The component vectors to a linear combination is given by the equation
A = 20 i^ + 14 j^ - 23 k^
What is the product of vectors?The dot product, or inner product, of two vectors, is the sum of the products of corresponding components. Equivalently, it is the product of their magnitudes, times the cosine of the angle between them . The dot product , also known as the inner product, of u and v to be the number u ⋅ v given by
u ⋅ v = u₁v₁ + u₂v₂ + u₃v₃
An equivalent definition, typically used in physics, is
u ⋅ v = ∣u∣ ∣v∣ cos θ,
where θ is the angle between u and v
Two nonzero vectors are perpendicular, or orthogonal, if and only if their dot product is equal to zero
Given data ,
Let the component vectors be represented as A
The value of A is
< 20 , 14 , -23 > be equation (1)
On simplifying the equation to the linear combination , we get
< 20 , 14 , -23 > = 20 i^ + 14 j^ - 23 k^
So , the linear combination of the vectors is given by the equation ,
A = 20 i^ + 14 j^ - 23 k^
Hence , the equation is 20 i^ + 14 j^ - 23 k^
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Erika sells bicycles at a store. She is paid a monthly salary plus a bonus on each bike she sells. Her monthly pay is modeled in the table. Choose the linear equation below that best represents this data.
Answer: Show the table
Step-by-step explanation:
SHow the table
Find the greatest common factor of the
following monomials:
gh5
OOHO
Clear all
10g5h4
Enter the correct answer.
?
DONE
To find the greatest common factor (GCF) between monomials, take each monomial and write it's prime factorization. Then, identify the factors common to each monomial and multiply those common factors together.
What is monomial?Monomial is defined as an expression that has a single non-zero term. It consists of different parts like the variable, the coefficient, and its degree. The variables in a monomial are the letters present in it. The coefficients are the numbers that are multiplied by the variables of the monomial. The degree of a monomial is the sum of the exponents of all the variables. Let us consider an expression 6xy2. The variables, the coefficient, and the degree of this monomial are shown in the table given below. Observe the table to learn the various parts of the monomial 6xy2.In algebra, a monomial is an expression that has a single term, with variables and a coefficient. For example, 2xy is a monomial since it is a single term, has two variables, and one coefficient. Monomials are the building blocks of polynomials and are called 'terms' when they are a part of larger polynomials. In other words, each term in a polynomial is a monomial.To learn more about coefficients refer to:
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Nathaniel is searching for a four-leaf clover in a field. He finds 2 four-leaf
clovers during the first 12 minutes of his search. If Nathaniel spends a total of
180 minutes searching in the field, predict the number of four leaf clovers
Nathaniel will find.
Answer:
30 clovers
Step-by-step explanation:
If Nathaniel find 2 four-leaf clovers in the first 12 minutes of his search, the rate at which he finds the four-leaf clovers is:
[tex]\implies \sf Rate=\dfrac{2\;clovers}{12\;minutes}=\dfrac{1}{6}\;clovers\;per\;minute[/tex]
To predict the number of four-leaf clovers Nathaniel will find in 180 minutes, multiply the found rate by 180 minutes:
[tex]\implies \sf \dfrac{1}{6} \times 180=30\;clovers[/tex]
Therefore, Nathaniel will find 30 clovers in 180 minutes based on the rate at which he found 2 clovers.
[tex] \sf \longmapsto \: Prediction \: of \: 4 \: leaf \: clovers=2/12×180
\: [/tex]
[tex] \sf \longmapsto \: Prediction \: of \: 4 \: leaf \: clovers=30clovers[/tex]
. If Mario was 32 years old 8 years ago, how old was he x years ago?
Answer: He was 32 years old 8 years ago, than a) x-40 b) x-24 c) 40-x d) 24-x e) 24+x
Step-by-step explanation:
Mario was '40 - x' years old when he was 'x' years old.
If he was 32 years old, 8 years ago, then he is 40 now as (32+8) equals 40.
