The distance between London and Paris is 290.38km
To get the distance between London and Paris, we will see the cosine formula as shown:
c² = a² + b² - 2ab cosФ
Given the following parameters:
a = 939kmb = 882 kmФ = 18⁰Substitute into the formula to have:
c² = a² + b² - 2ab cosФ
c² = 939² + 882² - 2(939)(882) cos18
c² = 1,659,645 - 1575326.21
c² = 84,318.79
c = 290.38km
Hence the distance between London and Paris is 290.38km
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Which function is represented by the graph? f(x) = â’|x â’ 3| 4 f(x) = â’|x 3| 4 f(x) = â’|x â’ 4| 3 f(x) = â’|x 4| 3.
Functions are used to represent graphs, and vice versa.
The function represented by the graph is [tex]f(x) =- |x + 4| + 3[/tex]
The graph (see attachment) is an absolute value graph.
An absolute value graph is represented as:
[tex]f(x) =a |x - h| + k[/tex]
Where
[tex]Vertex = (h,k)[/tex]
The vertex is the minimum or the maximum point on the graph.
So, we have:
[tex]Vertex = (-4,3)[/tex]
The function becomes
[tex]f(x) =a |x + 4| + 3[/tex]
The function also passes through the point (-1,0).
So, we have:
[tex]0 =a |-1 + 4| + 3[/tex]
[tex]0 =a |3| + 3[/tex]
Remove the absolute bracket
[tex]0 =3a + 3[/tex]
Subtract 3 from both sides
[tex]3a =- 3[/tex]
Divide both sides by 3
[tex]a =- 1[/tex]
Substitute -1 for (a) in [tex]f(x) =a |x + 4| + 3[/tex]
[tex]f(x) =- |x + 4| + 3[/tex]
Hence, the function represented by the graph is [tex]f(x) =- |x + 4| + 3[/tex]
Read more about absolute value graphs at:
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You and your sister are buying your mom a birthday gift. You paid $54 and your sister paid $22. What percentage did each sister contribute to the total cost of the gift?
Answer:
$54 = 71%, $22 = 29%
Step-by-step explanation:
54+22=76
54/76 = 0.7105
22/76 = 0.2894
100,105,110.25… recusive formula
Answer:
a[1] = 100
a[n] = 1.05·a[n -1]
Step-by-step explanation:
The given terms do not have a common difference, but do have a common ratio. Each is 1.05 times the previous. This is expressed in a recursive relation as ...
a[1] = 100
a[n] = 1.05·a[n -1]
A triangle has sides with lengths of 4 meters , 5 meters, and 7 meters . Is it a right angle ?
Answer:
No
Step-by-step explanation:
6.4 divided by 43.52
Answer:
0.14705882352
Step-by-Step:
Just use a calculator and your answer should pop up.
An online T-shirt store is having a sale. The original price of each T-shirt is p dollars. The store sells 20 T-shirts and earns a total of (20p−60) dollars.
a. Factor the expression using the GCF.
20p−60=
b. The discount per T-shirt is $
. what is the discount
Answer:20 (p-3)
Step-by-step explanation:
a wall that is 1.4m long has started lean and makes an angle of 80’o with the ground. A 2.0m board is jammed between the top of the wall and the ground to help prop the walk up. What angle does the board make with the
ground?
AB is a line segment.
The midpoint of the line segment AB has coordinates (3, 5)
Point A has coordinates (9, 2)
Work out the coordinates of point B.
Answer:
(-3,8)
Step-by-step explanation:
Lets say two points are (x1,y1) and (x2,y2), the midpoint will be:
((x1+x2)/2,(y1+y2)/2)
Plugging the point A in, we get: the midpoint, (3,5) as (((9+x2)/2),(2+y2)/2)
We can assign x2 and y2 as variables.
(9+x2)/2=3
9+x2=6
x2= -3
(2+y2)/2=5
2+y2=10
y2=8
therefore we get the point (-3,8)
There are better ways and this is the "formulaic (ig) way" to do this
The midpoint of a line segment means a point which lies in the mid of the given line segment. The coordinate of point B is (-3,8).
What are the coordinates of the midpoint of the line segment AB?The midpoint of a line segment means a point which lies in the mid of the given line segment.
Suppose we've two endpoints of a line segment:
A(p,q), and B(m,n)
Then let the midpoint be M(x,y) on that line segment. Then, its coordinates are:
x = (p+m)/2
and
y = (q+n)/2
The coordinate of the midpoint (x,y)=(3,5), while the coordinate of A(p,q)=(9,2). Thus, the coordinate of point A are,
x=(p+m)/2
3=(9+m)/2
6=9+m
m = -3
y = (q+n)/2
5 = (2+n)/2
10=2+n
n=8
Hence, the coordinate of point B is (-3,8).
