Write a recursive definition for each sequence. 100,10,1,0.1,0.01, ............

Answers

Answer 1

This recursive definition can also be written using a closed-form formula:

\($$a_n=\frac{10^3}{10^{n-1}}$$\)

A recursive definition for the sequence 100, 10, 1, 0.1, 0.01, ... can be given as follows:

Given a sequence of real numbers a₁, a₂, a₃, ..., we can recursively define a new sequence b₁, b₂, b₃, ... by setting

b₁ = a₁/10, b₂ = a₂/10, b₃ = a₃/10, ...

Then we can define the sequence a using a recursive formula as follows:

a₁ = 100a₂ = 10a₃ = 1a₄ = 0.1a₅ = 0.01aₙ = aₙ₋₁/10

where n is a positive integer greater than or equal to 6.

This formula gives the nth term of the sequence without requiring any previous terms to be computed.

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Related Questions

Latisha noticed that she has the same number of nickels, dimes, quarters, and half dollars in her drawer.the coins total $12.60.
a.How many of each coin does she have?
b.The nickels and dimes total what amount?
c.The quarters and half dollars total what amount?

Answers

Answer:

A. 14

B. $2.10

C. $10.50

N ideal gas expands from 15.5 to 21.4 l at the constant temperature of 325 k. if the change in entropy of the gas is 24.2 j/k, how many mol were there of the gas

Answers

The answer is , there were approximately 0.97 moles of the gas during the isothermal expansion.

we can determine the number of moles of the ideal gas by utilizing the formula for the change in entropy (∆S) during an isothermal expansion:
∆S = n * R * ln(V2/V1)
Here, n is the number of moles, R is the ideal gas constant (8.314 J/(mol·K)), V1 is the initial volume (15.5 L), and V2 is the final volume (21.4 L). We are given ∆S as 24.2 J/K. To find n, rearrange the formula:
n = ∆S / (R * ln(V2/V1))
Now, plug in the values:

n = 24.2 / (8.314 * ln(21.4/15.5))
Calculating this expression gives:
n ≈ 0.97 moles
So, there were approximately 0.97 moles of the gas during the isothermal expansion.

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Consider the mountain known as Mount Wolf, whose surface can be described by the parametrization r(u, v) = u, v, 7565 − 0.02u2 − 0.03v2 with u2 + v2 ≤ 10,000, where distance is measured in meters. The air pressure P(x, y, z) in the neighborhood of Mount Wolf is given by P(x, y, z) = 26e(−7x2 + 4y2 + 2z). Then the composition Q(u, v) = (P ∘ r)(u, v) gives the pressure on the surface of the mountain in terms of the u and v Cartesian coordinates.

(a) Use the chain rule to compute the derivatives. (Round your answers to two decimal places.)

∂Q ∂u (50, 25) =

∂Q ∂v (50, 25) =

(b) What is the greatest rate of change of the function Q(u, v) at the point (50, 25)? (Round your answer to two decimal places.)

(c) In what unit direction û = a, b does Q(u, v) decrease most rapidly at the point (50, 25)? (Round a and b to two decimal places. (Your instructors prefer angle bracket notation < > for vectors.) û =

Answers

A) The function Q changes as we vary u and v near the point (50, 25).

B) The greatest rate of change of Q at the point (50, 25) is approximately 9418.14 meters per unit change in the input parameters.

C) Q decreases most rapidly at the point (50, 25) in the direction of the vector < -0.925, -0.380 >, which has magnitude 1 and points in the direction of the negative gradient of Q.

To begin, we have the function Q(u, v) = (P ∘ r)(u, v), where P(x, y, z) = 26e(−7x2 + 4y2 + 2z) and r(u, v) = u, v, 7565 − 0.02u2 − 0.03v2. This means that we first need to evaluate P at the values of x, y, and z given by r(u, v), and then substitute u and v into the resulting expression to obtain Q(u, v).

To compute the partial derivative of Q with respect to u, we use the chain rule:

∂Q ∂u = (∂P ∂x ∂x ∂u + ∂P ∂y ∂y ∂u + ∂P ∂z ∂z ∂u) evaluated at r(u, v).

Similarly, to compute the partial derivative of Q with respect to v, we use:

∂Q ∂v = (∂P ∂x ∂x ∂v + ∂P ∂y ∂y ∂v + ∂P ∂z ∂z ∂v) evaluated at r(u, v).

Plugging in the values of u = 50 and v = 25 into these expressions and evaluating them using the given formulae for P and r, we obtain:

∂Q ∂u (50, 25) = -8707.47

∂Q ∂v (50, 25) = -3482.99

Next, we want to find the greatest rate of change of Q at the point (50, 25). To do this, we compute the magnitude of the gradient of Q at this point:

|∇Q(50, 25)| = √( (∂Q/∂u)² + (∂Q/∂v)² )

Plugging in the values of the partial derivatives that we found earlier, we obtain:

|∇Q(50, 25)| = √( (-8707.47)² + (-3482.99)² ) = 9418.14

Finally, we want to find the unit direction in which Q decreases most rapidly at the point (50, 25). This is given by the negative of the unit vector in the direction of the gradient of Q at this point:

û = -∇Q(50, 25) / |∇Q(50, 25)|

Plugging in the values of the partial derivatives that we found earlier and simplifying, we obtain:

û = <-0.925, -0.380>

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Joey likes beer and whisky and spends £75 in total on drink. His utility function for whisky (w) and beer (b) is = 5 + .
He can buy beer at £2 a can but the liquor store tries to discourage overconsumption of spirits by charging higher prices for larger quantities: the cost in dollars of bottles of whisky works out at !.
a. How many cans of beer and how many bottles of whisky does Joey consume?
b. Illustrate your answer with a clearly labelled diagram showing Joey's budget constraint and his indifference curve passing through the optimal consumption bundle.
c. Joey's friend Ross shops at the same liquor store and spends the same amount on drink. Jim, however, insists on drinking beer and whisky together. His utility function is = min{5, } How much beer and whisky does Jim buy?​

Answers

So what even is this make it shorter and I should be able to answer it
Joey spends £75 in total on drink. The cost of beer is £2 per can, and the cost of whisky is £6 per bottle.The budget constraint is: 2b + 6w = 75In summary, to fully answer the questions, we would need the specific numerical values for the utility function and the budget constraint.

To answer the questions, we need to understand the utility functions and budget constraints for both Joey and Jim. Let's break it down step by step:

Joey's Utility Function and Budget Constraint:

Joey's utility function for whisky (w) and beer (b) is given by: U(w, b) = 5 + (w^0.3 * b^0.7)

w: The quantity of whisky (in bottles) consumed by Joey

b: The quantity of beer (in cans) consumed by Joey

Joey spends £75 in total on drink. The cost of beer is £2 per can, and the cost of whisky is £6 per bottle.

To find how many cans of beer and bottles of whisky Joey consumes, we need to maximize his utility function while staying within his budget constraint.

Joey's Budget Constraint:

Joey's total expenditure on drink (E) is given by: E = 2b + 6w

And we know that E = £75.

So, the budget constraint is: 2b + 6w = 75

Now, we can solve this problem using optimization techniques. However, without specific numerical values for the utility function and budget constraint, it's not possible to determine the exact quantities of beer and whisky consumed by Joey. We can only find the optimal consumption bundle if the specific values are given.

Joey's Indifference Curve and Budget Constraint Diagram:

To illustrate Joey's optimal consumption bundle, we would need to plot his indifference curve (representing his preferences) and his budget constraint (showing all possible affordable combinations of beer and whisky). However, without the exact values, we cannot draw the diagram.

Jim's Utility Function and Consumption:

Jim's utility function for beer (b) and whisky (w) is given by: U(b, w) = min{5, (w^0.3 * b^0.7)}

Jim's utility function shows that he insists on drinking beer and whisky together, and his utility is the minimum of 5 and the product of whisky and beer raised to certain powers.

Again, without specific numerical values for the utility function, we cannot determine the exact quantities of beer and whisky consumed by Jim.

In summary, to fully answer the questions, we would need the specific numerical values for the utility function and the budget constraint. With those values, we could then calculate the optimal consumption bundles for both Joey and Jim.

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16 days 5 hours 23 minutes. how many minutes and hours come out in total?

Answers

Answer:

389 hours and 23 minutes

Step-by-step explanation:

16x24=384

384+=5=389

and 23 minutes

suppose there are two candidates for elected office. explain how the facts that a) voting might not be compulsory and b) resources are needed to finance reelection campaigns affect the conclusions of the median voter model.

Answers

The fact that voting might not be compulsory will make the voter ranks the candidate as their proximity, and the median voter wins the vote

The fact that resources are needed to finance reelection campaigns will make the probability of the median voter be in danger

According to median voter model theorem, at-least there must be two candidates

Being that we have two candidates for elected office, let's see how the following may affect the conclusions of the median voter model:

Part a

Voting might not be compulsory:

Here, voter ranks the candidates as per as their proximity, and the median voter will win the vote.

Part b

Resources are needed to finance re-election campaign :

When resources are needed to finance reelection campaign, none can cast their votes and it will distort this strategy. So the probability of median voter is in danger.

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what the prime factorization on 75?

Answers

Answer:

3*5^2

Step-by-step explanation:

75 is divisible by 3

75/3 = 25

25 is not divisible by 3, but it is divisible by 5.

25 = 5^2.

25/25 = 1. We are done.

is it less, greater or equal pls help (will give brainleist)

is it less, greater or equal pls help (will give brainleist)

Answers

Answer: less than
4*2/3 = 2.6666
So
4*2/3 is less than 4

One number 1 more than 3 times another. The sum of the numbers is 5. Find the two numbers.

The tWO numbers are__
and__

Answers

Answer: x=3.75   y=1.25

Step-by-step explanation:

Let the numbers we are looking for be x and y

Hence,

x=3y

x+y=5

x=3y

x=5-y

Thus,

3y=5-y

3y+y=5

4y=5

Divide both parts of the equation by 4:

y=1.25

Hence,

x=3(1.25)

x=3.75

In a senior class, 17% play chess, 31% play checkers, and 11% play both. Find the probability of a senior who plays chess also plays checkers

Answers

The probability of a senior who plays chess also playing checkers is approximately 0.647 or 64.7%.

Let A be the event that a senior plays chess, and let B be the event that a senior plays checkers. We are given that:

P(A) = 0.17 (17% play chess)

P(B) = 0.31 (31% play checkers)

P(A ∩ B) = 0.11 (11% play both)

We want to find P(B|A), which is the conditional probability of playing checkers given that the student already plays chess. By Bayes' theorem, we have:

P(B|A) = P(A ∩ B) / P(A)

Plugging in the values we know, we get:

P(B|A) = 0.11 / 0.17 ≈ 0.647

Therefore, the probability of a senior who plays chess also playing checkers is approximately 0.647 or 64.7%.

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Can someone help me with this!!!!!!

Can someone help me with this!!!!!!

Answers

Answer:

The answer is 17.58

Find the values of x for which the series converges. (Enter your answer using interval notation.) [infinity] (x − 5)^n/6^n (No Response) Find the sum of the series for those values of x.

Answers

The sum of the geometric series infinity ∑ (n = 0) (x - 5)ⁿ / 6ⁿ is {6 / (1 - x)}.

What is geometric series?

A geometric series in mathematics is made up of an unlimited number of terms with a fixed ratio between them.

As per data given,

The geometric series is infinity ∑ (n = 0) (x - 5)ⁿ / 6ⁿ

Rewrite geometric series,

infinity ∑ (n = 0) (x - 5)ⁿ / 6ⁿ = infinity ∑ (n = 0) {(x - 5)/6}ⁿ

Common ratio is r = (x - 5)/6

We know a geometric series converges when the radius is less than 1, so we have

I r I = I (x - 5)/6 I < 1

I x - 5 I < 6

-6 < x - 5 < 6

-1 < x < 11

Therefore, the series converges on ( -1, 11)

The sum of the series is, by using the formula {a / 1 - r}.

Substitute values in formula respectively,

a / 1 - r = 1 / {1 - (x - 5)/6}

           = 6 / {6 - (x - 5)}

           = 6 / (1 - x)

Hence, the sum of the geometric series infinity ∑ (n = 0) (x - 5)ⁿ / 6ⁿ is {6 / (1 - x)}.

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A researcher randomly selects and interviews fifty male and fifty female teachers.
a. systematic
b. convenience
c. random
d. stratified
e. cluster

Answers

The sampling method described in the scenario is d. stratified sampling.

In stratified sampling, the population is divided into distinct subgroups or strata based on certain characteristics or variables. The researcher then randomly selects samples from each stratum in proportion to their representation in the population. This approach ensures that the sample is representative of the population's diversity.

In this case, the researcher has divided the population of teachers into two strata: male teachers and female teachers. By randomly selecting 50 male teachers and 50 female teachers, the researcher is ensuring that both genders are represented in the sample.

The researcher's intention is to have a sample that reflects the gender distribution of teachers in the population accurately. Therefore, stratified sampling is the appropriate method in this scenario.

Other sampling methods, such as systematic sampling, convenience sampling, random sampling, and cluster sampling, are not applicable because they do not specifically address the need to ensure proportional representation of genders in the sample.

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for iq tests with a mean of 100 and a standa for iq tests with a mean of 100 and a standard deviation of 15, a score of 73 would represent a classification of:

Answers

The classification for a score of 73 on an IQ test with a mean of 100 and standard deviation of 15 is "below average".

For intelligence level tests with a mean of 100 and a standard deviation of 15, a score of 73 would address a characterization of less than ideal knowledge.

To comprehend this order, it is vital to realize that level of intelligence scores are normalized, meaning they depend on a dispersion where the typical score is 100 and the standard deviation is 15. This dissemination is frequently alluded to as a typical circulation, with most of scores falling inside one standard deviation of the mean.

A score of 73 is one and a half standard deviations underneath the mean (100-15-15=70). This places it in the seventh percentile, meaning just 7% of the populace would score lower.

As indicated by most intelligence level grouping frameworks, a score of 73 would fall inside the scope of marginal scholarly working or low normal knowledge. It is essential to note, nonetheless, that intelligence level scores are only one proportion of knowledge and ought not be utilized in segregation to decide an individual's scholarly capacities.

In outline, a score of 73 on a level of intelligence test with a mean of 100 and a standard deviation of 15 would address sub optimal knowledge and fall inside the scope of marginal scholarly working or low normal insight.

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PLZ ANSWER THIS. I really need help from smart people.

PLZ ANSWER THIS. I really need help from smart people.

Answers

Answer:

2x-3y<7

Step-by-step explanation:

Hope it helps (:

Si una llave entrega 32 litros en 5 minutos . cuantos tardara dicha llave en llenar 288 litros? porfa es urgente:c

Answers

The time required to fill 288 liters of water would be 288/6.4 = 45 minutes.Therefore, the time taken by the key to fill 288 liters of water is 45 minutes.

The given data in the problem is that a key delivers 32 liters of water in 5 minutes. We are required to calculate how much time it will take to fill 288 liters of water.So, let's proceed with the solution,Step 1: We need to find out how many liters of water is filled in one minute. We can use the unitary method to solve the problem. We know that 32 liters of water is filled in 5 minutes. Hence, in one minute, the amount of water filled would be32/5 = 6.4 litersStep 2: Now, we need to find the time required to fill 288 liters of water. Again, we can use the unitary method. We have found out that the amount of water filled in one minute is 6.4 liters. Therefore, the time required to fill 288 liters of water would be 288/6.4 = 45 minutes.Therefore, the time taken by the key to fill 288 liters of water is 45 minutes.

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I need to know what are the answers for 5,6,7.

I need to know what are the answers for 5,6,7.

Answers

Question 5:

The first question gives us the following points:

\(\lbrace(-1,-2),(3,0)\rbrace\)

To calculate the slope, we use the following formula:

\(m=\frac{y_2-y_1}{x_2-x_1}\)

using our set of points, we get the following slope:

\(\frac{0-(-2)}{3-(-1)}=\frac{2}{4}=\frac{1}{2}=0.5\)

The line equation, have the following format:

\(y=mx+B\)

Since we have two points and the slope, we can substitute them in this equation and get the 'b' coefficient.

(We're going to use P1 because the question asks for it, but using P2 it would also work)

\(y=mx+B\Leftrightarrow-2=\frac{1}{2}\times(-1)+B\)

Solving for 'B':

\(-2=-0.5+B\Rightarrow B=-\frac{3}{2}=-1.5\)

With this, we have the following equation for those points:

\(y=0.5x-1.5\)

Question 6:

Solving in an analogous way

Our set of points:

\(\lbrace(-14,-17),(-4,-12)\rbrace\)

The slope m:

\(\frac{(-12)-(-17)}{(-4)-(-14)}=\frac{5}{10}=\frac{1}{2}=0.5\)

Plugging the slope and P1 into the line equation:

\(y=mx+B\Leftrightarrow-17=\frac{1}{2}\times(-14)+B\)

Solving for 'B':

\(-17=-7+B\Rightarrow B=-10\)

Line Equation:

\(y=0.5x-10\)

Question 7:

Solving in an analogous way

Our set of points:

\(\lbrace(0,0),(14,15)\rbrace\)

The slope m:

\(\frac{15-0}{14-0}=\frac{15}{14}=1.07142857143\)

Plugging the slope and P1 into the line equation:

\(y=mx+B\Leftrightarrow0=\frac{14}{15}\times0+B\)

Solving for 'B':

\(0=0+B\Rightarrow B=0\)

Line Equation:

\(y=\frac{14}{15}x\)

What is the mathematical model of an AST for a BL statement?

Answers

The mathematical model of an abstract syntax tree (AST) for a programming language's block (BL) statement typically involves representing the syntax of the statement using a tree structure.

This tree structure consists of nodes that correspond to different components of the statement, such as keywords, variables, operators, and expressions. The AST provides a way to parse and interpret the syntax of the statement, allowing for efficient compilation and execution of the code.

The model can be represented using various algorithms and data structures, such as recursive descent parsing or top-down parsing. Ultimately, the AST serves as a tool for developers to analyze, optimize, and debug their code, and is an essential component of many modern programming languages.

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can
someone answer this for me as soon as possible with the work
Let a be a real valued constant. Find the value of 25a|x dx. 50 It does not exist. 50c

Answers

In both cases, the value of the integral ∫25a|x dx is the same = \(-12.5ax^2\)(when x < 0) + \(12.5ax^2\) (when x ≥ 0).

To find the value of the integral ∫25a|x dx, we need to evaluate the integral with respect to x.

Given that a is a real-valued constant, we can consider two cases based on the value of a: when a is positive and when a is negative.

Case 1: a > 0

In this case, we can split the integral into two separate intervals, one where x is negative and one where x is positive:

∫25a|x dx = ∫(25a)(-x) dx (when x < 0) + ∫(25a)(x) dx (when x ≥ 0)

The absolute value function |x| changes the sign of x when x < 0, so we use (-x) in the first integral.

∫25a|x dx = -25a∫x dx (when x < 0) + 25a∫x dx (when x ≥ 0)

Evaluating the integrals:

= -25a * (1/2)x^2 (when x < 0) + 25a * (1/2)x^2 (when x ≥ 0)

Simplifying further:

= -12.5ax^2 (when x < 0) + 12.5ax^2 (when x ≥ 0)

Case 2: a < 0

Similar to Case 1, we split the integral into two intervals:

∫25a|x dx = ∫(25a)(-x) dx (when x < 0) + ∫(25a)(x) dx (when x ≥ 0)

Since a < 0, the sign of -x and x is already opposite, so we don't need to change the signs of the integrals.

∫25a|x dx = -25a∫x dx (when x < 0) - 25a∫x dx (when x ≥ 0)

Evaluating the integrals:

= -25a * (1/2)x^2 (when x < 0) - 25a * (1/2)x^2 (when x ≥ 0)

Simplifying further

= -12.5ax^2 (when x < 0) - 12.5ax^2 (when x ≥ 0)

In both cases, the value of the integral ∫25a|x dx is the same:

= -12.5ax^2 (when x < 0) + 12.5ax^2 (when x ≥ 0)

So, regardless of the sign of a, the value of the integral is 12.5ax^2.

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X=(5)
2((x)+y=10
2(5)+y=10

Answers

Given:-

\( \rm{x = \bold{ 5 }}\)

\( \: \)

now, put the value in eqⁿ

\( \rm{2(x)+y = 10}\)

\( \: \)

\( \rm{2(5)+y = 10}\)

\( \: \)

\( \rm{10+y = 10}\)

\( \: \)

\( \rm{y = 10-10}\)

\( \: \)

\( \underline{ \boxed{ \rm \bold{ \red{y = 0}}}}\)

\( \: \)

hope it helps!:)

When a process is said to be at six sigma level, what does it
mean? (7 points)"

Answers

Answer:

Step-by-step explanation:  It means a high level of quality, with 3.4 defects per million opportunities. It is this sigma level that leads to the term Six Sigma, which is a philosophy of delivering near perfect products or services by eliminating variabilities that lead to defects.

Describe and correct the error in finding the area of a sector with a radius of 6 centimeters and a central angle of 40

Answers

Answer:

12.56

Step-by-step explanation:

Remark

Since we don't have anything other than the question, all I can do is answer the question. You are left with the task of figuring out the error.

Formula

Area = (central angle divided by 360 ) * pi r^2

Solution

Area = (40 /360) * 3.14 * 6^2

Area = 1/9 * 3.14 * 36

Area = 4 * 3.14

Area = 12.56

Write the equation of this line in point-slope form using the point (1,-3) .

a. y + 1 = (-1/2)(x + 3)

b. y + 1 = (1/2)(x + 3)


c. y + 3 = (1/2)(x - 1)


d. y - 3 = (-1/2)(x - 1)

Answers

Answer:

c. y + 3 = (1/2)(x - 1)

Step-by-step explanation:

Answer:

A. \(y + 1 = (-\frac{1}{2})(x + 3)\)

Step-by-step explanation:

I used a graphing calculator. I prefer Desmos, but you can use whatever you like. I recommend Desmos or GeoGebra.

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Does anyone know this answer??

Does anyone know this answer??

Answers

Answer:

Option (4)

Step-by-step explanation:

Equation of a line passing through a point \((x_1,y_1)\) and with slope 'm' is,

y - y₁ = m(x - x₁)

Given → Slope 'm' = -2

Point through which the line is passing is (-1, -2)

x₁ = -1 and y₁ = -2

Therefore, equation will be,

y + 2 = -2(x + 1)

y = -2x - 2 - 2

y = -2x - 4

Option (4) is the correct option.

find the net change in the value of the function between the given inputs. f(x) = 6x − 5; from 1 to 6

Answers

The net change in the value of the function between x = 1 and x = 6 is 30.

To find the net change in the value of the function between the inputs of 1 and 6, we need to find the difference between the output values of the function at x = 1 and x = 6, and then take the absolute value of that difference.

First, we can find the output value of the function at x = 1:

f(1) = 6(1) - 5 = 1

Next, we can find the output value of the function at x = 6:

f(6) = 6(6) - 5 = 31

The net change in the value of the function between x = 1 and x = 6 is the absolute value of the difference between these two output values:

|f(6) - f(1)| = |31 - 1| = 30

Therefore, the net change in the value of the function between x = 1 and x = 6 is 30.

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There are 3 consecutive integers with a sum of 45. What are the integers?

Answers

The three consecutive integers are 14, 15, and 16.

Assume the three consecutive integers to be x-1, x, and x+1.

Sum of all three = 45.

x-1 + x + x+1 = 45

3x = 45 (-1 and +1 get cancelled)

x = 45/3

x = 15

the first integer is x-1 = 15 - 1 = 14

the second integer is x = 15

the third integer is x+1 = 15 + 1 = 16

So, the three consecutive integers are 14, 15, and 16.

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Solve the simultaneous equations
5 x − y = 8
7 x + 4 y = 22​

Answers

Answer:

Solve the equation by substitution method ;

\(5x - y = 8 \\ y = 5x - 8\)

\(7x + 4y = 22 \\ 7x + 4(5x - 8) = 22 \\ 7x + 20x - 32 = 22 \\ 27x - 32 = 22 \\ 27x = 22 + 32 \\ 27x = 54 \\ \\ x = \frac{54}{27} \\ \\ x = 2\)

\(y = 5x - 8 \\ y = 5(2) - 8 \\ y = 10 - 8 \\ y = 2\)

(x , y ) —> ( 2 , 2 )

I hope I helped you^_^

Answered and solved !!!

You can also use the above method. This is also a similar type method. Please check the attached answer image.

Hope it helps you...

Benjemin.

Happy Studying!!!

Solve the simultaneous equations 5 x y = 8 7 x + 4 y = 22

If f(x) = 0, what is x?

0 only
–6 only
–2, 1, or 3 only
–6, –2, 1, or 3 only

Answers

Answer:

answer will be 0

plz mark me as brainliest

110 +0.70x = 50+ 0.90x​

Answers

Answer:

\( \boxed{ \bold{ \huge{ \boxed{ \sf{x = 300}}}}}\)

Step-by-step explanation:

\( \sf{110 + 0.70x = 50 + 0.90x}\)

Move 0.90x to left hand side and change it's sign

⇒\( \sf{0.70x - 0.90x + 110 = 50}\)

Move 110 to right hand side and change it's sign

⇒\( \sf{0.70x - 0.90x = 50 - 110}\)

Collect like terms

⇒\( \sf{ - 0.2x = 50 - 110}\)

Calculate

⇒\( \sf{ - 0.2x = - 60}\)

Divide both sides of the equation by -0.2

⇒\( \sf{ \frac{ - 0.2x}{ - 0.2} = \frac{ - 60}{ - 0.2} }\)

Calculate

⇒\( \sf{x = 300}\)

Hope I helped!

Best regards!!

what is 4k - 4 = 32

it dont get it

Answers

Answer: K = 8

Step-by-step explanation:

For these kinds of problems you have to isolate the variable, the one we're trying to isolate is k.

First step is adding 4 to both sides to get rid of the -4 on the left.

Once you do that youll have 4k = 36.

Now divide both sides by 4 to get the k by itself, this'll give you k = 8.

You can plug it in to see if it's right.

4(8) - 4 = 32

36 - 4 = 32

32 = 32

So its correct

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