This is 9th-grade math

Answer:

The square root of 120 is 10.9544512 :)

Answer:

a = -2

Step-by-step explanation:

7a + 10 = 2a​

subtract 2a from both sides

5a + 10 = 0

subtract 10 from both sides

5a = -10

divide both sides by 5

a = -2

hope this helps

For the first problem, there are no feasible solutions. In the second problem, the optimal solution is x₁ = 0, x₂ = 0, x₃ = -10, with the minimum value of Z = -30.


To demonstrate that the first problem has no feasible solutions using the Big M method and the simplex method, we will first convert the problem into standard form. The standard form of a linear programming problem involves converting all inequalities into equations and introducing slack, surplus, and artificial variables as needed.
1. Convert the inequalities to equations:
2x₁ + x₂ + s₁ = 2  (Constraint 1)
X₁ - x₂ - s₂ = 2    (Constraint 2)
X₁, x₂, s₁, s₂ ≥ 0
2. Introduce artificial variables and a big M:
Z = 90x₁ + 70x₂ - M(a₁ + a₂)  (Objective function)
2x₁ + x₂ + s₁ + a₁ = 2     (Constraint 1)
X₁ - x₂ - s₂ + a₂ = 2     (Constraint 2)
X₁, x₂, s₁, s₂, a₁, a₂ ≥ 0
3. Set up the initial simplex tableau:
       | 2x₁  |  x₂  | s₁ | s₂ | a₁ | a₂ | RHS |
Z       | -90  | -70  |  0 |  0 |  M |  M |  0  |
S₁      |   2  |   1  |  1 |  0 |  1 |  0 |  2  |
S₂      |   1  |  -1  |  0 | -1 |  0 |  1 |  2  |


4. Identify the pivot column (entering variable):
The most negative coefficient in the Z row is -90, so x₁ will enter the basis.
5. Identify the pivot row (leaving variable):
To determine the pivot row, calculate the ratio of the RHS to the positive coefficients in the entering column. Choose the smallest nonnegative ratio.
Ratios:
S₁: 2/2 = 1
S₂: 2/1 = 2
The smallest ratio is 1, so the pivot row is s₁.

6. Perform the pivot operation:
Divide the pivot row by the pivot element (1) to make the pivot element equal to 1:
       |  x₁  |   x₂   | s₁ |  s₂ |  a₁ |  a₂ | RHS |
Z       | -90  |  -70   |  0 |  0  |  M  |  M  |  0  |
X₁      |   1  |  0.5   |0.5 |  0  |0.5  |  0  |  1  |
S₂      |   1  |  -1    |  0 | -1  |  0  |  1  |  2  |

Perform row operations to make all other entries in the pivot column equal to zero:
       |  x₁  |   x₂   |  s₁ |  s₂ |  a₁ |  a₂ | RHS |
Z       |   0  |  15    | -90 |  0  | -45 |  90 | -90 |
X₁      |   1  |   0    |  1  |  0  |  1  |  0  |

 2  |
S₂      |   0  |  -2    | -1  | -1  | -0.5|  1  |  0  |

7. Check for optimality:
Since there are negative coefficients in the Z row, the current solution is not optimal. We need to continue iterating.
8. Repeat steps 4-7 until an optimal solution is reached:
The next pivot column is x₂ (coefficient: 15).
The next pivot row is s₂ (ratio: 0/(-2) = 0).
Perform the pivot operation:
       |  x₁  |  x₂  |  s₁ |  s₂ |  a₁ |  a₂ | RHS |
Z       |   0  |  0   | -90 |  15 | -75 |  75 | -180|
X₁      |   1  |  0   |  1  | -0.5| 0.5 | -0.5| 1   |
X₂      |   0  |  1   |  0  | -0.5| -0.5|  0.5| 0   |

The coefficients in the Z row are now nonnegative, but the artificial variables (a₁ and a₂) remain in the basis. This indicates that the original problem is infeasible since the optimal value of the objective function is negative.
Therefore, the first problem has no feasible solutions.

Now, let’s solve the second problem using the Big M method and the simplex method.
1. Convert the inequalities to equations:
-x₁ + x₂ + s₁ = 10    (Constraint 1)
2x₁ - x₂ + x₃ + s₂ = 10   (Constraint 2)
X₁, x₂, x₃, s₁, s₂ ≥ 0
2. Introduce artificial variables and a big M:
Z = 3x₁ + 2x₂ + 7x₃ + M(a₁ + a₂)   (Objective function)
-x₁ + x₂ + s₁ + a₁ = 10   (Constraint 1)
2x₁ - x₂ + x₃ + s₂ + a₂ = 10   (Constraint 2)
X₁, x₂, x₃, s₁, s₂, a₁, a₂ ≥ 0
3. Set up the initial simplex tableau:
       | -x₁ |  x₂  | x₃ | s₁ | s₂ | a₁ | a₂ | RHS |
Z       |  -3 |  -2  | -7 |  0 |  0 |  M |  M |  0   |
S₁      |  -1 |   1  |  0 |  1 |  0 |  1 |  0 |  10  |
S₂      |   2 |  -1  |  1 |  0 |  1 |  0 |  1 |  10  |

4. Identify the pivot column (entering variable):
The most negative coefficient in the Z row is -7, so x₃ will enter the basis.
5. Identify the pivot row (leaving variable):
Calculate the ratio of the RHS to the positive coefficients in the entering column. Choose the smallest nonnegative ratio.
Ratios:
S₁: 10
/1 = 10
S₂: 10/1 = 10
Both ratios are the same, so we can choose either. Let’s choose s₁ as the pivot row.
6. Perform the pivot operation:
Divide the pivot row by the pivot element (1) to make the pivot element equal to 1:
       | -x₁ |  x₂ |  x₃  | s₁ |  s₂ | a₁ | a₂ | RHS |
Z       |  -3 | -2  | -7   |  0 |  0  |  M |  M |  0   |
S₁      |  -1 |  1  |  0   |  1 |  0  |  1 |  0 |  10  |
S₂      |   2 | -1  |  1   |  0 |  1  |  0 |  1 |  10  |

Perform row operations to make all other entries in the pivot column equal to zero:
       | -x₁ |  x₂ |  x₃  |  s₁ |  s₂ | a₁ | a₂ | RHS |
Z       |   0 |  3  | -7   |   3 |  0  | -3 |  0 | -30  |
X₃      |   1 | -1  |  0   |  -1 |  0  | -1 |  0 | -10  |
S₂      |   0 | -3  |  1   |   2 |  1  |  2 |  1 |  30  |

7. Check for optimality:
Since there are no negative coefficients in the Z row, the current solution is optimal.
9. Read the solution:
The optimal solution is:
X₁ = 0
X₂ = 0
X₃ = -10
S₁ = 10
S₂ = 30
A₁ = 0
A₂ = 0
The minimum value of Z is -30.
Therefore, the second problem is feasible and has an optimal solution with x₁ = 0, x₂ = 0, x₃ = -10, and Z = -30.

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The surface area of the given square pyramid would be = 22.44 cm².

To calculate the surface area of the square pyramid the formula given below is used:

Surface area = a²+ 2al

where a² = area of base = (3²)= 9cm

a = side of base= 3cm

l = slant height. = 2.24cm

Surface area = 9+2(3×2.24)

= 9+ 2(6.72)

= 9+ 13.44

= 22.44 cm²

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The variables for the tree diagram involving the probabilities in this problem are given as follows:

A probability is calculated as the number of desired outcomes divided by the number of desired outcomes.

For nodes a and b, they are relative to the first ball, hence:

If the first ball is green, 6 out of the remaining 9 balls are green and the probabilities of the second ball are given by nodes c and d, as follows:

If the first ball is not green, 7 out of the remaining 9 balls are green and the probabilities of the second ball are given by nodes e and f, as follows:

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Answer:

.31

Step-by-step explanation:

Answer:

78.4

Step-by-step explanation:

9.8*8

=78.4 bags of leaves

Answer:

Step-by-step explanation:

15 - x = 3x + 3

15 - x = 3•x + 3

4x = 12

x = 3

Sorry, I change the b and a into x's if that's fine with you.

Answer:

18.8%

Step-by-step explanation:

For calculating this, focus on one part of the table :

There are 32 students who do not like sandwiches, and 6 of them do not like pies. Take this a proportion :

Students who don't like sandwiches also don't like pie is the 2 nd box on 2 nd line

Probability

Option D

The triangle's vertices will therefore be A'(4, 6), B'(0, 0), and C'(-2,4) if it is mirrored across the y-axis and then dilated by a scale factor of 2.

The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller). For instance, we can increase the size of a rectangle with sides of 2 cm and 4 cm by multiplying each side by, let's say, 2.

Given

In line with the posed question.

Triangle ABC's vertices are A(-2, 3), B(0, 0), and C. (1, 2).

As we are aware,

The x-coordinates of each point must be negative while keeping the y-value constant in order to reflect a triangle over the y axis.

As a result, when triangle ABC is mirrored across the y-axis, its vertices are

A'(2,3)

B'(0, 0)

C'(-1, 2)

The vertices of the triangle will also change when it is dialated by a scale factor of 2.

A'(4, 6)

B'(0, 0)

And, C'(-2, 4)

The triangle's vertices will therefore be A'(4, 6), B'(0, 0), and C'(-2,4) if it is mirrored across the y-axis and then dilated by a scale factor of 2.

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There are 8 different trips that can be made from City X to City Z, passing through City Y.

To find the number of different trips that can be made from City X to City Z, passing through City Y, we can use the multiplication principle of counting.

First, we need to choose one of the 2 major roads from City X to City Y. Then, for each of these roads, there are 4 major roads from City Y to City Z, and we need to choose one of these roads.

By the multiplication principle of counting, the total number of different trips from City X to City Z, passing through City Y, is the product of the number of choices at each stage. Thus, we get:

Number of different trips = Number of roads from City X to City Y x Number of roads from City Y to City Z

= 2 x 4

= 8

This calculation shows how the multiplication principle of counting can be used to find the total number of possible outcomes in a multi-stage process where the number of choices at each stage is known.

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Complete question is:

Automobile Trips. There Are 2 Major Roads From City X To City Y And 4 Major Roads From City Y To City Z. How Many Different trips can be made from City X to City Z, passing through City Y?

Answer:

6.45

Step-by-step explanation:

I am not staring at zero.  I am starting at 6.4, so I take 6.4 and add that to half way between 6.5 and 6.4.

6.4 + 1/2(6.5-6.4)  Combine in the parentheses

6.4 + 1/2(.5)  Take half of .5

6.4 + .05  add

6.45

Answer:

A.

Line

Step-by-step explanation:

In geometry a straight line is defined as the shortest distance between any two given points. Using the concept of locus, a Line is defined as the locus of all points that are equidistant from two given points.

On the other hand, the locus definition of a circle is the locus of a point that moves at a fixed distance from a center point. This fixed distance is called the radius of the circle.

Answer:

its proportional

Step-by-step explanation:

Answer:

x = -5 and x = 1

Step-by-step explanation:

4( x2 + 4x + 4 ) = 36

4x2 + 16x + 16 = 36

4x2 + 16x - 20 = 0

x2 + 4x - 5 = 0

Answer:

C. x = -5, and x = 1

Step-by-step explanation:

You have the equation 4(x + 2)2 = 36

You then isolate 4 out of the equation using division on both sides

You are left with (x+2)2 = 9

Next, take square roots

\(\sqrt({x} +2) ^{2}\) = \(\sqrt{9}\)

This leaves you with x + 2 ± 9

So, x = -2 + 3 = 1

or

x = -2 - 3 = -5

Answer:

72

Explanation:

First, we can find the top and bottom smaller squares of the rectangular prism. Since we are working with a variety of rectangles, we only need to use the equation L×W.

To start with, let's multiply 2×3, which gives us 6, the surface area of both the bottom and top rectangles, so now we need to multiply it by 2 to account for both of them. 6×2=12

Now, we'll find the surface area of the bigger rectangles in the middle, which are 6 by 3, so again we will need to multiply length times width, then by 2 to count both rectangles. 6×3=18×2=36

Finally, we can find the surface area of the smaller rectangles in the middle, which are 6 by 2. 6×2=12, then multiply by 2 since there are 2 of those rectangles, 12×2=24

Now to find the total surface area, we need to add the gathered surface area from each shape, 12+36+24=72

Answer:

ur answer is 199 thank me later

Answer:

194 ft²

Step-by-step explanation:

Area of rectangle R1 = length * width

                                  = 8 * 5

                                  = 40  square feet

Area of rectangle R2 = 14 * 11

                                    = 154 square feet

Area of the figure = 40 + 154 = 194 ft²

Answer: Option C.

Step-by-step explanation:

Ok, first, a linear function is something of the shape of:

y = a*x + b.

And the graph of those functions is a line, as the name implies, so we can discard that option.

So this must be a non-linear function, you can see that is a function because each value of x has only one value of y related to it.

Second, in a Venn diagram you will see that the set of functions is contained into the set of relationships, this means that all the functions are relationships, but not all the relationships are functions, and we know that this is a non-linear function, so this also must be a relationship.

Then the correct option is C, nonlinear, and a relationship.

As we have proved that the line created works exclusively with the three points by justifying how the x-value and y-value fit into the equation for the line.

Let's start by defining what a linear function is. A linear function is an equation of the form y = mx + b, where m is the slope of the line and b is the y-intercept. The slope represents the rate of change of the line, and the y-intercept represents the value of y when x is equal to zero. To create a linear function, we need two points on the line.

Now, let's create another linear function using points B and C:

slope (m) = (y₂ - y₁) / (x₂ - x₁) = (6 - 4) / (5 - 3) = 1

y-intercept (b) = y - mx = 4 - 1 * 3 = 1

Therefore, the linear function that passes through points B and C is also y = x + 1. We can check if point A lies on this line by substituting its x and y values into the equation:

2 = 1 + 1

This is true, so point A lies on the line created by points B and C. Therefore, we have also proved that the line created works exclusively with these three points.

In conclusion, we have created two linear functions using three points and proved that they work exclusively with those three points.

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The probability they choose all democrats is 0.01805

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

Republicans = 11

Democrats = 8

Number of selections = 4

If the selected people are all democrats, then we have

P = P(Democrats) * P(Democrats | Democrats) in 4 places

using the above as a guide, we have the following:

P = 8/19 * 7/18 * 6/17 * 5/16

Evaluate

P = 0.01805

Hence, the probability they choose all democrats is 0.01805

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Answer:

14

Step-by-step explanation:

-6+x=1

8

-6+x=1×8

x=8+6

x= 14 ans

Answer:

The equation is y= 0.08 x+55

Step-by-step explanation:

Let's use total cost y= Variable cost + fixed cost.

Here fixed cost =$55

And variable cost  for each minute =0.08

That's variable cost for x minutes =0.08

So, total cost y=0.08 x+55

The slope of the line passing through the points (-5, -4) and (-13, 2) is -3/4.

Slope is simply expressed as a change in y over the change in x.

It is expressed as

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

Given the points:
(-5, -4) and (-13,2)​

Point (-5, -4):

x₁ = -5

y₁ = -4

Point (-13,2)​:

x₂ = -13

y₂ = 2

Plug the given x and y values into the slope formula and simplify.

\(m = \frac{y_2 - y_1}{x_2 - x_1}\\\\m = \frac{2 - (-4)}{-13 - (-5)}\\\\m = \frac{2 + 4}{-13 + 5}\\\\m = \frac{6}{-8}\\\\m = -\frac{3}{4}\)

Therefore, the slope of the line is -3/4.

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The solutions to the equation x(0) = sin(tx) are not even, as the sine function is an odd function, not an even function.

To show that solutions to x 0 = sin(tx) are even, we need to demonstrate that f(-x) = f(x), where f(x) = sin(tx).

First, let's evaluate f(-x):

f(-x) = sin(t(-x))

Using the property of sine function, we can rewrite this as:

f(-x) = -sin(tx)

Now let's evaluate f(x):

f(x) = sin(tx)

We can see that f(-x) = -f(x), which means that f(x) is an odd function.

However, we want to show that f(x) is an even function. To do this, we need to show that f(x) = f(-x).

Substituting the value of f(-x) in f(x) we get:

f(x) = -sin(tx)

f(-x) = -sin(tx)

We can see that f(x) = f(-x), which means that f(x) is an even function.

Therefore, we have shown that solutions to x 0 = sin(tx) are even.
Hi! To show that the solutions to the equation x(0) = sin(tx) are even, we'll examine the properties of the sine function.

Given the equation x(0) = sin(tx), we want to demonstrate that sin(tx) is even, meaning that sin(tx) = sin(-tx). This can be shown by using the properties of sine and even functions.

Recall that an even function f(x) satisfies the property f(x) = f(-x) for all x in its domain.

Now, consider the sine function sin(-tx). Using the oddness property of sine, we can rewrite this as sin(-tx) = -sin(tx). Since sin(tx) = -sin(-tx), we can see that the sine function does not satisfy the even function property.

Therefore, the solutions to the equation x(0) = sin(tx) are not even, as the sine function is an odd function, not an even function.

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An essential concept in mathematics and can be applied to a variety of fields such as physics, economics, and engineering.

The slope of a line in a Cartesian plane is a numerical representation of its steepness and inclination relative to the x-axis.

The slope of a straight line refers to the rise or fall of the y-coordinate as it moves from left to right along the x-axis.

There are a few different ways to interpret the slope of a line, but generally it can be thought of as the rate at which the dependent variable changes with respect to the independent variable.
When the slope is positive, the line rises from left to right, indicating that the dependent variable is increasing as the independent variable increases.

In other words, there is a direct relationship between the two variables.

Conversely, when the slope is negative, the line falls from left to right, indicating that the dependent variable is decreasing as the independent variable increases.

This means that there is an inverse relationship between the two variables.
The magnitude of the slope can also provide information about the relationship between the variables.

If the slope is close to zero, then the relationship between the two variables is weak or nonexistent.

However, if the slope is large in magnitude (i.e. close to 1 or -1), then there is a strong relationship between the variables.

A slope of zero indicates that there is no change in the dependent variable as the independent variable changes, while a slope of undefined means that the line is vertical and has no slope.
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Answer:

9(x - 5)

Step-by-step explanation:

Just write the equation according to the sentence. It's THAT SIMPLE.

Answer:

d

Step-by-step explanation:

Answer:

2 2/3

Step-by-step explanation:

we know that the kg in each bag is 2 2/3

Answer:

this is the answer ( x,y ) = ( -7,-3 )