The distance between the two points is approximately 19.18 units
The length of the line segment connecting any two points is referred to as their distance. In coordinate geometry, the distance formula is usedto calculate the distance between two points.
In 1731, the distance formula itself was first made public. Pythagorean distance is another name for Euclidean distance. The Pythagoras is used to derive the distance formula.
If two point are given as A [tex](x_1,y_1)[/tex] and B [tex](x_2,y_2)[/tex] then the distance between the two points or the length of AB is calculated using the formula:
[tex]AB = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}[/tex]
The co ordinates of the two points are given as [tex](5\sqrt{3},7\sqrt5 )[/tex] and [tex](-\sqrt{3},-\sqrt{5} )[/tex].
Therefore distance between the points will be given by:
[tex]=\sqrt{(5\sqrt{3} - \sqrt{3} )^2 + (7\sqrt{5} -(-\sqrt{5} )^2}\\=\sqrt{(4\sqrt{3})^2+(8\sqrt{5})^2 }\\=\sqrt{48+320}\\=\sqrt{368}\\\approx19.18[/tex]
The distance between the two points is approximately 19.18 units.
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The term containing b^6 in the expansion of (a + b2)10
The term containing b^6 is -210 a^6 b^6
The given expansion can be solved by using the Binomial expansion
The binomial expansion for two terms (a + b) raised to the power n is given by
(a+b)^n = Σ[tex]a^{n-k} * b^k[/tex] * n!/k!(n-k)!
To find term contain b^6 we use the formula
Use the formula T r+1 =(−1) ⁿCr [tex]a^{n-r} * b^r[/tex]
Putting n=10,
we get 10-r=6
r=4
Therefore,
it is the fourth term ,
T = (-1)^3 10!/4!6! [tex]a^{10-6} * (b^2)^4[/tex]
= -1 x 10x9x8x7/4x3x2=-210 [tex]a^6 b^6[/tex]
Hence the term containing b^6 is -210 a^6 b^6
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NEED ANSWER PLS HURRY !!
Answer:it's the second option
Step-by-step explanation:
-x is already -1 so why would factoring it make it -1 again
Karen worked her 40 regular hours last week, plus 6 hours at the time-and-a-half rate. Her gross pay was $650. What was her hourly rate?
As Karen worked for 40 regular hours and 6hours overtime at the rate of 1.5 regular hours and her gross pay was $650 then her hourly rate is $13.27 (approximately).
As given,
Regular working hours =40 hours
Overtime at the rate of (1.5 of regular hours) = 6 hours
Gross pay =$650
Let 'h' be the hourly rate
Required equation
40h + 6(1.5h) =650
⇒ 40h +9h=650
⇒49h=650
⇒h=$13.27(approximately)
Therefore, as Karen worked for 40 regular hours and 6hours overtime at the rate of 1.5 regular hours and her gross pay was $650 then her hourly rate is $13.27 (approximately).
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Completing the square first gets brainliest maths Question plus 30 points.
Answer:
Hello,
Step-by-step explanation:
a)
[tex]x^2-2x-6=x^2-2x+1-1-6\\\\=(x-1)^2-7\\[/tex]
b)
[tex]x^2-2x-6=(x-1)^2-7\\\\=(x-1-\sqrt{7} )(x-1+\sqrt{7} )\\\\\\\boxed{x=1-\sqrt{7} \ or\ x=1+\sqrt{7} }\\[/tex]
A more
at a lower cost
business generally achieves greater profits
Answer:
What do you need help with?
Step-by-step explanation:
Consider a data set with at least three data values suppose the highest value is increased by 10 and the lowest is decreased by five
plss give your self a answer
Find the probability that there are no T when a fair coin is flipped three times.
The probability that no Tails is achieved on flipping a fair coin for three consecutive times is [tex](\frac{1}{8})[/tex].
As per the question statement, we are to flip or toss a fair coin thrice consecutively.
