elimination method -2x-7y=13 and 3x+6y=15​

The value of x found after solving the equation using algebra tiles is -3.

What is algebra tiles?

Algebra tiles are mathematical manipulatives that help students comprehend the principles of algebra and strategies to think algebraically. For introductory algebra pupils at the level of elementary school, middle school, high school, and college, these tiles have demonstrated to offer solid examples.

Solving the equation for value of x

−x + (−3) = x + 3              

-x -3 = x + 3                  

subtracting x from both sides

(-x -3) -x = (x + 3) -x

-2x -3 = 3                      

Adding 3 to both sides

-2x -3 + 3 = 3 + 3

-2x = 6

Dividing by 2 both side.

x = -3

Therefore the value of x = -3

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Answer:

-3

Step-by-step explanation:

H₀: The mean reported number of good friends is the same across marital statuses. H₁: There is a difference in the mean reported number of good friends among marital statuses.

In the context of the ANOVA table reporting F = 0.80 for comparing the reported number of good friends among different marital statuses (married, widowed, divorced, separated, never married), the null and alternative hypotheses can be specified as follows:

Null Hypothesis (H₀): There is no significant difference in the mean reported number of good friends across the different marital statuses.

Alternative Hypothesis (H₁): There is a significant difference in the mean reported number of good friends across the different marital statuses.

The null hypothesis assumes that any observed differences in the mean reported number of good friends among the marital statuses are due to chance or random variation. On the other hand, the alternative hypothesis suggests that there is a meaningful difference in the mean reported number of good friends among the different marital statuses. The ANOVA F-test is used to evaluate whether the observed variation between groups is statistically significant

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It is true that the null space of a is the solution set of the equation ax = 0.

The null space of a matrix A is Nul(A)= {x : Ax=0}. In other words, if A is m × n, then its null space consists of those vectors x ∈ Rn which solve the homogeneous equation Ax= 0.

Solving Ax=0 yields an explicit description of Nul(A).

Therefore, the Option A is correct.

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Answer:

8.64%

Step-by-step explanation:

Write it as a decimal

7/81 = 0.0864

0.0864 is the decimal representation for 7/81

For Percentage Conversion :

step 1 To represent 0.0864 in percentage, write 0.0864 as a fraction

Fraction = 0.0864/1

step 2 multiply 100 to both numerator & denominator

(0.0864 x 100)/(1 x 100) = 8.64/100

8.64% is the percentage representation for 7/81

Answer:

122.5

Step-by-step explanation:

If it triples her followers per 6 months then it gives her half of her followers in one month. So 35 times 3.5 which is 122.5

After \(7\) months, Ashton will have \(25,515\) followers.

Modelling is the process of creating a mathematical representation of a real-world scenario to make a prediction or provide insight.

We have,

Number of followers \(=35\)

So, Every month increase is triple i.e. \(3\) times for next \(6\) months.

So,

According to the question,

Every month increase \(=\ 3\ *\ Current\ Follower\)

So,

Followers after \(7\) months \(= 35*(3)^6\)

Because followers are increasing at the rate of three times per month,

So,

Followers after \(7\) months \(= 35*(3)^6=25,515\)

Hence, we can say that After \(7\) months, Ashton will have \(25,515\) followers.

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The technique often used to prove the correctness of a recursive function is **mathematical induction**.

Mathematical induction is a method of proof used to establish that a property holds for all natural numbers (or a well-ordered set). It consists of two steps:

1. **Base Case**: The base case establishes that the property holds for a specific initial value or base case. It typically involves showing that the property is true for the smallest possible input or base case of the recursive function.

2. **Inductive Step**: The inductive step demonstrates that if the property holds for a specific value, it also holds for the next value. This step involves assuming that the property is true for a certain input, and then proving that it holds for the subsequent input using the recursive definition of the function.

By proving that the base case is true and showing that the inductive step holds, mathematical induction establishes the correctness of a recursive function for all valid inputs.

The other options you mentioned, such as commutativity, diagonalization, and matrix multiplication, are not directly related to proving the correctness of recursive functions. Commutativity refers to the order of operations or elements, diagonalization is a technique used in mathematics and logic, and matrix multiplication is a mathematical operation for matrices. While these concepts may have applications in other areas of mathematics and computer science, they are not specifically used for proving the correctness of recursive functions.

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Answer:

1st  and second, unless you have already learned area of trapezoids. If you have, add third

Step-by-step explanation:

Answer: this is ez its

first

second

third

Step-by-step explanation:

The value of s is 8

First, we need to know that perpendicular bisectors are lines that divides into equal parts

From the diagram shown, we have that;

Line NO is equal to Line MO

This is represented as;

NO = 3s + 12

MO = 36

Equate the expressions, we get;

3s + 12 = 36

collect the like terms, we have;

3s = 36 - 12

subtract the value, we have;

3s = 24

Divide both sides by the coefficient of s in the equation;

s = 24/3

Divide the values

s = 8

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Answer:

It is: (f(2) - f(0))/(2 - 0)

f(2) = 250(0.5)(2) = 250

f(0) = 250 (0.5)(0) = 0

So: (250 - 0)/(2 - 0) = 250/2 = 175

The average rate of change is 175.

Step-by-step explanation:

The first scenario described is an example of a retrospective cohort study.  The second scenario suggests a retrospective cohort study as well. The third scenario represents a cross-sectional study, where researchers conduct a survey among high school students to assess the prevalence of obesity and diabetes.

1. In the first scenario, a retrospective cohort study is conducted by tracking individuals over a 20-year period. The study begins in 1960 and collects data on cigar smoking practices. After 20 years, the participants are followed up to determine if they developed any cancers. This type of study design allows researchers to examine the long-term effects of smoking Cuban cigars.

2. The second scenario involves a retrospective cohort study as well. The objective is to study the long-term neurological effects of a discontinued anesthetic agent. The researchers identify patients who received the drug before it was discontinued and then assess the occurrence of subsequent neurological disorders. This study design allows for the examination of the relationship between exposure to the anesthetic agent and the development of neurological disorders.

3. The third scenario represents a cross-sectional study. Researchers aim to assess the prevalence of obesity and diabetes among high school students during their junior year. They conduct a survey to gather information on the students' current weight, diabetes status, and other relevant factors. A cross-sectional study provides a snapshot of the population at a specific point in time, allowing researchers to examine the prevalence of certain conditions or characteristics.

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Answer:

A

Step-by-step explanation:

3(14║-10+3║)-║8-2║^2=3(14-║-7║)-║8-2║^2=3(14-7)-6^2=3(7)-36=21-36=-15

Answer:

-15

Step-by-step explanation:

See the steps below:)

In Japan, the average cost is $17.61 and in Switzerland, the average cost is $13.55.

An equation is a relationship between two or more variables expressed in equal to form. The equation of two variables look like ax + by=c. It is solved to find the value of variables.

According to the question, the equation are as under:

3x+2y=79.93----------------1

2x+3y=75.87 ----------------2

Multiply equation 1 by 2 and equation 2 by 3 and subtract the result from equation 2 from the result coming from equation 1.

6x+4y=159.86

6x+9y=227.61

Subtracting

6x+4y-6x-9y=159.86-227.61

-5y=-67.75

y=13.55

Put the value of y=13.55 in 3x+2y=79.93

3x+2(13.55)=79.93

3x+27.10=79.93

3x=79.93-27.10

3x=52.83

x=52.83/3

x=17.61

Hence the average cost in Japan is $17.61 and the average cost in Switzerland is $13.55.

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We are given two sets of paired observations, which we will use to calculate the sample mean difference and the standard error of the mean difference:

Sample mean difference = x1 -x2 = (214+186+182+200+210+204+187+210+190+182+215+198)/12 - (188+210+199+209+207+195+203+191+190+211+199+181)/12 = 4.75

Sample standard deviation of the differences = s = √[(Σd²)/(n-1)] where d = (x1 - x2) - (x1 - x2), and n is the number of pairs.

d1 = (214 - 188) - 4.75 = 21.25

d2 = (186 - 210) - 4.75 = -28.75

d3 = (182 - 199) - 4.75 = -22.75

d4 = (200 - 209) - 4.75 = -9.75

d5 = (210 - 207) - 4.75 = -1.75

d6 = (204 - 195) - 4.75 = 3.25

d7 = (187 - 203) - 4.75 = -20.75

d8 = (210 - 191) - 4.75 = 13.25

d9 = (190 - 190) - 4.75 = -4.75

d10 = (182 - 211) - 4.75 = -28.75

d11 = (215 - 199) - 4.75 = 10.25

d12 = (198 - 181) - 4.75 = 12.25

Σd² = 1734.875

s = √(1734.875/11) = 5.076

Standard error of the mean difference = s/√n = 5.076/√12 = 1.469

Using a t-distribution with 11 degrees of freedom and a 99% confidence level (α = 0.01), we find the t-value to be 3.106. Therefore, the 99% confidence interval for the true mean difference between the cholesterol levels for people who take the new drug is:

(4.75 - 3.106(1.469), 4.75 + 3.106(1.469))

= (0.885, 8.615)

So we are 99% confident that the true mean difference between the cholesterol levels for people who take the new drug lies between 0.885 and 8.615 mg/dL.

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The correct option is the third one; (14, 4); The vertex represents the maximum profit.

For a general quadratic equation

y = ax² + bx + c

The vertex is at the x-value:

x = -b/2a

Here the quadratic function is:

f(x)=  -x² + 28x - 192

The vertex is at:

x = -28/2*-1 = 14

Evaluating in x= 14 we get:

f(14) = -14² + 28*14 - 192 = 4

So the vertex is at (14, 4), and because the leading coefficient is negative, this is the maximum profit.

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To answer this question, we need to know the median and upper quartile of the data set. Once we have these values, we can determine what percentage of the data falls to the right of the median and to the left of the upper quartile.
Let's say the median of the data set is 50 and the upper quartile is 75. To find the percentage of measurements to the right of the median, we need to look at the data values that are greater than 50 and divide that number by the total number of measurements. Let's say there are 40 data values greater than 50 and a total of 100 measurements.

Then, the percentage of measurements to the right of the median would be:

(40/100) x 100% = 40%

To find the percentage of measurements to the left of the upper quartile, we need to look at the data values that are less than or equal to 75 and divide that number by the total number of measurements. Let's say there are 60 data values less than or equal to 75 and a total of 100 measurements. Then, the percentage of measurements to the left of the upper quartile would be:

(60/100) x 100% = 60%


Your answer:
1. 40% of the measurements lie to the right of the median.
2. 60% of the measurements lie to the left of the upper quartile (Q3).

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The percentage change in frequency is 0%.Hence, the natural frequency of torsional vibration of the custen is given by f = 25.7 / L₀^(1/2) and the percentage change in frequency is 0%.

We are given that:

Total moment of inertia of moving parts = I = 1 kgm²

Moment of inertia of air-screw = I = 18 kgm²

Outer diameter of hollow shaft = D₀ = 80 mm

Inner diameter of hollow shaft = Dᵢ = 35 mm

Length of hollow shaft = L = 0.30 m

Stiffness of the crank-throw = K = 2.5 × 10⁴ Nm/rad

Shear modulus of elasticity = G = 83000 N/mm²

We need to calculate the natural frequency of torsional vibration of the custen.

The formula for natural frequency of torsional vibration is: f = (1/2π) [(K/L) (J/GD)]^(1/2)

Where, J = Polar moment of inertia

J = (π/32) (D₀⁴ - Dᵢ⁴)

The formula for equivalent length of hollow shaft is given by:

q₁ = q₁₁ + q₁₂

Where, q₁₁ = (π/32) (D₀⁴ - Dᵢ⁴) / L₁q₁₂ = (π/64) (D₀⁴ - Dᵢ⁴) / L₂

L₁ = length of outer diameter

L₂ = length of inner diameter

For the given shaft, L₁ + L₂ = L

Let L₁ = L₀D₀ = D = 80 mm

Dᵢ = d = 35 mm

So, L₂ = L - L₁= 0.3 - L₀...(1)

For the given crank-throw, q₁ = (π/32) (D⁴ - d⁴) / L, where D = 80 mm and d = 80 mm

Hence, q₁ = (π/32) (80⁴ - 35⁴) / L

Therefore, q₁ = (π/32) (80⁴ - 35⁴) / L₀...(2)

From the formula for natural frequency of torsional vibration, f = (1/2π) [(K/L) (J/GD)]^(1/2)

Substituting the values of K, J, G, D and L from above, f = (1/2π) [(2.5 × 10⁴ Nm/rad) / (L₀) ((π/32) (80⁴ - 35⁴) / (83000 N/mm² (80 mm)³))]^(1/2)f = (1/2π) [(2.5 × 10⁴ Nm/rad) / (L₀) (18.12)]^(1/2)f = 25.7 / L₀^(1/2)...(3)

Now, if we assume that the air-screw mass is infinite, then the moment of inertia of the air-screw is infinite.

Therefore, the formula for natural frequency of torsional vibration in this case is:

f = (1/2π) [(K/L) (J/GD)]^(1/2)Substituting I = ∞ in the above formula, we get:

f = (1/2π) [(K/L) (J/GD + J/∞)]^(1/2)f = (1/2π) [(K/L) (J/GD)]^(1/2)f = 25.7 / L₀^(1/2)

So, in this case also the frequency is the same.

Therefore, the percentage change in frequency is 0%.Hence, the natural frequency of torsional vibration of the custen is given by f = 25.7 / L₀^(1/2) and the percentage change in frequency is 0%.

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Answer:

-3

Step-by-step explanation:

Answer:1/4

Step-by-step explanation:

Answer:

y=2x+3 is perpendicular. Just take away the negative

Step-by-step explanation:

Answer:

y= 2x-3

Step-by-step explanation:

The series ∑((-1)ⁿ⁺¹/(2n⁴) from n=0 to infinity is converges.

To test the convergence or divergence of the series ∑((-1)ⁿ⁺¹/(2n⁴) from n=0 to infinity, we can use the alternating series test.

The alternating series test states that if a series has the form ∑((-1)ⁿ)bₙ or ∑((-1)ⁿ⁺¹)bₙ.

where bₙ is a positive sequence that converges to zero as n approaches infinity, then the series converges.

We have ∑(-1)ⁿ⁺¹/2n⁴.

Let's analyze the sequence bₙ=1/2n⁴

The sequence bₙ = 1/(2n⁴) is always positive.

As n approaches infinity, 1/(2n⁴) approaches zero.

Therefore, we can apply the alternating series test to our series. T

The alternating series ∑((-1)ⁿ⁺¹/(2n⁴) converges because the sequence bₙ=1/2n⁴ satisfies the conditions of the alternating series test.

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Answer:

I think it is C. or D.

Step-by-step explanation:

I dont know for sure but they come close. Hope this helped you!!

Answer:

the answer to your question is x=3

Answer:

Option A: x = 3

Step-by-step explanation:

The lowest part of the parabola has an x-value of 3.

The matrix equation Ax = b, where A and b are given matrices, has no solution when k = -1. It has exactly one solution when k ≠ -1. For any other value of k, the equation has infinitely many solutions.

To determine the solutions of the matrix equation Ax = b, we need to perform row operations on the augmented matrix [A | b]. Let's denote the given matrix [1 2 3; 0 1 1; 1 0 1] as A and the vector [6+k; 5-k; b] as b.

When k = -1, the augmented matrix becomes:

[1 2 3 | 6-1]

[0 1 1 | 5+1]

[1 0 1 | b]

Performing row operations, we can reduce this matrix to the following row-echelon form:

[1 2 3 | 5]

[0 1 1 | 6]

[0 0 0 | b-11]

Since the last row contains all zeros except for b-11, the system has no solution when k = -1.

For k ≠ -1, the augmented matrix becomes:

[1 2 3 | 6+k]

[0 1 1 | 5-k]

[1 0 1 | b]

Performing row operations, we can reduce this matrix to the following row-echelon form:

[1 0 1 | b-3k]

[0 1 1 | 5-k]

[0 0 0 | -b+k-1]

Since the last row contains all zeros except for -b+k-1, the system has infinitely many solutions for any value of k ≠ -1. This is because the system reduces to an equation with a free variable, which implies infinitely many possible solutions.

In conclusion, the matrix equation Ax = b has no solution when k = -1, exactly one solution when k ≠ -1, and infinitely many solutions for any other value of k.

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f(p) where p is the price in thousands. f(250) means the average number of days before being sold for $250,000. Lets take a look at the answers and see which fits the best:

1. The house sold for $250,000. (This is what the 250 stands for, but we need to find what f(250) means and not just 250)

2. The house stayed on the market for an average of 250 days before being sold. (Nope, not even close)

3. This is the average number of days the house stayed on the market before being sold for $250,000. (Yes! This seems right, f(250) is the average number of days before being sold for $250,000)

4. The house sold on the market for $250,000 and stayed on the market for an average of 250 days before being sold. (Nope, we are not told anywhere that it takes 250 days to be sold)

This means that our answer has to be 3) This is the average number of days the house stayed on the market before being sold for $250,000.

I hope I've helped! :)

Answer:

f(p) where p is the price in thousands. f(250) means the average number of days before being sold for $250,000. Lets take a look at the answers and see which fits the best:1. The house sold for $250,000. (This is what the 250 stands for, but we need to find what f(250) means and not just 250)2. The house stayed on the market for an average of 250 days before being sold. (Nope, not even close)3. This is the average number of days the house stayed on the market before being sold for $250,000. (Yes! This seems right, f(250) is the average number of days before being sold for $250,000)4. The house sold on the market for $250,000 and stayed on the market for an average of 250 days before being sold. (Nope, we are not told anywhere that it takes 250 days to be sold)This means that our answer has to be 3) This is the average number of days the house stayed on the market before being sold for $250,000.

Answer:

8.7521 × 10^4

Step-by-step explanation:

this should be right

Answer:

Hope it helps

Step-by-step explanation:

1: B

2: B

3: D

4: C

5: A

As per the given data, r'(t) · r''(t) = \(108e^{(2t)} - 72e^{(-2t)} + 72te^{(2t)\).

To discover t(zero), we want to alternative 0 for t inside the given feature r(t). This offers us:

\(r(0) = 3e^{(2(0)}), 3e^{(-2(0)}), 3(0)e^{(2(0)})\\\\= 3e^0, 3e^0, 0\\\\= 3(1), 3(1), 0\\\\= 3, 3, 0\)

Therefore, t(0) = (3, 3, 0).

To find r''(0), we need to locate the second one derivative of the given feature r(t). Taking the by-product two times, we get:

\(r''(t) = (3e^{(2t)})'', (3e^{(-2t)})'', (3te^{(2t)})''= 12e^{(2t)}, 12e^{(-2t)}, 12te^{(2t)} + 12e^{(2t)}\)

Substituting 0 for t in r''(t), we have:

\(r''(0) = 12e^{(2(0)}), 12e^{(-2(0)}), 12(0)e^{(2(0)}) + 12e^{(2(0)})\\\\= 12e^0, 12e^0, 12(0)e^0 + 12e^0\\\\= 12(1), 12(1), 0 + 12(1)\\\\= 12, 12, 12\)

Therefore, r''(0) = (12, 12, 12).

Finally, to discover r'(t) · r''(t), we need to calculate the dot made of the first derivative of r(t) and the second spinoff r''(t). The first spinoff of r(t) is given by using:

\(r'(t) = (3e^{(2t)})', (3e^{(-2t)})', (3te^{(2t)})'\\\\= 6e^{(2t)}, -6e^{(-2t)}, 3e^{(2t)} + 6te^{(2t)\)

\(r'(t) · r''(t) = (6e^{(2t)}, -6e^{(-2t)}, 3e^{(2t)} + 6te^{(2t)}) · (12, 12, 12)\\\\= 6e^{(2t)} * 12 + (-6e^{(-2t)}) * 12 + (3e^{(2t)} + 6te^{(2t)}) * 12\\\\= 72e^{(2t)} - 72e^{(-2t)} + 36e^{(2t)} + 72te^{(2t)\)

Thus, r'(t) · r''(t) = \(108e^{(2t)} - 72e^{(-2t)} + 72te^{(2t)\).

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Answer:

Step-by-step explanation:

3

2/3  is the probability that the product of the two spinners' numbers is even.

How does probability explain work?

The simple definition of probability is the likelihood that something will occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out.

                       Statistics is the study of events that follow a probability distribution. There are four primary categories of probability: axiomatic, classical, empirical, and subjective.

An even number comes from multiplying an even and even, even and odd, or odd and even. Since an odd number only comes from multiplying an odd and odd, there are less cases and it would be easier to find the probability of spinning two odd numbers from 1.

            =  1 - 2/4 . 2/3

             =  1 - 1/3

            =  2/3

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The probability of selecting a user who chooses cinnamon and is under 13 years old is: 0.18 or 18% (rounded to two decimal places).

In the problem, we are given the number of users who choose bacon and are under 13 years old, which is 8. We are also given the number of users who choose plain and are under 13 years old, which is 5. Therefore, the total number of users under 13 years old is 8 + 5 = 13.

Next, we are asked to find the probability of selecting a user who chooses cinnamon and is under 13 years old. We know that the number of users who choose cinnamon and are under 13 years old is 3. Therefore, out of the total 13 users under 13 years old, the probability of selecting a user who chooses cinnamon and is under 13 years old is:

The total number of users under 13 years old is 8 (choose bacon) + 5 (choose plain) = 13.

The number of users who choose cinnamon and are under 13 years old is 3.

Therefore, the probability of selecting a user who chooses cinnamon and is under 13 years old is:

3 / 13 ≈ 0.23 or 23% (rounded to two decimal places)

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