Answer:
a^2+2ab+b^2
Step-by-step explanation:
(a+b)^2
(a+b)(a+b)
a(a+b)+b(a+b)
(a^2+ab)+(ab+b^2)
a^2+2ab+b^2
Find the magnitude and direction of the following vector.
-F G: F<-4,0> and G(-6,-4)
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).
What exactly would a distance formula imply?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).
More details about the distance formula can be found here.
brainly.com/question/24386522
#SPJ4
[tex]y+\frac{4}{5} =1\frac{2}{5}[/tex]
Solve each system by elimination. 2x + 3y = 7 , -2x + 5y = 1
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).
Learn more about solving systems of equations by elimination here: https://brainly.com/question/28405823
#SPJ4
Can you please look at the photo and tell me which statement isn’t true.
Answer:
D
Step-by-step explanation:
point P is in plane Z not plane X
Factor x^2-4x-63=-6x?
the diagram shows a rectangle 0.5cm length, 7cm width. four of these rectangles are put together?
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.
To learn more about Rectangle from the given link:
https://brainly.com/question/15019502
#SPJ9
2t + 17 < 5 or t + 7 2 13
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
Write an explicit formula for each sequence. Then generate the first five terms. a₁ =100, r=-20
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
Learn more about geometric sequence here:
https://brainly.com/question/23756814
#SPJ4
x11 =[tex]\frac{x}{11}=\frac{13}{65}[/tex] 1365
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.
Learn more about expression solutions here:
https://brainly.com/question/17374100
#SPJ9
Which statement is NOT true about a regular 16-gon?
a) It is a convex polygon.
b) It has 16 congruent sides.
c) The sum of the interior angle measures is 2880 degrees.
d) The sum of the exterior angles, one at each vertex, is 360 degrees
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
Joseph is mixing 5 1/2 gallons of orange drink for his class picnic. Every 1/2 gallon requires 1 packet of orange drink mix. How many packets of orange drink mix does Joseph need?
Joseph needs 22.4 packets of orange drink mix which requires one packet of orange drink mix for every half gallon.
What is Ratio?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.
Learn more about the Ratio here:
brainly.com/question/1504221
#SPJ1
Multiple the question bellow
2t² +t-3 = 0 ….???………????????
Lesson 8: Factors, Multiples, GCF and LCM
Math
MIN-LESSON
6. Leon is making goodie bags for his birthday party and wants to make sure he has enough for everyone
that is attending. He has 72 coloring books, 90 markers, and 180 pieces of chocolate.
a. What is the greatest number of goodie bags that he can make?
b. How many of each item will go into each bag?
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
What is the greatest number of goodie bags he can make?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
To learn more about highest common factor, please check: https://brainly.com/question/26073850
#SPJ1
i need help on
4-9x=14
Answer:The answer is x=-10/9 or -1 1/9
Step-by-step explanation:
A rectangle has a width of 12 and a length of 18. Find its area.
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:
Solve for the value of p
Answer:
[tex]p=11[/tex]
Step-by-step explanation:
[tex](5p+7)+(3p-5)=90\\8p+2=90\\8p=88\\p=11[/tex]
Brainliest Answer Please
Can anyone help me solve this math problem, I don’t understand these at all
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.
Learn more about relative frequency here:
https://brainly.com/question/3857836
#SPJ9
Moving to
estion 1
Identify the inequality or equality that describes the following situation. Juan has over 77 marbles.
The inequality or equality that describes the following situation is; m ≤ 77 marbles.
What is a solution set to an inequality or an equation?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.
Learn more about inequalities here:
https://brainly.com/question/27425770
#SPJ1
Determine whether each function is linear or quadratic. Identify the quadratic, linear, and constant terms. f(x)=-2(3+x)²+2 x²
The given function f(x)=-2(3+x)²+2x² , is a linear function.
Where:
Its quadratic term is 0x².Its linear term is -12xConstant is -18What is a function?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
-12x: linear term-18: constant0x²: quadraticLearn more about functions in:
https://brainly.com/question/13473114
#SPJ4
Four students have volunteered to fold pamphlets for a local community action group. Which student is the fastest?
a. Deron
b. Quinn
c. Neiva
d. Sarah
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.
Which is a rational function?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.
To learn more about rational function refer to:
https://brainly.com/question/1851758
#SPJ4
Identify a pattern and find the next three numbers in the pattern.
4,20,100,500, . ..
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.
What is meant by pattern?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
To learn more about identifying patterns, refer to:
brainly.com/question/24565868
#SPJ4
a woman works a basic week of 40 hours and her basic rate is $8.50 an hour.calculate her basic wage..
Answer:
$340 per week
Step-by-step explanation:
$40 hours a week
$8.50 per hour
40x8.5=weekly pay
40x8.5=340
If 8 + 13 = 21, then 21 = 8 +
The complete equation is 8 + 13 = 21, then 21 = 8 + 13
What is commutative property of additionThe 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
Learn more about commutative property of addition here:
#SPJ1
Find the magnitude and direction of the following vector.
-AB : A<-1,10> and B(1,-12)
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).
What basically does a distance formula mean?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).
More information on the distance formula can be found here.
https://brainly.com/question/24386522
#SPJ4
Let g be a translation 4 units down and a horizontal shrink by a factor of 1/4 of the graph of f(x)=x
Answer:
X is the value of cordinatinate so X is 1
How many times larger is
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
Formula; f(x)=x
1. x+1=
Step-by-step explanation:
1.x+1
1+1 is 2
1.x+1 and is 22+X and is 2xsubtract 8/9 - (-2/3)
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
January 19: On January 1, North Country Hotel and Resort hired an independent contractor to develop scheduling software. This is a year contract for $120,000/annual. The contractor is paid bi-weekly on Fridays. The first pay period is for the week January 1-5 and January 8-12. Payday is January 19. Independent contractors are not employees, so the accounts payable department would normally issue the checks and generate a 1099 at the end of the year. Calculate the first paycheck payment to the independent contractor and record the journal entry. For our example, you can use Salaries and Wages Expense and Cash accounts.
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.
Find out more about accrued wages and salaries on:brainly.com/question/6693966
#SPJ1
