Which statements are true about the ordered pair (5, −6) and the system of equations?

{x+y=−1
3x−y=21

Select each correct answer.

The ordered pair (5, −6) is a solution to the first equation because it makes the first equation true.

The ordered pair (5, −6) is a solution to the second equation because it makes the second equation true.

The ordered pair (5, −6) is not a solution to the system because it makes at least one of the equations false.

The ordered pair (5, −6) is a solution to the system because it makes both equations true.

Ronnie cut a total of 9 inches of wood. This is determined by multiplying the number of sections he cut (12) by the length of each section (3/4 inch).

Ronnie cut 12 sections of wood, each measuring 3/4 inch to make his birdhouse's roof. In order to find out the total length of wood he used, we need to multiply the number of sections he cut by the length of each section. This is a basic multiplication problem in fractions.

So, 12 (sections) x 3/4 (inches/section) = 9 inches.

This means Ronnie cut a total of 9 inches of wood to make the birdhouse roof.

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They both have 24 in common, She bought 3 packs of hotdogs and two packs of hotdog buns.

We have given that,

At a local store, hot dogs come in packages of 8, and hot dog buns come in packages of 12.

Let's first analyze the word problem we have here.

It is stating that she, Arpitha, bought the minimum packs of hotdogs and minimum packs of buns to get an equal number of buns to hotdogs.

We can find the multiples they have in common.

8, 16, 24, 32, 40

12, 24, 36, 48, 60

They both have 24 in common, She bought 3 packs of hotdogs and two packs of hotdog buns.

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The probability that the commuter doesn't get stopped all week long is approximately 0.44.

To find the probability that the commuter doesn't get stopped all week long, we need to find the probability of not getting stopped on each day and then multiply those probabilities together. Since the commuter estimates that he gets stopped on about 15% of work days, the probability of not getting stopped on a single day is 1 - 15% = 85%. To find the probability of not getting stopped all week, we raise 85% to the power of 5, since there are 5 work days in a week:

Probability of not getting stopped all week = (85%)5 = 0.85 * 0.85 * 0.85 * 0.85 * 0.85 = 0.44370515625.

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The probability that the commuter doesn't get stopped by the train all week long is 44%.

This question falls under the category of probability in mathematics. The commuter estimates he'll get stopped 15% of work days, which implies that he'll have a smooth commute 85% of the time (100% - 15%). In a 5-day work week, the probability that he doesn't get stopped at all can be computed by multiplying the probability of not getting stopped each day. Therefore, the answer is (0.85)^5 or approximately 0.44, which represents 44%.

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Answer:

The correct answer is twelve.

Step-by-step explanation:

The values of a would make the expression 36, 49 and 81.

The correct options are b, c, and d.

For variable x : ax² + bx + c = 0, where a≠0 is a standard quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.

To factor the expression x² - a completely, we need to write it as a product of two binomials.

This can be done using the difference of squares formula, which states that a² - b² = (a + b)(a - b).

If we apply this formula to x² - a, we get:

x² - a = (x + sqrt(a))(x - sqrt(a))

This is a factorization of x² - a into two binomials, where the constant term a is represented by the square root of a.

For the expression x² - a to be completely factored, both factors must be irreducible (meaning they cannot be factored any further). This requires that a be a perfect square.

Out of the given options, 36, 49, and 81 are perfect squares.

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Answer:

78,000

Step-by-step explanation:

9.75 is 7.8 times larger than 1.25.

However, we have powers of 10.  In the first number, 10 is raised to the 6th power; in the second number, 10 is raised to the 2nd power.  This means that the first number is 10⁴ times bigger than the second one, or 10000 times bigger.

This means in total, the first number is 7.8(10000) = 78000 times larger than the second one.

This can be confirmed by dividing the two; 9.75(10⁶)÷1.25(10²) = 78000

Answer:

78000

Step-by-step explanation:

The total travel time one way is 288 minutes.

To find the total travel time one way, we need to add up the time spent on each part of the journey. The salesman spends 1 hour and 48 minutes commuting from his house to the airport. Let's convert this to minutes, which gives us 60 + 48 = 108 minutes.

Next, we add the flight time. The question doesn't specify the duration of the flight, so we can't determine that. We'll assume it takes 2 hours, which is 120 minutes. Finally, we add the time spent on the bus. Again, the question doesn't provide this information, so let's assume it takes 1 hour (60 minutes) by bus.

Adding up the commute time, flight time, and bus time, we get 108 + 120 + 60 = 288 minutes. Therefore, the total travel time one way is 288 minutes.

the right answer is 44.

Answer:

44 degrees.

Step-by-step explanation:

We are asked to find the measure of angle Q using law of cosines.

Law of cosines:

[tex]c^2=a^2+b^2-2ab\times cos(C)[/tex]

Upon substituting our given values in above formula we will get,

[tex]24^2=20^2+34^2-2\times 20\times 34\times cos(Q)[/tex]

[tex]576=400+1156-1360\times cos(Q)[/tex]

[tex]576=1556-1360\times cos(Q)[/tex]

[tex]576-1556=1556-1556-1360\times cos(Q)[/tex]

[tex]-980=-1360\times cos(Q[/tex]

Upon dividing both sides of our equation by -1360 we will get,

[tex]\frac{-980}{-1360}=\frac{-1360\times cos(Q}{-1360}[/tex]

[tex]0.7205882352941176=cos(Q)[/tex]

Now we will use arccos to solve for the measure of angle Q.

[tex]cos^{-1}(0.7205882352941176)=Q[/tex]

[tex]43.896932391182=Q[/tex]

[tex]Q\approx 44[/tex]

Therefore, the measure of angle Q is 44 degrees.

There are 36 boys in the school choir.

The numerical relationship between two values that demonstrates how frequently one value contains or is contained within another.

Given:

There are 18 girls in the school choir.

The ratio of girls to boys is 1 to 2.

That means,

Girls / boys = 1/2

Substituting the values,

18 / boys = 1/2

Boys = 2 x 18

Boys = 36

Therefore, there are 36 boys.

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$2500 is invested at an interest rate of 4.5% per year, compounded daily for 2 years will amount to $5225.

Borrowers are required to pay interest on interest in addition to principal since compound interest accrues and is added to the accrued interest from prior periods.

We know the formula for compound interest is,

A = P(1 + r/100)ⁿ.

Where, A = amount, P = principle, r = rate, and n = time in years.

Given,  $2500 is invested at an interest rate of 4.5% per year, compounded daily, and assuming it is for 2 years.

∴ The amount compounded daily will be,

A = P(1 + (r/365)/100)ⁿˣ³⁶⁵ as compounded daily.

A = 2500(1 + (4.5/365)/100)²ˣ³⁶⁵.

A = 2500( 1 + 0.00101)⁷³⁰.

A = 2500(1.00101)⁷³⁰.

A = 2500×2.09 dollars.

A = 5225 dollars.

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To calculate the future value of an investment of $2500 at a 4.5% interest rate compounded daily for 5 years, we use the compound interest formula. Assuming 5 years of growth, the future value would be approximately $3117.14.

If $2500 is invested at an interest rate of 4.5% per year, compounded daily, we need to find the value of the investment after a certain number of years. The formula to calculate the future value of an investment with daily compounding is given by:

FV = P × (1 + r/n)^(n×t)

where:

To calculate the future value, we plug in the values into the formula. However, the number of years, t, has not been specified, so we'll need that to give a final answer. For our purposes, let's assume the student asks for the value after 5 years. Using the formula:

FV = $2500 × (1 + 0.045/365)^(365×t)

FV = $2500 × (1 + 0.00012328767)^(1825)

FV = $2500 × 1.246856823

FV = $3117.14 (rounded to the nearest cent)

After 5 years, the investment would be worth approximately $3117.14.

One benefit of applying statistical forecasting methods is the ability to make informed predictions and decisions based on historical data.

Statistical forecasting methods utilize historical data and mathematical models to make predictions about future outcomes. By analyzing patterns, trends, and relationships within the data, statistical forecasting methods can provide valuable insights and estimates for various industries and fields.

One key benefit of applying statistical forecasting methods is the ability to make informed decisions and plan for the future. By utilizing historical data and statistical models, organizations can anticipate future demand, sales, or resource needs. This enables them to optimize their operations, allocate resources efficiently, and make strategic decisions.

Statistical forecasting methods also provide a level of objectivity and reliability in the prediction process. These methods are based on rigorous mathematical techniques and statistical principles, ensuring that the forecasts are grounded in sound methodology. This allows decision-makers to have confidence in the accuracy and validity of the forecasts, reducing uncertainty and aiding in effective planning.

Overall, applying statistical forecasting methods provides a systematic and data-driven approach to predicting future outcomes. It enables organizations to anticipate and adapt to changing circumstances, optimize their resources, and make informed decisions, leading to improved efficiency, profitability, and overall performance.

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Final answer:

The total duration of the appointment was 2 hours and 45 minutes.

Explanation:

To determine how long the appointment lasted, we need to calculate the time difference between the start time and the end time. The appointment started at 2:30 pm and ended at 5:15 pm.

First, take note of the start time: 2:30 pm.

Then, take note of the end time: 5:15 pm.

Calculate the hours by subtracting the start hour from the end hour: 5 pm - 2 pm = 3 hours.

Next, calculate the minutes by subtracting the start minutes from the end minutes: 15 minutes - 30 minutes. Since you cannot have a negative number of minutes, you need to borrow an hour from the 3 hours calculated, making it 2 hours, and add 60 minutes to the 15 minutes. Now, 75 minutes - 30 minutes = 45 minutes.

Combine the total hours and minutes: 2 hours and 45 minutes

Answer:

The number written in standard form is [tex]131,480,000[/tex]

Step-by-step explanation:

we have

[tex]1.3148*10^8[/tex]

we know that

[tex]10^8=100,000,000[/tex]

substitute

[tex]1.3148*10^8=1.3148(100,000,000)[/tex]

Remember that

When multiplying decimals by 10, move the decimal point one space to the right

In this case move the decimal point eight spaces to the right

[tex]1.3148(100,000,000)=131,480,000[/tex]

therefore

The number written in standard form is [tex]131,480,000[/tex]

Answer:

Correct option is:

C. [tex](x-\sqrt{3})(x^2+3+x\sqrt{3} )[/tex]

Step-by-step explanation:

x^3-3sqrt(3)

=  [tex]x^3-3\sqrt{3} \\\\=x^3-\sqrt{3}^3[/tex]

= [tex](x-\sqrt{3})(x^2+3+x\sqrt{3} )[/tex]

(since, [tex]a^3-b^3=(a-b)(a^2+b^2+ab)[/tex])

Hence, the correct option is:

   C.    [tex](x-\sqrt{3})(x^2+3+x\sqrt{3} )[/tex]

Answer:

The factored form of given polynomial is [tex]x^3(4x^2-5x-9)[/tex]

Step-by-step explanation:

Given the polynomial [tex]4x^5 - 20x^4 - 36x^3[/tex]

We have to factor the above polynomial completely.

[tex]4x^5 - 20x^4 - 36x^3[/tex]

Take [tex]x^3[/tex] common from each term.

[tex]x^3(4x^2-5x-9)[/tex]

Here, the quadratic polynomial is prime i.e it cannot be factored into lower degree polynomial. It has complex roots.

Hence, the factored form of given polynomial is [tex]x^3(4x^2-5x-9)[/tex]

Answer: 4x^3(x^2 - 5x - 9)

Proof of validity is shown below.

Answer:

The function is given to be :

f(x) = 7 - 4.5x

Now, to make a correct input-output table for the given function write the given function in the form of y and x

⇒ y = 7 - 4.5x

Now, in this equation x is independent variable and y  is dependent variable.

So, give the input values to the variable x and note down the output values of variable y.

The required table is :

x      0         1           2             3

y      7        2.5       -2           -6.5