What is x, the distance between points A and A'? 2. 4 units 4. 8 units 13. 6 units 14. 4 units.
The distance between points A (3, -5) and A' (2, -3) is 2.4 units.
Given that,
The points A (3, -5) and A' (2, -3).
We have to determine,
The distance between point A and A'.
According to the question,
The distance between two points is determined by using the distance formula.
[tex]\rm Distance \ formula = \sqrt{(x_2-x_2) ^2+ (y_2-y_2)^2[/tex]
Then,
The distance between points A (3, -5) and A' (2, -3) is,
[tex]\rm Distance = \sqrt{(2-3) ^2+ ((-3)-(-5))^2}\\\\ Distance = \sqrt{(-1) ^2+ (2)^2}\\\\ Distance = \sqrt{1+4}\\\\Distance = \sqrt{5}\\\\Distance = 2.4 \ units[/tex]
Hence, The distance between points A (3, -5) and A' (2, -3) is 2.4 units.
For more details refer to the link given below.
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Answer:
13.6 units
Step-by-step explanation:
Edge
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]
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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 ]]
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:
Building For safety, the angle a wheelchair ramp makes with the horizontal should
be no more than 3.5º. What is the maximum height of a ramp of length 30 ft? What
distance along the ground would this ramp cover? Round to the nearest tenth of
a foot.
Answer: 8.6
Step-by-step explanation:
8.57142857143 --> 8.6
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.
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.
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
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.
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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i have two Questions.
1. Find the unit rate of 90 miles/2 hours, in feet per second.
2.Find the unit rate of 120 miles in 8 hours, in feet per second.
(extra credit: Extra Credit: How many unique handshakes can be made between 5 people?)
Step-by-step explanation:
ww have that 90 miles /2 hours is given and we are asked to find it in feet per second.
[tex] \frac{90 \: mi}{2 \: hrs} \times \frac{5280 \: ft}{1 \: mi} \times \frac{1 \: hr}{60 \: min} \times \frac{1 \: min}{60 \: sec} = 66[/tex]
So we get
66 fps.
2.
[tex] \frac{120 \: miles}{8 \: hours} \times \frac{5280}{1 \: mile} \times \frac{1 \: hour}{60 \: min} \times \frac{1 \: min}{60 \: seconds} = 22[/tex]
So we get 22 fps.
Extra credit There is 5 people and 2 hands so we use the combinations formula.
n!/r!(n-r)!. where n is the number of objects (the number of people) and r is the things taken at the time( the hands)
Subsitue
[tex] \frac{5 \times 4 \times 3 \times 2 \times 1}{2 \times 1 \times 3 \times 2 \times 1} [/tex]
[tex] \frac{20}{2} = 10[/tex]
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:
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
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:
What two numbers multiplied together makes -15 then you add them together to make 2
Answer:
-3 and 5
Step-by-step explanation:
-3*5=-15
-3+5=2
Answer:
-3 and 5
Step-by-step explanation:
-3×5 I'd -15
also -3+5 is 2
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
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)
Solve geometry perimeter
7.62
Step-by-step explanation:
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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calculate the height of the tree the answer is not 46
The distance between two cities is 180 km. The distance was
covered by a car at a rate of 50 km/h, by a bus at 45 km/h, by a
truck at 40 km/h, and a by a bicycle at 25 km/h. What is the constant of
variation?
Answer:
Step-by-step explanation:
he distance between two cities is 180 km.
Speed = distance/time
v = s/t from this we can calculate for time
Time = distance /speed
This distance was covered by a car at a rate of 50 km/h
Time taken by the car to cover this distance of 180km
= 180/50 = 3.6 hours
This distance was covered by a bus at 45 km/h
Time taken by the bus to cover this distance of 180km
= 180/45 = 4 hours
This distance was covered by a truck at 40 km/h
Time taken by the truck to cover this distance of 180km
= 180/40 = 4.5 hours
This distance was covered by a bicycle at 25 km/h
Time taken by the truck to cover this distance of 180km
= 180/25 = 7.2 hours
Therefore:
speed and time are directly proportional.
Speed, s is inversely proportional to time, t
xy = k (inverse variation) or y/x = k (direct variation), where k is the constant of variation
Introducing constant of variation, k
s = k/t
When s = 25, t = 7.2
25 = k/7.2
k = 7.2× 25 = 180
So
s = 180/k
Please help me solve this problem
Answer:
15
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
What is solution for 7y+9+6y=46
Answer:
combine like terms
7y + 6y
13y + 9
Step-by-step explanation:
here is the solution
13y + 9
Dalia's family bought 5 adult tickets and 2 student tickets to the school play for $65. Shay's family bought
3 adult tickets and 6 student tickets for $69. How much does each type of ticket cost?
Answer:
Lets say a is adult tickets and s is student tickets. for dalias family its:
5a + 2s = 65
for shay
3a + 6s = 69
-15a -6s = -195
-15a = -195
Step-by-step explanation:
Lisa is getting paid 96$ per hour, her salary per hour increases by 12%, how much is she getting paid now after in increases by 12% ?
Answer:
96$/12×100
=8 × 100
=800$
Answer:
After the raise, I believe she is now getting paid 107.52$ per hour,
Step-by-step explanation:
12% of 96$ is 11.52$
11.52$ + 96$ = 107.52$
I am not sure if all calculations are correct, but I hope this helps! :)
What is the answer step by step explanation please.
w (3w + 2) + 5w
Answer:8w^2+2
w(3w+2)+5w
First distribute the w to the parentheses:
3w^2+w
Add on the 5w to the new equation:
3w^2+2w+5w
Combine like terms:
8w^2+2
Joe had some money. He spent $200 on clothes, 2/5 of his remaining money on a pair of boots and saved the rest. He saved $126. How much money did Joe have at first?
Answer:
im sorry i dont get it
Step-by-step explanation:
Find the greatest common factor of 11a4
and
5y.
A piece of metal with a length of 2. 83 cm was measured using four different devices. Which of the following measurements is the most accurate? 2. 837 cm 2. 829 cm 2. 812 cm 2. 805 cm.
Answer:
2.829 mm
Step-by-step explanation:
Correct: 2.83 mm
Measured(mm) Difference (mm)
2.837 0.007
2.829 -0.001 Smallest deviation from actual.
2.812 -0.018
2.805 -0.025
The measurement of the piece of metal that is the most accurate is 2.837 cm.
Given that,A piece of metal with a length of 2.83 cm was measured using four different devices.
We have to determine,Which of the following measurements is the most accurate?
According to the question,A piece of metal with a length of 2.83 cm was measured using four different devices.
Accuracy is the degree to which the measured value is close to the correct value.
The difference between the accepted value and the measured value of the quantity is called the error of measurement.
The measurement for the first device is,
[tex]=2.83 - 2.837\\\\=-0.007[/tex]
The measurement of the first device is -0.007.
The measurement for the second device is,
[tex]=2.83 - 2.829\\\\=-0.001[/tex]
The measurement of the second device is -0.001.
The measurement for the third device is,
[tex]=2.83 - 2.812\\\\=-0.018[/tex]
The measurement of the third device is -0.018.
The measurement for the fourth device is,
[tex]=2.83 - 2.805\\\\=-0.025[/tex]
The measurement of the fourth device is -0.02.
Hence, The measurement that is the most accurate is 2.837 cm.
For more details about Substitution refer to the link given below.
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