Use the replacement set to find the solution set to the inequality c+5<16 {10,11,12}

Answer:

  (x, y) = (3, -7)

Step-by-step explanation:

You want to solve these equations, -x+y=-10 and 3x+4y=-19, using elimination.

The "elimination" method of solving a system of equations combines the equations in such a way that one of the variables is eliminated. Here, we can eliminate the x-variable by adding 3 times the first equation to the second:

  3(-x+y) +(3x+4y) = 3(-10) +(-19)

  7y = -49 . . . . . . . . . simplify; note x is eliminated from the equation

  y = -7 . . . . . . . . . . . divide by 7

The value of x can be found from the first equation by substituting for y:

  -x +(-7) = -10

  x = 10 -7 = 3 . . . . . . . add x+10 to both sides

The solution to these equations is (x, y) = (3, -7).

The solution is x=3, y = -7

From the question, we have

-x+y=-10 ...........(i)

3x+4y=-19 ..............(ii)

Multiplying equations (i) by 3, we get

-3x+3y=-30................(iii)

Adding both the equation (ii) and (iii), we get,

3x+4y-3x+3y  = -19-30

⇒7y = -49

⇒y = -7

Substituting the value of y in equation (i), we get

-x+y=-10

⇒-x-7=-10

⇒x=3

Elimination Method:

One method for resolving a system of linear equations is the elimination method. In this approach, the equation in one variable is obtained by either adding or subtracting the equations. We can add the equation to delete a variable if its coefficients are the same and have the opposite sign from the other variables. Similar to this, we can subtract the equation to get the equation in one variable if the coefficients of one of the variables are the same and their signs are the same.

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Answer:

4 and 7

Step-by-step explanation:

There are probably several ways to do this but this is how I did it:

First, I listed all the number combinations, that added together equaled 11.

This is what it looked like:

1, 10

2, 9

3, 8

4, 7

5, 6

6, 5

7, 4

I stopped here since the next step would be to double the first number and 8*2 would already be more than 15.

Then, I doubled the first number and added the second number to it, when I saw that didn't equal 15, I eliminated that possibility and moved on to the next set of numbers. When I reached 4, 7 I saw that 4*2 equaled 8 and 8 plus 7 equals 15 so I had the answer.

There are probably much more efficient ways to do this but this is how I did it.

Hope it helped!

The first number is 4 and second number is 7.

Let us consider that first number is x and second number is y.

            \(2x+y=15\\\\x+y=11\)

Substitute \(y=11 - x\)in equation \(2x+y=15\)

        \(2x+11-x=15\\\\x=15-11=4\)

So,   \(y=11-x=11-4=7\)

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The statement "When eliminating a loop-carried dependency that adds a constant, the closed-form direct solution will likely contain a multiplication" is true because eliminating a loop-carried dependency that adds a constant simplifies the equation, but to obtain a closed-form direct solution, we need to express the result as a function of the current iteration's variables only

When eliminating a loop-carried dependency that adds a constant, the closed-form direct solution will likely contain a multiplication. This is because the loop-carried dependency adds a constant to the result of the previous iteration, which means that the current iteration's result is a function of both the current iteration's variables and the previous iteration's result.

By eliminating this dependency, we remove the need to use the previous iteration's result, which simplifies the equation. However, to obtain a closed-form direct solution, we need to express the result as a function of the current iteration's variables only, which often involves a multiplication. This is because multiplication is a fundamental mathematical operation that allows us to combine variables in a way that preserves their individual values.

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True. When eliminating a loop-carried dependency that adds a constant, the closed-form direct solution will likely contain a multiplication. This is because the loop-carried dependency is typically expressed as an addition, and removing it would result in a product of the loop index and the constant.

when eliminating a loop-carried dependency that adds a constant, the closed-form direct solution will likely contain a multiplication. This is because the process often involves applying mathematical transformations that result in multiplications to simplify the loop and eliminate dependencies.

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However, I can explain the process of simplifying the given functions using the Karnaugh Map (K-Map) method and provide you with the minimized SOP and POS forms.

1. For Function 1, we have the following grouped and labeled K-Maps:
  - K-Map for variables a, b, and e (4x4 grid)
  - K-Map for variable d (2x2 grid)
2. To obtain the minimized SOP forms of Function 1, we need to analyze the grouped cells in the K-Maps and write the corresponding Boolean expressions. By applying the K-Map method, we can obtain six possible minimized SOP forms for Function 1.

3. For Function 2, we have the following grouped and labeled K-Maps:
  - K-Map for variables a, b, c, and e (4x4 grid)
  - K-Map for variable d (2x2 grid)
4. To obtain the minimized POS forms of Function 2, we need to analyze the grouped cells in the K-Maps and write the corresponding Boolean expressions. By applying the K-Map method, we can obtain three possible minimized POS forms for Function 2.

Please note that the specific expressions and grouped cells for each function can be obtained by visually examining the K-Maps. It would be best to refer to a resource that allows you to draw and label the K-Maps to get the accurate results for Function 1 and Function 2.

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we have

Multiply in cross

that means

there 4 times 1/8 in 1/2

so

1/8+1/8+1/8+1/8=1/2

Answer:

3 friends ( unless u mean 3/4 instead of 34 then its 2 friends)

Step-by-step explanation:

Answer:

116=1

Step-by-step explanation:

I hope this helps you!

Answer:

D) b = 3, m = -2/3

Step-by-step explanation:

1. The y-intercept, b, is the coordinate where a line intersects with the y-axis.

2. Given the information above, we can easily cross of A and C because they don't have their y-intercept as 3.

3. Now, since this line is going downward (or you can say it's a negative line), it's obviously going to have a slope that's negative.

Answer:

the square of the hypotenuse is 149 squared

Step-by-step explanation:

c= the square root of a^2+b^2=the square root of 7^2+10^2=12.20656

Answer:

There are many options, like:

14/1 or 28/2...

Step-by-step explanation:

First write the system:

(21 x 8) / 12

Then simplify the brackets:

(168) / 12

= 14

Then you can put 14 over 1 as an example of proportionality:

14/1 : (21 x 8) / 12

Or multiply it by 2, 3 etc.:

42/3 : (21 x 8) / 12.

Answer:

Step-by-step explanation:

9

Answer:

One expression for the length of one of the equal sides

is x = (934 - 214) / 2.

Step-by-step explanation:

The perimeter is the sum of the 3 sides of the triangle.

Let the length of one of the equal sides be x cm

So, we have:

2x + 214 = 934

2x = 934 - 214 = 720

x = 720 /2 = 360 cm.

Answer:

median: 44

first quartile: 25

third quartile: 61.5

interquartile range: 36.5

Step-by-step explanation:

For the given data set median is 44, first quartile is 25, third quartile is 61.5 and interquartile range is 36.5.

The Interquartile Range (IQR) formula is a measure of the middle 50% of a data set. The smallest of all the measures of dispersion in statistics is called the Interquartile Range. The difference between the upper and lower quartile is known as the interquartile range.

Formula to find the interquartile range is Interquartile range = Upper Quartile - Lower Quartile =Q2=Q3-Q1

The given date set is 28,46,25,76,18,25,47,83,44.

The data in order 18,25,25,28,44,46,47,76,83.

Here,

Median =44

First quartile=Q₁=25

Third quartile=Q₃= (47+76)/2

= 61.5

Now, interquartile range (IQR)

= Q₃-Q₁

= 61.5-25

= 36.5

Therefore, for the given data set median is 44, first quartile is 25, third quartile is 61.5 and interquartile range is 36.5.

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Answer:

------------------

25 minutes is 10 times the 2 1/2 = 2.5 minutes.

Therefore David would swim 10 times greater distance in 25 minutes:

The matching choice is B.

Answer:

option C

Step-by-step explanation:

hope this help u

Answer:

Below.

Step-by-step explanation:

First check if the function will factor. If so it is quickly solved this way.

Secondly, if it won't factor you can either use Completing the Square or the quadratic formula. I have troubling remembering the formula so I use completing the square.

There are 4 different methods to solve a quadratic equation Factoring, using square roots, completing the square, and the quadratic formula are the four ways to solve a quadratic problem.

A quadratic equation is an algebraic expression in the form of variables and constants.

A quadratic equation has two roots as its degree is two.

Factoring, using square roots, completing the square, and the quadratic formula are the four ways to solve a quadratic problem.

If you have a parabola's vertex shape or a parabola-like curve from a data collection, this is a useful visual tool. You may locate the point at which the quadratic function f(x) = ax² + bx + c intersects the x-axis by graphing it.

Factoing In some situations, employing this method can be advantageous over graphing, solving squares, or applying the quadratic formula. However, some quadratics are challenging to factor, and in those situations, the quadratic formula might be more useful.

Completing the square is lengthy, but it is effective. This procedure can be streamlined by using the quadratic formula. Additionally, the square approach is used to convert several circle equations into their correct form.

Qudratic formula method always works.  It is derived from using the previous method (complete the square) on a general quadratic in standard form: ax² + bx + c = 0.  The only drawback is that the calculations can become tedious, as they involve multiplication, addition, radicals, and division.

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a) A ⊕ B in hexadecimal is 0xd1520a1c3c3b3d9d. b) The probability is 1 is 1/2. c) the probability is 1/4.

a) To calculate the XOR (⊕) of two hexadecimal numbers A and B, we perform a bitwise XOR operation on each corresponding pair of digits.

Given A = 0xdf495f4d7475a088 and B = 0x0b270551bb6fedd5, the XOR operation can be performed as follows:

A ⊕ B = 0xdf495f4d7475a088 ⊕ 0x0b270551bb6fedd5

Calculating the XOR of each pair of corresponding digits, we get:

A ⊕ B = 0xd1520a1c3c3b3d9d

Therefore, A ⊕ B in hexadecimal is 0xd1520a1c3c3b3d9d.

b) Since A was generated uniformly at random from all 8-byte strings, each bit has an equal probability of being 0 or 1.

The probability that the second binary digit of A is 1 is 1/2, as there are two possible values (0 or 1) and each value has an equal probability.

c) To calculate the probability that the second binary digit of AB is 1, we need to consider the XOR operation on the corresponding bits of A and B.

Observing the XOR operation, we can see that the second binary digit of AB will be 1 only if one of the bits in A and B is 1 and the other is 0. This occurs with a probability of 1/2 * 1/2 = 1/4.

Therefore, the probability that the second binary digit of AB is 1 is 1/4.

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Answer:

x= -7

Step-by-step explanation:

the labeled angles are alternate-interior angles which are congruent

we can solve for 'x' by creating this equation:

x+139 = 132

x = -7

Equation in slope-intercept form for the required line which passes through (-2, 2) and perpendicular to  y= -5x-8 is equal to y = 5x+12.

As given in the question,

Line passes through the point ( -2, 2)

Required line is perpendicular to the given line y = -5x -8.

Let the point by ( x₁ , y₁) = ( -2, 2)

Standard equation of line is

y =mx +c

Slope = m

Slope of given line is -5

Lines are perpendicular

Slope of required line is 5

Required equation in slope-intercept form is:

y -2 =5(x-(-2))

⇒ y -2 = 5x +10

⇒ y= 5x +12

Therefore, equation in slope-intercept form for the required line which passes through (-2, 2) and perpendicular to  y= -5x-8 is equal to

y = 5x+12.

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Using the Laplace transform, the solution to the given initial value problem y" - 4y - 60y = 0; y(0) = 12, y'(0) = 24 y(t) is "y(t) = 6e^(8t) + 6e^(-8t)."

To use the Laplace transform to solve the given initial value problem, we need to follow these steps:

1. Apply the Laplace transform to both sides of the equation. Recall that the Laplace transform of the derivative of a function is given by sF(s) - f(0), where F(s) is the Laplace transform of f(t). Similarly, the Laplace transform of the second derivative is s^2F(s) - sf(0) - f'(0).

Taking the Laplace transform of the given equation, we have:

s^2Y(s) - sy(0) - y'(0) - 4Y(s) - 60Y(s) = 0

Substituting the initial values y(0) = 12 and y'(0) = 24, we get:

s^2Y(s) - 12s - 24 - 4Y(s) - 60Y(s) = 0

2. Combine like terms and rearrange the equation to solve for Y(s):

(s^2 - 4 - 60)Y(s) = 12s + 24

Simplifying further, we have:

(s^2 - 64)Y(s) = 12s + 24

3. Solve for Y(s) by dividing both sides of the equation by (s^2 - 64):

Y(s) = (12s + 24) / (s^2 - 64)

4. Decompose the right side of the equation into partial fractions. Factor the denominator (s^2 - 64) as (s - 8)(s + 8):

Y(s) = (12s + 24) / ((s - 8)(s + 8))

Using partial fractions decomposition, we can write Y(s) as:

Y(s) = A / (s - 8) + B / (s + 8)

where A and B are constants to be determined.

5. Solve for A and B by equating numerators:

12s + 24 = A(s + 8) + B(s - 8)

Expanding and rearranging the equation, we get:

12s + 24 = (A + B)s + (8A - 8B)

Comparing the coefficients of s on both sides, we have:

12 = A + B        (equation 1)
0 = 8A - 8B       (equation 2)

From equation 2, we can simplify it to:

A = B

Substituting this result into equation 1, we get:

12 = 2A

Therefore, A = 6 and B = 6.

6. Substitute the values of A and B back into the partial fractions decomposition:

Y(s) = 6 / (s - 8) + 6 / (s + 8)

7. Take the inverse Laplace transform of Y(s) to find the solution y(t):

y(t) = 6e^(8t) + 6e^(-8t)

Therefore, the solution to the given initial value problem y" - 4y - 60y = 0; y(0) = 12, y'(0) = 24 y(t) is:

y(t) = 6e^(8t) + 6e^(-8t)

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The solution to the equation is x = 105/14 and y = -27/2

Simultaneous equations are two or more algebraic equations with the same unknown variables and the same value of the variables satisfies all such equations. This implies that the simultaneous equations have a common solution.

We use different methods to solve simultaneous equations. Some of the common methods are:

By substitution method

-7x + -5y = 15 ----- 1

7x + 3y = 12 ----- 2

from equation 1

7x = -15 -5y ----- 3

substitute 7x in equation 2

-15 - 5y + 3y = 12

-2y = 12 + 15

-2y = 27

y = -27/2

To find x, substitute y in equation 3

7x = -15 - 5(-27/2)

7x = -15 + 135/2

Multiplying both sides by 2

14x = -30 + 135

14x = 105

x = 105/14

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The fraction is 47/200. The decimal is 0.235.

A percentage can be written in a fraction form by putting 100 on the denominator. For example, the fraction corresponding to x % is x/100.

For converting a percentage into a decimal first it should be converted into fractions as fractions can only be converted into decimal.

For example, the decimal for the fraction 50% is 0.5, which is given by writing 50% as 50/100 = 0.5 after putting decimal on 2 places left to 50.

So here the given percentage is 23.5%.

The corresponding fraction is 23.5/100 = 235/1000 = 47/200 after eliminating the decimal on the numerator and simplifying.

Now the corresponding decimal is, 0.235. Since 1000 is in the denominator for 235/1000, we can simply find the decimal by putting decimal point on 3 places left to 235.

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Answer:

yes 15cm is 3cm more than 12cm

Step-by-step explanation:

Answer:

118.3

Step-by-step explanation:

The formula for the area is a triangle is base*height/2

Area = 18.2*13/2 = 118.3

Answer:

118.3

1/2b×h

1/2(13)x18.2

6.5×18.2

118.3m^2

Answer:

|x| = –15

– |–x| = 9

– |x| = 12

The equation of the transformed exponential function g(x) is g(x) = 2^-x - 1

From the question, we have the following parameters that can be used in our computation:

Parent function: y = 2^x

The graph of the transformed exponential function g(x) passes through the points  (-2,3), (-1,1), (0,0), (1,-0.5) and (2, -0.75)

So, we have the following transformation steps:

1st Transformation:

Reflect y = 2^x across the y-axis

So, we have

y = 2^-x

2nd Transformation:

Translate y = 2^-x down by 1 unit

So, we have

y = 2^-x - 1

This means that

g(x) = 2^-x - 1

Hence, the equation of the function g(x) is g(x) = 2^-x - 1

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