The magnitude of the vector JK is estimated to be 2√13.
The given vector JK's direction is - Ф = 33.69° (angle lies in the fourth quadrant with having direction in clockwise)
What is the definition of a distance formula?The algebraic demonstration of the coordinate-based distances between two points (in coordinate system). Using rectangular coordinates, the Pythagorean theorem is employed to determine distances among points in 2- and 3-dimensional Euclidean space.
Now, in answer to your questioning;
J and K have coordinates of (8,1) & (2,5), respectively.
The following is the distance formula for the points J & K:
JK² = (x₂ - x₁)² + (y₂ - y₁)²
JK = √[(x₂ - x₁)² + (y₂ - y₁)²]
The given of coordinates of J and K's are-
(x₁,y₁) = (8,1) and (x₂,y₂) = (2,5).
Substituting the given values in the distance formula;
JK = √[(2 - 8)² + (5 - 1)²]
JK = √[(-6)² + (4)²]
JK = √[36 + 16] = √52
JK = 2√13 (magnitude of the vector JK)
Now, estimate the vector JK's direction.
The angle formed by a vector with a horizontal line defines its direction.
Use one of the given equation to find the direction of a vector.
tan Ф = Δy/Δx
Where, x = horizontal change
and, y = vertical change
tan Ф = (y₂ - y₁)/(x₂ - x₁)
= (5 - 1)/(2 - 8)
tan Ф = 4/(-6) = -2/3
Ф = 33.69° (angle lies in the fourth quadrant with having direction in clockwise)
As a result, the distance between J and K is found to be 2√13, that is the same as a magnitude of the given vector JK.
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Hey, I am confused on this question. The question is, Find the median of the data set without the outliner. Then, find the median of the data set with the outliner.
Complete the equation so that it has no solution.
3x + 2.5 = 12x – ___x + ____
GEOMETRY The length of a rectangle is twice the
width. Find the area, if the perimeter is 60 centimeters.
Draw a picture, define a variable, write an equation, and
solve the problem.
The telephone company offers two billing plans for local calls. plan 1 charges 31$ per month for unlimited calls and plan 2 charges 13$ per month plus 0.09$ per call.use an inequality to find the number of monthly calls for which plan 1 is more economical than plan 2.
Using an inequality, Plan 1 is more economical than Plan 2 given that the number of monthly phone calls is greater than 200.
If Plan 1 charges 31$ per month for unlimited calls, then the total cost per month of using Plan 1 is also 31$.
Plan 1 = 31$
If Plan 2 charges 13$ per month plus 0.09$ per call, we can express the total cost per month of using Plan 2 as:
Plan 2 = 13 + 0.09x
where x is the number of monthly phone calls
Inequality refers to the relationship between two non-equal expressions. It can be denoted by > for greater than, < for less than, >/= for greater than and equal to, and </= for less than and equal to.
If Plan 1 is more economical than Plan 2 then the monthly cost of Plan 1 is less than the monthly cost of Plan 2.
Plan 1 < Plan 2
31 < 13 + 0.09x
Solving for x.
31 - 13 < 13 + 0.09x - 13
18 < 0.09x
200 < x
x > 200
the number of monthly phone calls > 200
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seven caculators cost $170.00
a. What is the solution of the system?
Use substitution.
x-2y+z = -4
-4x+y-2z = 1
2x+2y- z = 10
By substitution, the solution of the system of equations, x - 2y + z = -4, -4x + y -2z = 1 and 2x + 2y - z = 10, is (x , y , z) = (2 , 1 , -4).
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 substitution method, given three equations in x, y, and z,
x - 2y + z = -4 (equation 1)
-4x + y -2z = 1 (equation 2)
2x + 2y - z = 10 (equation 3)
Using the equation 1, find the value of one variable, lets say x, in terms of the other variables.
x - 2y + z = -4 (equation 1)
x = 2y - z - 4 (equation 4)
Substitute the equation 4 to equation 2 and 3 and find the value of another variable, lets say y, in terms of the other variable.
