The sum of 32 and 48 can be expressed in different ways using the Distributive Property.

Answer:

1) solve x+1/x = 5

\( \frac{x + 1}{x} = 5\)

\(x + 1 = 5x\)

\(x - 5x = - 1\)

\( - 4x = - 1\)

\(x = \frac{ -1}{ - 4} \)

\(x = \frac{1}{4} \)

2) solve x³+1/x³

\(x {}^{3} + \frac{1}{x {}^{3} } \)

substitute x = 1/4 into the expression

\(( \frac{1}{4} ) {}^{3} + \frac{1}{( \frac{1}{4}) {}^{3} } \)

\( \frac{1}{64} + \frac{1}{ \frac{1}{64} } \)

\( \frac{1}{64} + \frac{64 \times 1}{1} \)

\( \frac{1}{64} + 64\)

\( \frac{4097}{64} \: or \: 64.02\)

Answer:

a. x(2+3x)b.x= 0, −2/333. a. 2x2(3x−1) b.x= 0, 1/335. a. (x−1)(x−7)b.x= 1, 7 37. a. (x−3)(x+4)b.x= 3, −439. a.

Step-by-step explanation:

The Maclaurin series for the function f(x) = arctan(3x²) / x is:

\(f(x) = 3x - 9x^{5/3} + 243x^{9/5} - 6561x^{13/7} + ...\)

The Maclaurin series for the function f(x) = arctan(3x²) / x.

To do this, we will use the Maclaurin series of arctan(u), which is given by:

\(arctan(u) = u - (u^3)/3 + (u^5)/5 - (u^7)/7 + ...\)

Now, let's find the Maclaurin series for f(x) = arctan(3x²) / x by substituting u = 3x²:

\(f(x) = (arctan(3x²)) / x = [(3x²) - (3x²)^3/3 + (3x²)^5/5 - (3x²)^7/7 + ...] / x\)

Now, simplify the series by dividing each term by x:

\(f(x) = 3x - 9x^5/3 + 243x^9/5 - 6561x^13/7 + ...\)

So, the Maclaurin series for the function f(x) = arctan(3x²) / x is:

\(f(x) = 3x - 9x^{5/3} + 243x^{9/5} - 6561x^{13/7} + ...\)

for such more question on  Maclaurin series

https://brainly.com/question/7846182

#SPJ11

The real values of $c$ for which $4x² + 14xc + c$ is the square of a binomial are $c = 0$ and $c = \frac{4}{49}$.

To determine the real values of $c$ for which the expression $4x² + 14xc + c$ is the square of a binomial, we need to find the conditions under which it can be factored as $(ax + b)²$, where $a$ and $b$ are constants.

Expanding $(ax + b)²$, we have $(ax + b)² = a²x² + 2abx + b²$. Comparing this with $4x² + 14xc + c$, we can set up the following equations:

$a² = 4$ (equating the coefficients of $x²$)

$2ab = 14c$ (equating the coefficients of $x$)

$b² = c$ (equating the constant terms)

From the first equation, we find that $a = \pm 2$. Substituting this value into the second equation, we have:

$2(\pm 2)b = 14c$

$\Rightarrow \pm 4b = 14c$

$\Rightarrow b = \pm \frac{14c}{4}$

$\Rightarrow b = \pm \frac{7c}{2}$

Finally, substituting the values of $a$ and $b$ into the third equation, we get:

$\left(\pm \frac{7c}{2}\right)² = c$

$\Rightarrow \frac{49c²}{4} = c$

$\Rightarrow 49c² = 4c$

$\Rightarrow 49c² - 4c = 0$

$\Rightarrow c(49c - 4) = 0$

Now, we can solve this equation to find the values of $c$:

$c = 0$: This is one possible solution.

$49c - 4 = 0 \Rightarrow 49c = 4 \Rightarrow c = \frac{4}{49}$: This is another possible solution.

Therefore, the real values of $c$ for which $4x² + 14xc + c$ is the square of a binomial are $c = 0$ and $c = \frac{4}{49}$.

Learn more about binomial here:

https://brainly.com/question/30339327

#SPJ11

The value of 19 cubes is equal to 6859. The correct option is D.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the number is 19. The cube of 19 will be calculated as:-

19³ = 19 x 19 x 19

19³ = 6859

The cube of 19 is calculated by multiplying the number three times. Hence, the cube of 19 is 6859.

To know more about an expression follow

https://brainly.com/question/1615668

#SPJ2

Answer:

A

Step-by-step explanation:

A linear function is a straight line when graphed so is not B.

For confirmation of A note how for each increase of 3 in x we get the same increase of 5 in y.

The concept of independent assortment is one of the fundamental principles of genetics that was first proposed by Gregor Mendel. According to Mendel's postulate of independent assortment, the alleles of different genes segregate independently of one another during the formation of gametes. This means that the inheritance of one trait does not affect the inheritance of another trait.

To test this postulate, Mendel conducted numerous experiments on pea plants and observed that the inheritance of different traits followed a predictable 1:2:1 ratio. This ratio indicated that the alleles for each trait were segregating independently of each other.

Overall, the content loaded Mendel's postulate of independent assortment is an important concept in genetics that helps explain how genetic variation is generated. The 1:1:1:1 testcross ratio is one of the many ways in which this postulate can be tested and supported.

Learn more about independent assortment here: brainly.com/question/29556097

#SPJ11

Two pairs of polar coordinates for the point (3, -3) can be determined using the formula r = √(x^2 + y^2) and θ = arctan(y/x). The pairs of polar coordinates are (3√2, -45°) and (3√2, 315°).

To find the polar coordinates, we first need to calculate the distance from the origin (r) using the formula r = √(x^2 + y^2), where x = 3 and y = -3. Plugging in the values, we get r = √(3^2 + (-3)^2) = √(9 + 9) = √18 = 3√2.

Next, we need to find the angle θ. We can use the formula θ = arctan(y/x), where y = -3 and x = 3. Plugging in the values, we get θ = arctan(-3/3) = arctan(-1) = -45° (in the fourth quadrant).

However, we can also add 360° to the angle to represent the same point in the first quadrant. So, adding 360° to -45° gives us 315°.

Therefore, the two pairs of polar coordinates for the point (3, -3) are (3√2, -45°) and (3√2, 315°).

To know more about Quadrant visit

https://brainly.com/question/26426112

#SPJ11

Answer:

30 first-class tickets were sold and 260 coach tickets were sold.

Step-by-step explanation:

Let a first-class ticket be represented by f and let a coach ticket be represented by c.

On a particular flight, a jumbo jet was carrying 290 passengers. So, the sum of the first-class tickets and coach tickets must sum to 290:

\(f+c=290\)

The total income was $95,280. Therefore:

\(680f+288c=95280\)

We can now solve the system of equations. First, we can simplify the second equation by dividing everything by 8:

\(85f+36c=11910\)

From the first equation, we can subtract f from both sides:

\(c=290-f\)

Substitute:

\(85f+36(290-f)=11910\)

Distribute:

\(85f+10440-36f=11910\)

Simplify:

\(49f=1470\)

So:

\(f=30\)

From the previous equation:

\(c=290-f\)

Substitute:

\(c=290-30=260\)

30 first-class tickets were sold and 260 coach tickets were sold.

A The amount of money in a savings account with an annual interest rate of 1.5%

Answer:

FLASE

Step-by-step explanation:

8 - 4(0) = 4(0)

8 - 0 = 0

8 ≠ 0

a) The limit as x approaches 0 of (sin(x) - cos(x) + 1) / (x^2 + 1) is equal to 1.

b) The limit as x approaches -1 is undefined.

a. As x approaches 0, both sin(x) and cos(x) approach 0. Thus, the numerator approaches 0 + 1 = 1. The denominator, x^2 + 1, approaches 0^2 + 1 = 1. Therefore, the overall limit is 1.

b. In the given question, it seems like the symbol "#" is used instead of "x." Regardless, let's assume the variable is x. The limit as x approaches -1 involves finding the behavior of the function as x gets arbitrarily close to -1.

If there is no additional information provided about the function or expression, we cannot determine its limit as x approaches -1. The limit might exist or not depending on the specific function or expression involved. It is essential to have more context or specific instructions to evaluate the limit accurately.

In summary, without further information, the limit as x approaches -1 is indeterminate or undefined.

Learn more about limit here: brainly.com/question/12211820

#SPJ11

The paper you mentioned, "Tensor decompositions for learning latent variable models" by A. Anandkumar, R. Ge, D. Hsu, SM. Kakade, and M. Telgarsky, is available as an arXiv preprint with the identifier arXiv:1210.7559.

In this paper, the authors explore the use of tensor decompositions for learning latent variable models. Tensor decompositions are mathematical techniques that can be used to analyze and extract meaningful information from high-dimensional data.

The authors propose a method that combines tensor decompositions with probabilistic graphical models to learn latent variable models. Latent variable models are statistical models that can capture hidden structures or factors in the data.

By leveraging tensor decompositions, the authors aim to provide a principled and efficient approach for learning latent variable models. The paper likely presents theoretical results, algorithms, and experimental evaluations to support their approach.

If you are interested in learning more about this topic, I recommend reading the paper in detail. It should provide a comprehensive explanation of the proposed method and its applications in learning latent variable models.

To know more about Tensor decompositions visit:

https://brainly.com/question/33290835

#SPJ11

Answer:

35

Step-by-step explanation:

i did the quiz

Answer:

35

Step-by-step explanation:

An example of a linear function table is y=3x

A linear function is used to relate an independent variable and a dependent variable by introducing a rate of change(function) of which the independent variable is equated to find the dependent variable. Linear functions are those whose graph is a straight line. The following is the form of a linear function. a + bx = y = f(x). One independent variable and one dependent variable make up a linear function. X and Y are the independent and dependent variables, respectively.

for example:

y=3x hence is the dependent variable as it depends on the change of x and 3 is the rate of change which is a constant and is determined by the division of the values of y/x hence to make a table of y over x of which y is determined by the rate of change the unrelated variable x, 3.

Read more about linear function tables at:

https://brainly.com/question/25173046

#SPJ4

The values of a, h and k on the function are given as follows:

The meaning of the transformations is given as follows:

A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.

The four translation rules for functions are defined as follows:

The parent function in this problem is given as follows:

y = 1/x.

Hence the meaning of the transformations is given as follows:

More can be learned about translations at brainly.com/question/28174785

#SPJ1

The area of the planned school garden have dimensions of g + 4 and g + 10 respectively.

An equation is an expression that shows the relationship between two or more variables and numbers.

Given the area of the planned school garden as:

A = g² + 14g + 40

A = g² + 10g + 4g + 40 = g(g + 10) + 4(g + 10)

A = (g + 4)(g + 10)

The area of the planned school garden have dimensions of g + 4 and g + 10 respectively.

Find out more on equation at: https://brainly.com/question/2972832

#SPJ4

Tenemos que resolver un ejercicio algebraico.

Veremos que la opción correcta es B: 47,886

Lo que sabemos es:

21,751 fans pusieron "me gusta"

83,464 pusieron "me encanta"

Asumimos que cada fan puede usar una sola de esas dos cosas.

Entonces el número total de fans es:

21,751 + 83,464 = 105,215

Tambien sabemos que entre los fans, hay 57,329 mujeres.

Entonces el resto serán hombres:

105,215 -  57,329 = 47,886

Podemos concluir que hay 47,886 hombres, por lo que la opción correcta es B.

Si quieres aprender más, puedes leer:

https://brainly.com/question/24585056

Answer:

$15

Step-by-step explanation:

The tip is 14.86

When estimating round to the nearest number so you’ll have 15

Answer:

Uhdhdb

Step-by-step explanation:

Jsjddj hdhdhhdb

Answer:

The answer would be Equation B:

x2 - 8x + 41

Step-by-step explanation:

Answer:

y = - 2x + 2

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m =

with (x₁, y₁ ) = (4, - 6) and (x₂, y₂ ) = (0, 2 )

m =  =  =  = - 2

The line crosses the x- axis at (0, 2 ) ⇒ c = 2

y = - 2x + 2 ← equation of line

The probability that 4  of the 9  computers are defective is given by expression 0.3665.

It may be calculated by dividing the number of positive outcomes by the total number of potential outcomes. It is the attribute or state of being probable, the degree to which something is likely to happen. In other words, it is a way to gauge how likely an event is to occur.

out of 18 phones, 6 are defective. 9 of the phones are selected at random without replacement.

the probability that 4 of the 9  phones are defective

18 phones- 6 defective , 12 non-defective

9 phones- 4 defective , 5 non-defective

Required probability = \(\frac{^6 C_4*^1^2C_5 }{^1^8C_9}\)

= 15x1188 / 48620

P = 0.3665

after rounding we get 0.3665.

Learn more about Probability:

https://brainly.com/question/30208803

#SPJ4

Complete question:

in a certain shipment of 18 computers, 6 are defective. 9 of the computers are selected at random without replacement. what is the probability that 4  of the 9  computers are defective? express your answer as a fraction or a decimal number rounded to four decimal places.

The length of the section that needs to be repaved is,

⇒ 4 / 21 miles

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

A road is 2/7 of a mile long

And, a crew needs to repave 2/3 of the road.

Now, The length of the section that needs to be repaved is,

⇒ 2/3 of 2/7

⇒ 2/3 × 2/7

⇒ 4 / 21 miles

Thus, The length of the section that needs to be repaved is,

⇒ 4 / 21 miles

Learn more aboput the multiplication visit:

brainly.com/question/10873737

#SPJ9

The planet that has the larger mass is the planet B and the measurements in standard forms are

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

Planet A = 5*10^26 kilograms

Planet B = 2*10^28 kilograms

Rewrite the masses properly

So, we have

Planet A = 5*10²⁶ kilograms

Planet B = 2*10²⁸ kilograms

The exponent 28 is greater than the exponent 26

This means that

2*10²⁸ is greater than 5*10²⁶

So, we have

Planet B has the larger mass

When the measurements are expressed in standard forms, we have

Planet A = 500000000000000000000000000 kilograms

Planet B = 20000000000000000000000000000 kilograms

Read more about standard forms at

https://brainly.com/question/1708649

#SPJ1

Answer:

A) 48° + 75°

Step-by-step explanation:

All triangles contain 180°

180° - 57° = 123°

A) 48° + 75° = 123°

B) 57° + 57° = 114°

D) 63° + 70° = 133°

A) 70° + 83° = 153°

\(\huge{\textbf{\textsf{{\color{pink}{An}}{\red{sw}}{\orange{er}} {\color{yellow}{:}}}}}\)

The answer is A. 48⁰ and 75⁰

Thr sum of all triangles is 180⁰

so, 180⁰ – 57⁰ = 123⁰

The sum of other two angles should be 123⁰,

so,...

48⁰ + 75⁰ = 123⁰