If he is 40 years old now, then he was '40 - x', x years ago.
Hence, '40 - x' is the answer to this sum.
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A cell tower is located 3 miles east and 6 miles north of the center of a small town. The cell tower has a coverage radius of 4 miles.
Start by drawing a diagram of this situation. Your diagram might include a coordinate plane, the cell tower, and a circle representing the cell tower's coverage boundary.
A house is located 7 miles north of the center of the town and is to the east of the cell tower. If the house lies on the boundary of the cell tower's coverage, how far east of the center of the town is the house?
The house is located 6.87 miles to the east of the cell tower.
What is Pythagoras theorem?“In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“.
Given:
Let the center of the town represent the origin (0,0).
Also 1 unit = 1 mile.
Since the cell tower is located 3 miles east and 6 miles north of the center of a small town, it is represented by A(3, 6)
The cell tower has a coverage of radius 4 miles. This can be represented by a circle with equation:
(x - a)² + (y - b)² = r². where (a,b) is the center of the circle and r is the radius.
Then, (x - 3)² + (y - 6)² = 4²
(x - 3)² + (y - 6)² = 16
b) The house is 7 miles north. It can be represented by y = 5 line.
To find the distance east of the house we have to substitute y = 5 and solve for x,
(x - 3)² + (y - 6)² = 16
(x - 3)² + (5 - 6)² = 16
(x - 3)² + 1 = 16
(x - 3)² = 15
(x - 3) = ±3.87
x= 3 ±3.87
x= 6.87 or 0.87.
Hence, the house is located 6.87 miles to the east.
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Which statement is true based on a graph of the line that passes through the given coordinates? (2, 1), (3,3), (5,7), (6,9) Please help
A. The line that passes through the given coordinates does not represent a proportional relationship because the line passes through the origin.
B. The line that passes through the given coordinates represents a proportional relationship because the line passes through the origin.
C. The line that passes through the given coordinates does not represent a proportional relationship because the line does not pass through the origin.
D. The line that passes through the given coordinates represents a proportional relationship because the line does not pass through the origin.
The line that passes through the given coordinates does not represent a proportional relationship because the line does not pass through the origin. Option C
What is a proportional relationship?We can say that a relationship is proportional when the relation does lead to a straight line graph and the graph would have to be able to pass through the origin.
Hence, even if we have a straight line graph but the graph does not pass through the origin of the graph then we can not say that the relationship that is existing between the coordinates that have been shown is proportional.
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A physically active adult weighing 170 pounds needs to consume about 2815 calories per day in order to maintain his or her weight. A nutritionist recommends that no more than 30% of those calories should come from simple sugars What is the maximum number of calories per day that should come from simple sugars?
Answer:
844.5 calories.
Step-by-step explanation:
If a physically active adult weighing 170 pounds needs to consume about 2815 calories per day in order to maintain his or her weight, and a nutritionist recommends that no more than 30% of those calories should come from simple sugars, the maximum number of calories per day that should come from simple sugars is:
2815 calories * 30% = <<281530.01=844.5>>844.5 calories
So, the maximum number of calories per day that should come from simple sugars is 844.5 calories.
Answer
844.5
Step-by-step explanation:
80+100=180
180÷100=1.80
1.80×2815=844.5
Write an equation of a line
Answer:
Step-by-step explanation:
Steps to find the equation of a line from two points:
1) Find the slope using the slope formula. ...
2) Use the slope and one of the points to solve for the y-intercept (b). ...
3) Once you know the value for m and the value for b, you can plug these into the slope-intercept form of a line (y = MX + b) to get the equation for the line.
Ratio is equivalent to the ratio of 120 to 36
120:36 is equivalent to 10:3
What is a ratio?The quantitative relation between two amounts shows the number of times one value contains or is contained within the other. for example-"the ratio of computers to students is now 2 to 1"The trick with ratios is to always multiply or divide the numbers by the same value.
