Which of the following equations describes the nth term for the sequence 3/5,1/5,1/15,1/45,\cdots2
A. an = 1/3 (3/5)n-1
B. an = 1/3 (3/5)n
C. an = 3/5 (1/3)n-1
D. an = 3/5 (1/3)n

After the taxes and rent, the remaining amount in his gross pay is $5,700

The term gross income is defined as also known as gross pay when it’s on a paycheck is an individual’s total earnings before taxes or other deductions.

Here we have given that Rene makes $38,000 per year and pays about 35% of his gross monthly income in federal and state taxes.

And as we all know that If you live in a metropolitan city, your HRA is equivalent to 50% of your basic salary.

Therefore, the remaining amount in his hand is calculated as,

=> $38000 - [35% of income + 50% of income]

Here the 35% of income is

=> 38000 x 35/100

=> 380 x 35

=> 13300

Similarly, the 50 percent of the income is

=> 38000 x 50/100

=> 380 x 50

=> 19000

Then the remaining amount is calculated by apply the values on it, then we get,

=> $38000 - [$13300 + $19000]

=> $3800 - $32300

=> $5700

To know more about percentage here.

https://brainly.com/question/13729841

#SPJ4

Therefore , the solution of the given problem of triangle comes out to be the relationship between s,t and u is u²= t²+s².

Given that it has three sides and three vertices, a triangle qualifies as a polygon. It is a fundamental geometric figure. Triangle ABC is the term used to refer to a triangle containing the vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are discovered. Triangles are polygons because they have three sides and three corners. The points where the three sides of the triangle converge are referred to as the triangle's corners. Three triangle angles are multiplied to yield 180 degrees.

Here,

Given : Triangle STU is a right triangle.

Thus,

We find :

sides s,t and u

the relationship between them is :

As it is a right triangle

So,

According to the pythagoras theorem,

=>u²= t²+s²

Therefore , the solution of the given problem of triangle comes out to be the relationship between s,t and u is u²= t²+s².

To know more about triangle visit:

https://brainly.com/question/2773823

#SPJ1

An equation to find the discount price, y dollars, of the pendant is y=2d.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The original price of the pendant was $200.

Let d represent the percent discount, written as a decimal.

The discount price, y dollars, of the pendant.

y=d% of 200

y=d/100 ×200

y=2d

Therefore, an equation to find the discount price, y dollars, of the pendant is y=2d.

To learn more about an equation visit:

https://brainly.com/question/14686792.

#SPJ1

Answer:

21/5

Step-by-step explanation:

cross multiply

21=5x

flip

5x= 21

divide both sides

The value of exponent x, if [tex]$\sqrt[\text X]{81} = 3[/tex], is 4, in the given equation.

Exponent is the process of expressing large numbers as powers, according to the definition. Accordingly, the exponent describes the number of times a number has been multiplied by itself. Using 6 as an example, multiply it by itself four times, or 6×6×6×6. 6⁴ can be used to represent this. In this case, the base is 6 and the exponent is 4. You can interpret this as 6 raised to the power of 4.

Exponents are represented by the symbol. The word "carrot" refers to this symbol (). 4 raised to a power of two, for instance, can be expressed as 4^2 or 4². Thus, 4^2 = 4 × 4 = 16. A few exponent-based numerical expressions are represented in the table below.

The value of x, if [tex]$\sqrt[\text X]{81} = 3[/tex]

3 × 3 = 9

9 × 3 = 27

27 × 3 = 81

Thus, The value of x, if [tex]$\sqrt[\text X]{81} = 3[/tex], is 4.

Learn more about Exponent

https://brainly.com/question/5497425

#SPJ1

The area of circle A to the area of circle B ratio is 100: 64, and the ratio of e: f is 13: 10.

The area of the circle is equal to the multiplication of the square of the circle's radius and π.

A = πr²

where 'r' is the radius

Circumference of circle A × 0.8 = circumference of circle B

So, taking r as the radius of A,

2πr =  circumference of circle A

2πr × 0.8 = circumference of circle B

So the radius of B is r × 0.8.

Now we can substitute that in the area equations :

Area of A = π×r²

Area of B = π × (r × 0.8)² = π × r² × 0.64

The circumferences of the A to B ratio is

Circumference of A : Circumference of B = (2 × π × r)/(2 × π × r × 0.8)

= 1: 0.8 = 100: 80,

The areas of circle A to circle B ratio is

Area of A : Area of B = (π × r²)/(π × r² × 0.64) = 1: 0.64 = 100: 64

e² = f² × 1.69

69% larger shows that f² is the 100% to which we must add 69% to obtain e². 100% + 69% Equals 169%, obtaining a factor of 1.69.

We have this equation:

e² = f² × 1.69

Apply the square root on both sides.

e = f × √(1.69) = f × 1.3

e/f = 1.3 = 1.3/1 = 13/10

the ratio e:f = 13: 10

Thus, the ratio of circle A's area to circle B's area is 100: 64 and the ratio of e: f is 13: 10.

To know more about ratio, here

https://brainly.com/question/13419413

#SPJ4

The equivalent expression would be; function G(t) = 86,400•3^t

What is a function in simple definition?

A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range.

The number of views on a viral video can be modeled by the function

G(t) = 2500(5) 2-4.

we have to find out an equivalent function of the form G(t) = ab.

Here, we want to make a transformation

From what we have;

G(t) = 2500(5)^(t - 4)

From indices, we know that;

x^(a + b) = x^a•x^b

Thus, we have it that;

G(t) = 2500•3^t•3^2

G(t) = (9 * 9600) * 3^t

G(t) = 86,400•3^t

learn more about of function here

https://brainly.com/question/23329742

#SPJ4

Answer:

3.656 ft

Round as needed

Step-by-step explanation:

cos∅ = adj/hyp

cos 83 = adj/30

multiply both sides by 30

30 * cos83 = adj

30 * 0.121869343405147 = adj

3.6560803022 = adj

≈ 3.656 ft

The solution to the system of linear equations is x = 10 and y = 22.

To solve this system of linear equations, we can use the substitution method.

First, we want to isolate one of the variables in either equation. Let's start with equation 1:

3x - 2y = 14

Add 2y to both sides to isolate x:

3x = 14 + 2y

Divide both sides by 3 to solve for x:

x = (14 + 2y) / 3

Now, substitute this expression for x into equation 2:

5x + y = 32

5(14 + 2y) / 3 + y = 32

Simplify:

70 + 10y + y = 32

Combine like terms:

11y = -38

Divide both sides by 11 to solve for y:

y = -38 / 11

y = -3.45454545...

Now, substitute -3.45454545... for y in the expression for x:

x = (14 + 2(-3.45454545...)) / 3

x = (14 - 6.9090909...) / 3

x = 7.09090909... / 3

x = 2.36363636...

x = 2.4 (rounded to nearest tenth)

Now that we have both x and y, the solution to the system of linear equations is x = 2.4 and y = -3.5.

Learn more about equation here

https://brainly.com/question/29657992

#SPJ4

Explanation is[tex]^{}[/tex] in a file

bit.[tex]^{}[/tex]ly/3gVQKw3

Answer: 107ft^2

Step-by-step explanation:

Calculate the area of both squares and add together.

Area =

(5x7) + (8x9) = 107ft^2

Answer:

4

Step-by-step explanation:

Answer:

A is your answer

Step-by-step explanation:

Answer:

8²+16²=x²

Step-by-step explanation:

because h²=base²+perpendicular ²

On solving the provided question we can say that equation formed is x/y = k, x = ky => y₂ = (10.5 × 3.2) / 5.6 => y₂ = 6

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

x/y = k, x = ky

where k is a constant.

Thus, x₁ / y₁ = x₂ / y₂

5.6 / 3.2 = 10.5 / y₂

5.6 × y₂ = 10.5 × 3.2

y₂ = (10.5 × 3.2) / 5.6

y₂ = 6

To know more about equation visit:

https://brainly.com/question/649785

#SPJ4

The answer to the given question is  x = -2, x = 2. The given problem can be solved by the following steps :

Step 1: Rewrite the equation in standard form: x2 + 7x - 4 = 0

Step 2: Find the factors of the coefficient of x and the constant term: -4 = -2 x -2, 7 = 7

Step 3: Set up the factors to solve the equation: (x + 2)(x - 2) = 0

Step 4: Solve each factor: x + 2 = 0, x - 2 = 0

Step 5: Find the solutions: x = -2, x = 2

Therefore, the final answer is x = -2, x = 2.

To know more about equation here

https://brainly.com/question/12918115

#SPJ4

Answer:

p = -7

Step-by-step explanation:

1) added up the like therms

-p -7 = 0

2) multiply by -1

p+7 = 0

3) add at both members -7

p+7-7 = -7

p= -7

Answer: 440 ft

Step-by-step explanation:

Given

A parade route is [tex]\frac{3}{4}[/tex] mile long

There are 8 refreshment stand at the end of the route

Suppose there are two refreshment stand, so the route is divided into 3 parts, similarly for three stands, the route is divided into 4 parts

For 8 stands, the route is divided into 9 parts

Distance between two stands is

[tex]\Rightarrow \dfrac{\frac{3}{4}}{9}\\\\\Rightarrow \dfrac{1}{12}\ \text{miles}[/tex]

We know, [tex]1\ \text{mile}\equiv 5280\ ft[/tex]

convert miles to feet

[tex]\Rightarrow \dfrac{1}{12}\times 5280\\\\\Rightarrow 440\ ft[/tex]

Answer:

2 prime numbers: 31 and 37

Step-by-step explanation:

31 and 37 are the only prime numbers between 30 and 40

Answer:

42 cm cubed

Step-by-step explanation:

6x4x4 to find volume of 96 when it is filled.

3x3x6 = 54 to find out what is cut out.

96-54 = 42 cm cubed.

Answer:

It will either invert the graph or stretch/compress the horizontal

Step-by-step explanation:

When a is negative It will invert the graph, and reflect it over the x-axis

By plugging in a=1 you get a normal absolute value function of x ( a V on the graph)

If a>1 then your graph will compress

If a<1 then your graph will stretch

Answer:

1/2

Step-by-step explanation:

The equations which show direct proportion between a and b are:

a=2b and a=b/2.

Direct proportion or direct variation is the relation between two quantities where the ratio of the two is equal to a constant value. It is represented by the proportional symbol, ∝. In fact, the same symbol is used to represent inversely proportional, the matter of the fact that the other quantity is inverted here.

Example: x and y are two quantities or variables which are linked with each other directly, then we can say x ∝ y. When we remove the proportionality symbol, the ratio of x and y becomes equal to a constant, such as x/y = C, where C is a constant.

Given, two variables a and b

If two variables a and b are in direct proportion

then,

a/b = constant.

1. a = b²

a/b = b

which is not constant

⇒ a is not in direct proportion with b.

2. a = 2b

a/b = 2

which is constant

⇒a is in direct proportion with b.

3. a = b/2

a/b = 1/2

which is constant

⇒ a is in direct proportion with b.

4. a=b+2

a/b = 1+2/b

which is not constant

⇒ a is not in direct proportion with b.

5. a = 2/b

ab = 2

⇒a is inversely proportional to b.

Hence, In equation a=2b and a=b/2, a is directly proportional to b.

Learn more about direct proportion here:

https://brainly.com/question/28730073

#SPJ1

Draw a line and locate the origin '0', mark the positive numbers on the right and the negative number on the left of '0' at an equal distance.

A number line is a horizontal straight line in which the integers are placed in equal intervals. All the numbers can be represented in a number line. This line can be extended indefinitely at both ends. 

A number line is a graphical representation of numbers on a straight line. It is used for comparing and ordering numbers. It can be used for representing any real number that includes every whole number and natural number.

Draw a line and locate the point ‘0’. This point is known as the origin. If the given number is positive, draw it on the right side of the origin. If it is a negative number, draw it on the left side of zero. Divide each unit into the values equal to the denominator of the given fraction.

To know more about fraction, here

https://brainly.com/question/10354322

#SPJ4

Answer:

B

Step-by-step explanation:

Answer:

x=8

Step-by-step explanation:

Add up the angles to 90 because angle GHI and angle IHJ should add up to 90°

3x+66=90

-66=-66

Solve for x.

3x = 24

3 = 3

x =8

Hope this helps.

Answer:

g=1.50x+12.50 / Cole can play 15 games

Step-by-step explanation:

Once writing the equation place 35 for the variable.( 35=1.50x+12.50) Then you would have to solve for x.(x=15) I hope this is correct