-4x + y -2z = 1 (equation 2)
-4(2y - z - 4) + y -2z = 1
-8y + 4z + 16 + y -2z = 1
-8y + y = 2z - 4z + 1 - 16
-7y = -2z - 15
y = -(2z + 15)/-7
y = (2z + 15)/7 (equation 5)
2x + 2y - z = 10 (equation 3)
2(2y - z - 4) + 2y - z = 10
4y - 2z - 8 + 2y - z = 10
4y + 2y = 2z + z + 10 + 8
6y = 3z + 18
y = (1/2)z + 3 (equation 6)
Substitute the value of y from equation 5 to equation 6 and solve for z.
y = (1/2)z + 3 (equation 6)
(2z + 15)/7 = (1/2)z + 3
2z + 15 = 7[(1/2)z + 3]
2z + 15 = (7/2)z + 21
2z - (7/2)z = 21 - 15
(-3/2)z = 6
z = -4
Substitute the value of z in either equation 5 or 6.
y = (1/2)z + 3 (equation 6)
y = (1/2)(-4) + 3
y = -2 + 3
y = 1
Finally, substitute the value of y and z to equation 4 and solve for x.
x = 2y - z - 4 (equation 4)
x = 2(1) - (-4) - 4
x = 2 + 4 -4
x = 2
Hence, the solution of the given system of equations is (x , y , z) = (2 , 1 , -4).
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Y=2000( 4/5) ^x what is the decay factor or growth factor
The exponential function is y=2000(4/5)ˣ. 0.8 is the decay factor and 0.2 is the decay rate.
Given that,
The exponential function is y=2000(4/5)ˣ.
Parts of exponential function.
The general equation for an exponential growth function is :
y=a(b)ˣ
a is the initial value.
1. If b>1, growth. Then b is growth factor. r is the growth rate is b=1+r.
2. If 0<b<1, decay. Then b is decay factor. r is the decay rate is b=1-r.
Now, from the given y=2000(4/5)ˣ.
2000 is the initial value.
4/5=0.8 which is 0<0.8<1
So, 0.8 is the decay factor.
Decay rate r is
b=1-r
r=1-b
r=1-0.8
r=0.2
Therefore, 0.8 is the decay factor and 0.2 is the decay rate.
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Solve each system by elimination.
4x - 6y = -26 , -2x+3y = 13
By elimination, the system of equations, 4x - 6y = -26 and -2x + 3y = 13, has infinite solutions.
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.
First, simplify the first equation by dividing it by -2.
4x - 6y = -26 ⇒ -2x + 3y = 13 (equation 1)
-2x + 3y = 13 (equation 2)
Since the simplified equation of the first equation is the same as the second equation, then the two lines are exactly the same or overlapping.
Hence, the system of equations has infinite solutions.
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please help! will mark brainliest!
|x-1|+5=2
Answer:
No solution is what I got if you solve for x
Step-by-step explanation:
Hope this helps!!
A bakery is making whole-wheat bread and apple bran muffins. for each batch of break they make $35 profit. for each batch of muffins, they make $10 profit. the break takes 4 hours to prepare and 1 hour to back. the muffins take 0.5 hours to prepare and 0.5 hours to bake. the maximum preparation time available is 16 hours. the maximum bake time available is 10 hours. let x =
The number of batches of muffins and bread to be made in order to maximize the profits is 16 and 2.
Considering the x to be the number of batches of bread and y be the number of batches of muffins.
In the problem, it is mentioned that the preparation of both the bread and muffin takes 4 hours and 0.5 hours since the maximum preparation time is 16 altogether
The inequality equation for it will be [tex]4x+0.5y\leq 16[/tex]
For baking the bread and muffin it takes 1 hour and 0.5 hours, the maximum baking time all together is 10
The inequality equation for it will be [tex]x+0.5y\leq 10[/tex]
The profit got from one batch of bread if 35 $ and from one batch of muffins is 10$
f(x,y)= 35x+ 10y
for f(0,0)= 0, f(0,20)= 200, f(2,16)= 230 , f(4,0) =140
So it requires 2 batches of bread and 16 batches of muffins.