Given here the ratio is 120:36≡10:3
Hence, 120:36 is equivalent to 10:3
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I need c15 and c16 doing please with working out thank you
Therefore , the solution to the given problem of circle comes out to be area = 25.1 sq cm and perimeter=12.5 cm.
What is the circle?Every position in a circle's plane is equally spaced from the centre and is considered to be a closed, double object. A line of reflected symmetry is created as a result of each line traversing the circle. Each angle also has an axis of symmetry that circles its center.
Here,
Given : Diameter = 8
Radius = 8/2 = 4cm
To find the semi circle area
=>semi circle area = πr²
=> 22/7 * 4² *1/2
=> 25.1 sq cm
To find the perimeter of semi circle :
=> 2πr /2
=> πr
=> 22/7*4
=>12.5 cm
Therefore , the solution to the given problem of circle comes out to be area = 25.1 sq cm and perimeter=12.5 cm.
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a
=
8.7
rounded to 1 DP
b
=
0.82
rounded to 2 DP
Find the maximum of
a
+
b
The maximum value considering DP of a and b is 9.52.
What is the decimal places of numbers?The decimal places of a number are the number of digits to be considered after the decimal point. E.g Round 4.7583 to 2 dp, we have;
4.76 3 dp
The maximum value of a sum of numbers is the highest value obtained when these numbers are added one to each other. The decimal places of each number is put into consideration in the process.
From the given question;
a = 8.7 and b = 0.82
Thus,
a + b = 8.7 + 0.82
= 9.52
a + b = 9.52
Therefore, the maximum of a + b = 9.52
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the instructions are on the image please help me and please hurry!
The elements in matrix X is attached below
What is MatrixMatrix is a mathematical construct consisting of an array of numbers, symbols, or expressions, arranged in rows and columns. It is most often used to represent linear relationships between two or more variables. Matrices are commonly used in science and engineering to represent systems of equations and in computer programming for representing data and performing operations on it.
In this problem, we can easily find x by reversing the variables and solve.
A - X = B
X = A - B
The elements in the matrix can be solved easily using an online calculator.
The value of x is attached below
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: 1/2 Log10 25/4 - 2 log10 4/5 + log10 320/125
To simplify this expression, you can first simplify the logarithms by using the properties of logarithms and the simplified expression is -0.00195
What is logarithm?A logarithm is a mathematical function that is used to determine the power to which a number must be raised in order to produce a certain value. The logarithm of a number "b" to base "a" is represented as loga(b) or logb. The logarithm of b to base a is equal to the exponent to which we must raise a to get b.
[tex]1/2 Log10 25/4 - 2 log10 4/5 + log10 320/125[/tex]
To simplify this expression, you can first simplify the logarithms by using the properties of logarithms.
[tex]1/2 log10 25/4 - 2 log10 4/5 + log10 320/125[/tex]
=[tex]1/2( log10 25 - log10 4) - 2 (log10 4 - log10 5) + (log10 320 - log10 125)[/tex]
= 1/2(1.397940008672037 - 0.6020599913279624) - 2*(-0.6020599913279624 - 0.6989700043360187) + (2.505149978319906 - 2.0969100130080566)
= 0.397940008672037 - 1.204120018655925 - 1.397940008672037 + 0.40825006983185
= -0.2 - 0.2062 + 0.40825
= -0.00195
So the simplified expression is -0.00195
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Complete question is: simplify the given equation: 1/2 Log10 25/4 - 2 log10 4/5 + log10 320/125
what percent of 50 is 25 with solution
Answer:
50%
What is a percentage?A percentage is a ratio, or a number expressed in the form of a fraction of 100. Percentages are often used to express a part of a total.
Looking at the problem, we can take 25, and divide 50 by it.
25 ÷ 50 = 0.5
0.5 is equal to 5/10, which is also equal to 50%, meaning that 50% of 50 is 25.
Mr. Hart recorded the ratio of the minutes spent driving to the miles driven while on a road trip.
Miles Driven
Number of
Minutes Number of Miles
? 40
75 60
100 80
Which graph represents these pairs of values?
The graph representing the given pairs is represented by the equation y = (4/5)x + 40.
What is expression?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.The general equation of a straight line is → y = mx + c{m} - slope {c} - intercept along the y - axis.
Given is that Mr. Hart recorded the ratio of the minutes spent driving to the miles driven while on a road trip.
The given table is as follows -
Number of Minutes {m} : 75 60
Number of Miles {M} : 100 80
The slope of this graph will be -
m = (80 - 60)/(100 - 75)
m = 20/25
m = 4/5
The equation of the line can be written as -
y = (4/5)x + c
For the point (75, 100) as follows -
100 = 4/5 x 75 + c
100 = 4 x 15 + c
c = 100 - 60
c = 40
The equation of the graph will be -
y = (4/5)x + 40
Refer to the graph attached.
Therefore, the graph representing the given pairs is represented by the equation y = (4/5)x + 40.
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A student wants to write an expression for, all of the elements which are in set A AND all of the elements in set B.” Which expression below matches the statement? (A ‘U B’). (A U B). (A n B) P(A n B)
A student wants to write an expression for, all the elements which are in set A and all the elements in set B. Then, the expression matches the statement is (A n B), which is read as A intersection B. Thus, option B is correct.
What is intersection?The intersection of two sets A and B, denoted by display by (A ∩ B). It is the set containing all elements of A that also belong to B, or, alternatively, all elements of B that also belong to A. The symbol is sued for the intersection is ∩. This is defined as that the element of A and B are is a single set.
Therefore, option B is correct.
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A book publisher find production cost associated 30 and fixed cost 25000 if each book is sold for 50 find cost function and profit function
The cost function is a function that describes the total cost of producing x number of books. The fixed cost of 25000 is a constant cost that does not depend on the number of books produced, so it is not included in the cost function. The cost function is therefore:
Cost function: C(x) = 30x
The profit function is a function that describes the profit made from selling x number of books. The profit is equal to the revenue from selling the books minus the cost of producing the books. The revenue from selling x number of books at a price of 50 each is 50x, so the profit function is:
Profit function: P(x) = 50x - 30x = 20x
This profit function tells you that for every book you sell, you will make a profit of 20.
i need help please i dont get this
Answer:
See attached
Step-by-step explanation:
You want the solution to the inequality -12x < -48 shown on a number line.
SolutionThe solution to the inequality is found by dividing by the x-coefficient
-12x < -48
x > 4 . . . . . . . divide by -12
When working with inequalities, you need to know that multiplying or dividing by a negative number reverses the inequality symbol.
GraphThe value x=4 is not included in the solution set, so an open circle is plotted at that point. All values of x greater than x=4 are included in the solution set, so the number line is shaded to the right of the open circle.
The graph of the solution is shown in the attachment.
__
Additional comment
Often, you can avoid multiplying or dividing an inequality by a negative number by rearranging it. Here, adding 12x+48 to both sides makes it be ...
48 < 12x
Now, you can divide by 12 without worrying about the inequality symbol:
4 < x . . . . . same as above
PLEASE HELP ASAP DUE TODAY
Answer:
y = -3/4x + 52
y + 6 = -3/4(x-8)
Step-by-step explanation:
y = mx + c
as long as the number is -3/4x , it represents slope -3/
Answer:
B. y = -3/4x + 52, C. y + 6 = -3/4(x - 8), and F. 3x + 4y = 9
Step-by-step explanation:
A. -3x + 4y = -34
y = 3/4x - 17/2
Slope = 3/4
INCORRECT
B. y = -3/4x + 52
Slope = -3/4
CORRECT
C. y + 6 = -3/4(x - 8)
y = -3/4x
Slope = -3/4
CORRECT
D. 4x + 3y = -22
y = -4/3x - 22/3
Slope = -4/3
INCORRECT
E. 4x - 3y = 48
y = 4/3x - 16
Slope = 4/3
INCORRECT
F. 3x + 4y = 9
y = -3/4x + 9/4
Slope = -3/4
CORRECT
G. y - 6 = 3/4(x - 8)
y = 3/4x
Slope = 3/4
INCORRECT
Terryl invests $1500 in two mutual funds. In the first year, one fund grows 3.8% and the other grows 6%. Write a polynomial to represent the value of Terryl’s investment after the first year if he invested x dollars in the fund with the lesser growth rate.
