Find an explicit rule for the nth term of the sequence.

-2, -8, -32, -128

Answer:

x = [tex]\frac{1}{2}[/tex] , x = 1

Step-by-step explanation:

Given

[tex]\frac{2x}{x+3}[/tex] + [tex]\frac{3}{x-3}[/tex] = [tex]\frac{8}{x^2-9}[/tex] ← denominator is a difference of squares

[tex]\frac{2x}{x+3}[/tex] + [tex]\frac{3}{x-3}[/tex] = [tex]\frac{8}{(x+3)(x-3)}[/tex]

Multiply through by (x + 3)(x - 3) to clear the fractions

2x(x - 3) + 3(x + 3) = 8 ← distribute left side and simplify

2x² - 6x + 3x + 9 = 8

2x² - 3x + 9 = 8 ( subtract 8 from both sides )

2x² - 3x + 1 = 0 ← in standard form

(2x - 1)(x - 1) = 0 ← in factored form

Equate each factor to zero and solve for x

2x - 1 = 0 ⇒ 2x = 1 ⇒ x = [tex]\frac{1}{2}[/tex]

x - 1 = 0 ⇒ x = 1

Answer:

x = -[tex]\frac{2}{3}[/tex]

y = 2

Step-by-step explanation:

The process of elimination is a method of solving a system of equations. One must first manipulate one of the equations such that one of the variables shared between the two equations has the inverse coefficient of the same variable in the other equation. Therefore, when one adds the equations, the variable cancels. One can solve for the variable using inverse operations, and then backsolve to find the value of the first variable.

When given the following system:

y = 3x + 4

y + 6x = 3x

Use inverse operations so that both equations are solve for one variable,

y = 3x + 4

y = -3x

Add the systems so that one of the variables (x) cancels, this process is called the process of elimination;

y = 3x + 4

y = -3x

_________

2y = 4

Inverse operations,

2y = 4

y = 2

Now backsolve, find the value of (x) by substituting the value of (y) into the equation:

y = -3x

2 = -3x

x = -[tex]\frac{2}{3}[/tex]

Answer: No solution.

Step-by-step explanation:

Answer:

I'm not sure but I thing the answer is 10

Step-by-step explanation:

Answer:

Step-by-step explanation:

7 x 5 = 35

35/2 = 17.5

[tex]17.5ft^{2}[/tex]

The area of the given triangle is 17.5 ft²

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.

Given a triangle with base=7ft and height =5ft

We know that area of a triangle = 1/2 × base × height

Therefore, the area of a triangle = 1/2 (7)(5) = 17.5 ft²

Hence, the area of the given triangle is 17.5 ft²

For more references on area, click;

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A right angled triangle with its side length is given. The sides of the triangle are 12ft , 13ft and 5ft. And we need to find out the value of cot A .

Here :-

We know :-

[tex]\tt\implies cot \theta = base / perpendicular [/tex]

Substitute the respective values :-

[tex]\tt\implies cot \theta = base / perpendicular\\\\\tt\implies\boxed{\red{\tt cot A = 12/5 }}[/tex]

Hence the required answer is 12/5.

Answer:

landslide

Step-by-step explanation:

Answer:

I believe that the answer might be the second one

Volcanic Eruption

Answer:

D

Step-by-step explanation:

We have to added up the like therms (the therms with the same literal parts)

x^2 + 2x^2 = 3x^2

3x - 4x = -x

2 + 1 = 3

3x^2 - x + 3

Answer:

D

Step-by-step explanation:

Edge 2022

Answer:

43.98

Step-by-step explanation:

The circumference of a circle with a radius of 7 units is approximately 43.98 units, which corresponds to option A.

The Circumference of a circle is defined as the product of the diameter of the circle and pi.

Given that the radius of the circle is 7 units, we can substitute this value into the formula:

To find the circumference of a circle, we can use the formula C = 2πr, where C represents the circumference and r represents the radius.

C = 2π(7) = 14π

Use the approximation π ≈ 3.14:

C ≈ 14(3.14) = 43.96

Rounding this value to the nearest hundredth, we get approximately 43.98 units.

Therefore, the circumference of a circle with a radius of 7 units is approximately 43.98 units.

