Find the values of x and y that satisfy the equation.

3x+6i=27+yi
x

Answer:

X=1

Step-by-step explanation:

Answer:

So the inverse function of f(x) = 2x + 3 is f⁻¹(x) = (x - 3) / 2.

Step-by-step explanation:

To find the inverse of a function, we switch the x and y variables and solve for y. So, we start with:

y = 2x + 3

Switching x and y, we get:

x = 2y + 3

Now, we solve for y:

x - 3 = 2y

y = (x - 3) / 2

So the inverse function of f(x) = 2x + 3 is f⁻¹(x) = (x - 3) / 2.

Answer & Step-by-step explanation:

To determine f's inverse function (x)= 2x + 3, we can follow these steps:

Step 1: Replace f(x) with y: y = 2x + 3

Step 2: Solve for x in terms of y:

y = 2x + 3

y - 3 = 2x

x = (y - 3) / 2

Step 3: Replace x with f^(-1)(x):

f^(-1)(x) = (x - 3) / 2

Therefore, the inverse function of f(x) = 2x + 3 is f^(-1)(x) = (x - 3) / 2.

Answer:

17) 23

18) 12

Step-by-step explanation:

17

x+15 = 7+2x

x-2x = 7-15

-x= -8

x=8

WX = x+15

= 8+15

= 23

18

2x = 3x-6

2x -3x = -6

-x = -6

x = 6

EF = 3x-6

= 3(6) -6

= 18 -6

= 12

the pH of the buffer is 3.74

To calculate the pH of a buffer containing 0.13 M lactic acid and 0.10 M sodium lactate, we will use the Henderson-Hasselbalch equation:

pH = pKa + log10([A-]/[HA])

Here, [A-] represents the concentration of the conjugate base, which is sodium lactate, and [HA] represents the concentration of the weak acid, which is lactic acid. Ka is given as 1.4 × 10⁻⁴.

First, we need to find the pKa. Since pKa = -log10(Ka):

pKa = -log10(1.4 × 10⁻⁴) = 3.85

Now, we can plug the values into the Henderson-Hasselbalch equation:

pH = 3.85 + log10(0.10 / 0.13)
pH = 3.85 + log10(0.769)
pH = 3.85 - 0.11 (approximately)

pH = 3.74

The pH of the buffer is approximately 3.74.

Visit here to learn more about conjugate base:

brainly.com/question/30225100

#SPJ11

Answer:

The answer is D (last bullet)

Answer: JNM=42

Step-by-step explanation:

The airplane should head approximately 4.76 degrees east of its intended direction to compensate for the crosswind and end up going due east.

To end up going due east, the airplane needs to counteract the effect of the crosswind and maintain a heading that compensates for the wind's direction and speed.

Since the crosswind is coming from the northeast, it forms a right triangle with the airplane's airspeed and ground speed vectors. The angle between the ground speed vector (due east) and the airspeed vector is the heading the plane should take.

Using trigonometry, we can calculate this angle. The opposite side of the triangle is the speed of the crosswind (50 km/hr), and the hypotenuse is the airspeed (600 km/hr).

Let's denote the angle as θ. We can use the sine function:

sin(θ) = opposite/hypotenuse

sin(θ) = 50/600

θ = sin^(-1)(50/600)

Evaluating this expression, we find θ ≈ 4.76 degrees.

Know more about speed vectors here:

https://brainly.com/question/11313073

#SPJ11

Answer:

Step-by-step explanation:

B

Answer:

y = −5x − 19

Step-by-step explanation:

Find the equation using slope-intercept form.

y = −5x − 19

The given parabolic equation is y = 4x - x² and the point is (1, 3). We are to determine the slope of the tangent line at (1, 3) and then obtain an equation of the tangent line.  we must first calculate the derivative of the given equation.

We can do this by using the power rule of differentiation. The derivative of x² is 2x. So the derivative of y = 4x - x² is dy/dx = 4 - 2x.Since we want to find the slope of the tangent line at (1, 3), we need to substitute x = 1 into the equation we just obtained. dy/dx = 4 - 2x = 4 - 2(1) = 2. Therefore, the slope of the tangent line at (1, 3) is 2.We can now write the equation of the tangent line. We know the slope of the tangent line, m = 2, and we know the point (1, 3).

We can use the point-slope form of the equation of a line to obtain the equation of the tangent line. The point-slope form of the equation of a line is given as: y - y₁ = m(x - x₁)where m is the slope, (x₁, y₁) is a point on the line.Substituting in the values we have, we get:y - 3 = 2(x - 1)We can expand this equation to obtain the slope-intercept form of the equation of the tangent line:y = 2x + 1Therefore, the equation of the tangent line to the parabola y = 4x - x² at the point (1, 3) is y = 2x + 1.

To Know about intercept visit:

brainly.com/question/14180189

#SPJ11

Answer:

Step-by-step explanation:

Shawndra y = 5x + 30

Juan: y = -10x + 150

-10x + 150 = 5x + 30

-15x + 150 = 30

-15x = -120

x = 8 weeks

Answer:

well im doing this for u can give the other person brainliest they really desrive it

Step-by-step explanation:

A scale factor of 8000 is required by the trucking company to hold 8,000 gallons of oil in the full-sized truck.

Given that the scale model of an oil truck can hold 1 gallon of oil, it implies that there is a ratio of 1:1 between the capacity of the scale model truck and the actual truck.To obtain the scale factor that must be applied to find the capacity of the full-sized truck, we will use the equation below;Scale factor = Actual capacity of the truck / Capacity of the scale model of the truckUsing the values given;Actual capacity of the truck = 8,000 gallonsCapacity of the scale model of the truck = 1 gallonScale factor = Actual capacity of the truck / Capacity of the scale model of the truckScale factor = 8000 / 1 = 8000

First, we can define the scale factor as the numerical ratio that shows the proportion between the sizes of two similar figures.In this case, we are dealing with two trucks that have the same shape and features, but different sizes. The scale model of the truck is smaller than the actual truck, and it can hold 1 gallon of oil, while the actual truck must hold 8,000 gallons of oil.So, to find the scale factor that the trucking company must apply, we can use the following equation:Scale factor = Actual capacity of the truck / Capacity of the scale model of the truckSince we know that the actual capacity of the truck is 8,000 gallons, and the capacity of the scale model of the truck is 1 gallon, we can substitute these values in the formula above:Scale factor = 8,000 / 1 = 8,000Therefore, the trucking company must apply a scale factor of 8,000 to obtain the full-sized truck that can hold 8,000 gallons of oil.

To know more about scale factor  visit :-

https://brainly.com/question/29464385

#SPJ11

\(\bold{\huge{\underline{ Solution }}}\)

Here,

\(\sf{ x + 2y = 13 ...eq(1)}\)

\(\sf{ x + 5y = 28 ...eq(2)}\)

By solving eq(1) :-

\(\sf{ x + 2y = 13 }\)

\(\sf{ x = 13 - 2y ...eq(3)}\)

Subsitute eq(3) in eq(2) :-

\(\sf{ (13 - 2y) + 5y = 28 }\)

\(\sf{ 13 - 2y + 5y = 28 }\)

\(\sf{ 13 + 3y = 28 }\)

\(\sf{ 3y = 28 - 13 }\)

\(\sf{ 3y = 28 - 13 }\)

\(\sf{ 3y = 15 }\)

\(\sf{ y = }{\sf{\dfrac{ 15}{3}}}\)

\(\sf{ y = }{\sf{\cancel{\dfrac{ 15}{3}}}}\)

\(\bold{ y = 5 }\)

Thus, The value of y is 5

Subsitute the value of y in eq(1) :-

\(\sf{ x + 2(5) = 13 }\)

\(\sf{ x + 10 = 13 }\)

\(\sf{ x = 13 - 10 }\)

\(\bold{ x = 3 }\)

Hence, The value of x and y are 5 and 3 .

\(\bold{\huge{\underline{ Let's \: Verify }}}\)

\(\sf{ x + 2y = 13 }\)

\(\sf{ 3 + 2(5) = 13 }\)

\(\sf{ 3 + 10 = 13 }\)

\(\sf{ 13 = 13 }\)

\(\bold{ LHS = RHS }\)

\(\sf{ x + 5y = 28 }\)

\(\sf{ 3 + 5(5) = 28 }\)

\(\sf{ 3 + 25 = 28 }\)

\(\sf{ 28 = 28 }\)

\(\bold{ LHS = RHS }\)

Let's use elimination method

We get

\(\\ \rm\Rrightarrow 2y-5y=13-28\)

\(\\ \rm\Rrightarrow -3y=-15\)

\(\\ \rm\Rrightarrow y=\dfrac{-15}{-3}\)

\(\\ \rm\Rrightarrow y=5\)

Putting on eq(1)

\(\\ \rm\Rrightarrow x+2y=13\)

\(\\ \rm\Rrightarrow x+2(5)=13\)

\(\\ \rm\Rrightarrow x+10=13\)

\(\\ \rm\Rrightarrow x=13-10\)

\(\\ \rm\Rrightarrow x=3\)

\(\LARGE{\underbrace{\underline{\rm{Verification:-}}}}\)

\(\\ \rm\Rrightarrow x+2y=13\)

\(\\ \rm\Rrightarrow 3+2(5)=13\)

\(\\ \rm\Rrightarrow 3+10=13\)

\(\\ \rm\Rrightarrow 13=13\)

And

\(\\ \rm\Rrightarrow x+5y=28\)

\(\\ \rm\Rrightarrow 3+5(5)=28\)

\(\\ \rm\Rrightarrow 3+25=28\)

\(\\ \rm\Rrightarrow 28=28\)

Hence verified!

To find a math game on coolmath.com or another math game site, you can simply go to the site and browse through the available games. Choose a game that seems interesting to you and fits your skill level. I can recommend a popular math game called "Number Munchers" available on coolmathgames.com.

Number Munchers is an educational game where you navigate a little green character around a grid filled with numbers. Your goal is to eat the correct numbers based on the given criteria, such as multiples of a specific number or prime numbers. The game helps improve math skills while being enjoyable.

The individual experiences with games may vary, as everyone has different preferences and levels of difficulty. I suggest trying it out with a child, family member, or friend and discussing your experiences afterward.

Learn more about prime numbers from the given link:

https://brainly.com/question/29629042

#SPJ11

Answer:

-6

Step-by-step explanation:

I hope this helps you out!

The Normal model is a good approximation for the sampling distribution.

a) According to the Central Limit Theorem, the theoretical mean and standard deviation for a sample size of 20 should be 0.05 and 0.02, respectively. For a sample size of 100, the theoretical mean and standard deviation should be 0.05 and 0.01, respectively.

b) The observed mean and standard deviation for a sample size of 20 was 0.052 and 0.021, respectively. For a sample size of 100, the observed mean and standard deviation was 0.051 and 0.012, respectively. These values are fairly close to the theoretical values.

c) Looking at the histograms in Exercise 1, I would be comfortable using the Normal model as an approximation for the sampling distribution at a sample size of 100.

d) The Success/Failure Condition states that the sample size should be large enough for the sampling distribution of the sample proportions to be approximately normal. Since I chose a sample size of 100, which satisfied the condition, I can be confident that the Normal model is a good approximation for the sampling distribution.

The sample size of 100 is large enough for the sampling distribution of the sample proportions to be approximately normal, and the observed mean and standard deviation is close to the theoretical values. Therefore, the Normal model is a good approximation for the sampling distribution.

Learn more about sampling distribution here:

https://brainly.com/question/30007465

#SPJ4

The students that will like exactly one of the two sports out of football and baseball is 200.

These are the fundamental set of set theory formulas. When there are two sets P and Q, the number of elements in one of the sets P or Q is denoted by n(P U Q). The number of elements in both sets P and Q is represented by the expression n(P ⋂Q). n(P U Q) is equal to n(P) + n(Q) - n (P Q).

Here,

F=140

B=144

F∩B=42

F-B=n(F)-n(F∩B)

=140-42

F-B=98

B-F=n(B)-n(F∩B)

=144-42

=102

So, the students that will like exactly one of the two sports,

=102+98

=200

There are 200 students who will only enjoy one of the two sports—football or baseball.

To know more about set,

https://brainly.com/question/28429487?referrer=searchResults

#SPJ4

The  difference between addition and subtraction of polynomials is that addition involves like terms  and subtraction  involves taking one polynomial away from another.

A polynomial is characterized as an expression that is composed of variables, exponents, and constants, that are combined utilizing numerical operations such as addition, subtraction, multiplication, and division (No division operation by a variable).In addition to polynomials, the like terms are included whereas, in subtraction, the like terms are subtracted. The addition of polynomials involves combining like terms to form a single expression, while subtraction involves taking one polynomial away from another. In addition, when subtracting polynomials, the sign of each term in the second polynomial needs to be changed (from positive to negative, or from negative to positive).

To know more about polynomials refer to the link  brainly.com/question/11536910

#SPJ4

Hi There!

Your Answer could be 8 don't trust me i might be wrong

Answer:

The value of \(x\):

\(x = 44\)

Step-by-step explanation:

Find the value of \(x\):

\(2(x + 10) = 3(x-8)\)

Use Distributive Property:

\(2(x + 10) = 3(x-8)\)

\(2x +20 = 3x - 24\)

-Subtract both sides by \(3x\) and combine both \(2x\) and \(-3x\) together:

\(2x +20 - 3x = 3x - 3x - 24\)

\(-x + 20 = -24\)

-Subtract both sides by \(20\):

\(-x + 20 - 20 = - 24 - 20\)

\(-x = -44\)

Divide both sides by \(-1\):

\(\frac{-x}{-1} = \frac{-44}{-1}\)

\(x = 44\)

So, the final answer would be \(x = 44\).

Answer: 3

Step-by-step explanation: 0.5 L W

0.5 L 1.5

1.5 Times 2 =3

To check the answer we do 0.5 x 3 x 1.5=2 which is the area

Answer:

\(\boxed{\red{500 + x \leqslant 4500}}\\ x \leqslant 4500 - 500 \\ \blue{\underline{x \leqslant 4000}}\)

Answer:

Less

Step-by-step explanation:

Because we don’t know the value of x.

Answer:

it could be angle DGF or CGA (they are both supplementary to angle CGD)

Step-by-step explanation:

Answer:

Volume of prism = 6.3 cm³

Step-by-step explanation:

Given:

Dimensions of parallels line = 2.3 and 1.2 cm

Height of prism = 1.8 cm

Width of prism = 2 cm

Find:

Volume of prism

Computation:

Volume of prism = Area of base x Width

Volume of prism = [(1/2)(sum of parallels line)(Height)]Width

Volume of prism = [(1/2)(2.3 + 1.2)(1.8)]2

Volume of prism = [(1/2)(3.5)(1.8)]2

Volume of prism = [(3.5)(1.8)]

Volume of prism = 6.3 cm³

The degrees of freedom for the following random sample is 19.

The quantity of values that can change in a statistic's final calculation is referred to as the number of freedom levels in statistics.

The estimation of statistical parameters can be done using many types of data or information. The number of independent data points needed to estimate a parameter is referred to as having two degrees of freedom.

The amount of flexibility in an estimate is typically defined as the number of distinct scores utilized in the estimate, minus the number of characteristics used as intermediate steps in the estimation of the parameter itself.

Now degrees of freedom is calculated for the confidence level by reducing the sample size by 1.

Hence sample size =20

Degrees of freedom = 20 -1 = 19

To learn more about sample visit:

https://brainly.com/question/13287171

#SPJ4

Answer:

18.8 feet

Step-by-step explanation:

You have to use trigonometry for this question.

So, the basic measurements we have are:

1. The angle of elevation = 42 degrees

2. Base length of the triangle(ie. the shadow  on the floor) = 20 ft

Now, imagine a right angled triangle with the base length as the shadow height, the height of the triangle as the height of the tree and the hypotenuse as the sun ray that causes the shadow. Also, the angle opposite the height is the 42 degrees.

So, we know the Adjacent length and we want to know the opposite length ( in respects with the angle given)

So, the trig ratio that compares the two is ‘Tan’

Now, form the equation:

Tan (42) = Opposite/ Adjacent = O/ A = O/20

Rearrange to solve:

O/20 = Tan(42)

O = Tan(42) x 20

Key these into a calculator and you get the answer: 18.800808...

Round to a suitable degree of accuracy.

18.8 ( 3s.f)

Answer:

Explanation:

The given polynomial is expressed as

16x^2 - 1

The standard form of a quadratic polynomial is expressed as

ax^2 + bx + c

By comparing both polynomials,

a = 16

b = 0

c = - 1

(a) The inter-event-time distribution for the processes \(N_1(t)\) and \(N_2(t)\) are \(X1_n=1 (1-p)^{(n-1)} p F(t)\)  and \(X1_n\)= \(1 p^{(n-1)} (1-p) F(t)\)

(b) The Laplace-Stieltjes transforms of the inter-event-time distributions for processes  \(N_1(t)\) and \(N_2(t)\) are given by

\(b F_1(s)\) = \(X_n p (1-p)^{(n-1)} bF(s)^n\) and \(bF_2(s)\)  = \(X_n (1-p) p^{(n-1)} bF(s)^n\)

(c) \(M_1(t)\) = pM(t) / (1 - (1-p)M(t))

\(M_2(t)\) = (1-p)M(t) / (1 - pM(t))

(d) As \(N_1(t)\) and \(N_2(t)\) has an exponential distribution with parameter (1-p) hence it is Poisson process.

(a) In the process \(N_1\)(t),

let \(F_1\) n(t) be the distribution function of the nth inter-event time, and

let \(F_2\) n(t) be the distribution function of the nth inter-event time (t).

Next, we have

\(F_1\)n(t) = P("the nth event is a renewal point of \(N_1\)(t)") P("the (n-1)th event is not a renewal point of \(N_1\)(t)") F(t)

= \(p (1-p)x^{(n-1)} F(t)\)

\(F_2\) n(t) = P("the nth event is a renewal point of \(N_2(t)\)") P("the (n-1)th event is not a renewal point of \(N_2(t)\)") F(t)

= \((1-p) p^{(n-1)} F(t)\)

The processes \(N_1(t)\) and \(N_2\) (inter-event-time )'s distribution is therefore provided by:

\(X1_n=1 (1-p)^{(n-1)} p F(t)\)  and \(X1_n\)= \(1 p^{(n-1)} (1-p) F(t)\)

respectively.

(b) The Laplace-Stieltjes transform of \(F_1(t)\) is given by:

\(bF_1(s)\) = E[\(e^{(-sT1)}\)]

= \(X_n\) P("the nth event is a renewal point of \(N_1(t)\)") \(e^{(-sT1_n)}\)

= \(X_n p (1-p)^{(n-1)} e^{(-sX_n)}\)

where

\(T1_n\) is the nth inter-event time in \(N_1(t)\),

\(X_n\) is the time of the nth event in N(t).

By using the fact that \(X_n = T1_1 + T1_2 + ... + T1_n,\) we have:

b\(F_1(s)\) = \(X_n p (1-p)^{(n-1)} e^{(-s(T1_1+T1_2+...+T1_n)} )\)

= \(X_n p (1-p)^{(n-1)} e^{(-sT1_1) } e^{(-sT1_2)} ... e^{(-sT1_n)}\)

= \(X_n p (1-p)^{(n-1)} bF(s)^n\)

where

bF(s) is the Laplace-Stieltjes transform of the distribution of the original process.

Similarly, the Laplace-Stieltjes transform of \(F_2(t)\) is given by:

\(bF_2(s)\) = \(E[e^{(-sT2)} ]\)

= \(X_n (1-p) p^{(n-1)} ex^{(-sX_n)}\)

\(bF_2(s)\)  = \(X_n (1-p) p^{(n-1)} bF(s)^n\)

(c) We observe that the inter-arrival durations of \(N_1(t)\) are exponentially distributed with parameter p, where is the rate of the original process, in order to determine the renewal function of  \(N_1(t)\) . Well, here we are:

\(M_1(t) = E[N_1(t)]\)

= ∑n=\(0^{\infty }\)\(P[N_1(t) = n]\)

= ∑n

=\(0^{\infty }\)\((1-p)^n p^n M(np)\)

where

M(t) is the renewal function of the original process.

By using the geometric series formula,

by simplifying this expression to:

M1(t) = p∑n=\(0^{\infty }\)\([(1-p)M(t)]^n\) = \(p[1 - (1-p)M(t)]^{-1}\)

The inter-arrival times of \(N_2(t)\) are exponentially distributed with parameter (1-p)λ, and we have:

\(M_2(t)\) = \(E[N_2(t)]\)

= ∑n

=\(0^{\infty }\)P[N2(t) = n]

= ∑n

=\(0^{\infty }\)\(p(1-p)^n M(np)\)

By using the geometric series formula,

We can simplify this expression to:

\(M_2(t)\) = (1-p)∑n

= \(0^{\infty }\)\([pM(t)]^n\)

= (1-p)\([1 - pM(t)]^{-1}\)

Therefore, we have:

\(M_1(t)\) = pM(t) / (1 - (1-p)M(t))

\(M_2(t)\) = (1-p)M(t) / (1 - pM(t))

(d) The inter-arrival times have an exponential distribution with parameter if N(t) is a Poisson process with rate. The inter-arrival times for \(N_1(t)\) are exponentially distributed with the constant-rate parameter p. \(N_1(t)\) is a Poisson process with rate p, therefore it is also.

The inter-arrival durations for \(N_2(t)\)similarly follow a similar exponential distribution with parameter (1-p), which is also a constant rate. With rate (1-p), \(N_2(t)\) is likewise a Poisson process.

For similar question on exponential distribution

https://brainly.com/question/13339415

#SPJ4