We are required to calculate the probability that no Tails is achieved during the above mentioned event.
To solve this question, first let us calculate all the possible outcomes of flipping a fair coin thrice consecutively. [We will denote a Heads outcome as "H" and a Tails outcome as "T"]
The total number of outcomes can be given by the formula [tex](2^{n})[/tex], where "n" is the number of times, the coin is tossed.
Here, (n = 3), therefore, total number of outcomes in our case [tex]=(2^{3})=8[/tex].
These 8 outcomes can be listed as [tex][{(H, H, H), (H, H, T), (H, T, H), (H, T, T), (T, H, H), (T, H, T), (T, T, H), (T, T, T)}][/tex]
And among the above listed 8, our favorable outcome is (H, H, H), i.e., 1 favorable outcome of 8.
Hence, probability that no Tails is achieved on flipping a fair coin thrice consecutively = [tex]\frac{1}{8}[/tex].
Probability: In Mathematics, probability is the chance to of the occurrence of a specific event among the occurrence of all possible events, and is measured by the ratio of the favorable cases to the whole number of cases possible.To learn more about Probability, click on the link below.
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6. Find the product: 6.45 x 19.3
nth term of -9, -5, -1, 3, 7
The nth term of the given sequence is 4n - 1.
What do we mean by the nth term?The nth term is a formula that allows us to locate any term in a series. The 'n' represents the term number. By substituting different values for the term number, we can create a sequence using the nth term ( n ).So,
-9 + 4 = -5-5 + 4 = -1-1 + 4 = 33 + 4 = 7As, (4 × 2) - 1 = 7Then, the nth term is 4n - 1Therefore, the nth term of the given sequence is 4n - 1.
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7,5+9287= x + 7?????
Answer:
X = 9287.5
Step-by-step explanation:
Solving steps
7.5+ 9287=x+7
Calculate
9294.5=x+7
Move the terms
-x=7-9294.5
Calculate
-x=-9287.5
Change the signs
Solution
X = 9287.5
Elroy's Balloon Emporium sells boxes of balloons. There are 500 balloons in a box. In January, they sell 3 boxes.In February they sell 6 boxes .If they started with 10 boxes, how many balloons do they have left to sell?
Answer:
500
Step-by-step explanation:
3+6=9
10-9=1
They sell 9 out of the 10 boxes. if each box has 500 balloons, then they have 500 left
Answer: 500 balloons
Step-by-step explanation: if you do 500 x 10 you get 5000 and then you do 3 x 500 + 6 x 500 then you get 4500 then subtract that from 5000
Write three different expressions that equivalent to 8 to the power 2 x 4 to the power of 2
Answer:
One could be: 8*8 times 4*4
Another could be: 8 to the second power times 4 to the second power
A third way to write this could also be: 8*4*8*4
Step-by-step explanation:
Hope its helpful
9x7/9-6+13 order of Operations
((9×7)÷9−6)+13
(63÷9−6)+13
(7−6)+13
1+13
14
Answer:
9 X 7 / 9 - 6 + 13
we can cut 9
=7-6 + 13
=1+13
=14
f(x) = x² - 6x-7
g(x) = x + 1
Answer:
(-1, 0) and (8, 9)
Step-by-step explanation:
x² - 6x-7 = x + 1
x² - 7x - 8 = 0
(x - 8)(x + 1) = 0
x = -1, 8.
When x = - 1, y = 0
and x = 8, y = 9
Find an expression which represents the difference when (- x - 3y) is subtracted
from (8a - 9y) in simplest terms.
Answer:
hello
Step-by-step explanation:
hi
MSA
my milkshake brings all the boys to the yard yeah right its better than yours yeah right its better than yours
Austin rented a truck for one day. There was a base fee of $17.99, and there was an additional charge of 73 cents for each mile driven. Austin had to pay $120.92 when he returned the truck. For how many miles did he drive the truck?
The miles for which Austin drove the truck is 141 miles
It is given that Austin rents a truck for one day
The daily rental base fee of the truck is $17.99
It is also given that additional charge of 73 cents per mile is charged.
It is also to be noted that 1$ =100 cents
Therefore, 73 cents in the form of dollar is 0.73$
Now it is given that total bill that is paid is $120.92
Now the total number of miles travelled by Austin is total bill minus the base fee and 73 cents multiplied by miles
Let the miles travelled by Austin be 'x'
Therefore, Miles travelled by Austin = 120.92$-17.99$
0.73 x =(120.92 -17.99) $
x= 102.93 / 0.73
x=141
Hence, the miles for which Austin drove the truck is 141 miles
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Please help me, I'll give brainliest.
In below Diagram,
The length of BE is 15 cm.
It is given that length of FA is 40 cm and CD is 24 cm.Use trigonometry or similar triangles.In ΔDAC,Tan(∠DAC) = DC/ACIn ΔEAB,Tan(∠EAB) = BE/AB∠DAC = ∠EABDC/AC = BE/AB(DC)(AB) = (BE)(AC)This is equation (1).In ΔDAC,Tan(∠FCA) = FA/ACIn ΔDAC,Tan(∠ECB) = BE/BC∠FCA = ∠ECBFA/AC = BE/BC(FA)(BC) = (BE)(AC)This is equation (2).From equations (1) and (2),(DC)(AB) = (FA)(BC)24(AB) = 40(BC)AB = BC(40/24)AB = BC(5/3)In equation (2), AC can be written as the sum of AB and BC.(FA)(BC) = (BE)(AB + BC)Use the known values.40(BC) = (BE)[(5/3)BC + BC]40(BC) = (BE)[(8/3)BC]40 = BE(8/3)BE = (40/8)*3BE = 5*3BE = 15cmTo learn more about trigonometry, visit :
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PLEASE HELP!!! I WILL GIVE BRAINLYEST!!
The dimensions of a room are given as 3.5 meters by 7.6 meters, to the nearest 10 cm. What area of carpet should be purchased to make sure it covers all the room?
Answer: Our carpet calculator will help you determine your approximate floor area in square metres. Simply measure the length and width of each room to the nearest 10cm, i.e. 5.4m x 3.7m, then enter your totals into the calculator and hit the 'calculate' button at the bottom.
For awkwardly shaped rooms (such as an L shape) divide the room into blocks, measure them separately and add them in as individual rooms.
Step-by-step explanation:
The total cost of a jacket and a pair of pants was $52.37. If the price of the jacket was $4.87 less than the pair of pants, what was the price of the jacket? Express your answer as a simplified fraction or a decimal rounded to two places.
The price of the jacket is $23.75
Let m be the price of a jacket and n be the price of pair of pants.
The total cost of a jacket and a pair of pants was $52.37
So, we get an equation,
m + n = 52.37 ................(1)
Also, the price of the jacket was $4.87 less than the pair of pants
So, we get an equation,
m = n - 4.87 .............(2)
Substitute above value of m in equation (1)
⇒ (n - 4.87) + n = 52.37
⇒ 2n - 4.87 = 52.37
⇒ 2n = 52.37 + 4.87
⇒ 2n = 57.24
⇒ n = 28.62
This means, the cost of a pair of pants is $28.62
Substitute above value of n in equation (2)
⇒ m = n - 4.87
⇒ m = 28.62 - 4.87
⇒ m = 23.75
This means, the cost of a jacket is $23.75
Therefore, the price of the jacket is $23.75
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Identify the Property of Operation that is being used.
3(a – 2) = 3a – 6
Question 1 options:
Distributive Property
Commutative Property
Identity Property
Associative Property
-------------------------------
(5 x 4) x 2 = 5 x (4 x 2)
Question 2 options:
Commutative Property
Distributive Property
Associative Property
Identity Property
-------------------------------
Simplify the expression.
9y + 6 – 7y - 3
Question 3 options:
-2y - 3
2y + 3
2y + 9
-2y + 9
-------------------------------
9y + 6 – 7y - 3
Question 3 options:
-2y - 3
2y + 3
2y + 9
-2y + 9
-------------------------------
a + b + 2a + 2b + 5 − b
Question 5 options:
3a + 2b + 5
3a + 4b + 5
2a + 4b + 5
2a + 2b + 5
Answer:
3×a-3×2=3a-6
3a-6=3a-6 proved
3.
The Moy family budgeted $32,650 to remodel their kitchen. They spent
$43,987. How much more or less is the amount spent than the amount
budgeted?
A $11,337 more
B $11,337 less
C $17,887 more
D $17,887 less
Answer:
A
Step-by-step explanation:
43987-32650= 11337
And it’s more
is b a scale copy of a yes or no explain your reasoning
Figure B is not a scale copy of figure A. The answer is NO. The corresponding lengths of both figures have different ratios.
How to Determine a Scale Copy of a Figure?If a figure is the scale copy of another figure, the corresponding side lengths of both figures would be proportional to each other, which means their ratios would be the same.
From the figure given, the ratios of their side lengths are:
18/9 = 2
12/12 = 1
30/15 = 2
This shows that their ratios are not the same.
Therefore, we can conclude that figure B is not a scale copy of figure A. The answer is NO. The corresponding lengths of both figures have different ratios.
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Ms. Francis is planning a birthday party for her daughter. There will be 22 children at the party, and in order to seat them all she needs to rent square card tables. Only 1 child can sit at each side of a card table.
Ms. Francis wants to arrange the tables in a rectangular shape so they look like one large table. The room is large enough that
the rectangle can be made with more than one row of tables.
Part A: How many different arrangements can Ms. Francis make to seat all 22 children?
Part B: What is the smallest number of tables that Ms. Francis needs to rent?
DIRECTIONS: To solve the problem, apply the steps of the Mathematical Problem-Solving Routine.
Understand
1. Try to visualize the situation. Consider drawing a diagram
2. State the problem in your own words.
3. What is the important information in the problem?
Plan
4. What strategy will you use to solve the problem? Why?
There are 5 possible arrangements to make seat all 22 children.
The smallest number of tables Ms. Francis is 10 tables.
Total number of children at the party = 22
When we picturize the scenario, each child need to get a side of the table.
So at least 22 sides should be there after arranging it into rectangles. Also the square card tables are arranged side to side to get rectangle rows.
It is also said that there can be multiple rows. So combining all these points, we can consider a row of 10 tables. Then the the squares on the ends contribute a total of 6 sides and the remaining 16 seats can be arranged by 8 square tables in between the end square tables. So a total of 10 square table is required to make a rectangle in one row.
For making 22 seats in 2 rows, the 4 square tables on the ends contribute 8 seats. For the remaining 12 seats add 7 square tables in each row, that is a total of 14 square tables. That is, for 2 rows, the square tables required is 14 + 4 = 18.
Similarly, for 3 rows, a total of 24 square tables are required.
For 4 rows, a total of 28 tables and for 5 rows, a total of 30 tables are needed.
We cannot make a 6 row because it will be same as a 5 row.
So 5 different arrangements can be made to seat all 22 children.
They are:
1 row → 1 x 10 = 10 tables
2 rows → 2 x 9 = 18 tables
3 rows → 3 x 8 = 24 tables
4 rows → 4 x 7 = 28 tables
5 rows → 5 x 6 = 30 tables
The smallest number of tables that Ms. Francis needs to rent is, therefore, 10 tables.
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-7=
n-10
3
2 step eq
3(n-10)=-7
Solve the equation in 2 step equation.
n=18.5
Given that 3(n-10)=7
step1: multiplication
Adding a number to itself as many times as the value of the other number is equivalent to multiplying two numbers by their sum.
3n-30=7
step2: adding 30 on both sides of the equation.
When objects are collected together, addition, a mathematical operation, describes how many total items there are in the collection.
2n-30+30=7+30
2n=37
step3: divide the equation by 2.
Basically, dividing is the act of dividing anything into equal sections or groups.
[tex]\frac{2n}{2} =\frac{37}{2}\\ n=\frac{37}{2} or 18.5[/tex]
Therefore, n=18.5
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PLEASE HELP ITS DUE TODAY Pleasee
[tex]scale \: from \: b \: to \: a = \frac{3}{2} \\ x = \frac{2}{3} \times 10.5 = 7[/tex]
1. What information can be seen most easily in the dot plot?
a dot plot can easily show all the data.
Step-by-step explanation:
In this example, a dot plot can easily show all the data. If the data set is very large (more than 100 values, for example) or if there are many different values that are not exactly the same, it may be hard to see all of the dots on a dot plot.
b. The cardinal number of (2, 4, 6, ..., 106) is
The cardinal number of (2, 4, 6, ..., 106) is 53.
The cardinal number of a set is the number of elements in the particular set.
We are given the set (2, 4, 6, ..., 106). As we can can clearly see, it is forming an Arithmetic Progression (AP).
Hence, let the number of elements or the cardinal number of the set be n.
Hence, according to the formula of AP, we can write,
2 + (n-1)(2) = 106
2(n-1) = 106 - 2
2(n-1) = 104
n - 1 = 104/2
n - 1 = 52
n = 52 + 1
n = 53
Hence, the cardinal number of the set is 53.
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I'm really confused about this equation. I'm trying to figure it out, but I'm lost and think I'm overthinking it
Jet A Travels at 417 mph and gets halfway to its destination in two hours. Jet B makes the same journey but makes it to the destination in 5 minutes. How fast is Jet B in MPH, or how much faster is Jet B than Jet A As A Multiplier?
Example: 417 * 48 = 20016 Or Jet B = X MPH
I think the answer is 417 * 48 = 20016 and Jet B= 20016
But I just need reassurance, or a definitive answer
Answer:
Jet B speed: 20,016 mphspeed multiplier: 48Step-by-step explanation:
You want the speed and speed multiplier for Jet B given that it makes a journey in 5 minutes that takes Jet A 2 hours for half the journey.
Speed multiplierFor the same distance, speed is inversely proportional to time.
speed multiplier = (speed B)/(speed A) = (time A)/(time B)
speed multiplier = ((2 h)/(1/2))/(5 min)
speed multiplier = (240 min)/(5 min) = 48
SpeedThe speed of Jet B is 48 times that of Jet A:
48(417 mph) = 20016 mph . . . . speed of Jet B
__
Additional comment
The time for the full trip by Jet A can be found using the proportion ...
partial time/partial distance = total time/total distance
If the total distance is "1 unit", then this proportion is ...
(2 h)/(1/2) = t/1 . . . . . where t/1 = t is the time for the full trip by Jet A
You will recognize the value (2 h)/(1/2) as the time value we used for Jet A in the above solution.
What unit would I use in this equation for science
Answer:
I think Dessicant
Step-by-step explanation:
i hope it helped you if I'm right :D
Solve for x.
-4x+60 < 72
OR 14z +11 <-31
The value of x is 3 and -3 respectively.
How to solve the inequalityGiven that;
4x+60 < 72 (1)14x +11 <-31 (2)From equation (1)
4x+60 < 72
First, collect like terms
4x < 72 - 60
subtract like terms
4x < 12
Make 'x' the subject
x < 12/ 4
x < 3
For equation (2)
14x +11 <-31
collect like terms
14x < -31 - 11
14x < -42
Make 'x' the subject
x < -42/ 14
x < -3
Thus. the value of x is 3 and -3 respectively.
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