The slope of the line shown on the
graph below is

Your answer is below.

4.9

The solution of the Venn diagram are represented below.

a. A = {4, 14, 8, 1, 12, 18, 6, 10}

b. B = {9, 15, 12, 18, 6}

c. (A ∪ B)' ∩ C = {5}

d. n{A ∪ B ∪ C}' =  {7, 11, 19, 17, 13}

e. A ∩ C = {6, 10}

f. n (A ∩ B ∩ C) =  {7, 11, 19, 17, 13}

A picture using circles or closed curves to illustrate mathematical or logical sets, and the intersections of the circles represent the shared components of the sets.

The given Venn Diagram represent the elements A, B and C.

a.

A = All elements shown in circle A,

A = {4, 14, 8, 1, 12, 18, 6, 10}

b.

B = All elements shown in circle B,

B = {9, 15, 12, 18, 6}

c.

(A ∪ B)' ∩ C

A ∪ B = Elements which are present in A and B,

A ∪ B = {4, 14, 8, 1, 12, 18, 6, 10, 9, 15}

(A ∪ B)' = remaining elements from A ∪ B.

(A ∪ B)' = {7, 11, 19, 17, 13, 5}

(A ∪ B)' ∩ C =  elements present in (A ∪ B)' and C

                    = {5}

d.

The union combines all the values in set. and ' shows the remaining values.

n{A ∪ B ∪ C}' =  {7, 11, 19, 17, 13}

e.

A ∩ C = values common in A and C,

A ∩ C = {6, 10}

f.

n (A ∩ B ∩ C) =  {7, 11, 19, 17, 13}

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9514 1404 393

Answer:

  (13.06, 16.41)

Step-by-step explanation:

Any point not on a perpendicular bisector of the line between towns will be closer to one town than the other. So, the intersection of perpendicular bisectors will be the equidistant from all towns. That point is the circumcenter of the circle circumscribing the triangle with the towns as its vertices. This can be found as the intersection of two perpendicular bisectors of the segments between the towns.

The midpoint of AB is ...

  (A +B)/2 = ((15, 3) +(25, 10))/2 = (40, 13)/2 = (20, 6.5)

The midpoint of AC is ...

  (A +C)/2 = ((15, 3) +(0, 20))/2 = (15, 23)/2 = (7.5, 11.5)

__

The differences between points are ...

  B -A = (25, 10) -(15, 3) = (10, 7)

  C -A = (0, 20) -(15, 3) = (-15, 17)

Then the perpendicular bisector equations can be written as ...

  bisector of AB  ⇒  10(x -20) +7(y -6.5) = 0

     10x +7x -245.5 = 0

  bisector of AC  ⇒  -15(x -7.5) +17(y -11.5) = 0

     -15x +17y -83 = 0

These have coefficients that aren't particularly nice, so a method similar to Cramer's Rule is suitable for solving this pair of equations. Using the "cross multiplication method", we have ...

  x = (7(-83) -17(-245.5))/(10(17) -(-15)(7)) = 3592.5/275 = 13 7/110 ≈ 13.06

  y = (-245.5(-15) -(-83)(10))/275 = 4512.5/275 = 16 9/22 ≈ 16.41

The point as far as possible from each town within the boundary of the island has coordinates (13.06, 16.41).

_____

Further detail regarding the solution

Here, we have written the equation for the perpendicular bisector this way. The difference in coordinates between points R and S can be called ...

  R -S = (∆x, ∆y)

The midpoint of segment RS can be called ...

  (R +S)/2 = (h, k)

Then the line that is a perpendicular bisector of RS can be written as ...

  ∆x(x -h) +∆y(y -k) = 0

This is the form that is used above.

__

The "cross multiplication method" for solving a pair of general-form linear equations ...

  ax +by +c = 0

  dx +ey +g = 0

will give the solution as ...

  1/(ae -db) = x/(bg -ec) = y/(cd -ga)

If you write the coefficients in two rows of four, the pattern of products and differences is easy to see.

  \(\left[\begin{array}{cccc}a&b&c&a\\d&e&g&d\end{array}\right]\)

Answer:

sum of five and 3 is divided by n

Answer:

5

Step-by-step explanation:

2 negatives always equal a positive.

We have to convert 4 1/3 into a improper fraction which is 13/3. Since we know 2 negatives equal a positive, we add both fractions. 13/3 + 2/3 ewuals 15/3 which equals 5.

If you take the point on the bridge directly beneath the lowest point on the cable to be the origin, then the parabola has equation

\(y = ax^2+bx+10\)

300 ft to either side of the origin, the parabola reaches a value of y = 90, so

\(a(300)^2+b(300)+10 = 90 \implies 4500a+15b = 4\)

\(a(-300)^2+b(-300)+10 = 90 \implies 4500a-15b = 4\)

Adding these together eliminates b and lets you solve for a :

\((4500a+15b)+(4500a-15b)=4+4 \\\\ 9000a = 8 \\\\ a = \dfrac1{1125}\)

Solving for b gives

\(4500\left(\dfrac1{1125}\right)+15b=4 \\\\ 4+15b = 4 \\\\ 15b=0 \\\\ b=0\)

So the parabola's equation is

\(y = \dfrac{x^2}{1125}+10\)

150 ft away from the origin, the cable is at a height y of

\(y = \dfrac{150^2}{1125}+10 = \boxed{30}\)

ft above the bridge.

Answer:

20

Step-by-step explanation:

617/28=  22 (rounded too)

617/32= 19 ( rounded too)

19-22 is teh amount of classes that can be filled with 28 to 32 students.

20 is correct because it is around the amount of classes that there can be. !4 is too little so the number of students should be smaller.

30 and 60 classes are to big. there would only be about 10 or 20 kids per class

Answer:

17th term

Step-by-step explanation:

For some nth term, both series have same term. So,

6n - 21 = 4n + 13

Subtract 4n from both sides

6n - 4n - 21 = 13

  2n - 21 = 13

Add 21 to both sides

2n = 13+21

2n = 34

Divide both sides by 2

n = 34/2

n = 17

Check:

6n - 21 = 6*17 - 21 = 102 - 21 = 81

4n + 13 = 4*17 + 13 = 68 + 13 = 81

17th term both the series is 81

Answer:

The answer is n = 17

Step-by-step explanation:

You first have to substitute a number for n. You put in a number and calculate. If the 2 are not equal, then it is not correct. When you substitute 17,

4(17) + 13 = 81. 6(17) - 21 = 81.

Because of this, 17 would be the correct term for n.

We are given the graph of a line and asked to find its equation. Recall that we can write the equation of a line as

where (x0, y0) is point on the line and m is the slope of the line.

From the graph, we can identify that points (-3, -2) and (5,4) are on the line. Now let us calculate the slope of the line.

Recall that given points (a,b) and (c,d), the slope of the line that passes through them is given by the formula

In our case we got a=-3, b=-2, c=5 and d=4. So we have

Now, we can use the fact that the point (5,4) is on the line. So we use it as our (x0,y0). So our equation would be

which is equivalent to

Now, we add 4 on both sides, so we get

so the equation of the line is

AnswerAnwser key

Step-by-step explanation:

Answer:

1) -6

2) -8

3) 125185623/1000000000 ( i didn't really understand this one but i hope i got it right)

4) 1

5) 0.94736842

6) 4/5 = 5/4

I can only do up to there for now .... sorry

but i can do the second part in a few mins.

Step-by-step explanation:

i really hope this is right....

Step-by-step explanation:

just multiply 7.6g times 10

The optimal solution is Z = -74, X = 4, Y = 2.

Maximize Z = 20X + 3Y

Subject to:

A1: 2X + Y + S1 = 10

R2: 3X + 3Y + S2 = 18

R3: 2X + 4Y + S3 = 20

X = 0, Y ≥ 0

The initial tableau for the simplex method is given below.

The column labels represent the variables, and the row labels represent the equations and slack variables. The bottom row (RHS) represents the right-hand side values of the equations.

To find the optimal solution, we'll perform the simplex method iterations:

Iteration 1:

Pivot column: Y (the most negative coefficient in the Z row)

Pivot row: S2 (smallest positive ratio of RHS to coefficient in the pivot column)

Performing row operations:

Divide row S2 by 3 to make the pivot element (coefficient of Y) equal to 1.

Row S2 = Row S2 / 3

Row S2: 1 | 1 | 0 | 1/3 | 0 | 6

Eliminate other elements in the pivot column:

Row Z = Row Z - (3 * Row S2)

Row S1 = Row S1 - (1 * Row S2)

Row S3 = Row S3 - (0 * Row S2)

Row Z: 20 | 0 | 0 | -3 | 0 | -18

Row S1: 1 | 0 | 1 | -1/3 | 0 | 4

Row S3: 2 | 1 | 0 | -2/3 | 1 | 14

Iteration 2:

Pivot column: X (the most negative coefficient in the Z row)

Pivot row: S1 (smallest positive ratio of RHS to coefficient in the pivot column)

Performing row operations:

Divide row S1 by 1 to make the pivot element (coefficient of X) equal to 1.

Row S1 = Row S1 / 1

Row S1: 1 | 0 | 1 | -1/3 | 0 | 4

Eliminate other elements in the pivot column:

Row Z = Row Z - (20 * Row S1)

Row S2 = Row S2 - (0 * Row S1)

Row S3 = Row S3 - (2 * Row S1)

Row Z: 0 | 0 | -20 | -2/3 | 0 | -74

Row S2: 1 | 1 | 0 | 1/3 | 0 | 6

Row S3: 0 | 1 | -2 | -2/3 | 1 | 6

Since there are no negative coefficients in the Z row, we have reached the optimal solution.

Final Solution:

Z = -74 (maximum value of the objective function)

X = 4

Y = 2

S1 = 0

S2 = 6

S3 = 6

Therefore, the maximum value of Z is -74, and the optimal values for X and Y are 4 and 2, respectively. The slack variables S1, S2, and S3 are all zero, indicating that all the constraints are satisfied as equalities.

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E = midpoint

DF = DE + EF

but, DE = EF because E is the midpoint

Substitution

9x - 10 = 92 + 92

Simplification

9x - 10 = 184

9x = 184 + 10

9x = 194

x = 194/9

x = 21.55

\( \huge\mathbb\orange{ANSWER} \)

\( \mathsf \purple{6x + 9 = 45}\)

\( \mathsf \pink{6x + 9 - 9 = 45 - 9}\)

\( \mathsf \purple{6x = 36}\)

\( \mathsf \pink{ \frac{6x}{6} = \frac{36}{6} }\)

\( \mathsf \purple{x = 6}\)

\( \mathbb\orange{Hope\: It\: Helps} \)

#13

#14

\(\\ \sf\longmapsto AB=\sqrt{(10-2)^2+(9-3)^2}\)

\(\\ \sf\longmapsto AB=\sqrt{8^2+6^2}\)

\(\\ \sf\longmapsto AB=\sqrt{10^2}\)

\(\\ \sf\longmapsto AB=10\)

#15

\(\\ \sf\longmapsto MN=\sqrt{(5-4)^2+(5+2)^2}\)

\(\\ \sf\longmapsto MN=\sqrt{1^2+7^2}\)

\(\\ \sf\longmapsto MN=\sqrt{1+49}\)

\(\\ \sf\longmapsto MN=\sqrt{50}\)

\(\\ \sf\longmapsto MN=5\sqrt{2}\)

Answer:

i hope it helped U ❤️❣️❤️❣️

A rhombus with MK = 24 m, JL = 20, ∠MJL = 50°. So, NK = 24 m, NL = 24.8 m, ML = 24.8 m, and JM = 20 m.

We need the information about the measurements or a description of the missing measures in the rhombus. We can make it MK = 24 m, JL = 20, ∠MJL = 50° for example. Since it's a rhombus, all sides are equal in length. Therefore, NK = MK = 24 m, JM = JL = 20 m, and ML = NL.

To find ML (or NL), we can use the Law of Cosines on the triangle MJL. In this case,

ML² = JM² + JL² - 2(JM)(JL)cos(∠MJL):

ML² = 20² + 20² - 2(20)(20)cos(50°)

ML² = 400 + 400 - 800cos(50°)

ML² ≈ 617.4

Taking the square root of both sides, we get ML ≈ √617.4 ≈ 24.8 m.

So, NK = 24 m, NL = 24.8 m, ML = 24.8 m, and JM = 20 m.

The complete question is The quadrilateral below is a rhombus. Given MK = 24 m, JL = 20, ∠MJL = 50°. Find NK, NL, ML, and JM. Any decimal answers should be rounded to the nearest tenth.

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Answer:

5.

Objective C

\(125x + 200 \geqslant 1200 \\ 125x \geqslant 1000 \\ x \geqslant 8\)

7

\(x \: \alpha \: y \\ y = kx \\ 2.00 = k \times 8 \\ k = \frac{2.00}{8} \\ k = 0.25\)

Answer:

Vertical angles are always congruent.

Step-by-step explanation:

Vertical angles are formed when two straight lines intersect each other, thereby forming two pairs of opposite angles, which are called vertical angles. Thus, a pair of these vertical angles formed are congruent to each other. So therefore, if two angles are said to be vertical angles, it follows that they are congruent to each other.

Using the diagram attached below, we can see two straight lines intersecting each other to form two pairs of vertical angles:

<a and <b,

<c and <d.

Thus, <a is congruent to <b, and <c is congruent to <d.

Therefore, the standby that is true about vertical angles is that:

Vertical angles are always congruent.

The ratio of the number of female attendants to the number of male attendants is 21/17

let

900 = 1200x + 800y / (x + y)

900x + 900y = 1200x + 800y

900x + 1200x = 800y + 900y

2100x = 1700y

x : y = 2100 / 1700

x : y = 21 ; 17

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Answer:

The answer is 5. Your best bet is honestly to count the spaces until they meet in the middle. The midpoint formula gets confusing on number lines.

Answer:

Step-by-step explanation:

You want to make 5.4 in three different ways.

You can add, subtract, multiply, or divide numbers to obtain a result of 5.4:

  2.9 +2.5 = 10.0 -4.6 = 2.0×2.7 = 10.8÷2 = 5.4

  √29.16 = ∛157.464 = 5.4

  \(\displaystyle\sum_{n=1}^\infty{10.8(3^{-n})}=5.4\)

Binding constraints directly influence the optimal solution in a linear Programming problem, whereas constraints with positive slack are non-binding and do not directly impact the solution.

binding constraints and positive slack in the context of linear programming. In a linear programming problem, we aim to find the optimal solution for an objective function, given a set of constraints. The terms "binding constraints" and "positive slack" are related to these constraints.

1. Binding constraints: These are constraints that directly impact the optimal solution of the problem. In other words, they "bind" the feasible region (the area where all the constraints are satisfied) and affect the maximum or minimum value of the objective function. Binding constraints are active constraints, as they influence the final solution.

2. Positive slack: Slack is the difference between the left-hand side and right-hand side of a constraint when the constraint is satisfied. If this difference is positive, it means that there is some "extra" or "unused" resource in that constraint. Positive slack indicates that the constraint is non-binding, meaning it does not directly impact the optimal solution. It shows that there is some room for the constraint to be further tightened without affecting the final outcome.

In summary, binding constraints directly influence the optimal solution in a linear programming problem, whereas constraints with positive slack are non-binding and do not directly impact the solution. Knowing the difference between these terms can help you better understand and analyze linear programming problems.

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Sοlving the equatiοn we get x=7

In mathematics an equatiοn is a mathematical statement which is built by twο expressiοns cοnnected by an equal ('=')sign. Fοr example, 3x – 8 = 16 is an equatiοn. Sοlving this equatiοn, we get the  x = 8.

Given that,

3/x²= x-4/3x² +2/x²

Tο sοlve the given equation  at first we will take LCM of the denominator of RHS

⇒ \(\frac{3}{x^{2} }\)=\(\frac{x-4+6}{3x^{2} }\)

⇒\(\frac{3}{x^{2} }\) = \(\frac{x+2}{3x^{2} }\)

By crο ss multiplicatiοn we get,

  x+2= 9

Subtracting 2 frοm both sides of equation we get

  x= 9-2

 x=7

Hence sοlving the equation we get x=7

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Answer:

If you start at 0, 51.  If you start with 2, 50.

Step-by-step explanation:

The amount of numbers that will be said are simply 100/2 which is 50 since counting by two is the same as the amount of even numbers up to 100.  If you start at 0, simply add an additional count, making 51.

Cheers.

Answer:

1, 2 and 3  (I, II and III)

Step-by-step explanation:

Since the slope is positive (3) in the equation y = 3x + 1, it means that the graph has a positive slope, meaning the line slopes up from left to right.

The y intercept is 1

the x intercept is:  

0 = 3x + 1

x = 1/3

Therefore, the graph of y = 3x + 1 lies in quadrants I, II and III.  Graph the equation to prove this.  

Answer:

the reciprocal of 0.25 is 4.