Learn more about the Circumference of the circle here:

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Answer:

x = 1.289

Step-by-step explanation:

11^x = 22

Take the log of both sides

xlog11 = log22

Divide both sides by log11

x = log22 / log11

Use calculator

x = 1.289

Answer:

Joe 5512

Maria 6890

Step-by-step explanation:

Joe  : Maria  : total

4           5         9

We have a total of 12402

Divide this by 9

12402/9 =1378

Multiply each number by 1378

Joe  :          Maria             : total

4*1378           5*1378         9*1378

5512                6890              12402

Answer:

V=82944

Step-by-step explanation:

FORMULA (Im guessing u just wanted answer but if u want formula there u go.

V= 1/3(a^2h)

Answer:

[tex]576 ~cubic ~centimeters[/tex]

Step-by-step explanation:

[tex]B=144cm^2[/tex]

[tex]h=12cm[/tex]

[tex]V=1/3~B*h[/tex]

[tex]=1/3(144)(12)[/tex]

[tex]=576 cm[/tex]

--------------------

hope it helps...

have a great day!!

Step-by-step explanation:

put 6x-10 in y=x-4

so

y = (6x-10) - 4

y = 6x-14

Answer:

8:30 am

Step-by-step explanation:

Answer:

8:30 a.m

Step-by-step explanation:

8:00

+ 30

_____

8:30 a.m

Answer:

D. 122 degrees

Step-by-step explanation:

The angle next to the 133 degree angle is equal to 47 degrees because they are linear pairs. (Linear pairs will always add up to 180 degrees).

The angle below the 75 degree angle is equal to 75 degrees because they are vertical angles. (Vertical angles will always be equal to each other).

Then by using the Triangle Exterior Angle Theorem. Your missing angle is equal to 47 degrees + 75 degrees = 122 degrees.

Answer:

120

Step-by-step explanation:

reduce the fraction from

[tex]48 \times \frac{250}{100 } [/tex]

to

[tex]48 \times \frac{5}{2} [/tex]

then multiply and you get 24 × 5 which is 120

Answer:

no thanks for your number

Step-by-step explanation:

Have a great day

Answer:

x ≈ 46.7°

Step-by-step explanation:

Using the sine ratio in the right triangle

sin x = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{OP}{NP}[/tex] = [tex]\frac{4}{5.5}[/tex] , then

x = [tex]sin^{-1}[/tex] ([tex]\frac{4}{5.5}[/tex] ) ≈ 46.7° ( to the nearest tenth )

Answer:

Step-by-step explanation:

circumference=2*pie*r

=2*3.14*7

=43.96 in.

========================================================

Work Shown:

C = 2*pi*r

C = 2*3.14*7

C = 43.96 inches is the approximate circumference, aka the distance around the circle.

Use more decimal digits in pi to get a more accurate circumference.

Answer:

Y =-25x +225

Step-by-step explanation:

First you can count the gradient first. Use then you can count y intercept

the total balloon are used is 2736

Answer: Upper right corner (northeast corner)

x-3y = 15

===================================================

Explanation:

The y intercept always occurs when x = 0.

If we plug x = 0 into 2x+y = -10 (northwest corner), then we solve for y to get...

2x+y = -10

2(0)+y = -10

0+y = -10

y = -10

We see that the y intercept here is -10, but we want -5 instead. So we can rule this out.

In the northeast corner, plugging x = 0 leads to,

x-3y = 15

0-3y = 15

-3y = 15

y = 15/(-3)

y = -5

We get the correct y intercept we're after. So we can stop here.

If you plugged x = 0 into the equation of the southwest corner, you'll get y =  5 which is fairly close but not quite what we want. The southeast corner equation leads to a y intercept of y = 5 as well.

Answer:

x - 3y = 15

Step-by-step explanation:

x - 3y = 15

-3y = -x + 15

y = 1/3x - 5

-5 is the y-intercept.

Answer:

if what

Step-by-step explanation:

if we dare or if we must

Answer:

If what?

Step-by-step explanokation:

So, I don't understand what the question is here. Please elaborate.

Answer:

D) y = -4/3x + 5

Step-by-step explanation:

Can be checked with a calculator or by replacing the variables into the equation.

Answer:

1. -1/2 1/2 1/4

2. -3.5 -3.6 -3.7

3. -1/10 -1/11 -1/12

hope this helps

have a good day :)

Step-by-step explanation: