On a piece of paper graph y = 2x-4 then determine which answers
matches the graph you drew

The Wronskian of the functions y1​=7x and y2​=2x is W(x) = 0. The functions y1​=7x and y2​=2x are linearly dependent. None of the given options satisfy the condition c1​y1​+c1​y2​=0.

The Wronskian (or Wrońskian) is a determinant introduced by Józef Hoene-Wroński (1812) and named by Thomas Muir (1882, Chapter XVIII). It is used in the study of differential equations, where it can sometimes show linear independence in a set of solutions.

The Wronskian of two functions y1​ and y2​ is defined as the determinant of the matrix [y1​, y2​; y1′​, y2′​], where y1′​ and y2′​ are the derivatives of y1​ and y2​ with respect to x. In this case, the functions are y1​=7x and y2​=2x, and their derivatives are y1′​=7 and y2′​=2. Evaluating the determinant, we get W(x) = |7x, 2x; 7, 2| = 0.

Since the Wronskian is zero for all values of x, the functions y1​=7x and y2​=2x are linearly dependent. This means that one function can be written as a scalar multiple of the other. In this case, y2​=2x is twice y1​=7x. None of the given options satisfy the condition c1​y1​+c1​y2​=0, so the correct statement is that the functions y1​=7x and y2​=2x are linearly dependent.

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Answer:

42

Step-by-step explanation:

substitute x = 7 into f(x)

f(x) = 6x = 6 × 7 = 42

42 lightbulbs are needed for 7 chandeliers

The volume of a sphere with a radius of 7 cm (or diameter of 12 cm) is 904.32 cubic centimeters.

To find the volume of a sphere with a radius of 7 cm, we can use the formula:

V = (4/3) * π * r^3

where V represents the volume and r represents the radius. However, you mentioned that the diameter of the sphere is 12 cm, so we need to adjust the radius accordingly.

The diameter of a sphere is twice the radius, so the radius of this sphere is 12 cm / 2 = 6 cm. Now we can calculate the volume using the formula:

V = (4/3) * π * (6 cm)^3

V = (4/3) * 3.14 * (6 cm)^3

V = (4/3) * 3.14 * 216 cm^3

V = 904.32 cm^3

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Answer: y = 6x

Step-by-step explanation:

Since this is a direct proportion, we will introduce the constant of proportionality here and this will be:

y = kx

Since y = 30 and x= 5,

30 = 5 × k

30 = 5k

k = 30/5

k = 6

Therefore, the equation that connects y to x will be:

y = kx

y = 6x

The equation that connects y to x is y = 6x.

Answer:  8.94 is the length of GI

Step-by-step explanation: The two triangles are similar, so the ratios of the sides to each other will be the same.

the unknown length of GI in triangle FIG corresponds to the known length 20 of IH in Triangle GIH, and the known length 4 of side FI in triangle FIG corresponds to GI in Triangle GIH. So the ratio looks like 4:x as x:20

4/x = x/20  multiply both sides by x and 20 to "cancel" the denominators.

20x(4/x) = 20x(x/20)

80 = x²    Calculate the square roots  

√x² = x . √80 = 8.94

Answer:

The Answer is 5

Step-by-step explanation:

Pink beads : White beads

30 : 35

( 30 / 5 ) : ( 35 / 5 )

6 : 7

To find the number of beads, You divide the number of pink beads available by the number of pink beads in the ratio:

= 30 / 6

= 5 necklaces

hope this helps :)

a) Diminishing returns start at x = 1,  where the marginal revenue will be less than the marginal cost

b)At x = 1, the company will earn R(1) = -32 + 6 + 18 + 4 = -4,000 dollars.

c) 0 ≤ x ≤ 25 implies that the Coffee Junction company has the capacity to spend a maximum of 25,000 dollars per month on advertisements.

a) At what level of advertising spending does diminishing returns start?

Diminishing returns refers to a situation when the marginal return on investment decreases as more resources are devoted to it. For instance, in case of Coffee Junction, increasing the advertising expenditure may lead to higher revenue, but the marginal revenue (revenue generated by each additional dollar spent) will gradually decrease.

b) How much revenue will the company earn at that level of advertising spending?

At x = 1, the company will earn R(1) = -32 + 6 + 18 + 4 = -4,000 dollars.

c) What does 0≤x≤25 tell us with respect to this problem?

In this problem, 0 ≤ x ≤ 25 implies that the Coffee Junction company has the capacity to spend a maximum of 25,000 dollars per month on advertisements.

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Answer:

8978.9

Step-by-step explanation:

MULTIPLY THE THE GIVEN AND

8.89  ×  1010 = 8978.9

THEN THE RESULT WOUD BE THE STANDARD NOTATION.

Ensuring that all rows impacted by the actions of a transaction are protected from changes until the entire transaction is completed is called "transaction isolation" or "atomicity."

Transaction isolation refers to the property of database transactions that ensures that a transaction appears to occur all at once, without any interference or changes from other concurrent transactions. It guarantees that the effects of a transaction are isolated and not visible to other transactions until the transaction is successfully completed and committed.

By enforcing transaction isolation, database systems maintain data integrity and prevent inconsistent or partial updates caused by concurrent transactions. It ensures that the changes made by a transaction are either applied in their entirety or not at all, providing a reliable and consistent view of the data to the users.

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Answer:

x = 76°

Step-by-step explanation:

76° and x are alternative interior angles, so they are congruent when lines a and b are parallel

Answer: y+6x = -34

Step-by-step explanation:

y-2= -6(x+6)                              (Ax+By=C is the goal)

y-2= -6x-36  (-6) x & (-6) 6

y=-6x-34 (Add 2 to both sides)

y+6x = -34   [Add 6x to both sides]

a) To simplify 4²×4-³, we can rewrite it as (4²)/(4³). Now, using the properties of exponents, we know that 4² is equal to 16 and 4³ is equal to 64. Therefore, the expression simplifies to 16/64, which can be further reduced to 1/4.

b) In (a²b ¹)² × (a ¹8¹), we can simplify the exponents by applying the power of a power rule. This gives us a²² × a⁸. Now, we can combine the terms with the same base by adding the exponents, resulting in a³⁰.

c) The expression (x-¹²2)+(0)³ can be simplified by evaluating the exponent of 0, which is always 0. Therefore, the expression simplifies to x-¹²2 + 0, which further simplifies to x-¹²2.

In summary, the simplified expressions are:
a) 1/4
b) a³⁰
c) x-¹²2

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The second data set represents the boxplot because in the box plot the measure of statistics is the same as the data set option second is correct.

A box and whisker plot is a method of abstracting a set of data that is approximated using an interval scale. It's also known as a box plot. These are primarily used to interpret data.

We have given a data set and a box plot shown in the picture.

From the boxplot we can see:

Minimum value = 2

Q1 = (2+4)/2 = 3

Median = (4+6)/2 = 5

Q3 = (8+10)/2 = 9

Maximum value = 10

The second data set:

{2, 3, 3, 4, 5, 5, 8, 10, 10}

Minimum value = 2

Q1 = (2+4)/2 = 3

Median = (4+6)/2 = 5

Q3 = (8+10)/2 = 9

Maximum value = 10

Thus, the second data set represents the boxplot because in the box plot the measure of statistics is the same as the data set option second is correct.

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Answer:  not sure. but as long as he saves his money wisely and doesn't spend frivilously

Step-by-step explanation:

Two triangles are congruent by Angle Angle Side (AAS). So the required option is AAS ( Angle Angle Side ).

If all three sides and all three angles of two triangles are equal, the triangles are said to be congruent. To make these triangles appear the same, they can be moved around, rotated, flipped, and turned. If they are moved, they will align. Triangles that are congruent share the same sides and angles. It is possible to determine whether two triangles are congruent using four congruency criteria. As a result, only three of the six variables may be used to assess if two triangles are congruent. Congruence in mathematics refers to the similarity between two figures based on their size and shape.

As in given figure,

one angle is equal and,

one sides is equal.

As one line intersects the other ,

So both the angles are equal ( By vertically opposite angles)

Hence, by Angle Angle Side (AAS)

Both are congruent to each other.

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Answer: b because I need more pints

Step-by-step explanation:

It might not be the write answer I guessed

Answer:

yp its d

Step-by-step explanation:

the equation for the level surface passing through the point (3, 0, 1) is x + 2y - 3z = 0. The given function is f(x, y, z) = (x - y + 2z) / (2x + y - z). We are asked to find an equation for the level surface passing through the point (3, 0, 1).

To find the equation for the level surface, we need to set the function equal to a constant value and solve for z.

Let's start by substituting the coordinates of the given point into the function:

f(3, 0, 1) = (3 - 0 + 2(1)) / (2(3) + 0 - 1)
           = 5 / 5
           = 1

So, the constant value for the level surface passing through (3, 0, 1) is 1.

Now, let's set the function equal to 1 and solve for z:

1 = (x - y + 2z) / (2x + y - z)

Cross-multiplying, we get:

2x + y - z = x - y + 2z

Rearranging the terms, we have:

x + 2y - 3z = 0

Therefore, the equation for the level surface passing through the point (3, 0, 1) is x + 2y - 3z = 0.

In summary, the equation for the level surface passing through the point (3, 0, 1) is x + 2y - 3z = 0.

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Answer: A. 10.8 km

Step-by-step explanation:

add up all the days:

1.3 + 1.75 + 2.25 + 2.5 + 3 = 10.8 km

Answer:

13/50

Step-by-step explanation:

26 percent in simplest form is the fraction 13/50. Since 'percent' means 'per hundred,' 26 percent would be equivalent to the fraction 26/100.

The maximum value of z is 0, and the values of the decision variables are x1 = 0, x2 = 10, x3 = 0, x4 = 0.

maximize: z = c1x1 + c2x2 + ... + cnxn

subject to

a11x1 + a12x2 + ... + a1nxn ≤ b1

a21x1 + a22x2 + ... + a2nxn ≤ b2

am1x1 + am2x2 + ... + amnxn ≤ bmxi ≥ 0 for all i

In our case,

the given LP is:maximize: z = 36x1 + 30x2 - 3x3 - 4x

subject to:

x1 + x2 - x3 ≤ 5

6x1 + 5x2 - x4 ≤ 10

xi ≥ 0 for all i

We can rewrite the constraints as follows:

x1 + x2 - x3 + x5 = 5  (adding slack variable x5)

6x1 + 5x2 - x4 + x6 = 10  (adding slack variable x6)

Now, we introduce the non-negative variables x7, x8, x9, and x10 for the four decision variables:

x1 = x7

x2 = x8

x3 = x9

x4 = x10

The objective function becomes:

z = 36x7 + 30x8 - 3x9 - 4x10

Now we have the problem in standard form as:

maximize: z = 36x7 + 30x8 - 3x9 - 4x10

subject to:

x7 + x8 - x9 + x5 = 5

6x7 + 5x8 - x10 + x6 = 10

xi ≥ 0 for all i

To apply the simplex algorithm, we initialize the simplex tableau as follows:

  |  Cj   |   x5   |   x6   |   x7   |   x8   |   x9   |   x10  |    RHS  |

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

z |  0    |   0    |   0    |  36    |   30   |   -3   |   -4   |    0    |

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

x5|   0   |   1    |   0    |   1    |   1    |   -1   |   0    |    5    |

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

x6|   0   |   0    |   1    |   6    |   5    |   0    |   -1   |   10    |

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

Now, we can proceed with the simplex algorithm to find the optimal solution. I'll perform the iterations step by step:

Iteration 1:

1. Choose the most negative coefficient in the 'z' row, which is -4.

2. Choose the pivot column as 'x10' (corresponding to the most negative coefficient).

3. Calculate the ratios (RHS / pivot column coefficient) to find the pivot row. We select the row with the smallest non-negative ratio.

Ratios: 5/0 = undefined, 10/(-4) = -2.5

4. Pivot at the intersection of the pivot row and column. Divide the pivot row by the pivot element to make the pivot element 1.

5. Perform row operations to

make all other elements in the pivot column zero.

After performing these steps, we get the updated simplex tableau:

  |  Cj   |   x5   |   x6   |   x7   |   x8   |   x9   |   x10  |    RHS  |

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

z |  0    |   0    |  0.4   |  36    |   30   |   -3   |   0    |   12    |

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

x5|   0   |   1    |  -0.2  |   1    |   1    |   -1   |   0    |   5     |

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

x10|   0  |   0    |   0.2  |   1.2  |   1   |   0    |   1    |   2.5   |

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

Iteration 2:

1. Choose the most negative coefficient in the 'z' row, which is -3.

2. Choose the pivot column as 'x9' (corresponding to the most negative coefficient).

3. Calculate the ratios (RHS / pivot column coefficient) to find the pivot row. We select the row with the smallest non-negative ratio.

Ratios: 12/(-3) = -4, 5/(-0.2) = -25, 2.5/0.2 = 12.5

4. Pivot at the intersection of the pivot row and column. Divide the pivot row by the pivot element to make the pivot element 1.

