Here are the first four terms of
an arithmetic sequence.
5 8 11 14

Find an expression, in terms of
for the..th term of the
sequence.

Answer: 300000000000000000

Step-by-step explanation:

50000x6000000000000 can be written as 3 times 10^17

So the answer is 300000000000000000

Hence, the coordinates of the new triangle are [tex]A(2,0),B(7,-2),C(2,-2)[/tex].

What is the coordinates?

A pair of numbers that describe the position of a point on a coordinate plane by using the horizontal and vertical distances from the two reference axes. Usually represented by [tex](x,y)[/tex] the x-value and y-value.

Here given coordinates are

[tex](-2,3),(3,1),(-2,1)\\\\(-2,0),(3,-2),(-2,-2)\\\\( - 2 , 0 ) , ( 3 , - 2 ) , ( - 2 , -2 )[/tex]

Suppose [tex]a[/tex] units on the horizontal and [tex]b[/tex] units on the vertical. Then, the new coordinate become

[tex]A(x,y)=A(x+a,y+b)[/tex]

As per the question triangle [tex]ABC[/tex] is translated [tex]4[/tex] units to the right and [tex]-3[/tex]units down.

So, [tex]a=4,b=-3[/tex] and the coordinates are

[tex]A(-2,3),B(3,1),C(-2,1)\\\\[/tex]

Then,

[tex]A(-2+a,3+b)=A(-2+4,3-3)=A(2,0)\\\\B(3+a,1+b)=B(3+4,1-3)=B(7,-2)\\\\C(-2+a,1+b)=C(-2+4,1-3)=C(2,-2)[/tex]

Hence, the coordinates of the new triangle are [tex]A(2,0),B(7,-2),C(2,-2)[/tex].

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The average number of customers waiting in the queue is 20

In this question, we have been given that the customers arrive at the rate of two per minute.

On average a customer waits 10 minutes in a queue.

We need to find the number of customers waiting in the queue on average.

Assume that the average number of customers waiting in the queue is N.

We have the average Rate of Arrival = 2 customers per minute

So, by the formula for average waiting time under the Single-Server Queue Model,

10 = N/2

N = 10 * 2

N = 20

The average number of customers waiting according to the single-server queue model given the above conditions is 20

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The solutions of the quadratic equation are:

x = (-1 + i√23)/4

x = (-1  - i√23)/4

For a general quadratic:

a*x^2 + b*x + c = 0

The solutions are given by the quadratic formula

[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac} }{2a}[/tex]

Here we have the quadratic equation:

2x^2 + x + 3 = 0

[tex]x = \frac{-1 \pm \sqrt{1^2 - 4*2*3} }{2*2} \\\\x = \frac{-1 \pm \sqrt{-23} }{4}[/tex]

So we will have two complex solutions, these are:

x = (-1 + i√23)/4

x = (-1  - i√23)/4

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If cos x= 2/3 and x is in quadrant I, then the exact value of sin(2x) is (4/3)sin x.

A branch of mathematics called trigonometry examines the connections between triangles' angles and sides. It is predicated on the idea of right triangles, where one angle is 90 degrees and two sides are perpendicular to one another. The six fundamental functions of trigonometry—sine, cosine, tangent, cotangent, secant,  cosecant. These values of functions can be used to address real-world angle and length issues, such as determining the height of a structure or the distance between two locations. Calculus, geometry, and other areas of mathematics are all strongly connected to trigonometry.Modeling actual phenomena like item motion, wave behaviour, and light dispersion is possible with these functions. Physics, engineering, and astronomy are just a few of the disciplines that use trigonometry extensively.

How to solve?

In quadrant I, cos x = 2/3 and sin x > 0.

sin(2x) = 2sin x cos x

sin(2x) = 2 * 2/3 * (sin x)

sin(2x) = (4/3)sin x

If sin x > 0, then sin(2x) = (4/3)sin x > 0.

The exact value of sin(2x) is (4/3)sin x

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The cost of the pyramid shape sign is $240.

A pyramid is a 3D figure that has a base made of a polygon and faces that are all triangular and connected. The conventional shape of a pyramid is created by joining each vertex of the base to a single common tip or apex. In this section, let's study more about pyramids.

We know the volume of a pyramid is (1/3)×length of the bese×width of the base×height.

∴ The volume of the pyramid with base length of 6feet, base width of 3feet and height 5 feet is,

= (1/3)×6×3×5 cubic feet.

= 30 cubic feet.

Given, The aluminum costs $8 per cubic foot.

∴ The total cost of the pyramid is = (30×8) = $240.

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Answer:

d = 5m

Step-by-step explanation:

Look at point (1, 5).

When the number of months is 1, the amount in dollars is 5.

The amount in dollars is always 5 times the number of months.

d = 5m

The value of x = 7 and y = 54.

What is a system of equations?

A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, often known as a system of equations or an equation system.

Here, we have

Given:  y = 6x+12 and y = x+47

We have to solve this equation and find the value of x and y.

y = 6x+12....(1)

y = x+47.....(2)

We put the value of y in equation (1) and we get

x + 47 = 6x + 12

6x -x = 47 -12

5x = 35

x = 7

Now, we put the value of x in equation(2) and we get

y = 7 + 47

y = 54

Hence, the value of x = 7 and y = 54.

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Answer:

[tex] slope=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} [/tex]

[tex] slope=\frac{8-1}{7-1} [/tex]

[tex] slope=\frac{7}{6} [/tex]

slope = 7/6

Answer:

a.) x=6 b.) y=-7 c.) a=0.25

Step-by-step explanation:

a.) 2(3x+2)=2x+28

6x+4=2x+28

subtract 4 on both sides

6x=2x+24

subtract 2x on both sides

4x=24

divide both sides by 4

x=6

b.) 5y+13=-43-3y

add 43 on both sides

5y+56=3y

subtract 5y on both sides

56=-8y

divide both sides by 8

-7=y or y=-7

c.) 4(2a+2)=8(2-3a)

8a+8=16-24a

add 24a on both sides

32a+8=16

subtract 8 on both sides

32a=8

divide both sides by 32

a=0.25

(hope you understood how I solved for each equation..)

Answer:

l

v

Step-by-step explanation:

80, 5, 30, 7, and 3,

From the given ratio, there is a total of 100,000 vending machines in Osaka.

What is the ratio?

By comparing two amounts of the same units, the ratio can be used to calculate how much of one item is included in the other. There are two different categories for ratios. The first is a part-to-part ratio, whereas the second is a part-to-whole ratio.

Given, the ratio of vending machines to people is 1 to 24

That means, for every vending machine, there are 24 people.

In the city of Osaka, there are about 2,400,000 people.

So, the number of  vending machines = 2400000/24 = 100000

Hence, there is a total of 100,000 vending machines in Osaka.

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The question is based on the calculus and the derivative for given equation [tex]t^{4} - 24t^{2} \\ \\[/tex] is t = 0.

Calculus is a discipline of mathematics that focuses on rates of change, to put it simply. For instance, you could wish to determine how quickly an automobile will slow down when it approaches a stop sign. Calculus can assist you in calculating that change. Calculus introduces movement into math, that's correct!

Calculus is a tool used by engineers to calculate things like rates of change and areas; in fact, calculus is the mathematical "backbone" for dealing with problems where variables change with time or some other reference variable. Calculus is concerned with two basic operations: differentiation and integration.

We are given

x(t) = [tex]t^{4} - 24t^{2} \\ \\[/tex]

we need to find its derivative only then we can comment on its increasing decreasing nature

x'(t) = [tex]4t^3 -48t\\\\[/tex]

we will check where derivative is zero

[tex]4t^3 - 48t = 0\\\\4t^2(t-4) = 0\\\\\\t = 0 \\\\t = 4\\[/tex]

hence increasing for all x E R except interval (0,4)

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Answer:

This would not form a triangle

Step-by-step explanation:

due to the triangle inequality theorem, in order to find out if three numbers can form a triangle, you have to have each pair of numbers add up to more than the remaining number. The first combination added is 5+10 which is 15, and that is not greater than 17, so the answer is no, this is not a triangle.

hope this helps! :3

The value of the angle y will be equal to 47.46. The correct option is A.

Supplementary angles are those that total 180 degrees. Angles 130° and 50°, for example, are supplementary angles because the sum of 130° and 50° equals 180°.

The angle is defined as the span between two intersecting lines or surfaces at or close to the point where they meet.

Given that the angle x is equal to 132.54°. The value of the angle y will be calculated as,

x + y = 180

132.54 + y = 180

y = 180 - 132.54

y = 47.46

Therefore, the value of the angle y will be equal to 47.46. The correct option is A.

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The correct statement regarding the exponential functions g(x) and h(x) is given as follows:

B g( x) ≥ h( x) on the interval –2 ≤ x ≤ 2.

The standard definition of an exponential function is given as follows:

y = ab^x.

In which the coefficients of the function are described as follows:

Function h(x) is defined as follows:

h(x) = 3^x - 2.

For the graphed function g(x), when x = 0, y = 4, hence the intercept of the function is given as follows:

a = 4.

When x = 1, y = 5, hence the rate of change of the function is obtained as follows:

b = 5/4.

b = 1.25.

Then function g(x) is given as follows:

g(x) = 4(1.25)^x.

Due to the higher intercept, g(x) ≥ h( x) at x = 0. This will change when they intersect, which from the image given at the end of the answer is at x = 1.906, which is approximately 2, hence statement B is correct.

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Answer:

a. 88

b. I disagree with Kris

Step-by-step explanation:

88 is by far the biggest outlier here being 11 numbers away from the second highest being 77. This means there is one kid that is much higher than the rest of the group.

Answer:

Step-by-step explanation:

1. Lin, Tyler, and Jada's information is missing.

2. 9 1/8 = 73/8

1 2/8 = 10/8

73/8 - 10/8 = 63/8.

His shoe length was 63/8 inches.

0.954 represents population of the town increases by 0.954 each year.

Two or more expressions with an Equal sign is called as Equation.

Given,

The population of a heard of buffalo after t

years is represented by the function

[tex]f(x)=2186(0.954)^{t}[/tex]

We need to find the what does the value 0.954 represent in this

situation.

In the given function 2186 represent the initial population.

t represents the time in years

and 0.954 represents population of the town increases by 0.954 each year.

Hence, 0.954 represents population of the town increases by 0.954 each year.

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Part a: y = -6x + 5 is : Not proportional.

Part b: y = 7/8x proportional:  proportionality constant = 7/8.

For the stated question;

Part a: y = -6x + 5

To check the proportional relation, put value of 'x' and find the corresponding value of 'y'.

The ratio = y/x must be same.

For x = 1, y = -1

y/x = -1

And, for x = 2, y = 7

y/x = 7/2

Thus, ratio is not equal, Not proportional.

Part b:  y = 7/8x

For x = 1, y = 7/8

y/x = 7/8

Now, For x = 2, y = 14/8

y/x = 7/8, both ratios are equal.

Thus,  y = 7/8x proportional:  proportionality constant = 7/8.

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The slope of the given function is 0.25. The function that has  the same slope is y = 0.25x + 5. Option B is the correct option.

What is a function?

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

Given table is

x         0          1            2             3

y      -0.5       -0.25      0           0.25

The slope of a function that passes through the points (x₁, y₁) and (x₂, y₂) is m = (y₂ - y₁)/(x₂ - x₁)

Assume that x₁ = 0, y₁ = -0.5, x₂ = 1, y₂ = -0.25

The slope of the function is [-0.25 - (-0.50)]/(1 - 0) = 0.25

Now compare the equation y = -0.25x - 2 with y = mx + c

m =  -0.25

The slope of the function is -0.25.

Now compare the equation y = 0.25x + 5 with y = mx + c

m =  0.25

The slope of the function is 0.25.

Now compare the equation y = 4x - 5 with y = mx + c

m =  4

The slope of the function is 4.

Now compare the equation y = -4x + 34 with y = mx + c

m =  -4

The slope of the function is -4.

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Answer:

Parallel: Y= -7/3x - 37/3

Perpendicular: Y=3/7x + 7

Step-by-step explanation:

Use the formula: Y - Y1 = M(X - X1) Plug in -7 as X1 and 4 as Y1 and your M value is your slope. (-7, 4) where it passes from.

Remember when the slope is parallel it's always the same slope in this case -7/3

When perpendicular flip it and change the sign 3/7

Answer:

top right

Step-by-step explanation:

6x3=18

The total Volume of tank = 35 liters

In three dimensions, everything takes up some space. What is being measured here is the area's volume. The volume of an object is the area occupied inside its three-dimensional boundaries. Sometimes it is referred to as the

According to the Given information

Volume of each marble = 0.04 liters

Number of marbles to be put in the water tank = 50 marbles

Volume of 50 marbles = 0.04 × 50 = 2 liters

Volume of water added to the tank = 33 liters

Total Volume of tank = 2 liters + 33 liters

                                    =     35 liters

SO,

The total Volume of tank = 35 liters

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The indications of the numbers in the linear equations that produces the number of apples in Annie's basket, n = 22·t + 12, are as follows;

The domain of the function n = 22·t + 12 is R⁺ which is the set of positive real numbers, including zero, [0, ∞)

A linear equation is a equation of the line of a straight line graph. The domain of a function is the set of the input values of the function.

The equation that describes the number of apples in Annie's basket, n = 22·t + 12

The number of minutes Annie spends picking apples = t

The number of apples in Annie's basket = n

The number 22 which is the coefficient of the variable t in the linear equation, which is the slope or the rate of change of the number of apples in Annie's, which indicates the number of apples Annie picks per minute.

The number 12 is the y-intercept of the equation y = 22·t + 12

The y-intercept is the value of the function where t = 0, which is the initial value of the function.

Therefore;

The domain of the function n = 22·t + 12, are the possible values of the independent or input variable, t, which is the set of positive integers including 0

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Answer:  [tex]f^{-1}(\text{x}) = \frac{2-\text{x}}{3}\\\\[/tex]

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

Work Shown:

[tex]f(\text{x}) = 2-3\text{x}\\\\\text{y} = 2 - 3\text{x}\\\\\text{x} = 2 - 3\text{y}\\\\\text{x} + 3\text{y} = 2\\\\3\text{y} = 2-\text{x}\\\\\text{y} = \frac{2-\text{x}}{3}\\\\f^{-1}(\text{x}) = \frac{2-\text{x}}{3}\\\\[/tex]

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

Explanation:

The process to find the inverse involves this outline.

This process is followed in the "work shown" portion above.

To confirm the answer, let g(x) be the inverse of f(x).

If they were inverses of each other, then these two properties would hold true:

Here's the verification for the first part.

[tex]f(\text{x}) = 2-3\text{x}\\\\f(g(\text{x})) = 2-3*g(\text{x})\\\\f(g(\text{x})) = 2-3*\frac{2-\text{x}}{3}\\\\f(g(\text{x})) = 2-(2-\text{x})\\\\f(g(\text{x})) = 2-2+\text{x}\\\\f(g(\text{x})) = \text{x}\\\\[/tex]

I'll let you do the other confirmation.

The length is 28.75 inch and width is 11.25 inch.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

Perimeter= 80 inches

let the width be x.

length= 3x- 5

Now, perimeter of a rectangle = 2( l+ w)

80= 2( x+ 3x- 5)

40 = 4x -5

45 = 4x

x= 11.25

and, length = 3(11.25)- 5 = 28.75

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The values obtained after solving the given equation is x  = 6 and y = 10.

Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.

This relationship is illustrated by the left and right expressions being equal to one another. The left-hand side equals the right-hand side is a basic, straightforward equation.

As per the information given in the question,

The given equations are,

-5x + 3y = 0   (i)

7x - 4y = 2    (ii)

Multiply equation (i) by -7 and equation (ii) by 5.

35x - 21y = 0       (iii)

35x - 20y = 10       (iv)  

Now, solve the equation for y, because 35x in positive and 35x in negative cancel out each other.

-y = -10

y = 10

Substitute y = 10 in equation (i)

-5x + 3(10) = 0

-5x = -30

x = 30/6

x = 5

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