RESOLVER LOS SIGUIENTES SISTEMAS DE ECUACIONES APLICANDO EL METODO DE SUSTITUCION
2x +3y = 2
-6x + 12y = 1

9514 1404 393

Answer:

  D.  f^-1(x) = 3 -7x

Step-by-step explanation:

Solve x = f(y) for y to find the inverse function.

  x = f(y)

  x = (3 -y)/7 . . . . . . use the function definition

  7x = 3 -y . . . . . . . .multiply by 7

  y = 3 -7x . . . . . . . add y-7x to both sides

Then the inverse function is ...

  [tex]\boxed{f^{-1}(x)=3-7x}[/tex]

Answer:

Dear the answer is 100% D

Good luck

9514 1404 393

Answer:

  sin(D) = cos(E) = (√3)/2

  cos(D) = sin(E) = 1/2

Step-by-step explanation:

The mnemonic SOH CAH TOA is intended to remind you of the relationships between trig functions and right triangle sides.

  Sin = Opposite/Hypotenuse

  Cos = Adjacent/Hypotenuse

For this diagram, this means ...

  sin(D) = cos(E) = (13√3)/26 = (√3)/2

  cos(D) = sin(E) = 13/26 = 1/2

Answer:

a) f(x,y) = - 1    minimum  at   P ( 0 ; -1 )

b) f (x,y) = 10  maximum at   P ( 3 , 1 ) and   f (x,y) = - 10 minimum at       Q ( - 3 , - 1 )

c)  Max  f ( x , y ) = 2   for points    P ( 1, 2 )  and T ( -1 , -2 )

Min  f ( x , y ) =  -2   for points   Q ( 1 , - 2 )  and R  ( -1 , 2 )

Step-by-step explanation:

A)  f(x,y) = x² - y²         subject to   x² + y² = 1      g(x,y) = x² + y²- 1

δf(x,y)/ δx  = 2*x                                                 δg(x,y)/ δx  =    2*x                      

δf(x,y)/ δy  = - 2*y                                                 δg(x,y)/ δy  =    2*y

δf(x,y)/ δx  = λ* δg(x,y)/ δx

2*x = λ*2*x

δf(x,y)/ δy  = λ* δg(x,y)/ δy

- 2*y = λ*2*y

Then, solving

2*x = λ*2*x           x = λ*x      λ = 1

- 2*y = λ*2*y         y = - 1

x² + y²- 1 = 0         x²  + ( -1)² - 1 = 0      x = 0    

Point  P ( 0 ; -1 )  ; then at that point

f(x,y) = x² - y²             f(x,y) = 0 - ( -1)²     f(x,y) = - 1    minimum

b)  f( x, y ) =  3*x  + y            g ( x , y )  = x² +  y²  = 10

  δf(x,y)/ δx  = 3                   δg(x,y)/ δx  =  2*x

 δf(x,y)/ δy   = 1                   δg(x,y)/ δy  =   2*y

δf(x,y)/ δx  =   λ * δg(x,y)/ δx      ⇒   3 = 2* λ *x    (1)

δf(x,y)/ δy   =  λ *  δg(x,y)/ δy     ⇒    1 = 2*λ * y    (2)

                                                           x² +  y²  - 10 = 0  (3)

Solving that system

From ec (1)     λ  =  3/2*x      From ec (2)     λ  = 1/2*y

Then    (3/2*x )  = 1/2*y          3*y  =  x

x²  +  y²  = 10     ⇒   9y²  + y²  = 10      10*y² = 10

y² = 1       y  ± 1       and    

y  =  1      x  = 3       P  ( 3 , 1  )       y  = - 1    x = -3    Q  ( - 3 , - 1 )

Value of  f( x , y )  at   P   f (x,y) = 3*x + y      f (x,y) =    3*(3) +1  

f (x,y) = 10  maximum at  P ( 3 , 1 )

Value of  f( x , y )  at  Q     f (x,y) = 3*x + y    f (x,y) =  3*(- 3) + ( - 1 )

f (x,y) = - 10 minimum at Q ( - 3 , - 1 )

c)  f( x, y ) =  xy                       g ( x , y )  =  4*x² + y² - 8

δf(x,y)/ δx  = y                         δg(x,y)/ δx  = 8*x

δf(x,y)/ δy = x                          δg(x,y)/ δy  =  2*y

δf(x,y)/ δx  =  λ * δg(x,y)/ δx   ⇒   y  =  λ *8*x    (1)

δf(x,y)/ δy =   λ * δg(x,y)/ δy   ⇒   x  =  λ *2*y    (2)

                                                      4*x² + y² - 8 = 0   (3)

Solving the system

From ec (1)  λ = y/8*x    and From ec (2)      λ = x/2*y        Then    y/8*x  =  x/2*y

2*y² = 8*x²       y² = 4*x²    

Plugging that value in ec (3)

4*x²  +  4*x² - 8 = 0

8*x² = 8     x² = 1        x ± 1      And y² = 4*x²

Then:

for x  = 1      y² =  4     y = ± 2

for x  = -1     y² =  4     y = ± 2

Then we get     P (  1 ; 2 )   Q  ( 1 ; - 2)

                          R ( - 1 ; 2 )  T  ( -1 ; -2)

Plugging that values in f( x , y ) = xy

P (  1 ; 2 )  f( x , y ) = 2            R ( - 1 ; 2 )  f( x , y ) = - 2

Q ( 1 ; - 2)  f( x , y ) = -2           T ( -1 ; -2 )  f( x , y ) = 2

Max  f ( x , y ) = 2   for points    P and T

Min  f ( x , y ) =  -2   for points   Q and R

Answer:

1. C

2. B

3 A

4. A

Step-by-step explanation:

#1

Brady starts off with 12 coins

And buys 6 more coins every year

So add 6 to find number of coins he will have the next year until we've done it five times ( because we want to find how many he will have after 5 years )

12 ( 1st year )

Add 6

12 + 6 = 18 ( 2nd year )

Add 6

18 + 6 = 24 ( 3rd year )

Add 6

24 + 6 = 30 ( 4th year )

Add 6

30 + 6 = 36 ( 5th year )

By the fifth year he will have 36 coins and the sequence would be

12, 18, 24, 30, 36

Which corresponds with answer choice C

2

15, 19, 23, 27, ?

We want to find the next term

To do so we must find the common difference

We can do this by subtracting the last given term by the term before it

27 - 23 = 4

Just to clarify we can do the terms before those

19 - 15 = 4

So the common difference is 4

Now to find the next term we simply add 4 to the last given term

27 + 4 = 31

The next term would be 31

3. Cumulative property of addition states that you can add any 3 numbers in a different order and they will be the same

a + b + 2 = 2 + a + b

Same variables and numbers just different order

Therefore this is an example of cumulative property of addition

4. The GCF ( greatest common factor ) is the greatest number that the two numbers can be divided by

18a and 24ab

Factors of 18

2 , 9 , 6, 3 , 1 and 18

Factors of 24

24, 1, 2, 12, 6, 4, 3 and 8

The greatest factor that both 18 and 24 have is 6

The GCF would be 6a ( not 6 ) because both numbers share a common variable (a) ( 18a , 24ab )

Answer:

[tex]3x^{2} -3x-11 = 0[/tex]

Step-by-step explanation:

Answer:

300

Step-by-step explanation:

[tex] \frac{1.5}{100} = 20000 \\ 20000 \div 100 = 200 \\ 200 \times 1.5 = 300[/tex]

if A banner ad created by Jonathan had CTR of 1.5% with 20,000 impression then 300 people clicked on the banner ad

percentage, a relative value indicating hundredth parts of any quantity.

A banner ad created by Jonathan had CTR of 1.5% with 20,000 impression.

We need to find how many people clicked on the banner ad.

Let us find the value of  1.5%  of 20000

Convert 1.5 % to decimal

1.5/100=0.015

Now multiply 0.015 with 20000

0.015×20000

300

Hence, if A banner ad created by Jonathan had CTR of 1.5% with 20,000 impression then 300 people clicked on the banner ad

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Answer:

first row you add 4 to get the next term. look at the difference in numbers.

second row the difference is 3 so you add 3 to get the next one.

3rd row the nth term is 3n so the one above would be 2n and the first /top nth term would just be n on its own - meaning one lot of it

4th row add 5 so 7-5= 2 being the 0th term. so just add 5 each time. so it would be 4n

bottom row the difference is 14 or to get that do 26-12

don't let it trick you out- after the third term it goes to the tenth so it would be best getting a piece of paper and working the whole of it out so u don't get confused

Answer:

Which video in YT has most number of views

Step-by-step explanation:

Answer:

c. 1.29

Step-by-step explanation:

Z-score:

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Andy 70578 60000 8200

This means that [tex]X = 70578, \mu = 60000, \sigma = 8200[/tex]

What is the z-score of Andy's salary?

This is Z, so:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{70578 - 60000}{8200}[/tex]

[tex]Z = 1.29[/tex]

So the correct answer is given by option c.

Answer:

f(x) has two imaginary roots and one real root.

Step-by-step explanation:

Complex roots:

I a complex number [tex]a + bi[/tex] is a root of a polynomial, it's conjugate [tex]a - bi[/tex] is also a root.

One root of a third degree polynomial function f(x) is -5 + 2i.

This means that -5 - 2i is another root of the polynomial, and thus, 2 of the roots are complex.

Third degree, so it has three roots, which means that the third root is real(not possible to have a complex root without it's conjugate), and thus, the correct answer is:

f(x) has two imaginary roots and one real root.

Answer:

B!

Step-by-step explanation:

just did it

Answer:

(4%) ... $8200

Step-by-step explanation:

x + y = 15000

.04x + .032y = 545.60

y = 15000 - x

.04x + .032(15000 - x) = 545.60

.008x = 65.6

x=8200

The cost a company pays a lender for a loan is called interest.

The account received an initial investment of 8200 with 4% interest.

The cost of borrowing money is called interest, and it is typically expressed as a percentage, such as an annual percentage rate (APR). Lenders may charge interest to borrowers for using their funds, or borrowers may charge interest to lenders for using their funds.

The cost a company pays a lender (creditor) for a loan is called interest. Although many different arrangements are possible, interest payments are typically based on the remaining balance of a loan and paid on a monthly basis. At a predetermined interest rate, interest is typically calculated as a percentage of the loan balance.

From the given information, we get

x + y = 15000 ........(1)

0.04x + 0.032y = 545.60 ..........(2)

From (1),

y = 15000 - x

substitute the value of y in the above equation, we get

⇒ 0.04x + 0.032(15000 - x) = 545.60

simplifying the above equation, we get

⇒ 0.008x = 65.6

x = 8200

Therefore, 8200 was initially invested in the account with 4% interest.

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Answer:

(a) A = 20(1.6)^t

(b) 210 rabbits

Step-by-step explanation:

Initial number of rabbits = 20

rate of growth, R = 60 % annually

(A) The general equation is  

[tex]A = P \left ( 1+\frac{R}{100} \right )^t\\\\A = 20\left ( 1+\frac{60}{100} \right )^t\\\\A = 20 (1.6)^t[/tex]

(B) Let the time, t = 5 years

So, the population after 5 years is

[tex]A = 20 (1.6)^5\\\\A = 209.7 = 210 rabbits[/tex]

Answer:

10 degrees

Step-by-step explanation:

The angle bisected so that mean it was divided into 2 parts, so if it's  20 degree angles bisected it's divided by 2:

20/2= 10°

So the measure of the original angle is 10° degrees!

Answer:40

Step-by-step explanation: i took the lesson this was the answer

Answer:

m∠TUV = 105

Step-by-step explanation:

From the question given above, the following data were obtained:

m∠TUN = 1 + 38x

m∠NUV = 66°

m∠TUV = 105x

m∠TUV =?

Next, we shall determine the value of x. This can be obtained as illustrated below:

m∠TUV = m∠TUN + m∠NUV

105x = (1 + 38x) + 66

105x = 1 + 38x + 66

Collect like terms

105x – 38x = 1 + 66

67x = 67

Divide both side by 67

x = 67 / 67

x = 1

Finally, we shall determine the value of m∠TUV. This can be obtained as shown below:

m∠TUV = 105x

x = 1

m∠TUV = 105(1)

m∠TUV = 105

Answer:

1.19

Step-by-step explanation:

1+0.02+0.05+0.12 = 1.19

Answer:

(Y-3)/(3+12)

(Y-3)/(15)

Y-1/5

so the answer is

(Y-1)

Answer:

[tex]y - 3 \: over \: 3 + 12 \\ y - 3.3 + 12 \\ y - 3.3 + 12 = y + 8.7 \\ y - 33 + 12 \\ y + 8.7[/tex]

Answer:

3/1 : 1/3

Step-by-step explanation:

Just simplify it.

Answer:

0.4204 probability, option b.

Step-by-step explanation:

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

[tex]f(x) = \mu e^{-\mu x}[/tex]

In which [tex]\mu = \frac{1}{m}[/tex] is the decay parameter.

The probability that x is lower or equal to a is given by:

[tex]P(X \leq x) = \int\limits^a_0 {f(x)} \, dx[/tex]

Which has the following solution:

[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]

The probability of finding a value higher than x is:

[tex]P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}[/tex]

Children arrive at a house to do Halloween trick-or- treating according to a Poisson process at the unlucky rate of 13/hour

13 arrivals during an hour, which means that the mean time between arrivals, in minutes is of [tex]\mu = \frac{13}{60} = 0.2167[/tex]

What is the probability that the time between the 15th and 16th arrivals will be more than 4 minutes ?

This is P(X > 4). So

[tex]P(X > 4) = e^{-0.2167*4} = 0.4204[/tex]

So the correct answer is given by option b.

Answer:

I guess this is the answer hope it helps

Answer:

10/9

23/3

Step-by-step explanation:

4x + 3y = 34

2x - 3y = 12

2x = 12 + 3y

2×(12 + 3y) + 3y = 34

24 + 6y + 3y = 34

24 + 9y = 34

9y = 10

y = 10/9

3×10/9 + 4x = 34

10/3 + 4x = 34

4x = (102 - 10)/3 = 92/3

x = (92/3)/4 = (92/3)/(4/1) = 92/(4×3) = 23/3

Answer:

[tex]\implies \dfrac{2}{10}< \dfrac{3}{10} [/tex]

Step-by-step explanation:

We need to compare the given two fractions .The given fractions are ,

[tex]\implies \dfrac{3}{10} [/tex]

[tex]\implies \dfrac{1}{5} [/tex]

Firstly let's convert them into like fractions . By multiplying 1/5 by 2/2 . We have ,

[tex]\implies \dfrac{1}{5} =\dfrac{1*2}{5*2}=\dfrac{2}{10} [/tex]

Now on comparing 2/10 and 3/10 we see that ,

[tex]\implies 2< 3 [/tex]

Therefore ,

[tex]\implies \dfrac{2}{10}< \dfrac{3}{10} [/tex]

Answer:

269 and 1/16 feet total (or 269.0625 feet to be precise)

Step-by-step explanation:

20 and 1/2 = 20.5

13 and 1/8 = 13.125

20.5 * 13.125 = 269.0625 feet = 269 and 1/16 feet

Answer:

19. 3x+5/2x+7 =5

or, 3x+5=5×(2x + 7)

or, 3x + 5 = 10x + 35

or, 5 - 35 = 10x - 3x

or, -30 = 7x

or, -30/7 = x

21. let x be the other number

we know,

or, x × 1/7 =2

or, x/7 =2

or, x = 14

therefore, the other number is 14.

Answer:

The ANSWER is 18*3= 54

Step-by-step explanation:

total angle inside pentagon = 540 degrees so 3(8x)+2(3x)=540 and that is 30x=540

Answer:

C = 144

Step-by-step explanation:

A 5 sided figure has the interior angle sum of 540 degrees

8x+8x+8x+3x+3x = 540

Combine like terms

30x= 540

30x/30 = 540/30

x = 18

<C = 8*18 = 144

Answer:

2.409

Step-by-step explanation:

㏑ 9 = 2.2

ln 200 = 5.3

[tex]ln 9 = log_{e}9\\ln 200 = log_{e}200[/tex]

[tex]log_{9}200 = \frac{log_{e}200}{log_{e}9}[/tex]

           = [tex]\frac{5.3}{2.2}[/tex]

           = 2.409

The approximate value of log 200 would be; 2.409

When we raise a number with an exponent, there comes a result.

Let's say you get  a^b = c Then, you can write 'b' in terms of 'a' and 'c' using logarithm as follows [tex]b = \log_a(c)[/tex]'a' is called the base of this log function. We say that 'b' is the logarithm of 'c' to base 'a'

We have given the values in 9 = 2.2 and 200 – 5.3

We need to find the approximate value of log, 200.

Therefore,

㏑ 9 = 2.2

ln 200 = 5.3

[tex]ln 9 = log_{e}9\\\\ln 200 = log_{e}200[/tex]

Using the logarithm property;

[tex]log_{9}200 = \dfrac{log_{e}200}{log_{e}9}\\ = \dfrac{ln 200}{ln 9}\\ = \dfrac{5.3}{2.2}[/tex]

=  2.409

Hence, the approximate value of log, 200 would be; 2.409

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