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A bakery is making whole-wheat bread and apple bran muffins. For each batch of break they make $35 profit. For each batch of muffins, they make $10 profit. The break takes 4 hours to prepare and 1 hour to back. The muffins take 0.5 hours to prepare and 0.5 hours to bake. The maximum preparation time available is 16 hours. The maximum bake time available is 10 hours. Let x = # of the batches of bread and y = # of batches of muffins. What constraints can be used to find the number of batches of bread and muffins that should be made to maximize profits?
Determine whether the events are mutually exclusive or not mutually exclusive. Then find the probability. Round to the nearest tenth of a percent, if necessary.
drawing an ace or a heart from a standard deck of 52 cards
According to the question, to calculate the probability of the event which states that to draw a card from the standard deck but the condition is getting either ace or heart.
The total number of the playing cards are [tex]52[/tex]
And total number of heart cards are [tex]13[/tex]
And total number of ace cards are [tex]4[/tex]
Therefore, the total number of favorable outcomes in which either heart or ace can be drawn: [tex]4+13[/tex]
As per question, the probability can be written as:
P(h or a) = P(a) + P(h) - P( a and h)
[tex]= \frac{4}{52} +\frac{13}{52} -\frac{1}{52} = \frac{16}{52} = \frac{4}{13} = 30.8%[/tex]
Hence, the probability of getting either an ace or heart card is [tex]\frac{4}{13}[/tex].
The given event is not mutually exclusive because it has [tex]30.8[/tex] percent which is not close to tenth of a percent.
What are mutually exclusive events?
Mutually exclusive events are those events which cannot happen at the same time. For instance, in any event nobody can run forward or backward together at the same time.
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Use each recursive definition to write an explicit formula for the sequence. a₁=-5, an =a n₋₁-1
The explicit formula for the given sequence is a(n) = -5 + (-1)(n - 1).
What is termed as recursive definition?
A recursive function is one that iterates or uses its very own previous term to determine subsequent terms, resulting in a series of terms.
The recursive formula for an arithmetic sequence is as follows.
a(1) = -5 and a(n) = a(n-1) -1
Remember that this formula provides us with two types of data.
1 is the first term.Add 4 to obtain any term out of its previous term. To put it another way, this same common difference is 4.Let's look for a formal formula again for sequence.
1) Remember that we can use the standard explicit form to represent a sequence in which the first term is A & common difference is B:
A + B(n - 1)
2) As a result, the sequence's explicit formula is a(n) = -5 + (-1)(n - 1).
Thus, by the use of recursive definition, the explicit formula for the sequence is a(n) = -5 + (-1)(n - 1).
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Write a two-column proof.
Given: X is the midpoint of WY and VZ.
Prove: VW=ZY
The two-column proof are:
The angle WXV is congruent to angle YXZ
Triangle WXV congruent triangle YXZ
In this question, we are given;
X as the midpoint of line segment WY and line segment VZ
Therefore, it is correct for us to conclude that;
segment XZ is congruent to segment XV, segment XW is congruent to segment XY
Thus, angle WXV is congruent to angle YXZ
Triangle WXV congruent triangle YXZ
We then conclude that;
VW = ZY
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Write the numbers in decreasing order. √14, √5/2, √9/16, 1,11
Given numbers[tex]\sqrt{14} , \sqrt{5/2} , \sqrt{9/16} , 1, 11[/tex] in decreasing order are as follows:
[tex]11, \sqrt{14} , \sqrt{5/2}, 1, \sqrt{9/16}[/tex] .
As given in the question,
Given numbers are as follow : [tex]\sqrt{14} , \sqrt{5/2} , \sqrt{9/16} , 1, 11[/tex]
Approximate value of all given numbers
[tex]\sqrt{14} =3.74\\\\\sqrt{5/2}= 1.58\\ \\\sqrt{9 /16} = 0.75\\ \\1 =1.00\\\\11=11.00[/tex]
Arrange the given numbers in decreasing order :
11 > 3.74 > 1.58 > 1 > 0.75
[tex]\implies 11 > \sqrt{14} > \sqrt{5/2} > 1 > \sqrt{9/16}[/tex]
Therefore, given numbers[tex]\sqrt{14} , \sqrt{5/2} , \sqrt{9/16} , 1, 11[/tex] in decreasing order are as follows: [tex]11, \sqrt{14} , \sqrt{5/2}, 1, \sqrt{9/16}[/tex] .
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Find the value of x to the nearest tenth. 58.9=2 x
x = 29 is the value of x.
What exactly is meant by a value?A value in mathematics is a number that indicates the result of a calculation or function.So, in the preceding example, you might also tell your teacher that 5 x 6 equals 30 or that x + y equals 9 if x = 6 and y = 3.A value is another term for a variable or constant.To find the value of x:
Given: 58.9 = 2xSimplify the equation to find the value of x.So,
58.9 = 2xx = 58.9/2x = 29.45Now, rounding to the nearest tenths gives x = 29.
Therefore, x = 29 is the value of x.
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if there are 12 gumdrops per scoop how much is each scoop
When there qre 240scoops and that there are 12 gumdrops per scoop, the number of gumdrop is 20 per scoop.
How to calculate the value?From the information, it was stated that there are 240scoops and that there are 12 gumdrops per scoop.
Therefore, the number in each scoop will be
= Total scoops /Number of gumdrop
= 240 / 13
= 20
Therefore, there are 20 gumdrops.
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There are 240scoops. If there are 12 gumdrops per scoop how much is each scoop
Evaluate the discriminant for each equation. Determine the number of real solutions. x²+4 x+5=0 .
The roots of the equation will be imaginary. Then the number of real solutions will be zero.
What is the discriminant of the quadratic equation?The discriminant represents the types of the root. And the discriminant (D) of the equation ax² + bx + c = 0 is given as
D = b² - 4ac
The type of roots will be given below.
D > 0, Real and Distinct rootsD = 0, Real and Equal rootsD < 0, Imaginary rootsThe equation is given below.
x² + 4x + 5 = 0
The discriminant of the given equation will be
D = 4² - 4 x 1 x 5
D = 16 - 20
D = - 4
D < 0
The roots of the equation will be imaginary. Then the number of real solutions will be zero.
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HELP MEEE, I NEED HELP FAST
if <3 measures 123°, what is the measure of <4?
Answer:57
Step-by-step explanation:180-123 I hope i have helped u have a wonderful day or night!
If $5 = 4 pound and Rs 342 = $3, how many pounds will be equal to Rs 8,550?
The amount of Rs8550 will be equal to 60 pounds.
What is currency exchange?The rate at which one currency will be exchanged for another is known as the exchange rate in the world of finance. The most frequent types of currencies are national currencies.
Given that $5 = 4 pounds and Rs 342 = $3, the amount RS 8550 will be calculated as below:-
$5 = 4 pounds
$1 = 4 / 5 pounds .............................( 1 )
Rs 342 = $3
$1 = 342 / 3 RS ..............................( 2 )
From the two equations:-
342 / 3 RS = 4 / 5 pounds
1 RS = ( 3 / 342 ) x ( 4 / 5 )
8550 RS = ( 8550 x 3 x 4 ) / ( 342 x 5 )
8550 RS = 60 pounds
Therefore, the amount of Rs8550 will be equal to 60 pounds.
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Explain why you need to vertically align the decimal points when summing decimal numbers.
Answer: It is irrelevant if multiplying or dividing decimal numbers. For addition and subtraction it is not sufficient: you need to line up the decimal points as well as the digits according to their place values. If you intend to simply align the decimal points then you may as well not bother.
Step-by-step explanation:
Rodney invests a sum of money, P, into an account that earns interest at a rate of r, compounded yearly. Gerald invests half that amount into an account that pays twice Rodney’s interest rate. Which of the accounts will have the higher ending balance after 1 year? Explain.
In the account of Rodney's will have the higher ending balance after 1 year.
Given that:
Rodney invests a sum of money, P, into an account that earns interest at a rate of r, compounded yearly.
Gerald invests half that amount into an account that pays twice Rodney’s interest rate.
To find:
Which of the accounts will have the higher ending balance after 1 year?
