Which of the following binomials is a factor of 22 + 7 −9 ?
A. − 3
B. + 1
C. 2 − 3
D. 2 + 9

Answer:

To determine whether (1, 5) is a solution of a given system, you need to substitute these values into the equations of the system and check whether the resulting statements are true.

For example, if the given system is represented by the equations y = 2x + 1 and y = x - 3, then you would substitute 1 for x and 5 for y in each equation and check whether the resulting statements are true.

Substituting these values into the first equation, we get:

5 = 2(1) + 1

5 = 2 + 1

5 = 3

This statement is not true, so (1, 5) is not a solution of this system.

On the other hand, if the given system is represented by the equations y = 2x + 1 and y = 5, then substituting the values (1, 5) into both equations would result in true statements, so (1, 5) would be a solution of this system.

I hope this helps! Let me know if you have any more questions.

Step-by-step explanation:

So there are 6 permutations possible with the letters "ABC". These are: ABC, ACB, BAC, BCA, CAB, CBA.

Permutations are a way of arranging objects in a specific order. The number of permutations of a set of n distinct objects is given by n!, where n! denotes the factorial of n.

In the case of the letters "ABC", there are three distinct objects: A, B, and C. Therefore, the number of permutations possible with these letters is:

3! = 3 x 2 x 1 = 6

This means that there are 6 possible ways of arranging the letters "ABC" in a specific order. These permutations are:

ABC

ACB

BAC

BCA

CAB

CBA

To see why there are 6 possible permutations, consider the first position. There are three letters to choose from, so there are three possible choices for the first position. Once the first letter is chosen, there are two letters left to choose from for the second position. Finally, there is only one letter left to choose from for the third position. Therefore, the total number of permutations is:

3 x 2 x 1 = 6

In summary, the number of permutations of a set of n distinct objects is given by n!, and in the case of the letters "ABC", there are 3! = 6 possible permutations: ABC, ACB, BAC, BCA, CAB, and CBA.

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Finite-state machines for given inputs: (a) 0s multiple of 3: 3-state machine. (b) At least four 1s: 4-state machine. (c) Exactly one 1: 2-state machine. (d) Begins with 000: 3-state machine. (e) Second is 0, fourth is 1: 4-state machine. (f) 01 pairs or 2 1s + 0s: 3-state machine. (g) Ends in 110: 3-state machine.

To construct finite-state machines that act as recognizers for the given inputs, we can follow these guidelines:

(a) For the set of all strings where the number of 0s is a multiple of 3, we can use a finite-state machine with three states. Start with the initial state, and transition to the next state whenever a 0 is encountered. After three transitions, go back to the initial state. If the machine ends in the accepting state, output 1.
(b) For the set of all strings containing at least four 1s, we can use a finite-state machine with four states. Start with the initial state, and transition to the next state whenever a 1 is encountered. If the machine enters the final state after four transitions, output 1.

(c) For the set of all strings containing exactly one 1, we can use a finite-state machine with two states. Start with the initial state and transition to the final state when the first 1 is encountered. Output 1 only if the final state is reached.

(d) For the set of all strings beginning with 000, we can use a finite-state machine with three states. Start with the initial state and transition to the next state whenever a 0 is encountered. If the machine reaches the final state after three transitions, output 1.

(e) For the set of all strings where the second input is 0 and the fourth input is 1, we can use a finite-state machine with four states. Start with the initial state and transition to the next state based on the inputs. Output 1 only if the machine reaches the final state.

(f) For the set of all strings consisting entirely of any number (including none) of 01 pairs or consisting entirely of two 1s followed by any number (including none) of 0s, we can use a finite-state machine with three states. Start with the initial state and transition based on the inputs. Output 1 only if the final state is reached.

(g) For the set of all strings ending in 110, we can use a finite-state machine with three states. Start with the initial state and transition based on the inputs. Output 1 only if the final state is reached.

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Finite-state machines (FSMs) can be constructed to act as recognizers for specific patterns in input strings. These are examples of how to construct FSMs as recognizers for different patterns in input strings. Each FSM is designed to produce an output of 1 when the input received matches the description provided.

Let's consider the given cases and construct FSMs for each one.

(a) The set of all strings where the number of Os is a multiple of 3:
To construct an FSM for this, we can keep track of the number of Os encountered so far. Initially, set the count to zero. When an O is encountered, increment the count by one. If the count becomes a multiple of 3, the FSM outputs 1; otherwise, it outputs 0. Reset the count to zero whenever a 1 is encountered.

(b) The set of all strings containing at least four 1s:
To create an FSM for this, we can keep track of the number of 1s encountered so far. Initially, set the count to zero. When a 1 is encountered, increment the count by one. If the count becomes equal to or greater than four, the FSM outputs 1; otherwise, it outputs 0.

(c) The set of all strings containing exactly one 1:
To build an FSM for this, we can have two states: a "no 1 encountered" state and a "1 encountered" state. Initially, start in the "no 1 encountered" state. Whenever a 1 is encountered, transition to the "1 encountered" state. If another 1 is encountered in the "1 encountered" state, transition to a third "more than one 1 encountered" state. In this case, the FSM outputs 0. Otherwise, if no additional 1s are encountered, the FSM outputs 1.

(d) The set of all strings beginning with 000:
To create an FSM for this, start in an initial state. When a 0 is encountered, transition to a second state. If two consecutive 0s are encountered in the second state, transition to a third state. Finally, if a third 0 is encountered in the third state, the FSM outputs 1; otherwise, it outputs 0.

(e) The set of all strings where the second input is 0 and the fourth input is 1:
To construct an FSM for this, start in an initial state. When the first input is read, transition to a second state. In the second state, transition to a third state if the second input is 0. In the third state, transition to a fourth state if the third input is not 0. Finally, in the fourth state, if the fourth input is 1, the FSM outputs 1; otherwise, it outputs 0.

(f) The set of all strings consisting entirely of any number (including none) of 01 pairs or consisting entirely of two Is followed by any number (including none) of Os:
To create an FSM for this, we can have multiple states to represent different scenarios. We start in an initial state and transition to a second state when a 0 is encountered. In the second state, transition back to the initial state if a 1 is encountered. If a 1 is encountered in the initial state, transition to a third state. In the third state, transition to a fourth state if an O is encountered. Finally, if an O is encountered in the fourth state, the FSM outputs 1; otherwise, it outputs 0.

(g) The set of all strings ending in 110:
To construct an FSM for this, start in an initial state. Transition to a second state if a 1 is encountered. In the second state, transition to a third state if a 1 is encountered again. Finally, if a 0 is encountered in the third state, the FSM outputs 1; otherwise, it outputs 0.

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The correct answer to a linear formulation is option a) the objective function and all constraints must be linear

A linear formulation refers to a mathematical model in which both the objective function and all constraints are expressed in linear terms. This means that the relationships between variables are represented by linear equations, or equations of the form ax + b = c, where a, b, and c are constant values and x is the variable.

The main advantage of linear formulation is that linear problems can be solved efficiently using linear programming techniques, which are well-established and widely used in various fields.

In conclusion, in a linear formulation, all variables and coefficients must be linear, and the relationships between variables are expressed as linear equations.

Therefore, The correct answer to a linear formulation is option a) the objective function and all constraints must be linear

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Answer:

y=5x

.-.-.-.

jhvghcfghvbkhhx

Answer:

D

Step-by-step explanation:

You find the slope by doing \(\frac{y_{2}-y_{1} }{x_{2}-x_{1}}\)

The slope is 5

Since the given values for np and nq are not suitable for the normal approximation (np < 5 or nq < 5), we cannot estimate P(fewer than 5) using the normal approximation.

In summary, we can use the normal approximation to estimate P(fewer than 5) when np > 5 and nq > 5.

To estimate P(fewer than 5), we can use the normal approximation to the binomial distribution by considering the mean (μ) and standard deviation (σ) of the binomial distribution. For a binomial distribution with parameters n and p, the mean is given by μ = np and the standard deviation is given by σ = √(npq).

In this case, n = 13 and p = 0.6, so np = 7.8 and nq = 5.2. Since both np and nq are greater than 5, we can proceed with the normal approximation.

To estimate P(fewer than 5), we can use the cumulative distribution function (CDF) of the normal distribution with parameters μ = np and σ = √(npq). We calculate P(X < 5) using the normal distribution and round the result to four decimal places:

P(fewer than 5) = P(X < 5) ≈ Φ((5 - μ) / σ)

Calculating the z-score as (5 - μ) / σ and using the standard normal distribution table or a calculator, we can find the corresponding probability value. However, since the given values for np and nq are not suitable for the normal approximation (np < 5 or nq < 5), we cannot estimate P(fewer than 5) using the normal approximation.

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The left turn departure sight distances for a passenger car taking a left turn from the minor road to the major road is 121.275

Here we given that a 2 lane highway with a grade of 6% has a posted speed limit of 50 mph and a design speed of 55mph. the minor road approach grade is -1.5%.

And we need to find the left turn departure sight distances for a passenger car taking a left turn from the minor road to the major road.

While we looking into the given question we have identified that the following are the values given in the problem,

=> Speed limit = 50 mph

=> design speed = 55mph

=> grade = -1.5%

As per the length of the sight triangle leg or ISD along the major road is

determined using the following equation:

=> ISD = 1.47 V t

=> ISD = 0.278 V t

Where:

ISD refers length of sight triangle leg along major road, ft (m)

V refers design speed of major road, mph (km/h)

t refers time gap for minor road to enter the major road, sec

When we apply the value, then we get,

=> ISD = 1.47 x 55 x  -1.5

=> ISD = -121.275

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Answer:

51

Step by-step explanation:

Dimes are .10 each so how many ,10's are in 5.10?

Answer:

\((x-2)(x-3)\)

Step-by-step explanation:

\(x^2-5x+6\)

\(x^2-3x-2x+6\)

\(x(x-3)-2(x-3)\)

\((x-2)(x-3)\)

0.00809

Step-by-step explanation:

1000 is divided in 8.09

That is why the answer is 0.00809

Answer: To minimize the time taken by the woman to reach point C, she should minimize the total distance traveled, which is the sum of the distance she walks and the distance she rows.

Let's call point B the point where the woman switches from walking to rowing. We can find the location of point B by drawing a straight line from A to the center of the lake, and then continuing that line on the other side of the lake to point C. Point B is the point where this line intersects the circle of the lake.

Since the radius of the lake is 4, the distance from A to the center of the lake is also 4. Therefore, the distance from A to B is also 4. The distance from B to C is also 4, since C is diametrically opposite to A.

Let's call the distance that the woman rows from B to C d. Then the distance that she walks from A to B is 4 - d.

The time taken to walk a distance of (4 - d) miles is:

t1 = (4 - d) / 10

The time taken to row a distance of d miles is:

t2 = d / 5

The total time taken is:

T = t1 + t2 = (4 - d) / 10 + d / 5

Simplifying, we get:

T = (8 + d) / 20

To minimize T, we need to find the value of d that minimizes (8 + d) / 20. We can do this by taking the derivative of (8 + d) / 20 with respect to d and setting it to 0:

d(T) / d(d) = 1/20

Setting this to 0, we get:

1/20 = 0

This is obviously not true, so there is no minimum value of T. However, we can see that as d gets larger, T gets larger, and as d gets smaller, T gets smaller. Therefore, the minimum value of T occurs at one of the endpoints of the interval [0, 4]. Since d cannot be negative, the only endpoint we need to consider is d = 4.

When d = 4, the woman rows the entire distance from B to C, and does not need to walk at all. Therefore, the total time taken is:

T = (8 + 4) / 20 = 0.6 hours

Therefore, the woman should walk to point B, and then row the rest of the way to point C, to arrive in the shortest possible time.

Step-by-step explanation:

Answer:

Rs 140

Step-by-step explanation:

Rs 25 is the amount of money she bought the apples

Rs 32 is the amount of money she sold the apples

32 - 25 = $7 profit per apple

7 Rs multiplied by 20 apples is equal to Rs 140 in profit.

Hope this helps!

Answer:

A=0.2

b=0.2 x 0.7=0.14

0.45 x 0.2=0.09

0.44

c=112

Step-by-step explanation:

On a graph, the absolute value of a number is always non-negative.

The absolute value of a number is defined as the distance of that number from zero on the number line. Since the distance can never be negative, the absolute value of a number is always non-negative.

This is reflected in the graph of an absolute value function. The graph of an absolute value function, |x| is a V-shape that opens upward, with the vertex of the V being the point where the absolute value function equals zero. The two arms of the V extend out from this point, going in opposite directions along the number line. The coordinates of the vertex (0,0) and the graph is always non-negative.

It's important to note that although the absolute value is always non-negative on a graph, the input value (x) can be both positive and negative. The output of the absolute value function (|x|) will always be positive.

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Answer:

hope it helps mark me brainlieast!

Step-by-step explanation:

For triangle ABC with sides  a,b,c  labeled in the usual way,

c2=a2+b2−2abcosC  

We can easily solve for angle  C .

2abcosC=a2+b2−c2  

cosC=a2+b2−c22ab  

C=arccosa2+b2−c22ab  

That’s the formula for getting the angle of a triangle from its sides.

The Law of Cosines has no exceptions and ambiguities, unlike many other trig formulas. Each possible value for a cosine maps uniquely to a triangle angle, and vice versa, a true bijection between cosines and triangle angles. Increasing cosines corresponds to smaller angles.

−1≤cosC≤1  

0∘≤C≤180∘  

We needed to include the degenerate triangle angles,  0∘  and  180∘,  among the triangle angles to capture the full range of the cosine. Degenerate triangles aren’t triangles, but they do correspond to a valid configuration of three points, namely three collinear points.

The Law of Cosines, together with  sin2θ+cos2θ=1 , is all we need to derive most of trigonometry.  C=90∘  gives the Pythagorean Theorem;  C=0  and  C=180∘  give the foundational but often unnamed Segment Addition Theorem, and the Law of Sines is in there as well, which I’ll leave for you to find, just a few steps from  cosC=  … above. (Hint: the Law of Cosines applies to all three angles in a triangle.)

The Triangle Angle Sum Theorem,  A+B+C=180∘ , is a bit hard to tease out. Substituting the Law of Sines into the Law of Cosines we get the very cool

2sinAsinBcosC=sin2A+sin2B−sin2C  

Showing that’s the same as  A+B+C=180∘  is a challenge I’ll leave for you.

In Rational Trigonometry instead of angle we use spreads, squared sines, and the squared form of the formula we just found is the Triple Spread Formula,

4sin2Asin2B(1−sin2C)=(sin2A+sin2B−sin2C)2  

true precisely when  ±A±B±C=180∘k , integer  k,  for some  k  and combination of signs.

This is written in RT in an inverted notation, for triangle  abc  with vertices little  a,b,c  which we conflate with spreads  a,b,c,  

(a+b−c)2=4ab(1−c)  

Very tidy. It’s an often challenging third degree equation to find the spreads corresponding to angles that add to  180∘  or zero, but it’s a whole lot cleaner than the trip through the transcendental tunnel and back, which almost inevitably forces approximation.

Answer:

370

Step-by-step explanation:

510 times 2 is 1020 - cost for 2 diamond and 2 silver

1300-1020 is 280 - cost for remaining 2 silver

280 divided by 2 = 140 - cost for each silver

510-140 is cost for 1 dimond = 370

Answer:

136.6 m per second squared

Step-by-step explanation:

acceleration = change in velocity×time

= 26.8×5.1

=136.6 m per sec squared

Answer:

Red Line

m = 1/2

b = 1

Blue Line

m = 1

b = -1

Green Line

m = 3

b = 0

Step-by-step explanation:

First off, we need to know what m and b are first.

m is the slope

b means y-intercept, or, when x is 0

And to find slope use "m = y2 - y1/x2 - x1" (remember, Rise over Run, not Run over Rise!)

Red line: if you count it, you get a point on the line each time you go up once and to the right twice. We can use Rise over run. Rise is y, or its name, go up, which is the 1. then the run which is 2. So, the slope is 1/2 or m = 1/2. and we can see that the y-intercept is 1. m = 1/2, b = 1

Blue Line: This is pretty much the same as the red line, see the slope it's rise once and run once so, the slope is 1/1 which is 1. Then the y-intecept is b which is when x is 0, we check the y-axis line and we see that the y-intercept is -1. m = 1, b = -1

Green Line: And once again, the same as Red Line and Blue Line, the slope is 3. Rise is 3 times, run is once, so, 3/1 which is 3. While the y-intercept is 0 since it is on (0,0). Meaning that it goes through the origin. m = 3, b = 0

Answer:110.5inches2

Step-by-step explanation:

to find the area of a triangle use the formula 1/2(base times height) where in this case  base is 17 and height is 13. applying this formula= 1/2(17x13)=1/2(221)=110.5inches2

The area of sector FGH is approximately 354.69 square units.