The polynomial that represents the value of Terryl’s investment after the first year if he invested x dollars in the fund with the lesser growth rate is;
p(x) = x(1 + 6/100)
g(x) = (1500 - x)(1 + 3.8/100)
How to find the compound interest?The compound interest is defined as a form of interest whereby the rate of interest is applied on the amount obtained after every given interval of time.
We are given that;
The total amount invested in the two mutual funds = $1500.
The growth rate of the first mutual fund = 6%.
The growth rate of the second mutual fund = 3.8%.
If the amount invested in the first mutual fund is x, then the amount invested in second mutual fund is 1500 - x.
The growth for both mutual funds can then be represented by;
First mutual fund; p(x) = x(1 + 6/100)
The second mutual fund; g(x) = (1500 - x)(1 + 3.8/100)
Thus, the polynomial expression for both the mutual funds are;
p(x) = x(1 + 6/100) and g(x) = (1500 - x)(1 + 3.8/100) respectively.
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In a village, the cases of a particular infectious
disease have been exponentially decreasing at
a rate of 95% per year since the people started
receiving the vaccine. If there were 200 cases
in the village to start with, predict the number
of cases after 2 years.
First, complete the equation:
Remaining Amount = 200(1-0.95)²
The number remaining in the village is 30.
How many people remain?We have to note that the case in which the population of the community is being reduced because of the fact that the community is being ravaged by disease is a case of a decrease in the population and is a problem of exponential decrease.
Then we would have that;
N =Noe^-rt
N = Number at time t
No = Initial number
r = spread rate
t = time taken
Then;
N = 200e^-0.95 * 2
N = 30
Thus, they would have only 30 people left.
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FIND THE SLOPE . THE PICTURE ATTACHED IS THE FULL QUESTION ,
Answer:
-12/5
Step-by-step explanation:
slope = change in y / change in x
change in y = 12 (from top to bottom) = 6 - (-6)
change in x = -5 (from top to bottom) = -2 -3
slope = 12/-5 = -12/5
Assume that AGHIE ALMN. Which of the following congruence statements
are correct? Check all that apply.
A. ZL 21
B. IG LM
C. THNM
D. ZN 21
E. GH = LM
F. ZME ZH
On solving the provided questions, we can say that the congruence of ABC=DEF, where A=D, B=E, and C=F.D because they are equal in length. F
What is congruence?A figure that can be put exactly on another is said to be "matching." When the bread is piled, it is the same size and shape. The term "match" describes things that are precisely the same shape and size. A pair of geometric figures is said to be congruent or to be in a congruent relationship if one of them can be reliably superimposed over the other.
B D and F.
B because they would go together if the statement were put in that particular sequence. ABC=DEF, where A=D, B=E, and C=F.D because they are equal in length. F due to the same cause as B.
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5x35 65x76 what the the total
The solution to the above math arithmetic is 5115.
Addition and subtraction are what?Finding the sum and difference of two integers are the two main addition and subtraction arithmetic procedures. They are both the other's polar opposite. An ordered group of integers with a shared difference between each word is known as an arithmetic sequence. The common difference, for instance, between the mathematical series 3, 9, 15, 21, and 27 is 6.
What exactly is an algebraic question?This grouping contains percent difficulties, decimal recognition, addition, subtraction, multiplication, and division as well as fraction and percent equivalences and estimate issues.
For instance, 5 + 6 = 11 and 11 - 6 = 5.
5x35 + 65x76=5115
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Ln 4 - Ln x = 2
Solve for x showing all steps. Round to the nearest hundredth.
Please give step by step instruction
Which expression is equivalent to 4(x + 2)?
12x
6x
4x + 2
4x + 8
Answer:
4x +2
Step-by-step explanation:
4( x + 2)
= 4*x +4*2
= 4x +2
Translate the following: "Four times a number n is equal to the difference between that number and 10"
Answer:
4n=10-n
n=2
Step-by-step explanation:
add n to both sides
5n=10
divide both sides by 5
n=10/5
n=2
which is a solution to (x-2)(x+10)=13
Answer:
answers 3
Step-by-step explanation:
took more thinking than it should've tbh (3-2=1) (3+10=13) 1x13=13
(HELP ASAP!)
In baseball, each time a player attempts to hit the ball, it is recorded. The ratio of hits compared to total attempts is their batting average. Each player on the team wants to have the highest batting average to help their team the most. For the season so far, Jana has hit the ball 7 times out of 10 attempts. Tasha has hit the ball 10 times out of 16 attempts. Which player has a ratio that means they have a better batting average?
Tasha, because she has the lowest ratio since 0.7 < 0.625
Tasha, because she has the highest ratio since 56 over 80 is greater than 50 over 80
Jana, because she has the highest ratio since 56 over 80 is greater than 50 over 80
Jana, because she has the lowest ratio since 0.7 < 0.625
Jana, because she has the highest ratio since 56 over 80 is greater than 50 over 80.
What is ratio?The numerical relationship between two values that demonstrates how frequently one value contains or is contained within another.
Given:
In baseball, each time a player attempts to hit the ball, it is recorded.
The ratio of hits compared to total attempts is their batting average.
Each player on the team wants to have the highest batting average to help their team the most.
For the season so far,
Jana has hit the ball 7 times out of 10 attempts.
Tasha has hit the ball 10 times out of 16 attempts.
To find the ratio of batting average:
We must find the same number of attempts.
So,
Jana has ratio 7/10.
So, 56 /80 = 0.7
Tasha has ratio 10/16.
So, 50 / 80 = 0.625
Therefore, Jana has the highest batting average.
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What are terms and common rations ? Can someone explain to me how to solve
For the arithmetic sequence 4 - 2(n - 1), we have that:
The first term is 4.The second term is 2.The third term is zero.The fourth term is -2.The fifth term is -4.The common difference is -2.For the geometric sequence 6 x 3^(n - 1), we have that:
The first term is 6.The second term is 18.The third term is 54.The fourth term is 162.The fifth term is 486.The common ratio is 3.How to model the arithmetic sequence?An arithmetic sequence is a sequence of numbers in which there is a common difference of the numbers, that is, the subtraction between consecutive terms of the sequence is always constant.
The nth term of an arithmetic sequence is given by the equation presented as follows:
[tex]a_n = a_1 + d(n - 1)[/tex]
In which:
[tex]a_1[/tex] is the first term.d is the common difference.The sequence in this problem is defined as follows:
4 - 2(n - 1)
Which has first term 4 and common difference -2, hence the terms are:
4, 2, 0, -2, -4, -6 and so on...
What is a geometric sequence?A geometric sequence is a sequence of numbers in which there is a common ratio of the numbers, that is, the quotient between consecutive terms of the sequence is always constant.
The nth term of a geometric sequence is given by the equation presented as follows:
[tex]a_n = a_1 \times q^{n - 1}[/tex]
In which:
[tex]a_1[/tex] is the first term.q is the common ratio.The sequence for this problem is given as follows:
6 x 3^(n - 1)
Which has first term of 6 and common ratio of 3, hence the terms are given as follows:
6, 18, 54, and so on...
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