Please Help solve simultaneous equations , I never got hang of it.

1. a+3b=5
3a+2b=8

2. 3m-4n= -14
2m+2n= 14
​

Answer:

x = -2

y = -3

Step-by-step explanation:

5x - y = -7

x + y = -5

6x = -12

x = -2

x + y = -5

-2 + y = -5

y = -5 + 2

y = -3

Answer:

(-2,-3)

Step-by-step explanation:

x + y = -5

y = -x - 5

5x - (-x - 5) = -7

5x + x + 5 = -7

6x = -12

x = -2

x + y = -5

-2 + y = -5

y = -3

Answer:

the answer is 2,808

Step-by-step explanation:

you have to multiply 78 by 36 because it is area

Answer:

-1/8, 69%, 5 and 50

Step-by-step explanation:

→ Convert -1/8 to a number format

-1/8 = -0.125

→ Convert 69% to a number format

0.69

→ Now place in order

-0.125, 0.69, 5, 50

The volume of a cylinder is 50πx

We know that

The volume (V) of a cylinder is,

V = πr²h

where

r is the radius of the cylinder

h is the height of the cylinder

From the question, we have

a cylinder with diameter 10 and height of 2x.

r = 10/2 =5

V = πr²h

V = π*5²*2x

V = 50πx

Multiplication:

Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious. In mathematics, the repeated addition of one number in relation to another is represented by the multiplication of two numbers. These figures can be fractions, integers, whole numbers, natural numbers, etc. When m is multiplied by n, either m is added to itself 'n' times or the other way around.

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The inverse of the statement is "If a number does not have exactly two distinct factors, then the number is not prime." Thus Option 2 is the answer.

   When a conditional statement is reversed, the hypothesis and conclusion are both negated. The hypothesis in the original statement is "a number with exactly two distinct factors," while the conclusion is "is prime."

  To make the inverse, we negate both sections. "A number does not have exactly two distinct factors" is the antonym of "A number that has exactly two distinct factors." "Is not prime" is the opposite of "is prime."

    As a result, the inverse statement is "If a number does not have exactly two distinct factors, then the number is not prime."

     It's crucial to remember that a statement's inverse could or might not be accurate. In this instance, the inverse is true since the definition of a prime number is incompatible with the fact that a number has more than two components if it has more than exactly two different factors.

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The percentage is calculated by dividing the required value by the total value and multiplying it by 100.

The monthly net income to keep housing a 30% of his budget is $7000.

The percentage is calculated by dividing the required value by the total value and multiplying it by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

We have,

Cost of monthly housing per month = $2100

$2100 = 30%

Monthly income = 100%

30% = 2100

Multiply 100/30 on both sides.

100/30 x 30% = 100/30 x 2100

100% = 7000

Thus,

The monthly net income to keep housing a 30% of his budget is $7000.

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Answer:

Undefined

Step-by-step explanation:

\(f(x)=2+|x-3|\\f'(x)=\frac{x-3}{|x-3|}\\f'(3)=\frac{3-3}{|3-3|}=\frac{0}{0}\)

Therefore, the function is not differentiable at x=3

Answer:

Its B I think

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Given:

The area of the triangle is 150 square ft.

The base length of the triangle is 20ft.

To find:

The height of the triangle.-

Explanation:

Using the area of the triangle formula,

Substituting the base and area we get,

Therefore, the height of the triangle is 15ft.

Final answer:

The height of the triangle is 15ft.

Answer:

The answer is (y - 1)^3 = (y - 1) (y^2 + y + 1)

Step-by-step explanation:

\((y - 1)^{3} = (y - 1)( {y}^{2} + y \: \: 1 + {1}^{2} ) \\ \\(y - {1)}^{3} = (y - 1)( {y}^{2} + y + 1)\)

The difference between the two investments after 35yrs is $4700 and  Bank of America is offering higher interest than 5/3rd banks.

