Solve the system of linear equations.
y=−2x−4
y=2x−4
(−1, 2)

(2, 2)

(−2, 0)

(3, 7)

(0,−4)

(7, 7)

(0, 4)

no solution

(1, 1)

infinitely many solutions

Answer:

D. 10 and 11

Step-by-step explanation:

This problem would use pythagorean theorem because we're finding the hypotenuse of a right triangle. This is its standard equation:

\(a {}^{2} + {b}^{2} = {c}^{2} \)

The legs represent \(a\) and \(b\) respectively, and \(c\) represents the hypotenuse. After plugging in the legs' respective values, the equation looks like this:

\(6^{2} + {9}^{2} = {c}^{2} →36 + 81 = {c}^{2} →117 = c^{2} \)

To isolate \(c\), you would find the square root of \(117\). In this case, we're just finding which integers\( \sqrt{117} \) is between. \(\sqrt{100}(=10)\) is the closest integer value below \(\sqrt{117}\) and \(\sqrt{121}(=11)\) is the closest integer value above \(\sqrt{117}\). So the answer is D. 10 and 11.

Answer:
1 : 10 is the answer.

Step-by-step explanation:

Total number of eggs in 2 boxes = 6 x 2 = 12

Total number of eggs in 20 boxes = 120

12 : 120

1 : 10

Answer:

1:6

Step-by-step explanation:

Answer:

most likely next spring

Step-by-step explanation:

Step-by-step explanation:

Answer:

3,6, and 9

Step-by-step explanation:

Answer:

1, 2, 3, 6, 9, 18

Step-by-step explanation:

1 x 18

2 x 9

3 x 6

Answer:

you need to write a problem with it

Step-by-step explanation:

for example,

Q4 will be 9n

n is the unknown number

9 is what n will be multiplyed with

multiplied since product means answer of a multiplication problem

hoped this helps

The smallest positive integer that is both a multiple of 7 and a multiple of 4, is 28 .

To find the smallest positive integer that is both a multiple of 7 and a multiple of 4, first find the multiples of both 4 and 7 to see which multiples are common between them and which are the lowest.

The multiples of 4 and 7 are:

Multiples of 4 :

4, 8, 12, 26, 20, 24, 28, 32, 36, 40,

Multiples of 7 :

7 , 14 , 21 , 28 , 35 , 42 , 49

The smallest positive integer that is both a multiple of 7 and a multiple of 4 is therefore 28.

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Answer:

Julia had 120 peas to start .

Answer:

  120 peas

Step-by-step explanation:

Before Julia gave Vlada 15 peas, the ratio of their numbers was 3:2. Afterward, Julia still had 10 more peas. You want to know the number Julia started with.

Let j represent the initial number of peas Julia had. Then Vlada had 2/3j peas. After the transfer, the difference was ...

  (j -15) -(2/3j +15) = 10

  1/3j -30 = 10

  1/3j = 40

  j = 120

Julia had 120 peas at first.

__

Additional comment

The transfer of peas decreases the difference by 30, so if it remains 10 it must have originally been 40. The difference in initial ratio units is 3-2 = 1, so Julia's initial 3 ratio units represent 3·40 = 120 peas.

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The given statement "Measuring the entire population is usually preferred over measuring a sample from the population" is False because measuring the entire population is often impractical or impossible.

When dealing with large populations, it is typically more feasible to gather data from a representative sample rather than measuring the entire population. This approach saves time, resources, and effort. Sampling allows statisticians to make reliable inferences about the population based on the characteristics observed in the sample.

Carefully chosen samples can accurately reflect the population's attributes and provide valuable insights.

However, it is crucial to ensure that the sample is representative and unbiased to avoid potential sampling errors and ensure the validity of the conclusions drawn from the data.

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Answer:

locations of A are 7, 17

Step-by-step explanation:

since B is positioned at 12 and AB = 5 , then

A = 12 - 5 or 12 + 5 = 7 , 17

(a) The smallest positive value of n for which a simple graph on n vertices and 2n edges can exist is 3. An example of such a graph for the smallest n is a triangle, where each vertex is connected to the other two vertices.

In this case, we have 3 vertices and 2n = 2 * 3 = 6 edges, which satisfies the condition.

To determine the smallest positive value of n, we need to consider the conditions for a simple graph:

1. Each vertex must be connected to at least one other vertex.

2. There should be no multiple edges between the same pair of vertices.

3. There should be no self-loops (edges connecting a vertex to itself).

Considering these conditions, we start by trying with the smallest possible n, which is 3. We construct a graph with 3 vertices and connect each vertex to the other two vertices, resulting in a triangle. This graph satisfies the conditions and has 2n = 2 * 3 = 6 edges.

(b) To prove that G is connected, we will use a proof by contradiction.

Assume that G is not connected, meaning it has two or more components. Let's consider two distinct components, C1 and C2.

Since G has at most two components, each component can have at most 10 vertices (20 vertices / 2 components). Let's assume C1 has x vertices and C2 has y vertices, where x + y ≤ 20.

Now, let's consider two vertices u and v, where u belongs to C1 and v belongs to C2. According to the given condition, deg(u) + deg(v) > 19.

Since deg(u) represents the degree of vertex u, it means the number of edges incident to vertex u. Similarly, deg(v) represents the degree of vertex v.

In C1, the maximum possible degree for a vertex is x - 1 (since there are x vertices, each connected to at most x - 1 other vertices in C1). Similarly, in C2, the maximum possible degree for a vertex is y - 1.

Therefore, deg(u) + deg(v) ≤ (x - 1) + (y - 1) = x + y - 2.

But according to the given condition, deg(u) + deg(v) > 19. This contradicts the assumption that G has at most two components.

Hence, our assumption that G is not connected is false. Therefore, G must be connected.

In conclusion, if a simple graph G has 20 vertices, at most two components, and every pair of distinct vertices satisfies the inequality deg(u) + deg(v) > 19, then G is connected.

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To find the dimensions of the largest room that can be built with a fixed perimeter of 600 feet.

We need to divide the perimeter by 2 and use that as the sum of two adjacent sides. Let's call the length of the rectangle "l" and the width "w".
So we have:  2l + 2w = 600
Simplifying:  l + w = 300
We want to maximize the area of the rectangle, which is given by:  A = lw
We can solve for one variable in terms of the other:  l = 300 - w
Substituting into the area equation:
A = (300 - w)w
A = 300w - w^2
To maximize the area, we need to find the value of w that makes the derivative of A with respect to w equal to 0:  dA/dw = 300 - 2w = 0
w = 150
So the width of the rectangle is 150 feet. Substituting back into the perimeter equation: l + 150 = 300
l = 150
So the length of the rectangle is also 150 feet.
Therefore, the largest room that can be built has dimensions 150 ft by 150 ft, and its area is:  A = lw = 150 * 150 = 22,500 ft^2
The dimensions of the largest rectangular room a carpenter can build with a fixed perimeter of 600 feet are 150 ft by 150 ft. The area of this room is 22,500 ft². This is because when the length and width are equal, the area of the rectangle is maximized.

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\(\huge \bf༆ Answer ༄\)

The Slope of the line is the rate of change shown in the graph.

Taking two points on the line (1 , 6) and (2 , 12)

Slope (m) is equal to : -

Hence, Rate of change is $6 / hour

\(꧁  \:  \large \frak{Eternal \:  Being } \: ꧂\)

Answer:

The correct answer is x>38

Step-by-step explanation:

The solution is : x = 77 and x > 38

In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex.

Given that,

Sum of all angles in a triangle is 180.

The angle PNO will hence be:

180 - 38 - 39 = 103 degrees.

The angle PNO + angle x = 180 degrees (straight line)

So 103 + x = 180,

therefore x = 180 - 103 = 77.

Which is also greater than 38,

so, x > 38 is also correct.

Hence the solution is : x = 77 and x > 38

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Answer:

Answer given below

Step-by-step explanation:

1. A = (0, 5) =  on y axis

2. B = (0, -3) = on x axis

3. C = (1, 2) = 1st quadrant

4. D = (-4, -3) = 3rd quadrant

5. E = (5, -5) = 4th quadrant

6. x axis

7. y axis

Answer:

31/21

Step-by-step explanation:

17/21+2/3

First step is to get both denominators equal so 3 should be multiplied by 7 to get 21 and 2 should also be multiplied by 7,

This leaves 17/21+14/21 which equals to 31/21

Answer:

Step-by-step explanation:

What you want to do is find a common denominator of this equation. You can actually use 21 as that denominator because 7×3=21.

You'll keep the 17/21 for your first value, and for the second...

multiply each side of 2/3 by 7/7. That will end up being 14/21.

Finally, you will add those two values up and get 31/21 or 1 10/21.

Answer:

9. A = Length by Width

Length = x

Width = 12x - 6y

A = x(12x - 6y)

A = 12x² - 6xy

10. A = ½bh

h = 2ab

A = ½(b)(2ab)

A = ab²

The solution to the equation is x = -2, -1.46, -1, x = 5.46

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

0 = x^{5}+x^{4}-20x^{3}-68x^{2}-80x-32

Express properly

So, we have

x^5 + x^4 - 20x^3 -68x^2 -80x - 32 = 0

Next, we plot the graph of x^5 + x^4 - 20x^3 -68x^2 -80x - 32 = 0 to determine the solution graphically

See attachment for graph

From the graph, we have

x = -2, -1.46, -1, x = 5.46

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The total cost of power generation for a specific load demand can be calculated by optimally allocating the load demand to each unit based on their power output limits. The allocation is done in a way that minimizes the overall cost while meeting the load demand.

In the given power system depicted in Figure 1, there are three units that are always running. Each unit has specific characteristics regarding their minimum power output (Pmin), maximum power output (Pmax), and incremental cost (Ci). Let's discuss the characteristics of each unit and calculate the total cost of power generation for a given load demand.

Unit 1:

Pmin = 200 MW

Pmax = 500 MW

Ci = $50/MWh

Unit 2:

Pmin = 150 MW

Pmax = 400 MW

Ci = $40/MWh

Unit 3:

Pmin = 100 MW

Pmax = 300 MW

Ci = $30/MWh

To calculate the total cost of power generation for a given load demand, we need to determine the optimal power output for each unit. We start by considering the units with the lowest incremental cost first.

Suppose the load demand is D MW. We allocate the load demand to the units as follows:

Step 1: Check if Unit 1 can meet the load demand within its power range. If yes, allocate the load demand to Unit 1 and calculate the cost:

Cost1 = Ci * P1, where P1 is the power output of Unit 1.

Step 2: If there is still remaining load demand, allocate it to Unit 2:

Cost2 = Ci * P2, where P2 is the power output of Unit 2.

Step 3: If there is still remaining load demand, allocate it to Unit 3:

Cost3 = Ci * P3, where P3 is the power output of Unit 3.

Finally, the total cost of power generation, Cost_total, is the sum of Cost1, Cost2, and Cost3:

Cost_total = Cost1 + Cost2 + Cost3

To find the optimal power output for each unit, we consider the load demand and compare it to the minimum and maximum power output limits for each unit. The power allocation is based on meeting the load demand while minimizing the overall cost of power generation.

In summary, given the characteristics of the three units in the power system (Pmin, Pmax, and Ci), the total cost of power generation for a specific load demand can be calculated by optimally allocating the load demand to each unit based on their power output limits. The allocation is done in a way that minimizes the overall cost while meeting the load demand.

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Answer:

Fraction: x= 4/5

Decimal: x= 0.8

Answer:

x = - 6    

Step-by-step explanation:

Equation

1/3 * (-9x +12) = 22                Multiply both sides by 3

Solution

3 * 1/3(-9x + 12) = 22*3

- 9x + 12 = 66                        Subtract 12 from both sides.

-9x = 66 - 12                         Combine

-9x = 54                                Divide by -9

x = 54/-9

x = - 6

Answer:

1) For \(x^2 + y^2 - 4x + 12y - 20 = 0\), the standard form is \((x-2)^2 + (y+6)^2 = 60\\\)

2) For \(x^2 + y^2 + 6x - 8y - 10 = 0\), the standard form is \((x + 3)^2 + (y - 4)^2 = 35\\\)

3) For \(3x^2 + 3y^2 + 12x + 18y - 15 = 0\),  the standard form is \((x + 2)^2 + (y+ 3)^2 = 18\\\)

4) For \(5x^2 + 5y^2 - 10x + 20y - 30 = 0\),  the standard form is \((x - 1)^2 + (y+ 2)^2 = 11\\\)

5) For \(2x^2 + 2y^2 - 24x - 16y - 8 = 0\),  the standard form is \((x - 6)^2 + (y+ 4)^2 = 56\\\)

6) For\(x^2 + y^2 + 2x - 12y - 9 = 0\), the standard form is \((x+1)^2 + (y-6)^2 = 46\\\\\)

Step-by-step explanation:

This can be done using the completing the square method.

The standard equation of a circle is given by \((x - a)^2 + (y-b)^2 = r^2\)

1) For \(x^2 + y^2 - 4x + 12y - 20 = 0\)

\(x^2 - 4x + y^2 + 12y = 20\\x^2 - 4x + 2^2 + y^2 + 12y + 6^2 = 20 + 4 + 36\\(x-2)^2 + (y+6)^2 = 60\\\)

Therefore, for \(x^2 + y^2 - 4x + 12y - 20 = 0\), the standard form is \((x-2)^2 + (y+6)^2 = 60\\\)

2) For \(x^2 + y^2 + 6x - 8y - 10 = 0\)

\(x^2 + 6x + y^2 - 8y = 10\\x^2 + 6x + 3^2 + y^2 - 8y + 4^2 = 10 + 9 + 16\\(x + 3)^2 + (y- 4)^2 = 35\\\)

Therefore, for \(x^2 + y^2 + 6x - 8y - 10 = 0\), the standard form is \((x + 3)^2 + (y - 4)^2 = 35\\\)

3)  For \(3x^2 + 3y^2 + 12x + 18y - 15 = 0\)

Divide through by 3

\(x^2 + y^2 + 4x + 6y = 5\)

\(x^2 + y^2 + 4x + 6y = 5\\x^2 + 4x + 2^2 + y^2 + 6y + 3^2 = 5 + 4 + 9\\(x + 2)^2 + (y+ 3)^2 = 18\\\)

Therefore, for \(3x^2 + 3y^2 + 12x + 18y - 15 = 0\),  the standard form is \((x + 2)^2 + (y+ 3)^2 = 18\\\)

4)  For \(5x^2 + 5y^2 - 10x + 20y - 30 = 0\)

Divide through by 5

\(x^2 + y^2 - 2x + 4y = 6\)

\(x^2 + y^2 -2x + 4y = 6\\x^2 - 2x + 1^2 + y^2 + 4y + 2^2 = 6 + 1 + 4\\(x - 1)^2 + (y+ 2)^2 = 11\\\)

Therefore, for \(5x^2 + 5y^2 - 10x + 20y - 30 = 0\),  the standard form is \((x - 1)^2 + (y+ 2)^2 = 11\\\)

5) For \(2x^2 + 2y^2 - 24x - 16y - 8 = 0\)

Divide through by 2

\(x^2 + y^2 - 12x - 8y = 4\)

\(x^2 + y^2 - 12x - 8y = 4\\x^2 - 12x + 6^2 + y^2 - 8y + 4^2 = 4 + 36 + 16\\(x - 6)^2 + (y+ 4)^2 = 56\\\)

Therefore, for \(2x^2 + 2y^2 - 24x - 16y - 8 = 0\),  the standard form is \((x - 6)^2 + (y+ 4)^2 = 56\\\)

6) For \(x^2 + y^2 + 2x - 12y - 9 = 0\)

\(x^2 + 2x + y^2 - 12y = 9\\x^2 + 2x + 1^2 + y^2 - 12y + 6^2 = 9 + 1 + 36\\(x+1)^2 + (y-6)^2 = 46\\\)

Therefore, for\(x^2 + y^2 + 2x - 12y - 9 = 0\), the standard form is \((x+1)^2 + (y-6)^2 = 46\\\\\)

For Plato / Edmentum

Just to the test and got it right ✅

The optimal values of these parameters are:

a. β₁ = 0

b. β₂ = 0

The linear regression y = β1 + β2x + e, assuming that the sum of squared errors (SSE) takes the following form:

SSE = 382 + 681 + 382 + 18β1β2

Derive the partial derivatives of SSE with respect to β1 and β2 and solve the optimal values of these parameters.

Given that SSE = 382 + 681 + 382 + 18β1β2 ∂SSE/∂β1 = 0 ∂SSE/∂β2 = 0

Now, we need to find the partial derivative of SSE with respect to β1.

∂SSE/∂β1 = 0 + 0 + 0 + 18β2 ⇒ 18β2 = 0 ⇒ β2 = 0

Therefore, we obtain the optimal value of β2 as 0.

Now, we need to find the partial derivative of SSE with respect to β2. ∂SSE/∂β2 = 0 + 0 + 0 + 18β1 ⇒ 18β1 = 0 ⇒ β1 = 0

Therefore, we obtain the optimal value of β1 as 0. Hence, the partial derivative of SSE with respect to β1 is 18β2 and the partial derivative of SSE with respect to β2 is 18β1.

Thus, the optimal values of β1 and β2 are 0 and 0, respectively.

Therefore, the answers are: a. β₁ = 0 b. β₂ = 0

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The statement "If a set of vectors {v₁, v₂, ...., vp} in Rⁿ is linearly dependent, then p>n" is False.

Let {v₁, v₂, ...., vp} be a set of p vectors in Rⁿ, then the following are equivalent statements:

1. The set of vectors is linearly dependent.

2. There exist constants c₁, c₂, ... cp, not all of them zero, such that:

c₁v₁+c₂v₂+...+cpvp = 0 (zero vector)

For the above to be possible, the following must hold true: p≥n

Because in Rⁿ, each vector has n components.

So, the total number of unknowns is p, while the total number of equations that we have is n.

Hence p≥n for the system of linear equations above to have a non-zero solution.

Hence, the statement "If a set of vectors {v₁, v₂, ...., vp} in Rⁿ is linearly dependent, then p>n" is False.

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The revolution of the gear having 200 teeth was 500 rpm.

The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.

Given that the rotational speed of a driven gear is inversely proportional to the number of teeth on a gear.

T1/T2 = R2/R1

As per the question, the required values as

T1 = 200

T2 = 50

R2 = 2,000 rpm

200/50 = 2,000 /R1

R1 = (2,000 × 50)/200

R1 = 500

Therefore, the revolution of the gear having 200 teeth was 500 rpm.

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Answer:

C. 48 \(ft^2\)

Step-by-step explanation:

The formula for finding the area of a triangle is:

\(\frac{1}{2}bh\)

The "\(b\)," is the base (10), and the "\(h\)," is the height (9.6), so plug it in:

\(\frac{1}{2} (10)(9.6)\\\)

\(\frac{1}{2} (96)\)

48 \(ft^2\)

The actual measurement of that side of the courtyard = 165 inches

In this question, we have been given Andre drew a plan of a courtyard at a scale of 1 to 60. in his drawing, one side of the courtyard is 2.75 inches.

We need to find the actual measurement of that side of the courtyard.

In order to calculate the real length,

real length = scale length / scale ratio

here, scale length = 2.75 inches

scale ratio = (1/60)

so, the real length would be,

real length = 2.75/ (1/60)

real length = 2.75 * 60

real length = 165 inches

Therefore, the actual measurement of that side of the courtyard = 165 inches

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The probability of selecting a T or a P on the second draw, given that an F was selected on the first draw is 0.39.

The probability of selecting a T or a P on the second draw, given that an F was selected on the first draw, can be calculated using conditional probability.

P(A|B) = P(A and B) / P(B)

P(A and B) = P(T or P on second draw and F on first draw) = P(T on second draw and F on first draw) + P(P on second draw and F on first draw)

= (3/9) x (4/10) + (2/9) x (4/10) = 14/90

To find P(B), we know that it is 0.4.

Therefore, the conditional probability of selecting a T or a P on the second draw, given that an F was selected on the first draw, is:

P(A|B) = P(A and B) / P(B) = (14/90) / 0.4 ≈ 0.39

So the probability of selecting a T or a P on the second draw, given that an F was selected on the first draw, is approximately 0.39.

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The standard deviation is 8.

Data dispersion in regard to the mean is quantified by a standard deviation, or. Data are said to be more closely grouped around the mean when the standard deviation is low and more dispersed when the standard deviation is high. A measure of a group of values' variance or dispersion in statistics is called the standard deviation. The values tend to be close to the set's mean when the standard deviation is low, while the values are dispersed over a larger range when the standard deviation is high. The dispersion of the data around the mean value is measured by the standard deviation. It might be helpful when comparing data sets that may have the same mean but a different range.

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Answer:

3\(\frac{727}{1000}\)

Answer:

1*4 = 4 in^2

Step-by-step explanation:

The area for this shape is calculated by multiplying width and length:

1*4 = 4 in^2