So, according the question
We have,
For Rodney,
p = Principle = P
r = Interest rate = r
t = time expressed in year = 1 year
n = Number of periods in a year = 1
We, know that the formula to calculate the compound interest for new balance of Rodney ,
B = [tex]p (1 + \frac{r}{n} )^{nt}[/tex]
Now, putting the values,
B = [tex]p (1 + \frac{r}{n} )^{nt}[/tex]
B = [tex]P(1+\frac{r}{1} )^{1\times 1)[/tex]
B = [tex]P (1 + r )[/tex]
B = P + Pr
Now, For Gerald,
p = Principle = P/2 ( Invest half of the money from Rodney )
r = Interest rate = 2r ( Twice the rate of Rodney's)
t = time expressed in year = 1 year
n = Number of periods in a year = 1
We know that the formula to calculate the compound interest for new balance of Gerald ,
B = [tex]p (1 + \frac{r}{n} )^{nt}[/tex]
Now, putting the values,
B = [tex]p (1 + \frac{r}{n} )^{nt}[/tex]
B = [tex]\frac{P}{2} (1+\frac{2r}{1} )^{1\times 1)[/tex]
B = [tex]\frac{P}{2} (1+ 2r)[/tex]
B = [tex]\frac{P}{2}[/tex] + Pr
Now compare the amounts of their accounts, so we can say that the amount of Rodney's account will have the higher ending balance after 1 year.
So, In the account of Rodney's will have the higher ending balance after 1 year.
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4(20+12) / (5-3)
What is this
Mr. Wong traveled 45 miles on a business trip. The cost to rent a car is 30.00 plus .75 per mile. How much did Mr. Wong pay for the car rental?
Mr. Wong paid 63.75 for the car rental.
The cost of rental car will be added one time to the total rent. The cost of trip will be calculated based on the distance covered.
So, forming the equation -
Total cost = 30 + 45 × 0.75
Performing multiplication on Right Hand Side of the equation to find the cost of business trip based on miles distance traveled
Total cost = 30 + 33.75
Performing addition on Right Hand Side of the equation to find the total cost based on one time rent of car and distance traveled
Total cost = 63.75
Hence, the total cost of car rental on business trip is 63.75.
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Imagine that an employer purchases a health insurance plan that costs $365 per month, but requires that the employee pay $35 per month toward the cost of the plan. If the employee's salary is
The sum of the annual salary and the annual contribution toward health insurance from the employer is $36,420.
Given,
Imagine that an employer purchases a health insurance plan that costs $365 per month, but requires that the employee pay $35 per month toward the cost of the plan.
The employee's salary is $36,000 per year.
We need to find what is the sum of the annual salary and the annual contribution toward health insurance from the employer.
How do we divide equally a total value into a number of items?
We divide the total value by the number of items.
Example:
$120 = 5 items
1 items = 120 / 5 = $24
We have,
Health insurance plan costs = $365
Employee pay = $35 per month.
The employee's salary = $36,000 per year.
The sum of the annual salary and the annual contribution toward health insurance from the employer;
= $36,000 + $35 x 12 months
= $36,000 + $420
= $36,420
Thus the sum of the annual salary and the annual contribution toward health insurance from the employer is $36,420.
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Regina left her office downtown and traveled 3 blocks west and 5 blocks north. Write a translation vector to describe her route.
The translation vector will be as follows:
(x, y) → (x - 3, y + 5)
Regina travelled 3 blocks west and 5 blocks north.
What is meant by translation vector?The interpretation vector is the distance through which a particle should be moved (made an interpretation of) to be in the following unit cell. The image for an interpretation vector is television. The television ought to be indicated toward the finish of the math.
The distance that an atom must travel in order to transfer to the following unit cell is known as the translation vector. A translation vector is denoted by the letter Tv. At the conclusion of the geometry, the Tv should be provided. Real or fake atoms shouldn't follow a Tv, but symmetry information and other things are acceptable.
Let us consider the direction similar to map where north is positive y-axis , east is positive x-axis , west is negative x-axis and south is negative y-axis.
Therefore the translation vector will be as follows:
(x, y) → (x - 3, y + 5)
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Determine which postulate can be used to prove that the triangles are congruent. If it is not possible to prove congruence, write not possible.
The triangles are congruent by SSS.
What exactly do you mean by congruent?
If two numbers can be placed exactly over one another, they are said to be "congruent." When placed one on top of the other, the two bread slices are the same size and form. Things that are precisely the same size and shape are said to be congruent.Given:
First Label the Diagram:
AB ≅ CD
AD ≅ BC
To Prove:
Δ ABC ≅ Δ CDA
Proof:
In Δ ABC and Δ CDA
AB ≅ CD ....……….{Given}
BC ≅ DA …………..{Given}
AC ≅ AC ……….{Reflexive Property}
Δ ABC ≅ Δ CDA ….{ By Side-Side-Side test}
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Write an explicit formula for each sequence. 1,4,7,10, . . . . .
According to the arithmetic progression, explicit formula for this sequence can.be depicted by:
aⁿ = a + ( n -1 ) d.
This sequence is in arithmetic progression, and an explicit formula for this sequence is
aⁿ = a + ( n -1 ) d
where n is the number of terms, d = the difference between two-term, and a is the first term of this sequence.
For example, We have to determine the 8th term of this sequence, so n = 8, and the difference between two correspondent numbers, ( 7 - 4 = 3 )
a⁸ = 1 + ( 8 - 1 ) 3 = 1 + 21 = 22.
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At the north campus of a performing arts school, 30% of the students are music majors. At the south campus, 80% of the students are music majors. The campuses are merged into one east
campus. If 65% of the 1000 students at the east campus are music majors, how many students did each of the north and south campuses have before the merger?
The number of students that did major in the north is 300 and the number of student that do major in the south is 700.
How to use percentage to find number of student that majors in music?At the north campus of a performing arts school, 30% of the students are music majors.
At the south campus, 80% of the students are music majors.
let
x = number of student at the north campus before the merger
Therefore,
1000 - x = number of students at the south campus before the merger
Hence, the equation for the music majors in the merger is as follows:
0.3x + 0.8(1000 - x) = 0.65(1000)
0.3x + 800 - 0.8x = 650
-0.5x = 650 - 800
-0.5x = -150
divide both sides by -0.5
x = -150 / -0.5
x = 300
Therefore, the number of students that did major in the north is 300 and the number of student that do major in the south is 700.
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Solve each system by elimination.
5c - 4t = 8 , 14 + 4t = 3c
Using elimination method, the solution of the given system of equations is (-3, -23/4)
A system of equations can be solved using:
graphical methodsubstitution methodelimination methodThe given system of equations is:
5c - 4t = 8 ...... (1)
14 + 4t = 3c ...... (2)
Re-arrange equation (2) to
-3c + 4t = -14 ........ (3)
To eliminate variable t, add equation (1) to equation (3):
5c - 4t = 8
-3c + 4t = -14 +
2c = -6
c = -3
Substitute c = -3 into equation (1)
5c - 4t = 8
5 . (-3) - 4t = 8
-15 - 4t = 8
Add 15 to both sides:
-4t = 23
t = -23/4
Hence, the solution is (-3, -23/4)
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Write a two-column proof.
Given: MS ≅ RQ, MS || RQ
Prove: Δ M S P ≅Δ R Q P
We can conclude that ΔMSP ≅ ΔRQP under SAS conditions.
What do we mean by a triangle's congruency?If all three corresponding sides and angles of two triangles are the same size, they are said to be congruent.These triangles can be moved, rotated, flipped, and turned to appear identical.If they are moved, they will coincide.When two triangles satisfy the five congruence conditions, congruence exists.They are the side-side-side (SSS), side-angle-side (SAS), angle-side-angle (ASA), angle-angle-side (AAS), and right angle-hypotenuse-side (RHS).So,
Given: MS ≅ RQ, MS || RQ
To Prove: ΔMSP ≅ ΔRQP
MS = RQ = (Given)SP = PQ = (Q is the midpoint)So, ∠MSP = ∠RQP (SAS)ΔMSP ≅ ΔRQP is proved.
Therefore, ΔMSP ≅ ΔRQP under SAS condition.
Know more about the congruency of a triangle here:
brainly.com/question/2938476
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