What is slope-intercept form?
O not this one
O a² +6² = = C
O Ax+By = C
O y = mx + b

[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]

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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.

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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.

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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.

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a=34.697, only one triangle is formed.

And B=40°.7'

A≈77°.79'.So, option A is correct.

Three edges and three vertices define a triangle as a polygon. One of geometry's fundamental shapes is this one.

Any three points determine a distinct triangle and a distinct plane in Euclidean geometry when they are non-collinear (i.e. a two-dimensional Euclidean space). To put it another way, each triangle is contained in a plane, and there is only one plane that includes that particular triangle. All triangles are contained in one plane if and only if all geometry is the Euclidean plane, however this is no longer true in higher-dimensional Euclidean spaces. Except as otherwise specified, the subject of this article is triangles in Euclidean geometry, more specifically, the Euclidean plane.

Given,

C​=61° 50, c​=31.2, b=23.6

Sine rule:

sin B/b=Sin C/c

sin B=b sin C/c

=(23.6 sin 61° 50)/31.2

sin B=0.65219

sin B=139.3

A+B+C=180

A=180-B-C

A=180-139.3-61.50

A= -20.8 which is not possible.

Because the angle must be positive.

sin B=sin 40.70

A+B+C=180

A=180-40.70-61.50

A=77.79'

sin A/a=sin C/c

a=c sin A/sin C

So, a=34.697

Only one triangle is formed

And B=40°.7'

A≈77°.79'

Hence, option A is correct.

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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.

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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.

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.

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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.

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Answer: 19

Step-by-step explanation:

Answer:19

Step-by-step explanation: 10 add the 9

Answer is 0

Given:- arithmetic sequence 20,18,16,14,....

To find:- 11th term of given arithmetic sequence

Arithmetic Progression (AP) is  sequence of numbers in order, in which the difference between any two consecutive numbers is  constant value. It is also known as Arithmetic Sequence.

The 11th term of the A.P. can be found by a formula, a(n)=a(1)+(n-1)d , where n is the number of terms, a(1) is teh first term of A.P and d is difference between any two continuously terms.

Number of terms to be found = 11

therefore, a(11) = a(1)+(n-1)d  

d=a(2)-a(1)

d=18-20

d=-2

putting value of d in above equation,

a(11) = 20 + (11-1)(-2)

a(11) = 20 -  20

a(11) = 0

hence the 11th term of arithmetic sequence 20,18,16,14,.... is 0.

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).

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.

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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.

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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

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%

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

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

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".

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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.

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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

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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.

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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.

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Answer:

15

Step-by-step explanation:

25 / 15 = 1.666...

9 x 1.666.... = 15

Answer:

Step-by-step explanation:

375

if they are simiar than 15 from abc would have been the same length

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

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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.

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Answer:

answer = 98.2808022923 i think

By solving a linear equation, we will see that the distance is 479.98 miles.

We know:

The rental has a base cost of $49.95 plus $1.19 per mile.

There is also an extra cost of $3.89 per gallon of gas, and with one gallon they can travel 18 miles, then there is another extra cost of:

$3.89/18 per mile.

Then, if you travel x miles, the total cost is given by the linear equation:

C(x) = $49.95 + ($1.19 + $3.89/18)*x

We want to find the value of x, number of miles, such that the total cost is $724.85, then we need to solve:

$724.85 = $49.95 + ($1.19 + $3.89/18)*x

Let's solve that for x:

$724.85 -  $49.95 = ($1.19 + $3.89/18)*x

$674.90 = ($1.19 + $3.89/18)*x

$674.90/($1.19 + $3.89/18) = x

479.98 = x

So the distance is 479.98  miles.

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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.

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