Most interest is compounded semiannually, quarterly, or monthly. Continuous compounding assumes that interest is compounded indefinitely and reentered on the balance sheet. The continuous compounding formula takes into account four variables.

For the given question,

5/3rd bank offers continuous interest:

For continuous interest, A = P\(e^{rt}\)

where,

P = the initial amount

A = the final amount

r = the rate of interest

t = time

e is a mathematical constant where e ≈ 2.7183.

A = 10000 × \(2.71^{0.042*35}\)

A =  10000 × 4.04

A = $40400 approximately

Interest = Amount - Principle

Interest = 40400 - 10,000

Interest = $30400

Bank of America offers compound interest:

For compound interest:

\(A = P(1 + \frac{r}{n})^{nt}\)

A = 10000 × 4.51

A = $45100

Interest = Amount - Principle

Interest = 45100 - 10,000

Interest = $35100

The above calculation explains Bank of America is offering higher interest than 5/3rd bank by $35100 - $30400 = $4700

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Answer:

64

Step-by-step explanation:

16 ÷ 12 = 1.33 (rounded to 2 decimal places)

1.33 = scale factor

1.33² = area scale factor

1.33² × 36 = 64 (rounded to a whole number)

Answer: 64 would be the area

Step-by-step explanation:

As P-value > significance level (i.e.,0.05), so, null hypothesis can't be rejected. There is no sufficient evidence to support our claim that there was a decrease in voter support for the new candidate after the unfortunate remarks were made.

We have two random samples related to election. For first Sample : Voters was interviewed 3 weeks before the start of a state-wide campaign for governor. Sample size, n₁ = 415

Sample mean, X₁ = 223

Sample proportion for sample one :

\(p₁ = \frac{X₁}{n₁ }= \frac{223}{ 415} = 0.537\)

Consider sample 2ⁿᵈ for several unfortunate remarks one week before the election.

Sample size, n₂ = 630

Sample mean, X₂ = 317

Let the significance level be 95% .

Sample proportion for sample two :

\(p₂ = \frac{X₂}{n₂ }= \frac{317}{630} = 0.503\)

A two-proportion Z-test is a statistical hypothesis test used to determine whether two proportions are different from each other. Consider the null and alternative hypothesis,

\(H₀ : p₂ = p₁

Hₐ : p₂ < p₁\)

Now, we have to check the hypothesis by two- proportion Z-test. Formula is,

\(Z = \frac{( p₁ - p₂)}{ \sqrt{p(1- p)( \frac{1}{n₁} + \frac{1}{ n₂}})}\)

p is mean of both the samples where k₁ is successes out of n₁ data in sample 1 and k₂ is successes out of n₂ data in sample 2.

\(p = \frac{k₂+ k₁} { n₂ + n₁} = 0.512\)

Now, plugging all known values in above formula,

\(Z = \frac{( 0.537 - 0.503)}{ \sqrt{0.512(1- 0.512)( \frac{1}{415} + \frac{1}{ 630}})}\)

\(Z = \frac{0.034}{ \sqrt{0.512(0.488)(0.00399 )}}\)

\(Z = \frac{0.034}{ 0.0316} = 1.076\)

The p-value or z-critical value for two tailed test is 0.2819. We see that 0.281>0.05 ( significance level). So, Null hypothesis can't be rejected. Therefore, null hypothesis is true i.e., there is no decrease in voter support for the new candidate.

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The general solution of the given system of equations is:

x = Ae^(7t), where A is a non-zero constant.

To find the general solution of the given system of equations, we need to solve the system and express the solutions in terms of the variables.

Given the system:

x' = (13 - 2 - 4)x

We can rewrite the system as:

x' = 7x

This is a linear first-order homogeneous system. The general solution can be found by solving the differential equation.

Separating variables, we have:

dx/x = 7 dt

Integrating both sides, we get:

ln|x| = 7t + C

Taking the exponential of both sides, we have:

|x| = e^(7t + C)

|x| = e^(7t) * e^C

Since e^C is a constant, we can write it as A, where A is a non-zero constant. So we have:

|x| = A * e^(7t)

Now, we consider the sign of x:

If x > 0, then x = A * e^(7t)

If x < 0, then x = -A * e^(7t)

Therefore, the general solution of the given system of equations is:

x = Ae^(7t), where A is a non-zero constant.

To describe the behavior of the solutions as t approaches infinity, we look at the exponential term e^(7t). As t increases, the exponential term grows exponentially, which means the solutions will also grow exponentially. Therefore, as t approaches infinity, the solutions will approach infinity or negative infinity, depending on the sign of the constant A.

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Answer:

\(m=\frac{-5}{3}\)

Step-by-step explanation:

We want to find the slope between the points (-2,5) and (1,0).

The slope (m) can be found using the formula \(\frac{y_2-y_1}{x_2-x_1}\), where \((x_1,y_1)\) and \((x_2,y_2)\) are points.

We are already given the values of the points, but let's label their values to avoid any confusion and mistakes.

\(x_1=-2\\y_1=5\\x_2=1\\y_2=0\)

Now, substitute into the formula.

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

\(m=\frac{0-5}{1--2}\)

Simplify this to:

\(m=\frac{0-5}{1+2}\)

\(m=\frac{-5}{3}\)

The slope is -5/3.

Answer:

D. Infinite solutions.

Step-by-step explanation:

Since they give us the equation for (y) we just implement that equation in place of (y) in the second equation

15x+3y=27 now becomes

15x+3(-5x+9)=27

Distribute the 3

15x-15x+27=27

15x and -15x cancel out

27=27

Infinite solutions since both sides are exactly equal.

Hope this helps! If you have any questions on how I got my answer feel free to ask. Stay safe!

Answer:

3.3 inches.

Step-by-step explanation:

We know that the scale of his building is 1 inch for every 400 ft.

And we also know that the actual length of the building is 1320 feet.

So, we can write the following proportion, with x being our unknown model length:

\(\frac{x}{1320}=\frac{1}{400}\)

Note the the lengths line up horizontally. The numerator is all the model lengths, while the denominator is the actual lengths.

Solve for x. Cross multiply:

\(1320=400x\)

Divide both sides by 400:

\(x=3.3\)

Therefore, the length of the model is 3.3 inches.

And we're done!

Answer:

it is your test we can't help you sorry

The use of a stakeholder management tool, such as the power interest grid or the stakeholder assessment matrix, may differ based on the chosen methodology. The methodology selected determines the approach, criteria, and prioritization used in assessing stakeholders and managing their engagement.

The choice of methodology for stakeholder management tools like the power interest grid or the stakeholder assessment matrix can impact how stakeholders are identified, assessed, and prioritized. The power interest grid is a tool that classifies stakeholders based on their level of power and interest in a project or organization. The methodology used to populate this grid can vary, such as through surveys, interviews, or a combination of methods. The methodology chosen can affect the accuracy and reliability of the data gathered, as well as the level of stakeholder involvement in the assessment process.

Similarly, the stakeholder assessment matrix is another tool that evaluates stakeholders based on their level of influence and impact on a project. The chosen methodology will determine the criteria used to assess stakeholders and assign them to different categories within the matrix. For example, one methodology might consider a stakeholder's financial investment, while another might focus on their expertise or social influence. The methodology selected can influence the outcomes of the assessment, such as the identification of key stakeholders or the prioritization of their needs and expectations.

In conclusion, the use of stakeholder management tools like the power interest grid or the stakeholder assessment matrix can differ based on the chosen methodology. The methodology determines the approach, criteria, and prioritization used in assessing stakeholders and managing their engagement. Careful consideration should be given to selecting a methodology that aligns with the specific project or organizational context to ensure effective stakeholder management.

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Answer:

We conclude that the inverse property of addition defines that adding a number and its opposite will be equal to zero.

Step-by-step explanation:

We know that adding a number and its opposite yields zero.

In other words, the inverse property of addition defines that adding a number and its opposite will be equal to zero.

For example,

Adding the number x and its opposite -x.

x + (-x) = 0

In other words, for every 'x', there is an additive inverse '-x' such that

x + (-x) = 0

Other examples such as:

5 + (-5) = 0

-1.33 + 1.33 = 0

It is clear that adding the number and its opposite produces zero.

Thus, we conclude that the inverse property of addition defines that adding a number and its opposite will be equal to zero.

Answer: $0.268

Step-by-step explanation: 5.36 divided by 20 = 0.268

Answer:

Step-by-step explanation:

$0.27

Okay, here we have this:

Considering the provided information, and figures, we are going to find the requested length, so we obtain the following:

Let us remember that if two figures are proportional, then they are proportional between corresponding segments, therefore we have:

Finally we obtain that the measure of PS is 21 units.

A parallel conversion is a method of implementing a new system in which the old and new systems run simultaneously for a period of time. While this approach can have its benefits, there are also potential problems that may arise.

One of the problems with a parallel conversion is that there is a higher risk, as there are two systems running at the same time, which can be costly and require additional resources. Another problem is that the old hardware might fail, which can cause data loss or delays in the conversion process. On the other hand, a lower risk may not be applicable in a parallel conversion because the risk factor is already high. Also, the users have to enter data into both systems, which can be time-consuming and prone to errors. Finally, an abrupt conversion is not applicable in a parallel conversion because both systems are running together. Overall, the parallel conversion method requires careful planning and execution to minimize the potential problems and ensure a smooth transition.

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Answer:

24 inches

Step-by-step explanation:

The probability of consuming at least one insect fragment in more than one bar is 0.3011.

Given that you consumed seven 28.35-gram (one-ounce) bars this week from a brand at the mean contamination level. The probability of finding one or more insect fragments in a 28.35-gram chocolate bar that is produced with the mean level of contamination is 0.4875.

The probability that you consume one or more insect fragments in a single bar is 0.4875The probability that you will not consume an insect fragment in a single bar is 0.5125

The probability that you will not consume an insect fragment in any of the seven bars is 0.5125⁷ = 0.0236The probability that you consume one or more insect fragments in more than one bar is 1 - 0.0236 = 0.9764The probability that you consume one or more insect fragments in more than one bar is 0.9764.

The probability that you consume one or more insect fragments in more than one bar is 0.3011.

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Firstly, OS is the radius of the circumference. So, OS = OR = OT = OP. So:

Similarly, we can find RQ by:

Because QS is tangent to the circumference, the angle m\(\begin{gathered} OQ^2=OS^2+QS^2 \\ 34^2=16^2+QS^2 \\ QS^2=34^2-16^2=1156-256=900 \\ QS=\sqrt[]{900}=30 \end{gathered}\)So, OQ = 34, QS = 30 and RQ = 18.

Answer:

4th answer is correct

Step-by-step explanation:

First, let us make x the subject.

\(\sf \frac{x+4}{4} =\frac{y+7}{7}\)

Use cross multiplication.

\(\sf 7(x+4)=4(y+7)\)

Solve the brackets.

\(\sf 7x+28=4y+28\)

Subtract 28 from both sides.

\(\sf 7x=4y+28-28\\\\\sf7x=4y\)

Divide both sides by 7.

\(\sf x=\frac{4y}{7}\)

Now let us find the value of x/4.

To find that, replace x with (4y/7).

Let us find it now.

\(\sf \frac{x}{4} =\frac{\frac{4y}{7} }{4} \\\\\sf \frac{x}{4} =\frac{4y}{7}*\frac{1}{4} \\\\\sf \frac{x}{4} =\frac{4y}{28}\\\\\sf \frac{x}{4} =\frac{y}{7}\)