Unit vector notation is a way of representing vectors in which magnitude of vector is equal to 1. A vector is mathematical object that has both magnitude (length) and direction, and can be represented as an arrow.
In unit vector notation, a vector is represented as a combination of a scalar (a numerical value) and a unit vector (a vector with a magnitude of 1 in the same direction).
The most common notation for unit vectors is to use a hat symbol (^) to indicate that a vector is a unit vector. For example, if we have a vector v, then its corresponding unit vector in the same direction would be represented as v. The unit vector in the x-direction is typically denoted as i, and the unit vector in the y-direction is denoted as j.
Unit vector notation is useful in many applications, including physics and engineering, where it is used to describe the direction of forces, velocities, and accelerations. It is also commonly used in computer graphics and game development, where it is used to represent the direction of movement or rotation of objects in a 3D space.
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Challenge A family wants to rent a car to go on vacation Company A charges $75.50 and 16 per mile Company B charges $50.50 and 10g per mile. How much more does Company A charge for x miles than
Company B?
For xmiles, Company A charges dollars more than Company B
(Simplify your answer. Use integers or decimals for any numbers in the expression)
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Using a system of equations, Company A charges 25 + 0.06x more than Company B.
What is a system of equations?A system of equations involves two or more equations whose solutions are found concurrently or at the same time.
A system of equations is also known as simultaneous equations.
Company A Company B Difference
Fixed charge $75.50 $50.50 $25 ($75.50 - $50.50)
Variable charge per mile $0.16 $0.10 $0.06 ($0.16 - $0.10)
Let the number of miles covered = x
Equations:The total cost of Company A (Equation 1) = 75.50 + 0.16
The total cost of Company B (Equation 2) = 50.50 + 0.1
The difference in total cost for x miles = 25 + 0.06w
Thus, for each mile of travel that the family rents the car, Company A will charge more than Company B by exactly 25 + 0.06w.
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How do you check the factorization of a polynomial?
Completely factorize the polynomial using any methods that are appropriate, then look for shared factors and the polynomial's roots. Next, double-check your work to confirm accuracy.
Follow these steps to determine a polynomial's factorization:
Completely factor the polynomial using any relevant techniques, including grouping, utilizing the difference of squares or cubes, or using the quadratic formula.
By multiplying them all together, you can verify that each factor is accurate. The final figure must match the initial polynomial.
Look for shared factors among the polynomial factors. If the polynomial has common components, remove them from the equation and rewrite it as the product of the common factors and the other factors.
The polynomial's roots can be verified by setting each factor to zero and calculating the variable. The roots ought to correspond to the original polynomial.
Verify your work a second time to make sure all relevant elements have been identified and taken into consideration.
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ez 25 points+brainliest: two times a number is plus another number is 18. three times the first number minus the second number is 7. what are the numbers?
The numbers required in the word problem are
x = 3 4/3 and y = 13 1/3.How to find the numbersLet's call the numbers x and y
From the first equation, we have:
2x + y = 18
From the second equation, we have:
3x - y = 7
Solving simultaneously by substitution method
3x - y = 7
3x = 7 + y
x = (7 + y)/3
substitute this expression for x into the first equation:
2x + y = 18
2((7 + y)/3) + y = 18
14/3 + 3y/3 = 18
14/3 = 18 - 3y/3
14/3 = 18 - y
collecting like terms
y = 18 - 14/3
y = 18 - 4 2/3
y = 13 1/3
substituting to solve for y
x = (7 + y)/3
x = (7 + 13 1/3)/3
x = 10 4/3/3
x = 3 4/3
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Part 1 : write an equation for the nth term of the given sequence
Part 2: What is the given term of the sequence?
The equation of the nth term is 4 + n.
The 75th term is 79.
What is an arithmetic sequence?It is a sequence where the difference between each consecutive term is the same.
Example:
5, 7, 9, 11, 13 is an arithmetic sequence.
We have,
5, 6, 7, 8, ,,,,,a(75),,,,,,,,
This is an arithmetic sequence.
a = 5
d = 1
Now,
The nth term of arithmetic is a + (n - 1)d.
So,
= 5 + (n - 1)1
= 5 + n - 1
= 4 + n
The nth term is 4 + n.
The 75th term.
i,e
For n = 75,
= 4 + n
= 4 + 75
= 79
Thus,
The equation of the nth term is 4 + n.
The 75th term is 79.
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help. I’m stuck with this
Answer:
$14
Step-by-step explanation:
i multiplied 2.80 times 5 and got 14.
i hope this helped :)
Identify the quadratic function(s). (Select all that apply.)
A. 2b(b - 7) + b = 0
B. (4a + 2)(2a - 1) + 1 = 0
C. 2y + 2(3y - 5) = 0
D. 8 - 5x = 4(3x - 1)
There are two quadratic functions as A. 2b(b - 7) + b = 0 and B. (4a + 2)(2a - 1) + 1 = 0.
What is a quadratic function?The quadratic function is defined as a function containing the highest power of a variable is two.
A. 2b(b - 7) + b = 0 is a quadratic function because it can be simplified to the form of ax² + bx + c = 0 where a, b, and c are constants and x is the variable. In this case, a = 2, b = -13, and c = 0.
B. (4a + 2)(2a - 1) + 1 = 0 is also a quadratic function because it can be simplified to the form of ax² + bx + c = 0. In this case, a = 8, b = -2, and c = 1.
C. 2y + 2(3y - 5) = 0 is not a quadratic function because it can be simplified to the form of mx + b = 0 where m and b are constants and x is the variable.
D. 8 - 5x = 4(3x - 1) is not a quadratic function because it can be simplified to the form of mx + b = 0 where m and b are constants and x is the variable.
Thus, the correct answer would be options A. 2b(b - 7) + b = 0 and B. (4a + 2)(2a - 1) + 1 = 0.
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A composite figure is shown.
A five-sided figure with two parallel bases. The top one is 5 centimeters. The vertical height between these bases is 2.7 centimeters. That vertical height intersects the bottom base, leaving 3 centimeters between it and the vertex to the left. The side on the right is the longest at 6.8 centimeters. There is a horizontal line connecting the vertex of the bottom base to the 6.8-centimeter side and that line is 3.4 centimeters.
Which of the following represents the total area of the figure?
24.52 cm2
31.49 cm2
42.07 cm2
49.04 cm2
The area of the shape is given as 24.52 cm2
How to solve for the areaWe have two triangles and 1 rectangle
we have to find the area of the triangles first and then solve for the area of the rectangle.
The area of a triangle = 1/2bh
for first triangle
area = 1/2 * 2.7 * 3
= 4.05
for second triangle
height = 6.8 - 2.7
= 4.1
area = 1/2 * 3.4 * 4.1
= 6.97
For the rectangle
area = l * w
= 2.7 * 5 = 13.5
The area = 13. 5 + 6.97 + 4.05
= 24.52 cm2
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Natalie flew home from vacation with a heavy bag. With the first airline she flew, Natalie had to pay $29 to check her bag, plus $4 for every pound that her bag was over the weight limit.
The next flight was with another airline that had the same weight limit. Natalie had to pay $6 per pound that her bag was over the weight limit, in addition to the checked bag fee of $23.
By coincidence, the fees ended up being the same with both airlines. How large was each airline's fee? How far over the weight limit was the bag?
The airline fees was $41 each
The over the weight limit of the bag is 3 pounds
How large was each airline's fee?Number pounds of Natalie's bag = x
Airline 1:
29 + 4x
Airline 2:
23 + 6x
Equate airlines 1 and 2
29 + 4x = 23 + 6x
collect like terms
29 - 23 = 6x - 4x
6 = 2x
divide both sides by 2
x = 6/2
x = 3 pounds
Hence,
Airline 1:
29 + 4x
= 29 + 4(3)
= 29 + 12
= $41
Airline 2:
23 + 6x
= 23 + 6(3)
= 23 + 18
= $41
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Simplify: - [tex]6\sqrt{63} -4\sqrt{28}[/tex]
Answer:10[tex]\sqrt{7}[/tex]
Step-by-step explanation:
PLEASE HELP, FIFTY POINTS!!!!!
Answer: Choose Option D (look at the image for the solution and make sure to give me brainliest)
Step-by-step explanation:
Help please…………………………………..
The limit as x approaches -2 is equal to 0. The correct option is B.
How to calculate the limit?The limit of the function f(x) = x² - 4 / x + 2 as x approaches 2 is equal to 0. This can be evaluated by plugging in x = -2 into the expression for f(x) and simplifying it:-
The limit of the function f(x) = x² - 4 / x + 2 as x approaches -2 is equal to 4. This can be evaluated by plugging in x = -2 into the expression for f(x) and simplifying it:
f(-2) = (-2)² - 4 / -2 + 2 = 4 - 4 / 0 = 0
So, the limit as x approaches -2 is equal to 0.
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What is 1.1 as a fraction?
We write the decimal as a fraction with the decimal value as the numerator and a power of 10 as the denominator, we get 1.1 as a fraction is 11/10.
To convert a decimal to a fraction, we write the decimal as a fraction with the decimal value as the numerator and a power of 10 as the denominator.
For 1.1, we can write it as:
1.1 = 11/10
Therefore, 1.1 as a fraction is 11/10.
Decimal numbers are a way to represent numbers that are not whole numbers or integers. A decimal number consists of two parts: a whole number part and a fractional part, separated by a decimal point. To convert a decimal number to a fraction, we need to write the decimal as a fraction with the decimal value as the numerator and a power of 10 as the denominator.
In the case of 1.1, we can write it as a fraction with a numerator of 11 (the decimal value) and a denominator of 10 (the power of 10 that corresponds to the first decimal place). We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 1 in this case. So the final fraction is 11/10.
Converting decimals to fractions is a useful skill in many areas of math, science, and engineering. It allows us to represent numbers in different ways and to perform calculations that involve fractions and decimals. Knowing how to convert between these two types of numbers can also help us understand the relationship between them and how they are used in real-world applications.
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The box-and-whisker plot below represents some data set. What percentage of the data values are greater than 72?
Answer:
In a box-and-whisker plot, the box represents the middle 50% of the data, with the median value marked by a vertical line inside the box. The "whiskers" extend from the box to the minimum and maximum values in the data set that are not considered outliers. Outliers are marked by individual points outside the whiskers.
To determine the percentage of data values that are greater than a given value, we need to look at the box-and-whisker plot to see where that value falls in the data set. If the value is outside the box, we know that at least 50% of the data values are either greater or less than that value, depending on whether the value is greater or less than the median. If the value is inside the box, we know that exactly 50% of the data values are greater and 50% are less than that value.
In the case of the value 72, we cannot determine the percentage of data values that are greater than it without knowing where it falls in the box-and-whisker plot. If it falls outside the box, we only know that at least 50% of the data values are greater than it. If it falls inside the box, we only know that exactly 50% of the data values are greater than it.
Step-by-step explanation:
Answer: Hello! I'm JK!.....
[tex]\frac{13}{75}[/tex]
Step-by-step explanation:
The range of the data is from 10 to 85.
[tex]\frac{85-72}{85-10}[/tex] = [tex]\frac{13}{75}[/tex]
So your answer is [tex]\frac{13}{75}[/tex]
I really hope this helps you. XoXoGoldenMaknae<3
what’s the answer to this question? i’ve been having a hard time figuring it out
Answer:
10.305
Step-by-step explanation:
First you calculate for the angle of 12ft down the wall secondly you calculate for the angle of 8ft down the wallthirdly you subtract the angle of the 8ft frpm the 12ftthe remainder it the angle that the projector needs to be tilted to focus on 8ft down the wallThere are 32 students in a 5th grade classroom. Each table seats 6 students. How many tables are needed so that every student has a seat?
5 tables 30 tables 6 tables 7 tables
To sit comfortably, the students need a total of 6 tables. The correct option is 3.
There are 32 students in a classroom. In 5th grade. Now to sit comfortably, the students need 6 tables. In each table, a total of 6 students can fit. In 5 tables, only 30 students can sit but two students will remain table less. With 1 extra table, 2 students can sir and each student from a table can sit in the las bench, i.e., 6th table.
The number of pupils in the classroom is 32. in grade five. The pupils now require 6 tables in order to sit comfortably. A total of 6 pupils can fit at each table. Only 30 pupils can fit at 5 tables, however 2 students will be tableless. With one extra table, two students can sit at the sixth table and each student from a table can use the last bench. Therefore, students need a total of 6 tables.
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Drag the tiles to the correct boxes to complete the pairs
[tex]\log _6 \sqrt[3]{6} \quad[/tex]=0.3 i.e 1/3
[tex]\log _2 64[/tex] =6
[tex]-3 \log _5 25 \quad[/tex]=-6
[tex]\log _2 \sqrt[4]{8} \quad[/tex] = 0.75
[tex]\log _3 \frac{1}{81}[/tex]=-4
What is a logarithm?Generally, A logarithm is a mathematical function that determines the power to which a given number (called the base) must be raised to obtain a certain value. In other words, a logarithm is the inverse operation of exponentiation.
For example, if we take the base 2 and the value 8, the logarithm of 8 to the base 2 (written as log2 8) is 3, because 2 raised to the power of 3 (i.e., 2^3) equals 8.
Logarithms are widely used in many fields of science, engineering, and mathematics, particularly in areas where large numbers or very small numbers are involved. They are also used in data analysis, signal processing, and many other applications.
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x[tex]x^{4} -41x^{2} +400=0[/tex]
Answer:
Values of x are ±4 and ±5
Step-by-step explanation:
Let y = [tex]x^{2}[/tex]
Which means: [tex]y^{2} = x^{4}[/tex]
Therefore:
A quadratic equation is formed:
[tex]y^{2} - 41y + 400 = 0[/tex]
The above quadratic equation can be simplified either by The Double Bubble Method or using the quadratic formula
Double Bubble Method:
[tex]y^{2} - 41y + 400 = 0[/tex]
The pair of factors of 400 that add together to give 41 are 25 and 16. Use these two factors to rewritre -41y:
[tex]y^{2} - 25y - 16y + 400 = 0[/tex]
Then do Factorization by grouping (i.e group the terms with common factors before factorizing):
[tex]y(y -25) - 16(y - 25) = 0[/tex]
[tex](y - 25)(y - 16) = 0[/tex]
The product of two expressions is zero, which means either of the two expressions is equal to Zero:
Either: [tex]y - 25 = 0[/tex]
Substituting [tex]y = x^{2}[/tex]:
= [tex]x^{2} - 25 = 0[/tex]
= [tex]x^{2} = 25[/tex]
= [tex]\sqrt{x^{2}} = \sqrt{25}[/tex]
∴ x = ±5
Or: [tex]y - 16 = 0[/tex]
Substituting [tex]y = x^{2}[/tex]
[tex]= x^{2} - 16 = 0[/tex]
[tex]= x^{2} = 16[/tex]
[tex]= \sqrt{x^{2}} = \sqrt{16}[/tex]
∴ x = ±4
∴Values of x are ±4 and ±5
The graph of a sinusoidal function has a maximum point at (0, 7) and then intersects its midline
at (3, 3).
Answer: 4cos(pi/6x)+3
Step-by-step explanation:
Find the area of the figure. Round your answer to the nearest hundredth.
5 ft
4 ft
14 ft
4 ft
The area of the figure nearest hundredth will be 84.13 square feet.
What is the area?The quantity area demonstrates the amount of a sector on a planar or hemispherical cup. Surface area refers to the area of an open surface or the border of a multi-object, whereas the area of a plane region or plane field refers to the area of a form or planar material.
The figure is the combination of the rectangle and the semicircle. Then the area of the figure is the addition of the rectangle and the semicircle. Then we have
A = L x W + (π / 8) D²
A = 14 x 5 + (3.14/ 8) (14 - 4 - 4)²
A = 70 + 0.3925 x 36
A = 70 + 14.13
A = 84.13 square feet
The area of the figure nearest hundredth will be 84.13 square feet.
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The missing diagram is given below.
Jay's world ascendants as an equation 56 is 14 more than the number 14 + P = 56 which statement best describes Jason's work
The statement that best describes Jace's work is D. Jace is correct. The phrase more than suggests addition, so Jace showed that 14 plus a variable equals 56.
How can the the correct sentence be known?The concept that will be used here is word problem solution , then we need to interprete it then perform the neccessary simplification. . We were told that the sentence as an equation is 56 is 14 more than a number.
14+ = 56
then we can represent the number as X
then input into the equation as:
14+X = 56
x=56-14
=42
Therefore, option D is correct.
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complete question:
Jace wrote a sentence as an equation.
56 is 14 more than a number.
14+ = 56
Which statement best describes Jace's work?
Jace is not correct. The phrase more than suggests using the symbol > and Jace did not use that symbol.
Jace is not correct. He was correct to use addition, but the equation should be 56+ p = 14
Jace is not correct. The first number in the sentence is 56, so the equation should start with 56.
Jace is correct. The phrase more than suggests addition, so Jace showed that 14 plus a variable equals 56.
Find the measure of the missing angles.
How do i find the excluded/extraneous values of this rational equation?
The extraneous values of the rational function are given as follows:
x = 7 and x = -3.
How to obtain the extraneous values of the rational function?The extraneous values of a function are the values of x that are outside the function's domain.
In this problem, we have a rational function, hence the extraneous values are the values that make the denominators zero, as follows:
x² - 4x - 21 = 0 -> (x - 7)(x + 3) = 0 -> x = -7 and x = -3.x + 3 = 0 -> x = -3.More can be learned about functions at https://brainly.com/question/24808124
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Elish was required to write a 600 word Literature essay. After working away for one hour, the word count on her computer showed that she had typed 240 words. What fraction of the essay does Elish still need to complete? Write your answer in simplest form
If Elish was required to write a 600 word Literature essay and word count on her computer showed that she had typed 240 words Elish still needs to complete 3/5 of the essay.
To find the fraction of the essay that Elish still needs to complete, we need to determine how many words she has left to write. We can do this by subtracting the number of words she has already written from the total required word count:
Words left to write = Total word count - Words already written
Words left to write = 600 - 240
Words left to write = 360
Now, to find the fraction of the essay that Elish still needs to complete, we can express the remaining words as a fraction of the total word count:
Fraction of essay left to complete = Words left to write / Total word count
Fraction of essay left to complete = 360 / 600
We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 120:
Fraction of essay left to complete = (360 ÷ 120) / (600 ÷ 120)
Fraction of essay left to complete = 3 / 5
This means that she has completed 2/5 of the essay so far (which is the equivalent fraction of 240/600).
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Select all the expressions that show breaking the addends 7 5/12 and 11 2/3 apart to make a whole.
A. 7 + 5/12 + 11 + 2/3
B. 7 + 5/12 + 8/12 + 11
C. 7 + 5/12 + 7/12 + 11 1/12
D. 7 + 5/12 + 5/12 + 11 3/12
E. 7 + 1/12 + 4/12 + 8/12 + 11
Colleen won the raffle at the zoo and gets to feed the dolphins! The dolphin trainer gives Colleen a bucket of fish to divide evenly among 3 dolphins. Each dolphin gets 6 fish. Which equation can you use to find the number of fish f in the bucket before Colleen feeds the dolphins?
Since the fish was share evenly amongst the 3 dolphins, and each one got 6, the equation will be:
f = d x n
where
f represents the fish
d represents the dolphin
n represents the number of fish each got.
Step by step explanationLet's assume that the number of fish in the bucket before Colleen feeds the dolphins is "f". To find out how many fish there were in the bucket, you can use the following equation:
f = 3 * 6
where 3 is the number of dolphins and 6 is the number of fish each dolphin gets. Solving for "f", you get:
f = 3 * 6
f = 18
So there were 18 fish in the bucket before Colleen fed the dolphins.
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You can rent a video game for $3.50. Your total cost of rentals for the month was $31.50.
This can be represented by the equation 3.5x = 31.5
What does the quantity 3.5x represent in this situation?
PLEASE BE ACCURATE!!! THANK YOU!!:)
According to the equation, when 9 video games are rented, the total cost is $31.5 which is expressed in the equation as 3.5x.
What is an equation?
A formula known as an equation uses the equals sign (=) to express how two expressions are equal. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. We have left hand side equal to right hand side in every mathematical equation. To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. A statement is not an equation if it has no "equal to" sign. It will be regarded as an expression.
Given,
The cost of renting a video game = $3.50
The total cost of rentals for the month = $31.50
The equation given is:
3.5x = 31.5
The term 3.5x in the equation represents the total cost of a month when the number of video games rented is x.
In this case x = 31.5/3.5 = 9
Therefore, according to the equation, when 9 video games are rented, the total cost is $31.5 which is expressed in the equation as 3.5x.
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Thomas has 6 sports video games in his collection for every 5 action games. Franklin has9 sports game for every 6 action games in his collection. Which friend has the least portion of action games?
The friend that had the least portion of action games would be = Thomas with 20 action games in total.
How to calculate the person with the least portion of games?The number of action games that Thomas has = 5
The number of sports video games for every action game = 6
Therefore the total number of sports game he has = 5×6 = 30.
The number of action games that Franklin has = 9
The number of sports video games for every action game = 6
Therefore the total number of sports game he has = 9×6 = 54.
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Please help in the math
Answer:
Step-by-step explanation:
reflict means to put the point in the other way but in the same point.
Helppppp asapp plsssssss I’ll give brainly
The opposite sides of FGHJ are parallel.
What is Quadrilateral?A quadrilateral is a four-sided polygon, having four edges and four corners.
FGHJ is a quadrilateral.
From the figure we can observe that opposite sides are equal which means the quadrilateral is a parallelogram.
A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.
The line segment FG≅JH
GH≅FJ
The sides are congruent and parallel.
Hence, the opposite sides of FGHJ are parallel.
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(SAT Prep) Find the value of x
2x
3x
Answer:
36°
Step-by-step explanation:
2x+3x=5x
5x=180°
x=180°:5=36°