What linear equation does each graph represent?
Draw an equation into each box to match the graph with its equation.

[tex]5y^2+17y-84 / y^3+12y^2+36y[/tex]  partial fraction decomposition is [tex]= -5y/(y² + 12y + 36) + 17/(y² + 12y + 36) - 84 (y³+12y²+36y)[/tex]

Partially decomposing a rational fraction, also known as partially expanding it, in algebra includes expressing the fraction as the sum of a polynomial and one or more fractions with a lower common denominator.

One technique for breaking down rational expressions into smaller partial fractions is partial fraction decomposition. This method serves the integration process better.

In order to integrate a rational function, it is condensed to a valid rational function. The integrand can be expressed as the sum of more elementary rational functions through the use of partial fraction decomposition.

Therefore, starting with the simplified solution and proceeding backwards, the final expression is “decomposed” into the original polynomial fractions.

[tex]= -5y²+ 17y-84 / y³+12y²+36y[/tex]

[tex]= -5y/(y² + 12y + 36) + 17/(y² + 12y + 36) - 84 (y³+12y²+36y)[/tex]

Learn more about fraction decomposition here:

https://brainly.com/question/30402740

#SPJ1

Answer:

answer = 98.2808022923 i think

Answer:

Step-by-step explanation:

1) She can use the CUADRATIC FUNCTION for to solve

2) She can use factorization for to solve

3) She can use the ZERO method for to solve

She can choose from the various combinations of 6 of 2, 5 to 3.Permutation is the name given to the various techniques of putting a group of objects in a sequential sequence.

Explanation:

2 of 6 = 6 of 2

3 to 5 = 5 to 3.

To learn more about Permutation refer to:

https://brainly.com/question/1216161

#SPJ1

Answer:

68%

Step-by-step explanation:

93 is 7 pts BELOW 100     this represents   -7 /15 = -.4666   Z-score

From Z-score table this  represents  .3192   ..or 31.92 % to the LEFT of the 93 ...... to the RIGHT is 100% - 31.92 %  = ~ 68%

The absolute minima of the function is at 12.85 and the absolute  maxima  is at 15.42.

Let the function be ,

f(t) = 5t + 5 cot( t/2 ).

first derivative of the function,

f'(t)

=  d/dt ( 5t + 5 cot(t/2))

= d/dt(5t) + d/dt ( 5 cot (t/2))

= 5 - 5/2cos^2(t/2)

Taking the derivative equal to 0,

f'(t) = 0

t = pi/2 , 3pi/2 f

On evaluating the equation wrt to obtained critical value,

we will get ,

absolute minimum value 12.85

absolute maximum value 18.56.

The extrema of a function are the maxima and minima. The maximum and minimum values of a function inside the specified ranges are known as maxima and minima, respectively. Absolute maxima and absolute minima are terms used to describe the function's maximum and minimum values, respectively, over its full range.

The terms "local maxima" and "local minima" refer to additional maxima and minima of a function that are not its absolute maxima and minima.

To learn more about maxima and minima

brainly.com/question/13766213

#SPJ4

Answer:

35 cm²

Step-by-step explanation:

Base of triangle = 10 cm

Height of triangle = 7 cm

Area of triangle = 1/2 x (base x height)

= 1/2 x (10 x 7)

= 1/2 x 70

= 35

So, area is 35 cm²

By spreading (by multiplying) that 3 back in, we may obtain our original expression 12.

What do you mean by Factoring of polynomial?

The process of multiplying polynomial factors is known as factoring polynomials. A polynomial of degree "n" in variable x is an equation of the form axn + bxn-1 + kcxn-2 +....+kx+ l, where each variable has a constant acting as its coefficient. A polynomial is an expression that has a constant and a variable together with an addition or a subtraction sign between them.

Factors of polynomials are zeros of polynomials that may be expressed as another linear polynomial. If we divide a given polynomial by any of its components after factorization, the residual will be zero.