We are given that m∠FGH is 102 degrees, and FG is 18 units. We can use this information to find the radius of the circle, which is the distance from the center of the circle to any point on the boundary. To do this, we first need to draw a diagram and label the parts.

In the diagram, O is the center of the circle, FG is a chord of the circle, and GH is an arc of the circle. We are given that m∠FGH is 102 degrees, so m∠FO is half of that, or 51 degrees. Since FO is perpendicular to FG, we can use trigonometry to find the length of FO, which is the radius of the circle.

We know that the sine of an angle is the opposite side divided by the hypotenuse, so:

sin(51) = FG / FO

FO = FG / sin(51)

FO ≈ 22.15

Now that we know the radius of the circle, we can use the formula for the area of a sector:

Area of sector = (angle / 360) x π x r²

In this case, the angle is 102 degrees, so:

Area of sector FGH = (102 / 360) x π x (22.15)²

Area of sector FGH ≈ 354.69 square units

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Answer:

Step-by-step explanation:

Siny= 4xy +x²

dy/dx(cos y) =4y+ 4x(dy/dx)+2x

making dy/dx the subject

dy/dx(cos y)-4x(dy/dx)=4y+2x

dy/dx(cos y -4x)=4y+2x

dy/dx=(4y+2x)/(cos y -4x)

I don't say you have to mark my ans as brainliest but if it has really helped u plz don't forget to thank me....

1. The outcomes in the sample space of choosing a letter from the word STARK are: S, T, A, R, K.

2. Number of outcomes in the sample space = 6 (from THANKS) × 5 (from STARK) = 30.

3. The Probability of choosing the letters AA is 0, as there are no occurrences of the letter A in both words together.

1. The outcomes in the sample space of choosing a letter from the word THANKS are: T, H, A, N, K, S.

  The outcomes in the sample space of choosing a letter from the word STARK are: S, T, A, R, K.

2. To find the number of outcomes in the sample space, we multiply the number of outcomes for each word.

  Number of outcomes in the sample space = Number of outcomes for the first word × Number of outcomes for the second word

  Number of outcomes in the sample space = 6 (from THANKS) × 5 (from STARK) = 30.

3. The probability of choosing the letters AA would be the number of favorable outcomes (which is 0 in this case) divided by the total number of outcomes in the sample space.

  Probability of choosing AA = Number of favorable outcomes / Total number of outcomes

  Probability of choosing AA = 0 / 30 = 0.

Therefore, the probability of choosing the letters AA is 0, as there are no occurrences of the letter A in both words together.

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700 * 25/100 = 175

SP = MP - Discount

SP = 700 - 175

SP = $525

Answer: 3

Step-by-step explanation:

\(Formula: \frac{y2 - y1}{x2 - x1}\)

Plug the numbers into the formula:

\(\frac{-6 - -3}{5-4}\) -> \(\frac{-6+3}{5-4}\\\)

Reduce:

\(\frac{3}{1} = 3\)

Answer:

-3

Step-by-step explanation:

the answer is -3

hope this helps

The equation of the line perpendicular to the tangent to the curve y=x^3-4x+1 at the point (2,1) is y = (-1/8)x + 9/8.

To find the equation of the line perpendicular to the tangent to the curve at (2,1), we need to first find the slope of the tangent line at that point.

The derivative of y=x^3-4x+1 is y'=3x^2-4, so the slope of the tangent line at (2,1) is y'(2) = 3(2)^2-4 = 8.

Since we want the line perpendicular to the tangent, we know that its slope will be the negative reciprocal of the tangent's slope. Therefore, the slope of the line we're looking for is -1/8.

Next, we use the point-slope form of the equation of a line to write the equation of the line with the slope we found and passing through the point (2,1):

y - 1 = (-1/8)(x - 2)

Simplifying and putting the equation in slope-intercept form:

y = (-1/8)x + 9/8

Therefore, the equation of the line perpendicular to the tangent to the curve y=x^3-4x+1 at the point (2,1) is y = (-1/8)x + 9/8.

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Answer:

R5 290

VAT is =15

\( \frac{15}{100} \times \frac{4600}{1} \)