Learn more about Midpoint:
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Find the value of x when 6-2x =5x-9x+16The value of x is
Answer:
5
Step-by-step explanation:
6-2x = 5x-9x+16
leave the x's together: (going over the equal signs changes the sign)
-2x-5x+9x = 16-6
2x = 10
x = 5
evaluate 2x+y for x=1/3 and y=2/3
a.1/3
b.2/3
c.4/3
d.5/3
Answer:
C. 4/3
Step-by-step explanation:
2 × ⅓ + ⅔
⅔ + ⅔ = 4/3
Use X as ⅓, and use Y as ⅔.
The side lengths of a triangle are 12, 14, and x units
Answer: x=14
Step-by-step explanation: have a good day
help i dont know how to do this !!!!!!!!!!!! for brainlist
Answer:
We can simplify everything to the power of 2:
[tex]8^{x+2} = 2^{3*(x+2)}=2^{3x+6[/tex]
[tex]16^{x+1} = 2^{4*(x+1)}=2^{4x+4[/tex]
As the two equations are equal to each other and they have common bases, their powers must be equal too. We can come up with this equation:
3x+6=4x+4
solve for x
x=2
D (last answer choice)
plug x=2 in and check and you will get 4096=4096
Simplify this expression.
2V5(13 +V2)
Answer:
26V^5+2V^7
Step-by-step explanation:
Help me I don’t know if it -7 and -12
Answer:
I think it's-12
I am not sure
Please ask to some one else please
Help please, and explanation.
According to my teacher the answer is not 1/4.
Answer:
1/9
Step-by-step explanation:
There are 3 even numbers. 2,4, and 6. There is a 1/3 chance of rolling one on each dice.
So 1/3*1/3=1/9
Answer plz school is stressful
Answer:
1 month.
Step-by-step explanation:
When reading a graph, the most important thing is knowing what the axes are. Here, the horizontal x-axis is months, and the vertical y-axis is the number of books read. Those are our 2 variables.
Now, a line on a graph shows the relationship between those 2 variables. At any given point on the line, it'll have an output value of y (books read) for whatever input value of x.
The question gives you the value on the y-axis (books read), so all you need to do is find the value of x that corresponds to that point on the line. I marked that point on the line in the attached image. Look directly below that point on the line, and you can see that 1 month corresponds to 4 books read.
Which table of values would produce the graph shown above?
help quick! Which BEST describes the tables?
Answer:
D. Neither table represents a function
Step-by-step explanation:
Functions require a key to go by. In this case, none of the two tables have a key from the start going down.
how many liters of a 30% antifreeze solution need to be added to 10 L of a 57% antifreeze solution to get 50% antifreeze solution. round to two decimal places.
i need help with this question, thx to anyone who helps! :)
Answer:
Golf balls
Step-by-step explanation:
There is a much higher chance of her picking an even number in the golf ball tank because there are way more golf balls with even numbers. (2, 4, 6, 8, etc.)
i have 9 animals 3 are girls what percent is girls?
Answer:
33 1/3%
Step-by-step explanation:
Because there are 3 girls and 9 total animals, you do: 3/9, which is 1/3. You divide to find the percent. 1/3=33.333333..... Because you have a repeating decimal, you do 33 and 1/3, because the repeating decimal is .33333.....
What is the greatest common factor of 3 and 33?
Answer:
3
Step-by-step explanation:
Step 1: Find the factors of 3 and 33.
3: 1, 333: 1, 3, 11, 33Step 2: Find the largest common factor they share.
As you can see, the largest common factor they share is 3.Therefore, the GCF of 3 and 33 is 3.
Find the value of the expression:
x(x-y)-y(y^2-x) for x=4 and y=2
Replacing x by 4 and y by 2, it is found that the value of the expression is of 8.
The expression given is:
[tex]x(x - y) - y(y^2 - x)[/tex]
We want to evaluate it for x=4 and y=2, hence, we replace x by 4 and y by 2, then:
[tex]4(4 - 2) - 2(2^2 - 4) = 4(2) - 2(0) = 8[/tex]
The value of the expression is of 8.
A similar problem, in which the objective is finding the value of an expression, is given at https://brainly.com/question/19548262
can somebody please tell me if this is correct or not
Answer:
I would have done it the same way. Believing it is correct.
Step-by-step explanation:
Answer: Looks precise
Step-by-step explanation:
can you identify the value of each digit ?
Answer:WHAT VALUE AND WHAT DIGIT
Step-by-step explanation:
13x+y=1
2x+6y=6
HELP PLZ
Answer:
(0,1)
Step-by-step explanation:
solve the first equation for y. y=1-13x
plug this into the other equation and solve for x.
2x+6(1-13x)=6
2x+6-78x=6
-76x+6=6
subtract 6 from both sides
-76x=0
x=0
plug this into the other original equation.
13(0)+y=1
y=1
(0,1)
calculate the height of the tree the answer is not 46
Hey Guys!
Try to solve this maths question.....
[tex]a + b + c = 4 \\ {a}^{2} + {b}^{2} + {c}^{2} = 10 \\ {a}^{3} + {b}^{3} + {c}^{3} = 22 \\ {a}^{4} + {b}^{4} + {c}^{4} = ? [/tex]
Don't copy from web and Don't spam
Need answer as well as explanation
Thank You!