(Note that words can also include variables and constants)

One of the variables or constants that is multiplied by another factor to create a phrase is called a factor. Factors 4 and x make up the phrase 4x. To factor is to divide the object of the multiplication. Therefore, factoring "disassembles" the result of multiplication.

We frequently need to factor a term in order to "solve" (that is, get the value of, say, x) an equation

For Example:

The operation of factoring falls in between multiplication and dividing. Let's examine the following statement:

3x + 12

We can factor out the third because 3x and 9 both share the number three:

3x ÷ 3 = x 12 ÷ 3 = 4

We set it aside what's left after factoring out 3:

3(x + 4)

By spreading (by multiplying) that 3 back in, we may obtain our original expression: x * 3 = 3x 4 * 3 = 12.

We now have: 3x + 12

Learn more about Factoring from the link below

https://brainly.com/question/26923098

#SPJ4

Answer:

HOPE IT HELPED

Step-by-step explanation:

Date is item 2

Who the check is being written to is item 1

Amount of check, written in numeric format is item 3

Amount of check written in word format is item 4

A description of what the check is for is item 5

The checking account owner's signature is item 6

Since the data in the table represent the height of an object over time, a model which best represents the data is: B. quadratic, because the height increases and then decreases.

In Mathematics, a quadratic equation can be defined as a mathematical expression (equation) that can be used to define and represent the relationship that exists between two or more variable on a graph.

Additionally, the standard form of a quadratic equation in mathematics is given by the following mathematical expression:

ax² + bx + c = 0

In Mathematics, the graph of all quadratic equations (functions) is either an upward or downward parabola, which is typically a u-shaped curve.

In conclusion, we can logically deduce that the graph of a quadratic equation (function) would always form a parabolic curve with the data value increasing on one end and decreasing on the other end as shown in the image attached below.

Read more on quadratic model here: https://brainly.com/question/11910490

#SPJ1

Complete Question:

The data in the table represent the height of an object over time.

Which model best represents the data?

quadratic, because the height of the object increases or decreases with a multiplicative rate of change

quadratic, because the height increases and then decreases

exponential, because the height of the object increases or decreases with a multiplicative rate of change

exponential, because the height increases and then decreases

The probability of not pulling hip hop CDs is equal to 3/5. The correct option is (A).

Probability is the branch of Mathematics that deals with the measurement of the chance of occurrence of a random event.

The probability of any event always lies in the close interval of 0 and 1 [0,1].

The zero value of probability indicates that the event will not happen while its value equal to one indicate that it will happen.

Given that,

The number of country, rock, hip hop, and jazz CDs are 10, 5, 12 and 3 respectively.

Then, the total number of CDs are 10 + 5 + 12 + 3 = 30

Now, the probability of not selecting hip hop is equal to the probability of selecting the remaining types of CDs which is given as,

P(Not hip hop CDs) = (10 + 5 + 3)/30    

                                 = 18/30

                                 = 3/5

Hence, the probability that the first CD that Kyle pulls from the box will not be hip hop is 3/5.

To know more about probability click on,

https://brainly.com/question/11234923

#SPJ1

Answer:

7/8

Step-by-step explanation:

First, we need to get 7/8 and 5/6 to the same denominator which is 48. 7/8 becomes 42/48 whilst 5/6 becomes 40/48

we can simply put them both with the same denominator and check, the larger numerator will be it.

so hmmm let's multiply one by the denominator of the other

[tex]\cfrac{7}{8}\hspace{5em}\cfrac{5}{6} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{7}{8}\cdot \cfrac{6}{6}\implies \cfrac{42}{48}\hspace{5em}\cfrac{5}{6}\cdot \cfrac{8}{8}\implies \cfrac{40}{48}\hspace{9em}\boxed{\cfrac{42}{48} ~~ {\Large \begin{array}{llll} > \end{array}}~~ \cfrac{40}{48}}[/tex]

The program for finding the two numbers in the array sum up to x is made.

Array A[n], x

Time Complexity:

As was covered in class, step one employs mergesort, which has an O(nlogn) complexity.

Since the worst-case scenario involves traversing through the full array, step three consumes O(n) time.

Total Running Time = O(nlogn + n) = O(nlogn)

Thus, the program for finding the two intergers in the array sum up to x is made.

To know more about the sorting, here

https://brainly.com/question/1385135

#SPJ4

Answer:

b!vch I am up b!vch I am up b!vch I am up

Answer:Answer to Solved In how many ways can the digits in the number 7, ... Question: In how many ways can the digits in the number 7, 600,000 be arranged?

1 answer

·

Top answer:

Concept used : The number of permutations (arrang...

Step-by-step explanation:

Answer:

Error: 131π

Surface Area = 131π=411.5 yd^2

Step-by-step explanation:

All the other steps were correct but 131π = 411.5486376, so there's no way the person should have gotten 411.3 yd^3.

Finally, if we round 411.5486376 to the nearest tenth, we get 411.5 yd^2.

Answer:

  a, b, d: No

  c: Yes

Step-by-step explanation:

You want to identify statements that are and are not the negation of "I am not drawing a rectangle."

The negation of a statement is a statement using the same subject and predicate, but with the opposite truth value.

The negation of ...

is the statement ...

Statements about circles are irrelevant, as are statements about any action other than drawing (or not drawing).

The probability that the next person will purchase more than one costume will be 1/30.

The probability of an event occurring is defined by probability.

Probability is also called chance because if you flip a coin then the probability of coming head and tail is nothing but chances that either head will appear or not.

As per the given,

Total visitors of a day = 81 + 6 + 3 = 90

The number of purchasing more than one costume = 3

Probability of purchasing more than one costume = 3/90 = 1/30

Hence"The probability that the next person will purchase more than one costume will be 1/30".

For more information about the probability,

brainly.com/question/11234923

#SPJ1

The value of the expression in the scientific notation will be 6.4 × 10⁴. Then the correct option is D.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The expression is given below.

⇒ [(8 × 10²) × (3.2 × 10⁵)] / (4 × 10³)

Simplify the expression, then we have

⇒ [(8 × 10²) × (3.2 × 10⁵)] / (4 × 10³)

⇒ [(25.6 × 10⁷)] / (4 × 10³)

⇒ 6.4 × 10⁷⁻³

⇒ 6.4 × 10⁴

The value of the expression in the scientific notation will be 6.4 × 10⁴. Then the correct option is D.

More about the Algebra link is given below.

https://brainly.com/question/953809

#SPJ1

The work that gravity does;

W = F.S = mgΔh

In light of the fact that gravity points downward and that displacement is also downward, their angle is 0 and their cosine 1, respectively.

W = mgΔh

g = 9.8 m/s²

Δh  = 4.6 m

m = 0.60 kg

W = 0.60 x 9.80 x 4.6

W = 2.7 J

The source of gravitational potential energy in relation to the ground is;

U = mgh

The release point therefore

Ug = mgh(0)

U0 = 0.60 x 9.8 x 6.1

U0 = 35.87 J

At the point of release

U(gf) = mgh(f)

U(gf) = 0.60 x 9.80 x 1.5

U(gf) = 8.820 J

Gravitational potential energy changes are;

ΔU(g) = U(gf) - U0

ΔU(g) =  8.820 J - 35.87 J

ΔU(g) = -27.05 J

Result, we can see that the work done through gravity is the opposite of how the gravitational potential energy has changed.

To know more about the gravitational potential energy, here

https://brainly.com/question/3120930

#SPJ4

Length is 4 ft and  width is is 3ft.

What is width ?

The "size" of a body is measured in geometry by its mean width; for more information on the various body measures, see Hadwiger's theorem. One must take into account -dimensional hyperplanes parallel to a specific direction in where is the n-sphere.

[tex]\begin{aligned}& w^2+(w+1)^2=5^2 \\& \frac{w^2+w^2+2 w+1}{}=25 \\& 2 w^2+2 w-21\end{aligned}[/tex]

[tex]\begin{aligned}& 2 w^2+2 w-24=0 \\& w^2+w-12=0\end{aligned}[/tex]

[tex]\begin{gathered}(w-3)(w+4)=0 \\w=3,-4\end{gathered}[/tex]

The width must be three because we can't have negative widths. Since the length is four feet, we have the dimensions of our poster.

To learn more about Length visit:https://brainly.com/question/8552546

#SPJ1

The amount which Cassie will pay the studio per month will be $115.

The equation by taking data from the question will be

6m - 40 = 650

6m−40=650

On solving this we get ,

6m = 610

m = 115

The regular cost per month is $115.

The above question is an example of multi-step equation.

Multi-step equations are algebraic expressions that must be solved using more than one operation, such as subtraction, addition, multiplication, division, or exponentiation. When solving multi-step equations, it is critical to understand the order of operations.

Solve an equation with a single unknown variable, x, by using algebraic operations on both sides of the equation to isolate x. The goal is to select an algebraic operation sequence that will leave x on one side of the equal sign and put everything else on the other side.

To learn more about multi-step equation

brainly.com/question/112509

#SPJ4

There will be 66 wolves there will be in 5 years according to given exponential function.

What is exponential equation?

The exponential function may be a function denoted by f(x)=\exp or e^. Unless otherwise fixed, the term usually refers to the positive-valued operate of a true variable

Main body:

given =  y=y₀ e^{0.027 t}

here , y₀ = 58

t = 5 years

y = 58 e^(0.027 * 5)

y = 58 e^(0.135)

y = 58 * 1.144537

y = 66.383133

y = 66

Hence there will be 66 wolves there will be in 5 years.

To know more about exponential equation, visit:

brainly.com/question/2456547

#SPJ4

The solution to the equation is x = -1.

What are arithmetic operations?

Arithmetic operations is a branch of mathematics that studies numbers and the operations on numbers that are useful in all other branches of mathematics. It consists primarily of operations like addition, subtraction, multiplication, and division.

To solve this equation, we need to use the order of operations to simplify the expression on the left side of the equal sign.

The order of operations tells us that we should perform operations within parentheses first, then perform any exponents or radicals, then perform any multiplications or divisions (working from left to right), and finally perform any additions or subtractions (also working from left to right).

Using the order of operations, we can simplify the left side of the equation as follows:

-1 - 7x - 6(-7 - x) = 36

(-1 - 7x) - 6(-7 - x) = 36

-1 - 7x - (-42 - 6x) = 36

-1 - 7x + 42 + 6x = 36

5x + 41 = 36

5x = -5

x = -1

Therefore, the solution to the equation is x = -1.

To learn more about the arithmetic operations visit,

https://brainly.com/question/13181427

#SPJ1

Answer:

168015

Step-by-step explanation:

b(c) = 2c³5c² - 6c - 13

b(7)=2(7)³5(7)²-6(7)-13

b(7)=2(343)5(7)²-6(7)-13

b(7)=(686) 5(49)-6(7)-13

b(7)=(686) (245)-6(7)-13

b(7)=(686) (245) -42-13

b(7)=168070-42-13

b(7)=168028-13

b(7)=168015

(Usually this is how you would solve it but because there was no sign between the 2c^35c^2 I got sort of confused so I just multiplied, if wrong I'm sorry..)

[tex]b(-7)=-168041[/tex].

[tex]b(c)=2c^{3} 5c^{2} -6c-13[/tex]

[tex]b(-7)=2(-7)^{3} 5(-7)^{2} -6(-7)-13[/tex]

[tex]b(-7)=2(-343) 5(49) -(-42)-13\\ \\b(-7)=-168070 +42-13\\ \\b(-7)=-168041[/tex]

The correct answer is therefore negative 1 divided by 7 raised to the sixth power, which is the same as 1/7^2. The other choices do not match this expression.

What is power?

The power (or exponent) of a number says how many times to use the number in multiplication. It is written as a small number to the right and above the base number.

The expression 7 raised to the negative second power times 7 raised to the third power is equivalent to 7 raised to the (negative second + third) power, which is 7 raised to the first power. This is equal to 7.

The quantity 7 raised to the first power all raised to the negative third power is equal to 7 raised to the (first + negative third) power, which is 7 raised to the negative second power.

Therefore, the expression that is equivalent to the quantity 7 raised to the negative second power times 7 raised to the third power all raised to the negative third power is 7 raised to the negative second power, which is 1/7^2 = 1/49.

Hence, The correct answer is therefore negative 1 divided by 7 raised to the sixth power, which is the same as 1/7^2. The other choices do not match this expression.

To learn more about the power visit,

https://brainly.com/question/28158010

#SPJ1

Dana Jones has amount after 7 years is $1560.97.

What is compounded continuously?

Theoretically, continuously compounded interest means that an account balance continuously earns interest as well as reinvesting that interest into the balance so that it too earns interest.

Given: Dana Jones invests $ 1100 at 5% interest compounded continuously for 7 years.

We have to find the amount after 7 years.

Consider, the formula

A = Pe^rt

where,

A is the amount after t years

P is the invested amount

r is the interest rate

t is the number of years

Plug P = 1100, r = 5% = 0.05, and t = 7 in the above equation.

[tex]A = 1100e^0^.^0^5^(^7^)\\A = 1560.9743\\A = 1560.97[/tex]

Hence, Dana Jones has amount after 7 years is $1560.97.

To know more about compounded continuously, click on the link

https://brainly.com/question/14303868

#SPJ4

Supplementary angles are two angles whose combined angle is 180 degrees. As shown below, the table of the proof that (1) is an addition to (3) can be completed.

Supplementary angles are two angles whose combined angle is 180 degrees. When a straight line crosses another line, two angles are created on either side of the initially imagined straight line. Two sets of additional angles make up those two-two angles. This implies that a straight line will be formed by the outside sides of any extra angles that are positioned next to one another.

For the demonstration that 1 is an addition to 3, the preceding table can be completed as shown below.

1) Line m in is parallel to line n;

2) ∠1 = ∠2  →  Corresponding angles

3) m∠1 = m∠2  →  Definition of Congruent angles

4) ∠2 and ∠3 for a linear pair  →  Adjacent angles on a straight line

5) ∠2 is supplementary to ∠3  →  Definition of linear pair

6) m∠2 + m∠3 = 180°  →  Definition of supplementary angles

7) m∠1 + m∠3 = 180°  →  Substitution Property

8) ∠1 is supplementary to ∠3

As a result, the table containing the proof that item 1 is an addition to item 3 can be completed as displayed above.

To know more about Supplementary Angles, visit:

https://brainly.com/question/2882938

#SPJ1

The series appears to be     166, 199, 232, 265, 298, 331

With examples, define sequence?

A list of numbers in a certain order is known as a sequence. A term is the name given to each number in a sequence.

                                      In a series, each term has a place (first, second, third and so on). Take the sequence 5, 15, 25, 35, as an example. Each number is referred to as a word in the sequence.

The last number of the common difference must end in 3

And this must be a 2 digit number

So....the first number must end in 6

The the 4th number must be 265

So..... the 5th number  must end in 8

And the last digit  of the last term must end in  1  [ and begin with 3 ]

Putting all this together  we have that

265  + 2d  =  331

2d  = 66   ⇒  d = 33

So  the first term must be  265 - 3 (66)  =  166

the series appears to be     166, 199, 232, 265, 298, 331

Learn more about sequence

brainly.com/question/21961097

#SPJ4