Encontrar 2 números cuya suma sea 49 y su diferencia sea 23

The value of the missing coefficient is 12

Lets explain how to factorize the difference of two cubes

- The factorization of the difference of two cubes like a³ - b³, is a

 product of a binomial and trinomial

- The binomial is the cube root of the first term and the second term

∵ The ∛a³ = a and ∛b³ = b

∴ The binomial is (a - b)

- We will find the trinomial from the binomial by square the 1st term

of the binomial and multiply the 1st term and the 2nd term of the

binomial with opposite sign of the binomial and square the 2nd

term of the binomial

∴ The trinomial is (a² + ab + b²

∴ The factorization of (a³ - b³) is (a - b)(a² + ab + b²)

* Lets solve the problem

∵ 8f³ - 216g³ is the difference of two cubes

∵ ∛(8f³) = 2f

∵ ∛(216g³) = 6g

∴ The binomial is (2f - 6g)

- Lets make the trinomial

∵ (2f)² = 4f²

∵ (2f)(6g) = 12fg

∵ (6g)² = 36g²

∴ The trinomial = (4f² + 12fg + 36g²)

∴ The factorization of 8f³ - 216g³ = (2f - 6g)(4f² + 12fg + 36g²)

∴ The value of the missing coefficient is 12.

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complete question:

Find the value of the missing coefficient in the factored form of 8f^3-216g^3

8f^3-216g^3=(2f-6g) (4f^2+?fg+36g^2)

The value of ? =

Answer:

m = 25 + 6n

Step-by-step explanation:

To write a function for the amount of money Makayla spent going to the movies during the club, you need to consider two things: the annual registration fee and the discounted ticket price. The annual registration fee is a fixed amount that does not depend on the number of movie tickets Makayla purchases. The discounted ticket price is a variable amount that depends on the number of movie tickets Makayla purchases. You can use a letter, such as n, to represent the number of movie tickets Makayla purchases. Then, you can write an expression for the amount of money Makayla spent on movie tickets, which is 6 times n, or 6n. To find the total amount of money Makayla spent going to the movies during the club, you need to add the annual registration fee and the amount of money spent on movie tickets. This gives you the expression 25 + 6n. You can use another letter, such as m, to represent the total amount of money Makayla spent going to the movies during the club. Then, you can write an equation that relates m and n, which is m = 25 + 6n. This equation is a function that models the amount of money Makayla spent going to the movies during the club as a function of the number of movie tickets she purchased.

Answer:

6

Step-by-step explanation:

To find the mean you've got to add 7, 9,4,3,9 and 4 (which gives you 36) and divide that by the number of figures/numbers (which is 6 numbers in total) and it gives you 6

let's recall that whenever omitted, the base is assumed to be 10.

[tex]\begin{array}{llll} \textit{logarithm of factors} \\\\ \log_a(xy)\implies \log_a(x)+\log_a(y) \end{array} ~\hspace{4em} \begin{array}{llll} \textit{Logarithm of exponentials} \\\\ \log_a\left( x^b \right)\implies b\cdot \log_a(x) \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\log_{10}(2)=m\implies \log(2)=m\hspace{5em}\log_{10}(3)=n\implies \log(3)=n \\\\[-0.35em] ~\dotfill\\\\ \log_{10}(24)\implies \log(24)\implies \log(8\cdot 3)\implies \log(2^3\cdot 3) \\\\\\ \log(2^3)+\log(3)\implies 3\log(2)+\log(3)\implies 3m+n[/tex]

The function for the concentration of the drug in the bloodstream indicates;

a. The concentration will be 0.5 mg/L when t = 20 - 6·√(11) and t = 20 - 6·√(11) hours

b. Please find the completed table of values in the following section

c. The domain is all positive values of t, including t = 0, which is [0, ∞)

d. The patient should receive the drug after about 19.78 hours

e. The shape of the concentration graph are similar, but the concentration of the oral drug is higher than the concentration of the drug administered intravenously

A function is a rule that maps input variables to output values.

a. The function modelling the concentration of the drug in the bloodstream after t hours indicates;

c(t) = 20·t/(t² + 4)
When the concentration is 0.5 mg/L, we get;

c(t) = 20·t/(t² + 4) = 0.5

(t² + 4) × 0.5 = 20·t

t² + 4 = 20·t ÷ 0.5 = 40·t

t² - 40·t + 4 = 0

t = (40 ± √((-40)² - 4 × 1 × 4))/(2 × 1) = (40 ± 12·√(11))/(2) = 20 ± 6·√(11)

The concentration will be 0.5 mg/L when t = 20 + 6·√(11) and t = 20 - 6·√(11)

b. The completed table of values, obtained using MS Excel can be presented as follows;

t     [tex]{}[/tex]  0      2      4      6      8       10      12       14      16      18       20

c(t)   [tex]{}[/tex]0      5      4      3      2.35  1.92   1.62    1.4     1.23   1.09    0.99

c. The denominator, t² + 4, indicates that the denominator is positive for all values of x, whereby the time is a natural, a possible domain for the function is the set [0, ∞)

d. The values in the table indicates that to maintain a concentration above 1 mg/L and below 8 mg/L, the patient must receive the next intravenous dose between the values obtained as follows;

The maximum value of the function is 5 mg/L when t = 2 hours, therefore, when c(t) = 1 mg/L, we get;

c(t) = 20·t/(t² + 4) = 1, which indicates that t = 10 ± 4·√6, which indicates that the time at which the concentration reduces to 1 mg/L again in the bloodstream is 10 + 4·√6 ≈ 19.78 hours

The patient should receive the next dose, after about 19.78 hours

e. The concentration of the oral drug, obtained from a similar question on the website, indicates that the maximum concentration is 64 mg/L, which is higher than the maximum concentration of the drug administered intravenously, which has a maximum concentration of 5 mg/L

However, the maximum bloodstream is reached at about the same period for both drugs administration methods

The concentration of the drug administered by oral administration in the first part is about four times the drug administered intravenously after 20 hours.

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Answer: x = 11

Step-by-step explanation:

     We know that vertical angles are congruent to each other. We will create an equation to help us solve. Then, will isolate the x-variable with inverse operations.

128° = 8x + 40°

8x + 40° = 128°

8x = 88°

x = 11

Answer:

A

Step-by-step explanation:

Note that the digit 5 in 50321 represents 50000 whereas the digit 5 in 42570 represents 500.

So, the total value is:

[tex]50000+500=50500[/tex]

Answer:

Step-by-step explanation:

Answer:

AB ≈ 8.1

Step-by-step explanation:

using the cosine ratio in the right triangle

cos40° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{AC}{AB}[/tex] = [tex]\frac{6.2}{AB}[/tex] ( multiply both sides by AB )

AB × cos40° = 6.2 ( divide both sides by cos40° )

AB = [tex]\frac{6.2}{cos49}[/tex] ≈ 8.1 ( to the nearest tenth )

The interest rate can drastically change the total amount paid to the lender, in the case of mortgages, up to thousands of dollars.The correct answer is c.

The interest rate of a loan is one of the most important factors to consider when shopping around for loans because it directly affects the cost of borrowing money. The interest rate determines the percentage of the loan amount that the borrower will have to pay back to the lender as interest over the loan's term.

A higher interest rate means that borrowers will have to pay more in interest over the life of the loan, increasing the total cost of borrowing. Conversely, a lower interest rate will result in lower interest payments and a reduced overall cost of the loan.

For example, in the case of a mortgage, which is a long-term loan, even a small difference in the interest rate can have a significant impact on the total amount paid to the lender. Over the course of a 30-year mortgage, a higher interest rate could result in thousands of dollars in additional interest payments.

Therefore, it is important to compare and consider different loan offers to find the best interest rate available. This can help borrowers save money and make more informed decisions about their borrowing options. The correct answer is c.

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Step-by-step explanation:

y= rad(x+3)

y²=x+3

x= y²-3

change the variables

y= x²-3

The solution to the conversions are: (1) 1.60934 km/min, (2) 20.8333 m/s, (3) 49.7097 mi/h, (4) 27.7778 m/s, (5) 118100.64 ft/h

1. 60mi/h to km/min  

First, convert miles to kilometers:

1 mile (mi) = 1.60934 kilometers (km)

60mi/h = 60 x 1.60934 = 96.5604km/h

Next, convert hours to minutes:

1 hour = 60 minutes

96.5604 km/h = 96.5604 km/h x (1 h / 60 min)

                        = 1.60934 km/min.

Therefore, 60 mi/h is equal to approximately 1.60934 km/min.

2. 75km/h to m/s

First, convert kilometers to meters:

1 kilometer = 1000 meters

75 km/h  = 75 km/h x (1000 m / 1 km)

               = 75000 m/h

Next, convert hours to seconds:

1 hour = 3600 seconds

75000 m/h = 75000m/h x (1 h / 3600 s)

                   = 20.8333 m/s.

Therefore, 75 km/h is equal to approximately 20.8333 m/s.

3. 80km/h to mi/h

First, convert kilometers to miles:

1 mile = 1.60934 kilometers

1 kilometers = (1/1.60934) mile

80 km/h = 80km/h x (1 mi / 1.60934 km)

              = 49.7097 mi/h.

Therefore, 80 km/h is equal to approximately 49.7097 mi/h.

4. 100km/h to m/s

First, convert kilometers to meters:

1 kilometer = 1000 meters

100 km/h = 100km/h x (1000 m / 1 km)

                = 100000 m/h.

Next, convert hours to seconds:

100000 m/h = 100000 x (1 h / 3600 s)

                    = 27.7778 m/s.

Therefore, 100 km/h is equal to approximately 27.7778 m/s.

5.  10m/s  to ft/h

First, convert meters to feet:

10 m/s = 10 x (3.28084 ft / 1 m)

           = 32.8084 ft/s.

Next, convert seconds to hours:

32.8084 ft/s = 32.8084 x (3600 s / 1 h)

                    = 118100.64 ft/h.

Therefore, 10 m/s is equal to approximately 118100.64 ft/h.

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the next two terms in the sequence would be 12 and 17.

The perimeter of the triangle ABC is 146.

Given that a triangle we need to find it perimeter,

We know that the tangents from a common point to the circle are equal,

Therefore,

DB = BE

EC = FC

FA = AD

So,

FA = AC - FC

FA = 52-13 = 39

Therefore,

FA = AD

AD = 39

Now,

9x-56 = 17x - 120

8x = 64

x = 8

DB = BE = 16

AB = 16 + 39 = 55

BC = 16+13 = 29

AC = 52

Perimeter = AC + BC + AB = 55 + 29 + 52 = 146

Hence the perimeter of the triangle ABC is 146.

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The graph of the exponential function y = 2ˣ and its inverse y = log₂ x are shown in figure.

Since, A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Here, Functions are,

⇒ y = 2ˣ

And, Its inverse function is,

⇒ y = log₂ x

Thus, The graph of the exponential function y = 2ˣ and its inverse y = log₂ x are shown in figure.

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The external circumference of the metal pipe is approximately 31.4 centimeters.

We know that the circumference of the circle that has a radius of r is defined as the product of diameter to the pie value.

The circumference of the circle = 2πr

We are given that  internal radius is 5cm and the thickness of the metal is 6mm.

The circumference of the external circle = 2πr

= 2 x 3.14 x 5

= 31.4

The circumference of the metal pipe is approximately 31.4 centimeters.

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Answer:

3, 2√2, √7

Step-by-step explanation:

compute the square roots of the next three prime numbers:

√7

√11

√13

Therefore, the next three terms of the sequence are:

{1, √2, √3, 2, √5, √7, √11, √13}

chatgpt

chat

Answer:

$762.53

Step-by-step explanation:

think of 710.98 as the whole.

then 7.25% = an increase of 0.0725.

710.98 X (1 + 0.0725)

= $762.53 (to nearest cent)

The weighted average of the points A, B, and C with weights 1, 4, and 1 respectively is (A + 4B + C) / 6.

To find the weighted average of the points A, B, and C with weights 1, 4, and 1 respectively, we first need to multiply each point by its corresponding weight and then add them together.

Finally, we divide the sum by the total weight.

The weighted sum of the points is:

(1 × A) + (4 × B) + (1 × C) = A + 4B + C

The total weight is:

1 + 4 + 1 = 6

Therefore, the weighted average of the points A, B, and C with weights 1, 4, and 1 respectively is:

(A + 4B + C) / 6

Note that the weight of B is four times that of A and C.

Therefore, the weighted average will be closer to B than A or C, reflecting the fact that B has a larger weight.

For example, if A = 3, B = 5, and C = 4, then the weighted average is:

(A + 4B + C) / 6 = (3 + 4 × 5 + 4) / 6 = 26 / 6 = 4.33.

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The fraction of the money the youngest boy does get is 5x/22.

Given that, three brothers share some money. The oldest 5/11 of the money.

Let the total money be x.

Share of oldest boy = 5/11 ×x

= 5x/11

Remainder = x-5x/11

Remainder = 6x/11

The next boy gets 7/12 of the remainder.

Share of next boy = 7/12 × 6x/11

= 7x/22

Share of youngest boy = 6x/11 - 7x/22

= (12x-7x)/22

= 5x/22

Therefore, the fraction of the money the youngest boy does get is 5x/22.

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6. Each ordered pair on the line represent the weight on Earth (pounds) and weight on Moon (pounds).

7. An equation to represent the relationship shown in the graph is [tex]y=\frac{1}{6} x[/tex].

8. Yes, this a proportional relationship.

9. In this problem situation, it is not all the points on the graph that make sense.

10. a. The weight of a person on Earth given a weight of 12 lb on the Moon is 72 lb.

b. The weight of a person on Earth given a weight of 21 lb on the Moon is 126 lb.

c. The weight of a person on Earth given a weight of 36 lb on the Moon is 216 lb.

In Mathematics, a proportional relationship produces equivalent ratios and it can be modeled or represented by the following mathematical equation:

y = kx

Where:

Part 7.

Next, we would determine the constant of proportionality (k) based on the data points provided as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = 10/60 = 20/120 = 30/180 = 40/240

Constant of proportionality, k = 1/6.

Therefore, the required equation is given by;

y = kx

y = x/6

Part 8.

Since the data points have a constant of proportionality, yes, it is a proportional relationship.

Part 9.

By critically observing the graph, it is not all the data points on the graph that make sense

Part 10.

a. When y = 12 lb, the weight of a person on Earth is given by;

x = 6y

x = 6(12)

x = 72 lb.

b. When y = 21 lb, the weight of a person on Earth is given by;

x = 6y

x = 6(21)

x = 126 lb.

c. When y = 36 lb, the weight of a person on Earth is given by;

x = 6y

x = 6(36)

x = 216 lb.

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Im sorry but I dont see a Box Plot.

Answer:

provide more data

Step-by-step explanation:

no solution

The number that belongs in the green box, using the law of cosines, is given as follows:

15.97º.

The Law of Cosines states that for any triangle with sides a, b, and c and angle C opposite to side c, the following equation is true to obtain the missing length:

c² = a² + b² - 2abcos(C)

For this problem, the parameters are given as follows:

c = 11, a = 12, b = 20.

Hence the missing angle measure is given as follows:

11² = 12² + 20² - 2 x 11 x 20cos(C)

440cos(C) = 423

cos(C) = 423/440

C = arccos(423/440)

C = 15.97º.

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Answer:

B

Step-by-step explanation:

square units (units for all area)

The y-intercept of the line is 2. the equation of the line in the form y=mx+b is y = 2x + 2.

To find the equation of the line in the form y=mx+b, we need to first find the slope (m) and the y-intercept (b).
Looking at the table:
x | y
--|--
1 | 4
2 | 6
3 | 8
We can use the formula for slope:
m = (y2 - y1) / (x2 - x1)
Let's use the first two points (1, 4) and (2, 6):
m = (6 - 4) / (2 - 1)
m = 2 / 1
m = 2
So the slope of the line is 2.
To find the y-intercept, we can use the formula:
b = y - mx
Let's use the first point (1, 4) and the slope we just found:
b = 4 - (2)(1)
b = 4 - 2
b = 2
So the y-intercept of the line is 2.
Putting it all together, the equation of the line in the form y=mx+b is:
y = 2x + 2.

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cos 30° can be evaluated using the trigonometric identity: cos 30° = cos(π/6) = (√3)/2.

Therefore, the exact value of cos 30° is (√3)/2.

Answer:

cos30 = √3 / 2

or cos30 ≈ 0.8660254037

a. The concentration would be 0.5 mg/L at approximately t = 40 hours.

b. The table representing the concentration of the drug in the bloodstream, t hours after administration is shown below.

c. A reasonable domain for this function is t ≥ 0.

d. The patient should receive the next intravenous dose of the drug in order to maintain a concentration above 1 mg/L and below 8 mg/L at t = 1.25 hour.

e. The concentration of the oral drug and the concentration of the intravenous drug would keep increasing over the first 20 hours after it is administered.

In order to determine the time when the concentration would be 0.5 mg/L, we would substitute the value of the concentration and then solve the quadratic function for time (t);

c(t) = 20t/(t² + 4)

0.5 = 20t/(t² + 4)

0.5(t² + 4) = 20t

0.5t² + 2 = 20t

0.5t² + 2 - 20t = 0

t² + 4 - 40t = 0

t² - 40t + 4 = 0

Time, t = 38.8998 ≈ 40 hours.

Part b

In this context, we would complete the table of values at various time (t) as follows;

t        0    2      4     6       8           10        12        14     16        18      20

c(t)    0    5      4      3     2.35      1.92     1.62     1.4    1.23     1.10    1.00

Part c

Since the concentration of the drug at time, t = 0 is equal to 0 mg/L and the concentration actually never becomes zero (0) for any value of time (t), we can reasonably infer and logically deduce that a reasonable domain for this quadratic function is t ≥ 0 or {0, ∞}.

Part d and e

Furthermore, the intravenous drug must be administered to the patient between the time interval 1.25 ≤ t ≤ 20 in order to maintain a concentration above 1 mg/L and below 8 mg/L.

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[tex]1\cdot2^2+1\cdot2^1+1\cdot2^0=4+2+1=7\\\\111_2=7_{10}[/tex]