Determine if the ordered triple is a solution to the system of equations.

1. 3x+4y-z=5. a) (-1, 2, 0)
5x-y + 3z=-7. b) (-2, -6, 3)
9x + 5y + 7z=-21


Please show step by step

The exact value of tan(θ ) in simplest radical form is 1/9 .

What is the trigonometric ratio?

Trigonometric ratios are the ratios of a right triangle's sides. The sine (sin), cosine (cos), and tangent (tan) are three often used trigonometric ratios. There are other trigonometric ratios which are reciprocals of these ratios.

Trigonometric ratios can be computed either using the provided acute angle or by calculating the ratios of the right-angled triangle's sides.

(-9,-1), is a point with x= -9 = adjacent side, y= -1 = opposite side

tan(θ ) = opposite side/adjacent side = -1/-9  = 1/9

1/9 can't be simplified further

So, the exact value of tan(θ ) in simplest radical form is 1/9 .

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System A: (1, -1)

System B: No solution

Answer:

System A

The system has a unique solution: x=1, y=-1

System B

The system has no solution

Step-by-step explanation:

System A

Use simultaneous equations to see if we can solve the system by multiplying the second equation by -1 and adding them together:

5x + 3y = 2

-4x - 3y = -1

We get (5-4)x+(3-3)y=(2-1), which simplifies to x=1

If x=1:

5+3y=2

3y=-3

y=-1

Since we have specific answers for x and y, we can say the system has a unique solution.

System B

If y is equal to both 5x+8 and 5x+5, that means

5x+8=5x+5

Subtracting 5x from both sides we get 8=5, which is illogical.

Therefore the system has no solution

Answer:f(4)=−2f(3)=(−2)∗(+640)=−1280

The object continues to roll without slipping, and the actual force of static friction stays constant.

A force that holds an object at rest is called static friction.

The definition of static friction is: The resistance people feel when they attempt to move a stationary object across a surface without actually causing any relative motion between their body and the surface they are moving the object across.

The range of static friction is 0 to the minimum force required to initiate motion.

The following is the formula to determine static friction: Normal Force x Static Friction Coefficient = Static Friction.

So, in the given situation the object keeps rolling without slipping, and the static friction's actual force remains constant.

Therefore, the object continues to roll without slipping, and the actual force of static friction stays constant.

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The total change in the stock market from the beginning of the day to the end of the day is 89.75

A fraction is written in the form of a numerator and a denominator where the denominator is greater than the numerator.

Example: 1/2, 1/3 is a fraction.

We have,

At the beginning of the day, the stock market goes up 30 1/2 points.

At the end of the day, the stock market goes down 120 1/4 points.

The total change in the stock market from the beginning of the day to the end of the day.

= 120(1/4) - 30(1/2)

= 481/4 - 61/2

= 120.25 - 30.5

= 89.75

Thus,

The total change in the stock market from the beginning of the day to the end of the day is 89.75

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The fundamental difference between t-test and z-score is: t-test is used to determine the difference in data sets, the standard deviation and the z-score is used to to draw data from a given population with different means and standard deviation. A) The t statistic uses the sample mean in place of the population mean

T-test is a statistic model which is used to find how averages of different data sets differ in case the standard deviation and Z-scores statistic helps to draw data from populations with different means and standard deviations and also place them on a common scale.

The z-core formula is:

Z₁=[tex]\frac{x-m}{s}[/tex]

Therefore the fundamental difference is that the t-test uses the variance in place of the population variance.

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Complete question:

Which of the following is a fundamental difference between the t statistic and a z-score?

A) The t statistic uses the sample mean in place of the population mean

B) All of the choices are differences between t and z.

C) The t statistic computes the standard error by dividing the standard deviation by n - 1 instead of dividing by n.

D) The t statistic uses the sample variance in place of the population variance.

Answer:

129723

Explanation:

[tex]1800(1+0.13)^{35} \approx 129723[/tex]

Answer:9/10

Step-by-step explanation:

make 3/4 equal to 3/20 by multiplying by 5

15/20 + 3/20 = 18/20

18/20 = 9/10

The graph of the line that represents the given equation, 3x - 4y = 8, is shown below

From the question, we are to graph the line that represents the given equation.

The given equation is

3x - 4y = 8

To graph the line, we will determine x-intercept and y intercept of the line.

The x-intercept in the point where y equals zero on the line

and

The y-intercept in the point where x equals zero on the line

Determining the x-intercept

3x - 4y = 8

Set y = 0

3x - 4(0) = 8

3x = 8

x = 8/3

The x-intercept is (8/3, 0)

Determining the y-intercept

3x - 4y = 8

Set x = 0

3(0) - 4y = 8

-4y = 8

y = 8/-4

y = -2

The y-intercept is (0, -2)

Using the x-intercept and y-intercept, the graph of the line is shown below

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Answer: the answer is A,B,E

Step-by-step explanation:

Answer: The answer is (four/seven)

Yes, because it forms a straight line.

Arithmetic; it's a linear function.

Step-by-step explanation:

2023 Edgen

Answer:

y = 10/17x - 7

Step-by-step explanation:

→ Write in standard form

y = 10/17x + c

→ Substitute in (17, 3)

3 = 10 + c

→ Solve for c

c = -7

→ Rewrite

y = 10/17x - 7

Given two calculations are different.

What is a square of a number?

The square of any number can be calculated by multiplying the number by itself twice.

Let 'a' be any number then the square of this number 'a' will be

                        a² = a × a

Now  - 3² = - (3) × (3)

               = -9  ----------(I)

and (-3)² = (-3) × (-3)

              = 9 ----------(II)

By observing (I) and (II) we can say that in the second case just because of the scope of brackets the square of -3 would result in 9.

But in the first case square of 3 would give 9 and because of the minus sign, it gave -9.

Hence, These two calculations are different.

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Answer:

-626.8

Step-by-step explanation:

78 -716 + (0.8)(14)

78 - 716 + 11.2

(78 -716) + 11.2

-638 + 11.2

-626.8

The divide rule will be;

⇒ Divisor = (Dividend - Remainder) / Quotient

What is Division method?

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

Vocabulary Use the terms divisor, dividend, quotient, and remainder.

Now,

If we have to find the divisor , then we can use the divide rule as;

⇒ Divisor = (Dividend - Remainder) / Quotient

Thus, The divide rule will be;

⇒ Divisor = (Dividend - Remainder) / Quotient

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Answer:

About 2.1 pounds a month.

Step-by-step explanation:

In this question, we know the amount of weight gained and the time it took, 20 pounds and 9.5 months.

to find the rate, we can do:

20/9.5

about 2.1

So, the answer will be:

about 2.1 pounds / month

The value of the quotient of the polynomial is 2x^2 + 2x + 10 and the remainder is 28

A method for solving a rational number that represents a polynomial divided by a monomial or another polynomial is called "dividing polynomials." In order to divide normally, we place the dividend and the divisor in the exact same manner.

Divide the first term of the dividend by the highest term of the divisor, which in this case is x (i.e., the term with the highest power of x).

Divide the divisor by the outcome you just got (the first term of the eventual quotient).

By following the above rules where

2x3-4x2+3x+2 is divided by the x-3, We get the following equation

where

quotient is 2x2+2x+10

and the remainder is 28

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The value of the digit 4 in the number 3.04 is 0.04.

What is the Place Value of a digit ?

Place value is the value a digit in a number represents based on the number's place within the whole.

Here, The place value of the digit 4 is hundredths.

So, Value of digit 4 =  4/100 = 0.04.

Hence, Value of digit 4 in 3.04 is 0.04.

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The quotient is 2x² + 10x − 5, and the remainder is 0.

What is synthetic division?

Synthetic division is a method in algebra for manually performing Euclidean division of polynomials that requires less writing and fewer calculations than long division. It is typically taught for division by linear monic polynomials, but the method can be applied to any polynomial.

The given polynomial is (2x³ + 4x² - 35x + 15) and we have to divide this polynomial by (x - 3).

By using synthetic division

   2x³ + 4x² - 35x + 15

Take the constant term of the divisor with the opposite sign and write it to the left

     3 |   [tex]x^3[/tex]    [tex]x^2[/tex]     [tex]x^1[/tex]      [tex]x^0[/tex]

        |   2     4     -35     15

   ----|----------------------------

Write down the first coefficient as it is

Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).

Add the obtained result to the next coefficient of the dividend, and write down the sum.

   3 |   2            4     -35     15

      |         3.2 = 6

 ----|----------------------------

         2           10    

Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).

Add the obtained result to the next coefficient of the dividend, and write down the sum.

 3 |   2      4     -35     15

    |           6       30

-----|----------------------------

         2    10       -5

Again, we get

3 |   2      4     -35     15

    |           6      30   -15

-----|----------------------------

         2    10     -5      0

We have completed the table and have obtained the following resulting coefficients: 2,10,−5,0.

Thus, the quotient is 2x² + 10x − 5, and the remainder is 0.

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The statement that is used to prove the congruence of angles PTR and STQ is given by:

Lines PQ and RS intersect at an angle less than a right angle.

Congruent angles are angles that have the same measure.

One example of congruent angles is for vertical angles, as these angles are opposite by the same vertex in crossing segments, with an angle less than a right angle of 90º, and then these two angles will be congruent.

The common vertex in the segment given at the end of the answer is of:

T.

The vertical angles are both acute angles, that is, angle measures that are less than 90º, which is the reason for the correct statement.

The diagram is given by the image presented at the end of the answer.

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Answer: First number is 16, second number is 17.

Step-by-step explanation
16 + 17 = 33

16 x 7 = 112
17 x 5 = 85

112 + 85 = 197

Answer:

I didn't know kindergardeners had Brainly.

No cup of ketchup remains.

Brown Sugar =1/4 C

Cider Vinegar = 1/2 C

Ground Cumin = 1tsp

Ketchup           = 2/3 C

Pepper             = 1tsp

Total Quantity of Ketchup =9 cups

1 batch of barbecue sauce =2/3 Cup

x batch of barbecue sauce =9 Cups

x batch of barbecue sauce = 9 Cups *1 batch of barbecue sauce

                                                               2/3 Cup

x batch of barbecue sauce =13[tex]\frac{1}2}[/tex] batches

we know that;

1 batch of barbecue sauce =2/3 Cup

Therefore,

The total number of ketchup Cups used = Total  batch of barbecue sauce *quantity for1 batch of barbecue sauce

               =       13[tex]\frac{1}2}[/tex] batches * 2/3 Cup

The total number of ketchup Cups used =  9 Cups  

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If an 80% confidence interval for a proportion is found to be (0.27, 0.33), then the sample proportion would be 0.30

Sampling is frequently used to estimate the proportion of a population that has a given attribute, such as the proportion of all faulty goods coming off an assembly line or the proportion of all individuals visiting a retail store who make a purchase before leaving. The percentages for the population and sample are written as p and p, respectively. Thus, if 43% of individuals visiting a business make a purchase before departing, p = 0.43; if 78 people enter the store and make a transaction, p=78/200=0.39.

The sample proportion is a random variable because it differs from sample to sample in ways that are impossible to anticipate in advance.

How to solve?

For this case the confidence interval is given by:

(0.27; 0.33)

We can find the estimaed proportion in the following way:

p = (0.27 + 0.33)/2 = 0.30

then the sample proportion would be 0.30

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There may be an association, but not a correlation unless the variables are quantitative. There could be a correlation between the average number of hours of TV watched per person and number of crimes committed per year. Even if there is a relationship, one does not cause the other.

Correlation is a statistical measure that expresses the extent to which two variables are linearly related (meaning they change together at a constant rate).

What are qualitative and quantitative variables?

The variables are classified as qualitative or quantitative as follows:

Qualitative variables assume labels as values.

Quantitative variables assume numbers as values.

The relevance of the variables according to association and correlation are given as follows:

Qualitative variables can have association.

Quantitative variables can have correlation.

The variables in this problem are given as follows:

Television watching -> yes/no -> qualitative.

Crimes committed -> yes/no -> qualitative.

As they are qualitative variables, they can have association, and thus there is no correlation between the two variables

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The distance between N and PS is 3.2.

What is the midpoint of the segment?

Take the distance between the two endpoints and divide it by two. This distance from either end is the line's midpoint. Alternatively, add the endpoints' x coordinates and divide by 2. Repeat for the y coordinates.

From the below figure,

N is the intersection of the red and blue circles.

I’ve drawn PQRS as the square (0,0), (4,0), (4,4), and (0,4).

Then the formula for the red circle is:

             (x-2)² + (y-4)² = 4.

The formula for the blue circle is

                  x² + y²- 16 = 0.

Solving for x and y yields intersections

               (0, 4) and (3.2, 2.4),

the first being S and the latter being N.

Hence, the distance between N and PS is 3.2.

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Step-by-step explanation:

b.) 8/7≈ 1.1

Final.) and then using the exponential decay formula, 18.1 will be left after

The area of the triangle in the image is 1/20 square centimeters.

This is a rather trivial problem.

On the image, we can see a triangle where the height and the base are known quantities.

Remember that for a triangle of height H and base B, the area is given by the formula:

A = B*H/2

Here we can see that:

H = (1/6) cm

B = (3/5) cm

Then we can replace these two fractions on the area formula, we will get:

A = (1/6 cm)*(3/5 cm)/2

A = (3/5*6 cm²)/2

A = (3/30*2 cm²)

A = (3/60 cm²) = (1/20 cm²)

That is the area of the triangle in the image.

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Answer:

Step-by-step explanation: