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Find the value of x

The exponential function to describe the given sequence of numbers, 10, 60, 360, 2160, 12960, ... is aₙ = 10 × [tex]6^{n-1}[/tex].

The given series 10, 60, 360, 2160, 12960, ... is a geometric progression.

a = 10

The common difference r = 60/10 = 6

As we know the general formula of the nth term of a geometric series is

aₙ = a × [tex]r^{n-1}[/tex]

Now, put the values of a = 10, r = 6 and n in the general formula,

aₙ = 10 × [tex]6^{n-1}[/tex]

Therefore, the required exponential function to describe the given sequence of numbers, 10, 60, 360, 2160, 12960, ... is aₙ = 10 × [tex]6^{n-1}[/tex].

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The domain and scope of the identity function are the same. Equation for the identity function is  f(x) = x, or y = x.

An statement, rule, or law in mathematics that specifies the connection between an independent variable and a dependent variable (the dependent variable. A relationship between a group of inputs and one output each is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. Y=X2 is an illustration of this. You only receive one output for y if you enter anything for x. The fact that x is the input value leads us to argue that y is a function of x.

identity function are the same.

Equation for the identity function is

f(x) = x, or y = x.

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Answer:

one solution

Step-by-step explanation:

The two lines cross at exactly one point.  That means there is one solution.

The monthly payment for this difference would be $1,361.21. An Adjustable Rate Mortgage (ARM) is a type of mortgage in which the interest rate on the loan changes over time.

An Adjustable Rate Mortgage (ARM) payment is based on various factors such as the loan amount, interest rate, and the terms of the ARM. The interest rate is usually tied to a specific financial index, such as the U.S.

Here is the calculation format for the difference in payments between year 2 and year 3 for Bart and April's mortgage:

Total amount to be paid for the mortgage: $315,000

Rate of interest: 5.85% (Depreciating rate)

Time = 2 years:

a. Remaining amount to be paid after 2 years:

Principal × (1 - Rate/100)^time

= $315,000 × (1 - 5.85/100)²

= $315,000 × (1 - 0.0585)²

= $279,223.01

Time = 3 years:

a. Remaining amount to be paid after 3 years:

Principal × (1 - Rate/100)^time

= $315,000 × (1 - 5.85/100)³

= $315,000 × (1 - 0.0585)³

= $262,888.46

Difference in payments from year 2 to year 3:

= Remaining amount after 2 years - Remaining amount after 3 years

= $279,223.01 - $262,888.46

= $16,334.55

The monthly payment for this difference would be $1,361.21, which is calculated by dividing the difference in payments by 12:

$16334.546/12 = $1361.21

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We can check if a function has an inverse function using horizontal  Line Test.

What is Function?

A relation between a collection of inputs and outputs is known as a function. In plain English, a function is an association between inputs in which each input is connect

horizontal  Line Test

Make f a function. Any horizontal line that crosses the f graph more than once indicates that f lacks an inverse. F does have an inverse if there are no horizontal lines that cross the graph of f more than once.

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Given:

A length of a side of an equilateral triangle = 32 cm

Formula Used:

If in an equilateral triangle with side length 'a' then,

Area of an equilateral triangle = [(√3)/4] × a2 

Calculations:

Area of an equilateral triangle = [(√3)/4] × 322

⇒ (1024 × √3)/4

⇒ 256√3 cm2

Answer:

y = x - 2

Step-by-step explanation:

Here m is the slope and b is the y-intercept.

Choose any two points on the line.            

 (2,0)  ; (0,-2)

Now, find the slope.

        [tex]\sf \boxed{Slope = \dfrac{y_2-y_1}{x_2-x_1}}[/tex]

                   [tex]= \dfrac{-2 - 0}{0 - 2}\\\\=\dfrac{-2}{-2}\\\\= +1[/tex]

m = 1.

Now, y = 1x +  b

The (2 , 0) passes through the line. Substitute x = 2 and y = 0 in the above equation and find the value of 'b'.

       0 = 1*2 + b

       0 =  2 + b

        -2 = b

Equation of line:

              y = x - 2

The rate exists water being poured into the cup when the water level is 9 cm exists [tex]$$1458 \pi \mathrm{cm}^3 s^{-1}$$[/tex].

To determine the derivative of a composite function in differential calculus, apply the chain rule formula. If y = f(g(x)), then according to the chain rule, the instantaneous rates of change of the functions f and g with respect to x produce the instantaneous rate of change of f with respect to x.

A composition of functions, such as the composition of the functions f and g, f(g(x)), can be used to determine the derivative using the chain rule.

Let us set up the following variables:

R, Radius of conical cup (cm) = 30 cm

H, Height of the conical cup (cm) = 10 cm

Our aim is to find dV/dt when h = 9 and we are given dh/dt = 2

By similar triangles we have

r : h = R : H

r/h = 30/10

⇒ r = 3h

The volume of a cone is 1/3π r²h, So:

V = 1/3π r²h

simplifying the equation, we get

= 1/3π (3h²)h

= 1/3π 9h²h

= 3π h³

Differentiating wrt h we get:

dV/dh = 9π h²

Applying the chain rule we have:

dV/dt = (dV/dh)(dh/dt)

= 9π h² × 2

= 18π h²

If h = 9 then

[tex]$\left[\frac{d V}{d t}\right]_{h=9}=18 \pi\left(9^2\right)=1458 \pi \mathrm{cm}^3 s^{-1}$$[/tex].

Therefore, the rate exists water being poured into the cup when the water level 9 cm exists [tex]$$1458 \pi \mathrm{cm}^3 s^{-1}$$[/tex].

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Earth's rotation is what causes day and night. As Earth rotates on its axis, half of the planet is facing the Sun, while the other half is facing away from the Sun.

The half of the planet facing the Sun experiences daylight, while the half facing away from the Sun experiences darkness. This cycle repeats itself every 24 hours, resulting in the day and night cycle that we experience.

Earth's rotation causes day and night by rotating on its axis, with half of the planet facing the Sun and the other half facing away from the Sun. This cycle of daylight and darkness lasts for  creating the day and night cycle that we observe.Earth's rotation is what causes day and night. As Earth rotates on its axis, half of the planet is facing the Sun, while the other half is facing away from the Sun.

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The inverse of ∼P→∼Q is P->Q.

Given ∼P→∼Q

Its inverse, ∼(∼P)→∼(∼Q), means that P→Q.

If the hypothesis is correct but the conclusion is untrue, a conditional statement is false. If the statement in the example above read, "If you achieve good marks then you will not get into a good college," it would be untrue. A conditional statement that has been modified or rearranged is referred to as a related conditional. An if-then statement, also known as a conditional statement, is a set of hypotheses followed by a conclusion. It is noted that p→q. Read this: if p, then q.

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The equation for new function is,

⇒ f (x) = ∛( 1/4x - 6) - 5

A relation between a set of inputs having one output each is called a function.

Given that;

The parent function is,

⇒ g (x) = ∛x

Now, After  reflected and stretched by 4, we get;

⇒ g (x) = f (1/4x) = ∛ 1/4x

And, After translated 6 units to the right, we get;

⇒ g (x) = f (x - 6) = ∛ 1/4x - 6

And, After 5 unit down, we get;

⇒ g (x) = h (x) - 5 = ∛( 1/4x - 6) - 5

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The value of x in this problem is 2.

Our given algebraic equation is 2.5 ( 6x - 4 ) = 10 + 4 ( 1.5 + 0.5x) and in this, we have to find the final value of x.

Use the transposing method to isolate the variable x and then solve for it.

distribute brackets on both sides of the equation.

= 2.5*6x - 2.5*4 = 10 + 4*1.5 + 4*0.5x

= 15x - 10 = 10 + 6 + 2x

collect terms in x to the left side and numeric values to the right side.

= 15x - 2x = 10 + 6 + 10

= 13x = 26

= x = 26/13 = 2

Therefore the final value of x in this equation will be 2.

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P= kd/u^2 is the equation which expresses the following relationship p varies derectly with d and inversly with the square of u.

Equation is a mathematical statement that expresses the equality of two expressions. An equation is written as an expression containing an equal sign, with each side of the equal sign representing a mathematical expression. The purpose of an equation is to show the relationship between two or more variables, such as a change in one variable resulting in a change in another. Equations are used to solve problems in mathematics, physics, economics, and many other fields.

The equation states that p is directly proportional to d, and inversely proportional to u squared. This means that as d increases, p increases, and as u increases, p decreases. The constant of proportionality, k, is a measure of the strength of the relationship between p, d, and u.

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According to triangle inequality theorem a triangle with two sides 7 units and 17 units, has a third side which measures 10 units.

What is Triangle Inequality Theorem?

According to triangle inequality theorem, the sum of the lengths of any two sides of a triangle is greater than the length of the third side.

The two sides of a triangle are -

a=7, b=x and c=17, where a, b and c are the sides of the triangle.

As, 17 is a bigger number so let it be the biggest side.

Now, according to triangle inequality theorem -

a + b = c

7 + x = 17

x = 17 -7

x = 10

Therefore, the third side of the triangle measures 10 units.

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Answer:

5 kg.

Step-by-step explanation:

2 kg for $0.96 is more expensive than 5 kg for $1.95

The ratio for cos (cosine) of angle θ is: cos(θ) =  adjacent side of θ / hypotenuse

We know that in right triangle the cosine of an angle is nothing but the ratio of the side adjacent of  given angle to the hypotenuse.

In right tirnagle for an angle θ, the ratio for cosine of angle θ would be:

cos(θ) =  adjacent side of θ / hypotenuse

Consider following right triangle PQR with angle PQR = 90 degrees

Here, PR is the hypotenuse.

Assume that angle QPR measure α degrees and angle PRQ measures θ degrees.

By definition of cosine of angle θ,

cos(θ) =  adjacent side of θ / hypotenuse

cos(θ) =  QR / PR

And by definition of cosine of angle α,

cos(α) =  adjacent side of α / hypotenuse

cos(α) = PQ / PR

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The expression is x + 9.Generally speaking, an expression is at its simplest form when it is most usable.

Explanation:

8x + 6+5 - x - 6x - 2

= x + 9.

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The perimeter expression of a rectangle has a perimeter represented by the expression 4x−8 is 2(2x - 4)

From the question, we have the following parameters that can be used in our computation:

Perimeter = 4x - 8

Factor out 2 from the expression

So, we have the following representation

Perimeter = 2 * 2x - 2 * 4

So, we have

Perimeter = 2(2x - 4)

Hence, the perimeter is 2(2x - 4)

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P (X)= [tex]x^3+4 x^2-3x+2[/tex]  moreover, [tex]\frac{P(x)}{x - 1} = x^{2} + 5x +2[/tex] as a result, the actual claim is  [tex]$p(x)=(x-1)\left(x^2+5 x+2\right)+\frac{4}{x-1}$[/tex]

The likelihood of an event occurring is determined by probability:       P(A) = f / N. Probability and odds are related, but probability is necessary for odds to exist. Prior to calculating the likelihood that an event will occur, probability is required.

The steps listed below can be used to determine an event's likelihood: Step 1: Identify an event that has only one outcome. Step 2: Compile a list of all potential outcomes, including any positive ones. Step 3: Subtract the number of favourable outcomes from the total number of outcomes that are feasible. The probability of A or B is equal to p(A or B) = p(A) + p(B) if occurrences A and B are mutually exclusive (B). A probability is a number that expresses the possibility or likelihood that a specific event will take place.

Therefore the correct answer is option A ) [tex]$p(x)=(x-1)\left(x^2+5 x+2\right)+\frac{4}{x-1}$[/tex]

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Answer:  -100

Step-by-step explanation:   -7(15)+5

It said x=15 so put 15 in and solve from there and that would be -100

HOPE THIS HELPS ANY I JUST completed FUNCTIONS AND MAN IT WAS FUN

We can solve the inequality to get:

h ≤ -3

And its graph can be seen below.

Here we have the following inequality:

-(1/3)*h ≥ 8

To solve the inequality, we need to isolate h.

So we can multiply both sides by -3 (notice that this will change the sign of the inequality symbol)

So we will get:

-3*(-1/3)*h ≤ -3*h

h ≤ -3

Now to graph this, we need to draw a closed circle at -3, and draw an arrow that gose to the left.

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Answer:

Step-by-step explanation:

8x+18=2x+x+4x-3

8x+18=7x-3

perimeter = x+21

Answer:

33 ounces

Explanation:

20% of 27.5 ounces is 5.5 ounces.

To find how much more juice the container has, we add 5.5 to 27.5, which equals to 33 ounces

Answer:

85+7.5v=160

7.5v=160-85

7.5v=75

V=75/7.5

V=10

Ryan would need to take 10 visits to get a free ticket.

4.68

find unit rate by dividing 208 cents by 16 which is 13 than multiply by 36

Answer:

16 inches of ribbon cost- $2.08

36 inches of ribbon cost- ?

36*$2.08/ 16

$74.88/16

= $4.68

Thus, 36 inches of ribbon would cost $4.68

The value of the legs of the triangle would be hypotenuse/√2.

You can use basic trigonometry to solve this problem. We know that the sine of the angle made by the hypotenuse and the base is equal to the ratio of perpendicular height and the hypotenuse, given that the angle is 45° the perpendicular will be equal to ⇒ hypotenuse × sin(45°).

That is perpendicular=hypotenuse/√2

Similarly, the cosine of the angle made by the hypotenuse and the base is equal to the ratio of base length and the hypotenuse, given that the angle is 45° the base will be equal to ⇒ hypotenuse × cos(45°)

That is base=hypotenuse/√2

Therefore, the value of the legs of the 45°-45°-90° triangle would be hypotenuse/√2.

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Answer:

60 degrees

Step-by-step explanation:

The total measure of a circle is 360 degrees.

360-140-100 = 120

Angles MON and NOP are equivalent which makes MN and NP equivalent.

120/2 = 60 degrees = MN

Answer: J' (8, -9); K' (8, -2); L' (3, -2); M' (3, -9)

Step-by-step explanation:

A rotation of 90 degrees counterclockwise is (x, y) -> (-y, x), so

J (-9, -8) -> J' (8, -9)

First, you take negative 8 (y) of J and make it positive 8 for the x of J'. Then, take -9 (y) of J and switch it to x of J'.

You repeat this process for the rest of the points. X switches to Y with the opposite sign and Y switches to X but stays the same.

K (-2, -8) -> K' (8, -2)

L (-2, -3) -> (3, -2)

M (-9, -3) -> (3, -9)

The number of grams of sugar that would be in a 200 ml glass of juice, given the carton, is 13. 2 grams of sugar

In a 250 ml glass of juice, we would see 16. 5 g of sugar. Given this information, we can find the amount of sugar in a 200 ml of juice by using direct proportion.

The amount of sugar in 200 ml of juice is :

= ( Amount of sugar in 250 ml x Quantity of juice ) / Quantity of base quantity of juice

= ( 16. 5 x 200 ) / 250

= 3, 300 / 250

= 13. 2 grams of sugar

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