Consider the 3 x 3 system of equations with unknown x,y and z given as follows 2x + 4y - 2z = 1 2x + 8y + 4z = 1 30x + 12y - 4z = 1. (1) 5.2.1 Write down the constant matrix of this system of equations. 5.2.2 Write down the coefficient matrix of this system of equations. 5.2.3 Calculate the determinant of the matrix given on 5.2.2. (3) (2)

The position in the sequence for the given sequence will be 2n + 1. Then the correct option is C.

Let a₁ be the first term and d be a common difference.

Then the nth term of the arithmetic sequence is given as,

aₙ = a₁ + (n - 1)d

The sequence is given below.

3, 5, 7, 9, 11, ...

The first term is 3. And the common difference is given as,

d = 5 - 3

d = 2

Then the position in the sequence for the given sequence will be given as,

aₙ = 3 + (n - 1) · 2

aₙ = 3 + 2n - 2

aₙ = 1 + 2n

The position in the sequence for the given sequence will be 2n + 1. Then the correct option is C.

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Answer: C

Step-by-step explanation: C

2 divided into 9 parts is 2/9.

Let's' explain this visually

Take this pizza, (image below)

Let's say we have two pizzas for 8 friends (including ourselves), so naturally, we'll cut the pizza's each into 9 slices, 1 for each, now everyone gets 1/9 of a pizza, but there are two pizzas, so if we add 1/9+1/9, we'll get two ninths.

Now 2/9=0.2 repeating!

This is how I got my answer sorry for the vague  explanation

Answer:

172

Step-by-step explanation:

I promise you that this is right!

Answer:

-1x + 9. This is the simplest form

Answer:

The area of the trapezoid shown above is 660 square inches.

Step-by-step explanation:

It already gives you the formula, so just plug in the numbers given.

\(h\) - height (20)

\(B_1\) - Base (30)

\(B_2\) - Other base (36)

\(\frac{1}{2}(20)(30+36)\\\frac{1}{2}(20)(66)\\=660\)

The axis of symmetry of the function f(x) = -(x - 9)(x - 21) is x = 15. Hence, option (d) is the correct answer.

The given function f(x) = -(x - 9)(x - 21) is in the form of the quadratic function of x.

So, we can use the formula for the axis of symmetry of the quadratic function which is given byx = -b / 2a

where a and b are the coefficients of the quadratic equation (ax² + bx + c = 0).

So, by comparing the given quadratic function f(x) = -(x - 9)(x - 21) with the general form ax² + bx + c, we have a = -1 and b = -30.

Now, substitute these values of a and b in the formula of axis of symmetry

x = -b / 2a

=> x = -(-30) / 2(-1)

=> x = 30 / 2

=> x = 15

Therefore, the axis of symmetry of the given function f(x) = -(x - 9)(x - 21) is x = 15.

Hence, option (d) is the correct answer.

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345.989554676 to 1 decimal place is 346.0

Decimals numbers are the numbers, which consist of two parts namely, a whole number part and a fractional part separated by a decimal point.

Example of decimal numbers are as follows;

12.4, 18. 9455, 56.7999, 6.7789, 9.067 etc.

When you round to the one decimal place, or to the nearest tenth, the number in the hundredth point place will determine whether you round up or down.

If the hundredths digit or second decimal number is a number between 5 and 9, round up to the nearest whole number. If it's a number between 0 and 4, you would "round down" by keeping the tenths place the same.

Therefore,

345.989554676 to 1 decimal place is 346.0

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The area of the parallelogram with sides measuring 44, 38, and an included angle of 35 degrees is approximately 1,008.77 square units.

To find the area of a parallelogram, we need to know the length of one side and the perpendicular height. However, in this case, we are given the lengths of two adjacent sides (44 and 38) and the measure of the included angle (35 degrees). To find the area, we can use the formula:

Area = side1 * side2 * sin(angle)

Plugging in the values, we have:

Area = 44 * 38 * sin(35 degrees)

To calculate this, we convert the angle from degrees to radians since the trigonometric functions in most programming languages work with radians. Using the conversion formula (radians = degrees * pi / 180), we find that 35 degrees is approximately 0.610865 radians.

Area = 44 * 38 * sin(0.610865)

Using a scientific calculator or a programming language, we can evaluate sin(0.610865) to be approximately 0.5815.

Area = 44 * 38 * 0.5815

≈ 1008.77 square units

Therefore, the area of the parallelogram is approximately 1,008.77 square units.

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The top right graph could show the arrow's height above the ground over time.

The initial and the final height are both at eye level, which is the reference height, that is, a height of zero.

This means that the beginning and at the end of the graph, it is touching the x-axis, hence either the top right or bottom left graphs are correct.

The trajectory of the arrow is in the format of a concave down parabola, hitting it's maximum height and then coming back down to eye leve.

Hence the top right graph could show the arrow's height above the ground over time.

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Answer:

x = -3.5 and y = -5.5

Step-by-step explanation:

y = x - 2 and y = 3x + 5

so x - 2 = 3x + 5

subtract one x from both sides:

-2 = 2x + 5

subtract 5 from both sides:

-7 = 2x

solve for x:

2x = -7, x = -3.5.

now find y:

y = x - 2 = -3.5 - 2 = -5.5

Answer:

it is option D because it make supplementry or 180°

On solving the provided question, we can say that the range is between the two sides' difference and their sum.

The variable's range is obtained by finding its largest observed value (maximum) and subtracting its smallest observed value (minimum). Variational bounds or possible range: various steel prices; various styles; The extent or magnitude of a procedure or action: insight. the maximum or expected range of a weapon's projectile. The range of a list or set is the number between the minimum and maximum. Prior to identifying the region, align all the numbers. Remove (remove) the lowest number from the highest number next. The list's range is provided in the solution.The solution provides the list's range.

T is length of the third side

\(18-13 < T < 18+13\)

\(5 yards < third side < 31 yards\)

The range is between the two sides' difference and their sum.

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To prove that two triangles are similar, one of the following conditions must be satisfied: 1) Three pairs of corresponding sides are proportional (SSS Similarity), 2) Two pairs of corresponding sides are proportional and the included angles are congruent (SAS Similarity), or 3) Two pairs of corresponding angles are congruent (AA Similarity).

SSS Similarity: If we can show that the ratios of the corresponding sides of two triangles are equal, then the triangles are similar. For example, if the ratios of the lengths of the corresponding sides of triangle ABC and triangle DEF are AB/DE, BC/EF, and AC/DF, and these ratios are equal, then the triangles are similar.

SAS Similarity: If we can prove that two pairs of corresponding sides of the triangles are proportional and the included angles between them are congruent, then the triangles are similar. For example, if AB/DE = BC/EF and angle BAC = angle EDF, then triangles ABC and DEF are similar.

AA Similarity: If we can demonstrate that two pairs of corresponding angles in the triangles are congruent, then the triangles are similar. For example, if angle A in triangle ABC is congruent to angle D in triangle DEF, and angle B in triangle ABC is congruent to angle E in triangle DEF, then the triangles are similar.

It is important to note that proving similarity based on these conditions does not require measuring the actual lengths of the sides or angles but rather establishing the proportional relationships or congruence between them.

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Answer:

A right triangle is a triangle that has 90 degrees angle in one of its parts. You are given two points that have coordinate:

x1,y1= (-2, 4)

x2,y2= (-1,1)

To make the angle 90 degrees, there is two possible third point coordinate:

1. x1, y2 = (-2,1)

2. x2, y1= (-1,4)

The right triangle would be option C: (-2,1)

Option A and B is not a right triangle

Step-by-step explanation:

Answer:

the coordinates of vertex E is (6,0)

C(2,0),compare this to(2,4)

same x.but y=0

(6,0)comparing to (6,12)

we get it

(a) The correct option is C

(b) The correct option is B

Given the expression:

To write this in logarithmic form, we first add 6 to both sides of the equation

From

Take logarithm of both sides

The exact value  of \(sin 2x\) is \(4√5/9.\)

Given that \(sec x = 3/2 and csc y = 3\)where x and y are in the 2x = 2 sin x quadrant, we need to find the exact value of sin 2x.

In the first quadrant, we have the following values of the trigonometric ratios:\(cos x = 2/3 and sin y = 3/5\)

Also, we know that sin \(2x = 2 sin x cos x.\)

Now, we need to find sin x.

Having sec x = 3/2, we can use the Pythagorean identity

\(^2x + 1 = sec^2xtan^2x + 1 = (3/2)^2tan^2x + 1 = 9/4tan^2x = 9/4 - 1 = 5/4tan x = ± √(5/4) = ± √5/2\)

As x is in the first quadrant, it lies between 0° and 90°.

Therefore, x cannot be negative.

Hence ,\(tan x = √5/2sin x = tan x cos x = √5/2 * 2/3 = √5/3\)

Now, we can find sin 2x by using the value of sin x and cos x derived above sin \(2x = 2 sin x cos xsin 2x = 2 (√5/3) (2/3)sin 2x = 4√5/9\)

Therefore, the exact value  of sin 2x is 4√5/9.

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Answer:

Step-by-step explanation:

Solution

Start with the product

The product is 7*x where x is a number but not specified.

Now add 6

Answer: 7x + 6      

This cannot be simplified any more than what it is now.

Represent the following sentences as an algebraic expression:

Assuming:

6 is added to the product of 7 and a number.

Product : 7 × x = 7x

Now we will add 6.

Add : 7x + 6.

Final Answer:

7x + 6.

\( \star\tiny\pmb{spbankingandsscseries} \small\star \)

Answer:

i dont know if its right but i think its 2.01

if im wrong im so sorry

The height is 2.0066 meter.

Number systems are systems in mathematics that are used to express numbers in various forms and are understood by computers. A number is a mathematical value used for counting and measuring objects, and for performing arithmetic calculations. Numbers have various categories like natural numbers, whole numbers, rational and irrational numbers, and so on. Similarly, there are various types of number systems that have different properties, like the binary number system, the octal number system, the decimal number system, and the hexadecimal number system.

A number system is a system representing numbers. It is also called the system of numeration and it defines a set of values to represent a quantity

Given:

height= 6 feet and 7 inches

Convert feet to meter

1 feet= 0.3048 meter

6 feet = 6* 0.3048

          =1.8288 meter

Now, convert inch to meter

1 inch= 0.0254 meter

7 inch = 0.0254 * 7

          =0.1778 meter

So,

6 feet and 7 inches= 1.8288 + 0.1778

                               = 2.0066 meter

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Answer:

\(-3 \frac{1}{3}t+6\)

Step-by-step explanation:

Given expression:

\(\sf 7\frac{1}{3}t-\left(10 \frac{2}{3}t-6\right)\)

Remove the parentheses:

\(\implies \sf 7\frac{1}{3}t-10 \frac{2}{3}t+6\)

Factor out the common term t:

\(\implies \sf \left(7\frac{1}{3}-10 \frac{2}{3}\right)t+6\)

Change the mixed numbers into improper fractions:

\(\implies \sf \left(\dfrac{7 \cdot 3+1}{3}-\dfrac{10 \cdot 3+2}{3}\right)t+6\)

\(\implies \sf \left(\dfrac{22}{3}-\dfrac{32}{3}\right)t+6\)

Subtract the fractions:

\(\implies \sf \left(\dfrac{22-32}{3}\right)t+6\)

\(\implies \sf \left(\dfrac{-10}{3}\right)t+6\)

Convert the improper fraction back into a mixed number:

\(\implies -3 \frac{1}{3}t+6\)

Answer:

Its 5

Step-by-step explanation:

-3 * 5 = -15 , i.e smaller than 15.

Here we have a program written in C++ language. Each // symbol is a relative comment explaining the reason for each command line (and is not included during the program execution).

The Program:

#include <iostream>

//c++ build in library

using namespace std;

//main code body starts here

int main()

{

 //declare variable to store phone numbers,its area code, prefix and line    number.

long pnumber;   //declare long variable

int ac, prefix, lnumber;

 //declare integer variables, where ac: Area Code and lnumber is the Line Number

cout<<"Enter a 10-digit Phone Number: "<<endl;

 //cout command prints on screen the desired message

 cin>>pnumber;

 //cin command enables the user to interact with the programm and enter information manually

//main body to obtain the desired output starts below

 //each 'division' is used to allocate the correct value at the correct

 //since prefix is used to get the desired output of ( )    -

 ac = pnumber/10000000;

 prefix = (pnumber/10000)%1000;

 lnumber = pnumber%10000;

 //main body ends here

 cout<<"Based on your 10-digit number"<<endl;

 cout<<"below you have (AreaCode), Prefix, and - line number "<<endl;

 cout<<"("<<ac<<")"<<""<<prefix<<"-"<<lnumber<<endl;

 //Prints on screen the desired output of the long 10 digit Number

 return 0; //ends program

}

-------------------------------------------------------------------------------------------------------

The Output Sample:

Enter a 10-digit Phone Number:

8019004673

Based on your 10-digit number

below you have (Area Code), Prefix, and - line number

(801) 900-4673

....Programm finished with exit code 0

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Answer:

x = 4

Step-by-step explanation:

Since, QS bisects \( \angle PQR\).

\(\therefore m\angle PQS = \frac{1}{2} \times m\angle PQR\\

\therefore (10x + 1)\degree = \frac{1}{2} \times 82\degree \\

\therefore (10x + 1)\degree = 41\degree \\

\therefore 10x + 1 = 41 \\

\therefore 10x = 41 - 1\\

\therefore 10x = 40\\

\therefore x = \frac{40}{10} \\

\huge \orange {\boxed {\therefore x = 4}} \)

Answer:

1,075

Step-by-step explanation:

4,870-2575=2295

2295-1220=1075

Answer:

4870 - (1220+2575) = 4870 - 3795 =1075

September he spent $1075

In these options, 0ption D that is, Multicollinearity, is not an assumption of the regression model.

The regression model is a statistical technique used to model the relationship between a dependent variable and one or more independent variables. There are several assumptions associated with the regression model, which should be satisfied for accurate and reliable results.

Option A, Linearity, assumes that there is a linear relationship between the independent variables and the dependent variable. It implies that the relationship can be represented by a straight line.

Option B, Independence, assumes that the observations or data points used in the regression model are independent of each other. This means that the value of one observation does not depend on or influence the value of another observation.

Option C, Homoscedasticity, assumes that the variance of the errors or residuals in the regression model is constant across all levels of the independent variables. It implies that the spread or dispersion of the residuals is consistent.

Option D, Multicollinearity, is not an assumption of the regression model. Multicollinearity refers to a high correlation between independent variables in the regression model, which can cause issues in estimating the individual effects of the independent variables.

Therefore, the correct answer is D) Multicollinearity, as it is not an assumption of the regression model.

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James takes about 120 steps per minute and each step is 2.75 feet long. To find his walking speed in miles per hour, James should use the following calculation.

Convert 120 steps/min to steps/hour by multiplying by 60 (minutes in an hour):120 x 60 = 7,200 steps/hour Convert 2.75 feet to miles by dividing by 5,280 (feet in a mile):2.75 ÷ 5,280 = 0.000520833 miles/step Multiply the distance per step by the number of steps per hour to get the total distance walked in one hour:0.000520833 x 7,200 = 3.75 miles/hour Therefore, James' walking speed is 3.75 miles per hour.

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Using it's concept, it is found that there is a 0.79 = 79% probability that he or she is content with the vacation allowance.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, 500 - 105 = 395 out of 500 employees are content with the vacation allowance, hence:

p = 395/500 = 0.79.

There is a 0.79 = 79% probability that he or she is content with the vacation allowance.

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Answer:Ava bought 2 1/4 pounds of ham for $7.65 at ShopRite last week. This week she bought 3 1/2 pounds of the same ham for $12.60 at Stop & Shop. Which store has the better price per pound for ham? How much less expensive is the ham at the store with the better price?

Step-by-step explanation:

Ava bought 2 1/4 pounds of ham for $7.65 at ShopRite last week. This week she bought 3 1/2 pounds of the same ham for $12.60 at Stop & Shop. Which store has the better price per pound for ham? How much less expensive is the ham at the store with the better price?

The sandwich and soup combos that can be served is 48.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

In this case, 1/3 liter of soup is served with each sandwich and soup combo.

Since the cook made 16 liters of soup to serve with sandwiches as part of the combo. The sandwich and soup combination will be:

= 16 ÷ 1/3.

= 16 × 3

= 48

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