Use the multinomial theorem to compute some polynomial expansions:
(a + b + c)² = a² + b² + c² + 2 (ab + ac + bc)
(a + b + c)³ = a³ + b³ + c³
… … … … … … + 3 (a²b + a²c + ab² + b²c + ac² + bc²)
… … … … … … + 6 abc
(a + b + c)⁴ = a⁴ + b⁴ + c⁴
… … … … … … + 4 (a³b + a³c + ab³ + b³c + ac³ + bc³)
… … … … … … + 6 (a²b² + a²c² + b²c²)
… … … … … … + 12 (a²bc + ab²c + abc²)
Now, given that
a + b + c = 4
a² + b² + c² = 10
it follows that
ab + ac + bc = (4² - 10)/2 = 3
We use this result to simplify the extra terms in the 3rd-degree expansion.
a²b + a²c + ab² + b²c + ac² + bc²
= a (ab + ac) + b (ab + bc) + c (ac + bc)
= a (ab + ac + bc) + b (ab + ac + bc) + c (ab + ac + bc) - 3abc
… … I underline the terms that are added and subtracted … …
= (a + b + c) (ab + ac + bc) - 3abc
= 4 • 3 - 3abc
= 12 - 3abc
Given that
a³ + b³ + c³ = 22
this tells us that
4³ = 22 + 3 (12 - 3abc) + 6abc
4³ = 58 - 3abc
and so
abc = (4³ - 58)/(-3) = -2
from which it follows that
a²b + a²c + ab² + b²c + ac² + bc² = 12 - 3 • (-2) = 18
Now we similarly simplify the extra terms in the 4th-degree expansion.
a³b + a³c + ab³ + b³c + ac³ + bc³
= a² (ab + ac) + b² (ab + bc) + c² (ac + bc)
= a² (ab + ac + bc) + b² (ab + ac + bc) + c² (ab + ac + bc) - a²bc - ab²c - abc²
= (a² + b² + c²) (ab + ac + bc) - (a²bc + ab²c + abc²)
= 10 • 3 - (a²bc + ab²c + abc²)
which means
4⁴ = a⁴ + b⁴ + c⁴
… … … … … … + 4 (30 - a²bc - ab²c - abc²)
… … … … … … + 6 (a²b² + a²c² + b²c²)
… … … … … … + 12 (a²bc + ab²c + abc²)
reduces to
136 = a⁴ + b⁴ + c⁴
… … … … … … + 6 (a²b² + a²c² + b²c²)
… … … … … … + 8 (a²bc + ab²c + abc²)
Now, we know a + b + c = 4 and abc = -2, so we have
a²bc + ab²c + abc² = abc (a + b + c) = -2 • 4 = -8
and so
136 = a⁴ + b⁴ + c⁴ + 6 (a²b² + a²c² + b²c²) + 8 • (-8)
200 = a⁴ + b⁴ + c⁴ + 6 (a²b² + a²c² + b²c²)
Finally, we know that ab + ac + bc = 3. Squaring this gives
(ab + ac + bc)² = 3²
a²b² + a²c² + b²c² + 2 (a²bc + ab²c + abc²) = 9
but we also know that a²bc + ab²c + abc² = -8, so
a²b² + a²c² + b²c² + 2 • (-8) = 9
a²b² + a²c² + b²c² = 25
Therefore, we end up with
200 = a⁴ + b⁴ + c⁴ + 6 • 25
⇒ [[[ a⁴ + b⁴ + c⁴ = 50 ]]
Explain the steps in solving 2.14x-12.18=-576 , and write the solution to the equation.
Answer:
x = 274 91/107
Step-by-step explanation:
This is called a "two-step linear equation" because it is solved in 2 steps.
Step 1. Identify the constant on the same side of the equation as the variable term, and add its opposite to both sides of the equation.
2.14x -12.18 +12.18 = 576 +12.18
2.14x = 588.18
__
Step 2. Identify the coefficient of the variable and multiply both sides of the equation by its reciprocal.
2.14x(1/2.14) = 588.18(1/2.14)
x = 274.850467... = 274 91/107 . . . the decimal fraction repeats
The solution to the equation is x = 274 91/107.
Answer:
x = 274 91/107
Step-by-step explanation:
Step-by-step explanation:
This is called a "two-step linear equation" because it is solved in 2 steps.
Step 1. Identify the constant on the same side of the equation as the variable term, and add its opposite to both sides of the equation.
2.14x -12.18 +12.18 = 576 +12.18
2.14x = 588.18
__
Step 2. Identify the coefficient of the variable and multiply both sides of the equation by its reciprocal.
2.14x(1/2.14) = 588.18(1/2.14)
x = 274.850467... = 274 91/107 . . . the decimal fraction repeats
The solution to the equation is x = 274 91/107.
Please help me solve this problem
Answer:
15
Step-by-step explanation: