A negative sign indicates the ______ of the number?

According to estimates, FG has a magnitude of 2√5.

The vector direction of FG is given as = 63.43°. (angle formed in the 1st quadrant with anti-clockwise direction).

The distance formula is used in complex numbers to show the plane in addition to its magnitude. Distance formulas can also be used to determine the actual the distances between two planes in three- and n-dimensional planes.

Now, in answer to the question posed;

F and G have coordinates of (-1,10) and (1,-12), respectively.

The formula for calculating the distance between points A and B is as follows:

FG² = (x₂ - x₁)² + (y₂ - y₁)²

FG = √[(x₂ - x₁)² + (y₂ - y₁)²]

The coordinates for the points F and G's  are-

(x₁,y₁) = (-4,0)   and (x₂,y₂) = (-6,-4).

Substituting the given values in the distance formula;

FG = √[(-6 + 4)² + (-4 + 0)²]

FG = √[(-2)² + (-4)²]

FG = √[4 + 16] = √20

FG  = 2√5 (magnitude of the vector FG)

Estimate the direction of this same vector FG now. The angle formed by a vector with a horizontal line defines its direction.

Use one of the following formulas to calculate the direction of a vector.

tan Ф = Δy/Δx

Where, x = horizontal change

and, y = vertical change

tan Ф = (y₂ - y₁)/(x₂ - x₁)

      = (-4 + 0)/(-6 + 4)

tan Ф = -4/(-2) = 2

Ф = 63.43°  (angle lies with in the first quadrant with anticlockwise direction).

As a result, the distance between F and G is determined to be 2√5. (the same as the magnitude of a given vector FG).

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Answer:

D

Step-by-step explanation:

point P is in plane Z not plane X

Answer:

B. 3x10^4

Step-by-step explanation:

9x10^-8 = 0.00000009

3x10^-12 = 0.000000000003

0.00000009 / 0.000000000003 = 30,000

3x10^4 = 3x10,000 = 30,000

The  greatest number of goodie bags he can make is 18.

The number of coloring books that would be in each bag is 4

The number of markers that would be in each bag is 5

The number of chocolate that would be in each bag is 18

The greatest number of goodie bags he can make can be determined by calculating the highest common factor of 72, 90, 180.

The factor of a number is a number that perfectly divides another number. For example, the factors of 18 are 1, 2, 3, 6, 9, 18. The highest common factor is the highest factor of two or more numbers. The highest common factor of 4 and 8 is 4.

Factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72.

Factors of 90 = 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90.

Factors of 180 = 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90 and 180.

Common factors = 1, 2, 3, 6, 9, 18

Highest common factor = 18

The number of coloring books that would be in each bag = 72 / 18 = 4

The number of markers that would be in each bag =90 / 18 = 5

The number of chocolate that would be in each bag = 180 / 18 = 18

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The complete equation is 8 + 13 = 21, then 21 = 8 + 13

The commutative property of addition states that a change in the arrangement or order of a number being added does not affect the sum of the numbers.

Example;

5 + 4 is equivalent to 4 + 5

2 + 3 is equivalent to 3 + 2

Given the expression;

8 + 13 = 21

Using the commutative property of addition, it can also be expressed as;

21 = 8 + 13

In this case, there's no net change in the equation.

Thus, the complete equation is 8 + 13 = 21, then 21 = 8 + 13

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Quinn, the student, is the fastest

Quinn: 30/60, or 1/2 page per second.

Quinn is the fastest student when it comes to folding pamphlets.

A polynomial divided by another polynomial is a rational function. The domain of a rational function is the set of all numbers excluding the denominator's zeros because polynomials are defined everywhere.

A rational function in mathematics is any function that can be defined by a rational fraction, which is an algebraic fraction in which both the numerator and denominator are polynomials.

Find the folding speed of the students per second.

Neiva: 1/3 pages per second.

Sarah: 2/10 or 1/5 pages per second.

Quinn: 30/60 or 1/2 pages per second.

Deron: 45/120 or 3/8 pages per second.

Among these students, Quinn is the fastest student in folding pamphlets.

Therefore, the correct answer is option b. Quinn.

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The inequality or equality that describes the following situation is; m ≤ 77 marbles.

If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality. Set of such values is called solution set to the considered equation or inequality.

Also set of values of the variable involved in the inequality for which the considered inequality holds true is called the solution set for that inequality.

We need to find the inequality or equality that describes the following situation; Juan has over 77 marbles.

Let the marbles juan has m then

The  inequality or equality that describes the following situation is;

m ≤ 77 marbles.

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Answer:

t < -6 (the other part of the question I don't understand)

Step-by-step explanation:

2t < 5 - 17

2t < - 12

t < - 12 /2

t < -6

Answer:

D.) 14/9

Step-by-step explanation:

Remove parenthesis and add

8/9 + 2/3

Get LCD of 9

8/9 + 6/9 = 14/9

Answer:

X is the value of cordinatinate so X is 1

Answer:The answer is x=-10/9 or -1 1/9

Step-by-step explanation:

The relative frequency of the data is being found.

We have the data:

Ages                 Number of students

15 - 18                              5

19 - 22                             5

23 - 26                            5

27 - 30                            10

31 - 34                             3

35 - 38                            10

We need to find the relative frequency of the data:

Total students = 5 + 5 + 5 + 10 + 3 + 10 = 38

Relative frequency = Number / Total × 100

So, we get that:

Ages                 Number of students            Relative frequency

15 - 18                              5                                      13.16 %

19 - 22                             5                                      13.16 %

23 - 26                            5                                      13.16 %

27 - 30                            10                                    26.32 %

31 - 34                             3                                       7.89 %

35 - 38                            10                                    26.32 %

Therefore, we get that, the relative frequency of the data is being found.

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Answer:

$340 per week

Step-by-step explanation:

$40 hours a week

$8.50  per hour

40x8.5=weekly pay

40x8.5=340

The Final value for the given question is 11 /5.

x / 11 = 13 / 65 is the given expression.

Here, we must determine the value of 'x' in the preceding expression.

We get by multiplying '11' on both sides

= x * 11 / 11 = 13 * 11  / 65

By canceling common numbers on the numerator and denominator we get

= x  = 13 * 11 / 65

= x = 11 / 5

Therefore, the correct value for x is 11 /5.

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Step-by-step explanation:

1.x+1

1+1 is 2

Answer:

216

Step-by-step explanation:

Assuming that it is in centimetres, what we have to do is multiply the width by the length. Therefore we have to do 12×18, which equals 216

Answer:Area = w multiplied by l

12*18

=216

pls mark brainliest

Step-by-step explanation:

AB has a magnitude of 9√6 according to estimates.

AB's vector direction is given as Ф = 84.80° (angle which lies in the 4th quadrant with clockwise direction).

In complex numbers, the distance formula is employed to demonstrate the plane as well as its magnitude. Furthermore, distance formulas can be used to calculate the distance between two planes in three-dimensional and n-dimensional planes.

Now, in response to the given question;

J and K have (-1,10) and (1,-12) coordinates, respectively.

The distance formula for the points A and B is as follows:

AB² = (x₂ - x₁)² + (y₂ - y₁)²

AB = √[(x₂ - x₁)² + (y₂ - y₁)²]

The coordinates for the points A and B's  are-

(x₁,y₁) = (-1,10)   and (x₂,y₂) = (1,-12).

Substituting the given values in the distance formula;

AB = √[(1 + 1)² + (-12 - 10)²]

AB = √[(2)² + (-22)²]

AB = √[4 + 484] = √486

AB  = 9√6 (magnitude of the vector AB)

Estimate this same vector AB's direction now. The direction of a vector is defined by the angle formed by it with a horizontal line.

To determine the direction of a vector, utilize one of the formula given.

tan Ф = Δy/Δx

Where, x = horizontal change

and, y = vertical change

tan Ф = (y₂ - y₁)/(x₂ - x₁)

       = (-12 - 10)/(1 + 1)

tan Ф = -22/(2) = -11

Ф = 84.80°  (angle which lies in the 4th quadrant with clockwise direction).

As a result, this same distance between A and B is discovered to be 9√6 (the same as the magnitude of a given vector AB).

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Answer:

c

Step-by-step explanation:

(a) A regular 16- gon is a convex polygon ← True

(b) It has 16 congruent sides ← True

(c)

the sum of the interior angles of a regular polygon is

sum = 180° (n - 2) ← n is the number of sides

here n = 16 , then

sum = 180° × 14 = 2520°

thus 2880° is False

(d)

the sum of the exterior angles of any polygon = 360° ← True

The pattern exists described as a sequence of repeating objects, shapes, or numbers. Patterns can also occasionally be referred to as a series.

The pattern follows the rule tn = t(n-1) × 5

The next three numbers in the pattern be 4, 20, 100, 500, 2500, 12500, 62500.

A recurring arrangement of numbers, forms, colors, and other elements constitutes a pattern in mathematics. The pattern can be connected to any kind of occasion or thing. When a group of numbers are arranged in a particular way, the arrangement is referred to as a pattern. Patterns can also occasionally be referred to as a series.

Let the numbers in the pattern be 4, 20, 100, 500, . . .

t2 = 4 × 5 = 20

t3 = 20 × 5 = 100

t4 = 100 × 5 = 500

t5 = 500 × 5 = 2500

t6 = 2500 × 5 = 12500

t7 = 12500 × 5 = 62500

Thus, the pattern follows the rule tn = t(n-1) × 5

The next three numbers be 2500,12500,62500

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Joseph needs 22.4 packets of orange drink mix which requires one packet of orange drink mix for every half gallon.

A ratio is defined as a relationship between two quantities, it is expressed as one divided by the other

We have been given that Joseph is mixing 5 1/2 gallons of orange drink for his class picnic.

And every 1/2 gallon requires 1 packet of orange drink mix.

We have to determine the number of packets of orange drink mix Joseph needs.

Let the number of packets of orange would be x

We can write this as a ratio as

1/2 gallon : 1 packet = 5 1/2 gallons : x packets

0.5 gallon : 1 packet = 11.2 gallons : x packets

⇒ x = 11.2/0.5

⇒ x = 22.4

Therefore, he needs 22.4 packets of orange drink mix.

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By elimination, the solution of the system of equations, 2x + 3y = 7 and -2x + 5y = 1, is (2 , 1).

A system of equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy all the equations.

There are three methods that can be used to solve system of equations.

1. Elimination

2. Substitution

3. Graphing

Using the elimination method, given two equations in x and y, a variable should be eliminated by adding/subtracting the two equations.

Adding the two equations will eliminate the variable x.

2x + 3y = 7     (equation 1)

-2x + 5y = 1    (equation 2)

0x + 8y = 8

y = 1

Substitute the value of y to any of the two equation and solve for x.

2x + 3y = 7     (equation 1)

2x + 3(1) = 7

2x = 7 - 3

2x = 4

x = 2

Hence, the solution of the system of equations is (2 , 1).

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The given function f(x)=-2(3+x)²+2x² , is a linear function.

Where:

 A function is a mathematical expression or equation that allows us to visualize graphically the behavior of a function. A function is not real when it cuts the vertical axis at the same point of x.

   A function can be linear or quadratic, this is evidenced by the higher exponential degree, in our case we have the following function:

f(x) = -2(3+x)²+2x² we solve the function that seems to be quadratic because it has the highest degree the number "2" in the variable, however we will solve its reduction.

We solve the trinomial and substitute

(3+x)² = (9 + 6x + x²)

-2(9 + 6x + x²) + 2x²

-18 - 12x - 2x² + 2x² + 2x²

0x² - 12x - 18 is a linear function

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The first paycheck payment to the independent contractor is $4,615.38

Dr. salaries and wages expense $4,615.38

Cr. salaries and wages payable                     $4,615.38

What is the amount of first  bi-weekly pay to the contractors?

On the basis that there are 52 weeks in a year, hence, there would be 26 bi-weeks in a year, in order to determine the amount of first paycheck payment to the independent contractor, we simply divide the annual cost of contract by 26 bi-weeks in a year.

first paycheck payment =annual contract fees/26 bi-weeks

first paycheck payment =$120,000/26

first paycheck payment =$4,615.38

The paycheck refers to first 2 weeks which ends on on 12th January, whereas the actual payment would occur a week later on 19th of January, as a result, the amount is owed until 19th January, which means that salaries and wages expense would be debited and salaries and wages payable would be credited until actual payment is made on the 19th of January.

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Given a₁ = 100, r=-20, the explicit formula of the geometric sequence is: a(n) = 100 . (-20)ⁿ⁻¹, and the first five terms are: 100, -2000, 40000,  -800000, 16000000

Let

a₁ = the first term

r = ratio

The n-th term of a geometric sequence is given by:

a(n) = a₁ . r^(n-1)

To find the explicit formula, substitute a₁ = 100, r=-20

a(n) = 100 . (-20)ⁿ⁻¹

The first 5 terms:

a₁ = 100

a(2) = 100 . (-20)²⁻¹

       = 100 . (-20)¹ = -2,000

a(3) = 100 . (-20)³⁻¹

       = 100 . (-20)² = 40,000

a(4) = 100 . (-20)⁴⁻¹

       = 100 . (-20)³ = -800,000

a(5) = 100 . (-20)⁵⁻¹

       = 100 . (-20)⁴ = 16,000,000

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Area of Rectangle :42 [tex]cm^{2}[/tex]

To calculate the shaded area, first calculate the overall area and then deduct the areas of the four little rectangles.

The following are the dimensions of the large rectangle:

The length is merely one of the little rectangles' length: 7

The width is equal to the length of one of the tiny rectangles plus the width of two of the small rectangles, thus 7 + 0.5 + 0.5 = 8.

As a result, the area of the largest rectangle is 7 × 8 = 56 cm^2.

We must now calculate the areas of the four smaller rectangles. It's simply length multiplied by width:

7 ×0.5 = 3.5

Because there are four rectangles, multiply by four:

14 cm squared = 3.5 ×4

Finally, the shaded area is calculated as 56 - 14 = 42 cm squared.

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Answer:

[tex]p=11[/tex]

Step-by-step explanation:

[tex](5p+7)+(3p-5)=90\\8p+2=90\\8p=88\\p=11[/tex]

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