Use the information below to complete the problem: p(x) = 1/(x+1) and q(x)= 1/(x-1) Perform the operation and show that it results in another rational expression. p(x) / q(x)

Step-by-step explanation:

To find the number of years it will take for Enola's investment to triple in value, we can use the formula for simple interest:

I = P * r * t

where I is the total interest earned, P is the principal (the initial amount invested), r is the interest rate, and t is the number of years.

Since the investment will triple in value, the total interest earned will be equal to two times the initial investment, or 2 * $8,600.00 = $17,200.00. Substituting these values into the formula and solving for t, we get:

$17,200.00 = $8,600.00 * 5.1% * t

t = $17,200.00 / ($8,600.00 * 5.1%) = 3.28 years

Rounding this value to the nearest tenth of a year, we get t = 3.3 years. Therefore, it will take approximately 3.3 years for Enola's investment to triple in value.

A) The Probability that comic D will perform fourth is; 1/6

B) The Probability that Comic F will perform first and Comic C will perform fourth is;  1/30

C) Probability that the comedians will perform in the following order, D, F, C, E, A, B is;  1/720

D) Probability that Comic A or Comic B will perform third is; 1/15

A) Probability that comic D will perform fourth;

Number of ways that this will succeed = 1 * 5!

Number of possible outcomes normally = 6!

Thus;

P(D is 4th) = 5!/6! = 1/6

B) Probability that Comic F will perform first and Comic C will perform fourth.

Number of ways that this will succeed = 1 * 1 * 4!

Number of possible outcomes normally = 6!

Thus;

P(F is 1st and C is 4th) = 4!/6! = 1/30

C) Probability that the comedians will perform in the following order, D, F, C, E, A, B;

There is only 1 way and as such the probability = 1/6! = 1/720

D) Probability that Comic A or Comic B will perform third;

(2!*4!)/6! = 1/15

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The angles m∠CEA and m∠AED are supplementary .hence the value of x will be 10 has been proved.

An angle is a geometry in plane geometry that is created by 2 rays or lines that have an identical terminus.

The identical endpoint of the two rays known as the vertex—is referenced as an angle's sides.

We are Given that m∠CEA and m∠AED are only two angles on a straight line thus they will be supplementary.

Therefore, we have

m∠CEA + m∠AED = 180°

8x + 10 + 6x + 30 = 180

14x + 40 = 180

14x = 140

x = 10

Hence "The value of x will be 10 that proved the angles m∠CEA and m∠AEDare complementary".

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Option (d) i.e y = 2x is correct option as this function is satisfying given values of y and x.

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. German mathematician Peter Dirichlet initially offered the standard concept of function in 1837.

y and x are coupled in such a way that there is a distinct value of y for each value of x, and this relationship is frequently represented as y = f(x), or "f of x." In other words, the same x cannot have more than one value for f(x).

We need to check by substituting value of y in every equation to check correct option.

(a) Substituting y=6 and x=3 in function

L.H.S = 6

R.H.S = 3x= 3×3=9

L.H.S≠R.H.S

So, it is not a correct option.

(b) Substituting y=6 and x=3 in function

L.H.S = 6

R.H.S = x-3= 3-3=0

L.H.S≠R.H.S

So, it is not a correct option.

(c) Substituting y=6 and x=3 in function

L.H.S = 6

R.H.S = x+2= 3+3=5

L.H.S≠R.H.S

So, it is not a correct option.

(d) Substituting y=6 and x=3 in function

L.H.S = 6

R.H.S = 2x= 2×3=6

L.H.S=R.H.S

So, it is correct option.

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Answer:29,921.25

Conner and Darian made a profit of $40,021.50 on the first day of their hot chocolate sale. They donated $10,050.25 of that money to their school, which leaves them with $40,021.50 - $10,050.25 = $29,971.25.

Conner and Darian each gave their dad $25.00, which means they gave a total of $25.00 * 2 = $<<25*2=50.00>>50.00 to their dads.

This means that Conner and Darian had $29,971.25 - $50.00 = $29,921.25 left to invest in their hot chocolate shop.

Answer:

y = 1/3x + 6

Step-by-step explanation:

The shape of the graph of a function is the shape assumed by the graph of the function after the dataset generated by using the function is plotted on the coordinate plane. The shape in the graph of the question is a triangular shape.

A function is a direction used to map the values of an input variable of the function to the output variables.

The points in the attaches graph which are connected by lines are;

(0, 1.5), and (4.5, 0)

The joining of the above points in the attached graph, and the origin forms a triangular shape.

Details about the shape of the graph of a function

The graph of a function such as f(x) = -x² + 2·x + 3, is obtained by finding the values of the output values of the function, f(x) for each input value of the function, x as follows;

x     [tex]{}[/tex]             f(x)

0     [tex]{}[/tex]              3

1     [tex]{}[/tex]               4

2     [tex]{}[/tex]              3

3     [tex]{}[/tex]              0

4     [tex]{}[/tex]              -5

5     [tex]{}[/tex]              -12

6     [tex]{}[/tex]              -21

7     [tex]{}[/tex]              -32

8     [tex]{}[/tex]              -45

Please find attached the graph of the sample function created with MS Excel

The graph of the function f(x) = -x² + 2·x + 3 has the shape of a parabola, which is the shape of a quadratic function.

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The big-o estimate for each of these functions are:

nlog(n^2 + 1) = o (n^2 logn)

It is a commonly used notation in algorithms and data structures domain to get an approximate upper bound of the time the algorithm in question will take to run.

For example, if you want to find the maximum element in a list of n elements, the worst case scenario is that the maximum is the last number. Then we write  O(n) .

If the function is not too unweildy, it's pretty easy to do.

Consider the function f(x) = 4x^3 + (7x^2)(log(x)) + 3x +8

Look for the highest order term - the term that grows faster than the other terms, as x gets larger. For this function, that term is 4x^3.

Now just get rid of the constant out front to get x^3.

Then put a Big O in front: O( x^3 ).

So we say that f(x) is O( x^3 ).

Since,

nlog(n^2 + 1 ) + n^2 logn is approximately equals to n^2logn

which implies,

nlog(n^2 + 1) + (n^2 logn) = O (n^2 logn)

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Answer:

To create a proportion using the form %/100 = is/of, we can first write the given information in the form %/100 = is/of. In this case, we know that 1 1/2% represents 15, so we can write:

1 1/2%/100 = 15/of

Next, we need to solve for the "of" value, which is the number we are trying to find. To do this, we can multiply both sides of the equation by 100 and then divide both sides by 1 1/2% to get:

(1 1/2%/100) * 100 = (15/of) * 100

of = (15/1 1/2%) * 100

Finally, we can evaluate the right-hand side of the equation to find the value of "of". Since 1 1/2% is the same as 1.5%, we can substitute 1.5 for 1 1/2% in the equation to get:

of = (15/1.5%) * 100

of = (15/0.015) * 100

of = 1000

Therefore, the number we are trying to find is 1000.

In summary, the proportion that represents the given word problem is:

1 1/2%/100 = 15/1000

Answer:

[tex]\textsf{Proportion}: \quad \sf \dfrac{1.5}{100}=\dfrac{15}{x}[/tex]

[tex]\textsf{Solution}: \quad \sf x=1000[/tex]

Step-by-step explanation:

Given proportion formula:

[tex]\sf \dfrac{\%}{100}=\dfrac{is}{of}[/tex]

Given word problem:

Let the unknown number be x.

Therefore:

Substitute these into the proportion formula to create a proportion to represent the given word problem:

[tex]\sf \dfrac{1.5}{100}=\dfrac{15}{x}[/tex]

To solve the proportion, cross multiply:

[tex]\implies \sf 1.5x=15 \cdot 100[/tex]

[tex]\implies \sf 1.5x=1500[/tex]

Divide both sides by 1.5:

[tex]\implies \sf \dfrac{1.5x}{1.5}=\dfrac{1500}{1.5}[/tex]

[tex]\implies \sf x=1000[/tex]

A fraction of the students who have brown hair is equal to 1/7.

You should shade only one (1) section on the pie chart to show the number of students with brown hair.

In Mathematics, a pie chart can be defined as a type of graph that is used for the graphical representation of the proportion relationship between each part or unit to a whole, especially by dividing a circle into various sectors or sections.

Based on the information provided in the table (see attachment), we can logically deduce the following parameters about the various hair color;

Number of brown hair = 1 brown hair.

Number of blonde hair = 4 blonde hair.

Number of black hair = 2 black hair.

Therefore, the total number of hairs is equal to 7 hairs.

For the fraction of students with brown hair, we have;

Fraction = 1/7.

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1/2 is the slope of the following when you simplify

The attached picture is of a similar problem. But different radii.

Notice how you can form 2 equilateral triangles, and that there are 4 semi circles (at AC, AD, BC, BD).

This is because points C and D lie on the circumference of the circles. So distance from centres( A and b) to C and D are the radius

To get the area of your shaded section, you would just need to add up the areas of the 4 semi circles and 2 equi. triangles.

To get the area of a semi circle, work out the area of one of the sectors, i.e sector ABC, then subtract area of an equilateral triangle.

(Note, due to symmetry all semi circles have same area)

________________________________________________________

For example, for the picture below:

Area of equi triangle = absinC = 1*1*sin60 = √(3)   --> (C is angle)

Area of sector = (angle/360) * πr² = (60/360) * π * (1)² = π/6

So area of 1 semi circle = Area of Sector - Area of equi triangle

                                       = π/6 - √(3)

Now you would just add the areas of 4 semi circles, and 2 equi triangles, and compare coefficients to get a, b, c.
______________________________________

Now you would do the same for your question, except radius is now 6cm instead of 1cm.

When the sequence limn→∞ (1 n! ∫x t = a f(n+1)(t)(x−t)n d t) converges to zero, as seen on the left side equation the Taylor series will accurately converge to f(x). For the Taylor series of f, this side is known as the integral form of the remainder (x).

Rn(x) = f(n+1)(c) (n + 1); thus, (x a)n + Rn(x)! when there is a c between a and x, (x a)n+1. The Taylor formula is the name given to the second equation. The residual of order n or error term for the Pn(x) over I approximation of f is known as the function Rn(x) (x). To integrate a Taylor Series function, expand the Taylor Series as usual before integrating each term. There is a general expression for the new series. Prior to determining the generic phrase, it is essential to avoid simplification.

Assume that f(x) is a real or composite function and that f(x) is a differentiable function of a real or composite neighborhood number. The following power series is then described by the Taylor series: F (x) = F a F ′ a 1! (x−a)+f”(a)2!

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Answer:

you would times them both so 4x543 =2172

Step-by-step explanation:

543 cubic centimeters has 0.543 L approximate displacement.

Engine displacement means the displacement of the piston inside cylinder from Bottom Dead Center into Top Dead Center in one cycle.

Basic formula to calculate engine displacement is =

V = π/4 x D² x H x N

Where :

D = Bore Diameter

H = Length of Stroke

N = Number of Cylinder

Since the question has already stated cubic centimeter, it has already shown the displacement. So, we can ignore above formula and the 4-cylinder engine information.

First, we state what is known. It is the displacement at cubic centimeter.

Cubic centimeter = 543 cc

Next, we change the unit of cubic centimeter (cc) into liter (L)

Displacement = cc / 1000 L

= 543 / 1000 L = 0.543 L

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The height of rectangular prism needed to reach the desired volume is 9 inches.

What is the volume of the rectangular prism?

The volume of a rectangular prism is the product of its three dimensions, that is volume = length × width × height.

V= l.w.h

l Length

w Width

h Height

Given :

volume of rectangular prism (v) 32,188.04 inches

length  of rectangular prism(l) 59.3 inches

width of rectangular prism(w) 59 inches

Since , V= l.w.h

32,188.04 = 59.3 * 59 * h

or h = 32188.04/59.3 * 59

or h = 32188.04/3498.2

or h = 9.2

Hence , the height of rectangular prism needed to reach the desired volume is 9 inches.

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One pair of vertical angles are 2 and 3.

One pair of supplementary angles are 1 and 3.

The angles that are in the same position on two parallel lines intersected by a transversal line on the parallel lines.

Corresponding angles are equal.

We have,

Vertical angles are:

1 and 4

2 and 3

6 and 7

5 and 8

Supplementary angles are:

1 and 3.

2 and 4.

6 and 8.

5 and 7.

Thus,

Vertical angles are 2 and 3.

Supplementary angles are 1 and 3.

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Step-by-step explanation:

(a). Radius = WX, WY or WT as they are all points going from the centre of the circle.

(b). Diameter = TX or XT as it goes through the circle points.

(c). Chord = UV or TX as it is two points that originate from the centre of the circle.

(d).  The diameter is two times the radius, as the radius (WY = 3) we can find out that the diameter is 3 * 2 so 6.

Answer:

70 degrees

Step-by-step explanation:

Triangle XBC is an isosceles triangle.

From the question given, you already know that angle XBC = 55 degrees. This means that angle XCB = 55 degrees. This is because the two sides XB and XC are of equal length, which means that the angles are also equal to each other.

Using this info, we can calculate angle BXC:

The sum of a triangle adds up to 180, so call the unknown angle x:

55 + 55 + x = 180

110 + x = 180

x = 180 - 110 = 70 degrees

Answer:

Step-by-step explanation:

first things first go back in the lesson or your notes if you wrote down some and if not go right some down and in the notes there would be the answer between pages 1-5 or maybe  6 IDR ( i dont remember )  but look thru those  pages and you will find the answer hope this helped. please mark me brainiest please.

see the attached solution

Answer:

[tex]\dfrac{-2x^4-6}{(x+1)(x-1)(x^2+1)}[/tex]

Step-by-step explanation:

Given expression:

[tex]\dfrac{2}{x+1}-\dfrac{2x}{x-1}+\dfrac{4}{x^2+1}[/tex]

The least common multiplier of the denominators is:

[tex](x+1)(x-1)(x^2+1)[/tex]

Adjust the fractions based on the least common multiplier:

[tex]\implies \dfrac{2(x-1)(x^2+1)}{(x+1)(x-1)(x^2+1)}-\dfrac{2x(x+1)(x^2+1)}{(x+1)(x-1)(x^2+1)}+\dfrac{4(x+1)(x-1)}{(x+1)(x-1)(x^2+1)}[/tex]

[tex]\textsf{Apply the fraction rule}: \quad \dfrac{a}{c} \pm \dfrac{b}{c}=\dfrac{a \pm b}{c}:[/tex]

[tex]\implies \dfrac{2(x-1)(x^2+1)-2x(x+1)(x^2+1)+4(x+1)(x-1)}{(x+1)(x-1)(x^2+1)}[/tex]

Simplify:

[tex]\implies \dfrac{2(x^3-x^2+x-1)-2x(x^3+x^2+x+1)+4(x^2-1)}{(x+1)(x-1)(x^2+1)}[/tex]

[tex]\implies \dfrac{2x^3-2x^2+2x-2-2x^4-2x^3-2x^2-2x+4x^2-4}{(x+1)(x-1)(x^2+1)}[/tex]

[tex]\implies \dfrac{-2x^4+2x^3-2x^3-2x^2-2x^2+4x^2+2x-2x-2-4}{(x+1)(x-1)(x^2+1)}[/tex]

[tex]\implies \dfrac{-2x^4-6}{(x+1)(x-1)(x^2+1)}[/tex]

The percentage increase is about 16.66%.

What is a percentage increase?

The percentage increase formula is the ratio of value increased to the original value and multiplied by 100. It is expressed in percentage. If there is an increase in the value of anything, then there is an increase in the percentage.

The initial amount was $18 and the final amount is $21.60.

By using the percentage increase formula, we can write

        Percentage increase = (final value - initial value)/|Final value| * 100

                                            = ((21.60 - 18)/21.60)*100

                                            = 16.66%

Hence, the percentage increase is about 16.66%.

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For figure {0}, the number of tiles will be equal to 2.

Function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function

Expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators

Equation : A mathematical equation is used to equate two expressions.

Given is a graph as shown in the image.

The line passes through point -

(3, 8) and (4, 10)

So, the slope of the line will be -

m = (10 - 8)/(4 - 3)

m = 2

y = 2x + c

For the point (3, 8), we can write -

8 = 6 + c

c = 2

For figure {0}, the number of tiles will be equal to 2.

Therefore, for figure {0}, the number of tiles will be equal to 2.

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The simple interest rate that Levi is being charged, given that he will have to pay back $ 45 and $ 15. 25 in 5 months, is  81.3 %

The simple interest rate can first be found by finding the monthly amount that Levi has to pay in fees which is :

= 15. 25 / 5 months

= $ 3. 05 fee per month

The amount that the fee would have been in a year is :

= 3. 05  x 12

= $ 36. 60

The simple interest rate is therefore :

= 36. 60 / 45

= 81.3 %

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Answer: (3,-6) x=3 y=-6

Step-by-step explanation:

1) The base rate for the empty bus is $120.

2) The variable cost (slope) for each person on board the bus is $2.

3) An equation to show the cost, c, of a bus with x number of people on it is C = 120 + 2x.

The total charge for taking 30 people aboard = $180

The total charge for taking 50 people on board = $220

The differences in the number of people and charges are 20 and $40, respectively.

Let x = the number of people boarding the bus and n = the fixed rate per bus.

30x + n = 180 ... Equation 1

50x + n = $220  ... Equation 2

Subtract Equation 1 from Equation 2:

20x = $40

x = $2 ($40/20)

The variable cost per person = $2 ($40/20)

The base rate for the empty bus = 30(2) + n = $180, where n is the base rate or fixed cost per bus.

= 60 + n = $180

n = $120

OR:

50(2) + n = $220

100 + n = $220

n = $120

The equation for the cost, c, of a bus with x number of people:

C = 120 + 2x

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Answer:

4y = (1/2)^x -5

Step-by-step explanation:

The first three equations are lines. All the variables have a power of just one (power of one is a math number that is not written) They are actually all written in slope-intercept form even. Line equations are linear function. Yay the words match!

You get a curve (not linear) when you have exponents, square roots or variables in the denominator of a fraction. Or as here, a variable for an exponent!

Answer:

ive did the math and its r= 4

Step-by-step explanation:

The relation between variables is represented by an equation ; y = 2.5x+15

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

Given that, Alexa joined a program at some coffee shop which offers her $15 per month, after which she will get her coffee at a discount rate which $2.5

We can represent the relationship as ;

y = 2.5x+15

Where, x (number of coffee) is an independent variable because it does not depend on any condition, and y (cost) is a dependent variable because it depends on the value of x.

Hence, the relation is described as y = 2.5x+15

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