5. Perform row operations to make all other elements in the pivot column zero.

After performing these steps, we get the updated simplex tableau:

  |  Cj   |   x5   |   x6   |   x7   |   x8   |   x9   |   x10  |    RHS  |

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

z |  0    |   0    |  0.8   |  34    |   30   |   0    |   4    |   0     |

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

x5|   0   |   1    |  -0.4  |   0.6  |   1    |   5   |   -2   |   10    |

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

x9|   0   |   0    |   1    |   6    |   5    |   0   |   -5   |   12.5  |

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

Iteration 3:

No negative coefficients in the 'z' row, so the optimal solution has been reached.The optimal solution is:

z = 0

x1 = x7 = 0

x2 = x8 = 10

x3 = x9 = 0

x4 = x10 = 0

x5 = 10

x6 = 0

Therefore, the maximum value of z is 0, and the values of the decision variables are x1 = 0, x2 = 10, x3 = 0, x4 = 0.

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The set of variables that is most likely to have a cause-and-effect relationship is option C: the weight of a box and the postage rate we have to pay to ship the box to California.

Based on the given sets of variables, the set most likely to have a cause-and-effect relationship is:
B. The height of a person and the weight of a person

This is because there is a general correlation between a person's height and their weight, as taller individuals tend to have higher weights. While this is not an absolute rule, there is a stronger cause-and-effect relationship in this set compared to the other options.

This is because the weight of the box is a likely cause of the postage rate, as the heavier the box, the more postage we will have to pay to ship it. In options A and B, there may be a correlation between the variables, but it is less likely that there is a direct cause-and-effect relationship. In option D, the make of a car is not a likely cause of its mileage, as there are many other factors that can affect a car's mileage.

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Answer:

a = 20

Step-by-step explanation:

122 = 4a + 42

4a = 80

a = 20

Hope this helps!

(a) A nonzero vector orthogonal to the plane through the points P, Q, and R is (9, -17, 35). (b) The area of triangle PQR is \(\sqrt\)(811) / 2.

(a) To determine a nonzero vector orthogonal to the plane through the points P, Q, and R, we can first find two vectors in the plane and then take their cross product. Taking vectors PQ and PR, we have:

PQ = Q - P = (5, 1, -2) - (-4, 0, 0) = (9, 1, -2)

PR = R - P = (6, 4, 1) - (-4, 0, 0) = (10, 4, 1)

Taking the cross product of PQ and PR, we have:

n = PQ x PR = (9, 1, -2) x (10, 4, 1)

Evaluating the cross product gives n = (9, -17, 35). Therefore, (9, -17, 35) is a nonzero vector orthogonal to the plane through points P, Q, and R.

(b) To determine the area of triangle PQR, we can use the magnitude of the cross product of vectors PQ and PR divided by 2. The magnitude of the cross product is given by:

|n| = \(\sqrt\)((9)^2 + (-17)^2 + (35)^2)

Evaluating the magnitude gives |n| = \(\sqrt\)(811).

The area of triangle PQR is then:

Area = |n| / 2 = \(\sqrt\)(811) / 2.

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Answer:

consider the < as = signs

and take -5 to the other side making it a +

x<0+5

x<5

Answer:

A. the number of bacteria colonies doubling every 80 minutes.

Step-by-step explanation:

A. 2 cells = 80 mins

B. 4 cells = 80 mins

how to check;

multiply both sides by 2 in equation A

2 × 2 = 80 × 2

4 cells = 160 mins

change the mins into hours

4 cells = 160 ÷ 60

4 cells.= 2 hrs 40 mins

coagulate results

equation A. is 4 cells = 2hrs 40 mins

equation B. is 4 cells = 4 hrs

therefore equation A. is faster

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The overall sample for the survey consists of 50 freshmen, 40 sophomores, 35 juniors, and 30 seniors, totaling 155 students.

To create an overall sample for the survey, the administrators selected a certain number of students from each class level. They randomly sampled 50 freshmen, 40 sophomores, 35 juniors, and 30 seniors. By combining these individual samples from each class, the administrators obtained an overall sample size of 50 + 40 + 35 + 30 = 155 students. This overall sample represents a portion of the student population from each class level and allows for a representation of students from different academic years in the survey.

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Answer:

6.2 Fahrenheit  

Step-by-step explanation: I took the test hopes this helps (And sorry for being late)

Answer:

6.2

Step-by-step explanation: