (x - x1)

-2 = y - 9 / x - 1

y - 9 = -2(x - 1)

y - 9 = -2x + 2

y = -2x + 11

Therefore the y-intercept is +11.

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Answer: A) Domain: All real numbers , Range: All real numbers

Step-by-step explanation: Since the line of the graph continued to infinity, the answer for both domain (goes from Left to right) and range (goes up to down) would be all real numbers

The volume of a rectangular box can be found by multiplying the length, width, and height of the box together. So if the volume of the box is x³+x²-4x-4 cubic inches, the length is x+1 inches, and the width is x-2 inches, we can set up the equation h = (x³+x²-4x-4) ÷ (x²-x-2).

The formula for the volume of a rectangular box is V = l × w × h, where l is the length, w is the width, and h is the height of the box. This formula can also be written as V = l×w×h.

In the question you provided, the volume of the rectangular box is given as x³+x²-4x-4 cubic inches, and the length and width are given as x+1 inches and x-2 inches, respectively. With this information, we can set up an equation using the formula for the volume of a rectangular box:

(x+1)(x-2)(h) = x³+x²-4x-4

where h is the height of the box in inches. To solve for h, we can divide both sides of the equation by (x+1)(x-2) to get:

h = (x³+x²-4x-4) ÷ (x+1)(x-2)

And Now we can simplify the expression using standard algebraic operations.

h = (x³+x²-4x-4) ÷ (x²-x-2)

You can now substitute any value of x to find the height of the box.

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An acute angle, θ, is in a right triangle such that sin of theta is equal to 3 over 8 period  The value of cot θ is (√55)/3.

To determine the value of cot(θ), Since is an angle in a right triangle and sin() = 3/8, we obtain:

cot(θ) = (√55)/3

In light of the fact that is an acute angle in a right triangle, we may calculate:

sin(θ) = 3/8

Keep in mind:

Hypotenuse = ((opposite cathetus)2 + (adjacent cathetus)2), where sin() = (opposite cathetus)/(hypotenuse)

Next, we have:

contrary cathetus = 3

Using the formula hypotenuse = 8 = (3 + neighboring cathetus)2,

In order to solve this for the nearby cathetus, we obtain:

(82 - 32) = 55 adjacent cathetus

And we are aware of:

(Cot) = (nearby cathetus) (opposite cathetus)

Next, we have:

cot(θ) = (√55)/3

The value of cot θ is (√55)/3.

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Answer:

1

Explanation:

Radius = C/2π

C is 6.28 and 2*pi is also 6.28

So 6.28/6.28 = 1.

Answer: the answer is 1

Step-by-step explanation:

Answer:

472

Step-by-step explanation:

Answer:

The Measure of angle 1 is 68

The Measure of angle 2 is 112

The Measure of angle 3 is 68

The Measure of angle 4 is 112

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

[tex]f(x)=a^x[/tex]

x  is the exponent, so [tex]f(b)=a^b \text{ and }f(c)=a^c[/tex].

That makes [tex]f(b) \cdot f(c) =(a^b)(a^c)=a^{b+c}[/tex].

b + c is the exponent, so it takes the place of x.

[tex]a^{b+c}=f(b+c)[/tex]

Answer:

First Question - 74.25

Second Question - 23.92

Hope this helps you out

Answer:

0.2 x 25 = 5

0.3 x 75=22.5

22.5+5=27.5

Step-by-step explanation:

If you list the number of tickets sold over time, the kind of sequence will you see is a geometric sequence.

What is a geometric sequence?

A geometric progression sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.

Here,

We assume that the variable x represents the number of tickets sold previously (initial year) and it sold 7 times as many tickets each year as it did the year before, a mathematical expression that models this situation is given by geometric sequence:

x, 7x, 49x, 343x, .....

Verification:

7/1 = 49/7 = 343/49 = 7

Hence, this is a geometric sequence.

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Answer:B all integers

Step-by-step explanation: took the test

The option second all integers are correct because for every value of the x the function will always give an integer value.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have a function

f(x)= 4[X-3]+ 2

f(x) represents the greatest integer function, which means for every value of the x the function will always give an integer value.

The function will be discontinuous for all integers.

Thus, the option second all integers are correct because for every value of the x the function will always give an integer value.

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Answer:

11.2

Step-by-step explanation:

First draw an imaginary straight line to separate the two shapes.

You will have a side of 10 in the traingle

And a side of 13 - 8 =5

Then

Using pythagoras theorem

Sqrt(10^2+5^2)=11.180

Answer:

2x−3=x

Move all terms containing x

to the left side of the equation.

Subtract x

from both sides of the equation.

2x−3−x=0

Subtract x

from 2x

x−3=0

Add 3

to both sides of the equation.

x=3

Answer:

50

Step-by-step explanation:

2000/40=50

Answer:

The train travels 50 miles per hour

Step-by-step explanation:

You can solve this by dividing 2,000 by 40.

Answer:

13

Step-by-step explanation:

He starts with 45 pencils (3x15) in total. Then he gives 32 to each student. He is left with 13 (45-32) pencils.

Answer:

x would be 18

Step-by-step explanation:

180 degrees in a traingle, subtract 90 for the right angle and then you are left with 5x = 90

x = 90/5

x = 18

find each angle using x from here

Answer:

Angle T is 36 degrees

Angle V is 54 degrees

Step-by-step explanation:

x=18

The angle that the golfer has between the spectator and the hole is 60°. Therefore, option A is the correct answer.

Law of Sines In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of any triangle to the sines of its angles.

The formula for sine rule is sinA/a=sinB/b=sinC/c

Given that, in a tournament, a professional golfer knows that she is 200 yards from the hole. A spectator is watching her play and is 140 yards away from the golfer.

Let the angle that the golfer has between the spectator and the hole be x

Here, sin 120°/200 =sin x/140

0.8660/200 =sin x/140

0.00433 = sin x/140

sin x=0.866

x=60°

Therefore, option A is the correct answer.

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Hi hi! The answer would be 22.7°, I took the test a while ago.

Answer:

17 is the correct answer

Answer:

I think it's the remaining students, 17.

Step-by-step explanation:

15 + 18 = 33 (students that like one subject but not the other)

33 + 5 = 38 ( adding 5 because of the 5 student that dislike both)

38 is the number of students that either don't like both subjects or like one but now the other, so now you would subtract it by the total number of students (55).

55 - 38 = 17

The remaining students are who I believe like both subjects. The remaining number of students are 17.

Answer:

Solution given:

function of g(x)=?

when

x=0

y=3

so

g(x)=-3f(x) is a function of g.

Let

Face changed to opposite means coefficient is negative

Streched by 3 [-6/-2=3]