Answers
[tex]a^2+b^2=c^2[/tex], where a and b are the lengths of the legs, and c is the length of the hypotenuse. In the context of the x-y plane, the legs of the triangle correspond to separate x and y values on the plane, and the hypotenuse corresponds to a straight line between two points on that plane.
To find the distance between the points you've listed, (2√5,4) and (1,2√3), we'll first need to find the "legs" of the triangle. To find the length of the x leg, we'll just need the distance between the x values of the points, which we find to be 2√5-1. We do the same for the y component, which ends up being 4-2√3. Now that we have our legs, we're ready to find the hypotenuse - or the distance.
Going back to Pythagorus's equation, we have:
[tex](2 \sqrt{5}-1)^{2}+(4-2 \sqrt{3})^{2}=d^2 [/tex]
where d, the hypotenuse of the triangle, means "distance."
To solve for d, we take the square root of both sides:
[tex]d= \sqrt{(2 \sqrt{5}-1)^2+(4-2 \sqrt{3} )^2} [/tex]
And from there, all that's left to do is solve the right side of the equation, which just ends up being rote calculation.
Edit: I'll go through the steps of that calculation here. We'll start by expanding each of the squared terms inside the radical:
[tex](2 \sqrt{5}-1)^2=(2 \sqrt{5}-1)(2 \sqrt{5}-1)=(2 \sqrt{5}-1)2 \sqrt{5}-(2 \sqrt{5}-1)[/tex]
[tex]=(2 \sqrt{5})^2-2 \sqrt{5}-2 \sqrt{5}+1=20-4\sqrt{5}+1[/tex]
[tex](4-2\sqrt{3})^2=(4-2\sqrt{3})(4-2\sqrt{3})=(4-2\sqrt{3})4-(4-2\sqrt{3})2\sqrt{3}[/tex]
[tex]=16-8\sqrt{3}-8\sqrt{3}+(2\sqrt{3})^2=16-16\sqrt{3}+12[/tex]
Putting those values back under the radical:
[tex] \sqrt{20-4\sqrt{5}+1+16-16\sqrt{3}+12} [/tex]
Collecting constants:
[tex] \sqrt{49-4\sqrt{5}-16\sqrt{3}} [/tex]
If you wanted an exact answer, this messy-looking thing would be it, and you can verify those results on WolframAlpha if you'd like. If you want an approximation, just enter that expression in to the online calculator of your choice, and it should give out the value of approx. 3.51325.
In general, if you want to solve for the distance between two points [tex](y_{1},x_{1}) [/tex] and [tex] (y_{2},x_{2}) [/tex], the formula is:
[tex]d= \sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2} [/tex]
Related Questions
3/9X18=? 7X3/4=? PLEASE HELP ME!!!!!!!!!!!!!!!!!!!!!!!!1
Answers
3/9 is 0.3333333333 0.333333333× 18 is 6
second one is 5.25
7×3 is 21 21 /4 is 5.25
Hope this helps,
♥Nikki♥
vicki drives to and from the gym 2 days a week. The distance from her home to the gym is 13 miles. Over the course of 2 days, her car uses 1/8 of a tank of gas. Complete each sentence. Vicki drives a total of blank mi a week. To find the total number of miles that Vicki can drive with 1 tank of gas, she can blank by 18 .
Answers
Vicki drives a total of 52 miles a week. To find the total number of miles vicki can drive with one tank of gas, she can divide by 18.
Hope This Helps You!
Good Luck :)
- Hannah ❤
One weekend, Nate compared his history homework to his younger sister Caroline’s social studies homework. He found that for every 2 1−3 pages he had to read for homework, Caroline had to read one page for homework. How many pages did Nate read for every three pages Caroline read?
Answers
Hope this helped! :)
he read 2 1/3 pages to her one
so 2 1/3 * 3 =
7/3 * 3 = 21/3 = 7 pages
How do you solve 2x cubed + 3x squared -2x -3 = 0
Answers
A package of dried fruit weighs 1/2 of a pound if one serving size is 1/8 of a pound how many servings would be in the package
Answers
If Sawyer makes $15 an hour, which equation represents his earnings? Question 1 options: W = 15h W = 15/h W = h/15 W = 15 + h
Answers
the graph shows the height of 10 sunflower grown in pjs garden
Answers
Answer:
B. [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
We have been given a graph that shows the height of the 10 sunflowers grown in PJ's garden. We are asked to find the probability that the 11th flower will be at least 60 inches.
[tex]\text{Probability}=\frac{\text{Total number of favorable outcomes}}{\text{total number of possible outcomes}}[/tex]
From the given experiment we can see that there are 5 sunflowers with height more than or equal to 60 inches, so total number of favorable outcomes is 5.
Since there are total 10 sunflowers, so total number of possible outcomes is 10. Upon substituting our given values in probability formula we will get,
[tex]P(\text{The 11th plant will be at least 60 inches})=\frac{5}{10}[/tex]
[tex]P(\text{The 11th plant will be at least 60 inches})=\frac{1}{2}[/tex]
Therefore, the probability that 11th plant will be at least 60 inches is [tex]\frac{1}{2}[/tex] and option B is the correct choice.
Hhhhhhheeeeeeelllllllppppppp
Answers
hope this helped!!!!
Relationship B has a greater rate than Relationship A. This graph represents Relationship A.
Which equations could represent Relationship B?
Select each correct answer.
y = 3x
y = 1.4x
y = 2.2x
y=12x
Answers
Answer:
Step-by-step explanation:
Answer:
y=2.2x
y=3x
Step-by-step explanation:
Took the test and got it correct
Whenever she visits Oakdale, Karin has to drive 55 kilometres due north from home. Whenever she visits Brookfield, she has to drive 48 kilometres due east from home. How far apart are Oakdale and Brookfield, measured in a straight line?
Please show work <3
Answers
of 60 books on a bookself, 24 are nonfiction what percent of the books are not nonfiction?
Answers
40% of the books are nonfiction which means 60% of the books on the bookshelf are not nonfiction.
Jami jogged 1/3 of a mile in 1/6 of an hour. What was her speed in miles per hour?
Answers
there are 6 1/6 per hour
multiply 1/3 by 6
1/3 * 6 = 6/3 = 2 miles per hour
PLS HELP ME ASAP algebra
Answers
which Statement describes what these four powers have in common? 4^0 (-2)^0 (1/3)^0
A. all the powers have a value a value of 0 because the exponent is zero
B. all the powers have the value of 1 because the exponent is zero
Answers
Answer:
Option B is correct
all the powers have the value of 1 because the exponent is zero
Step-by-step explanation:
Using the exponent rule:
[tex]a^0 = 1[/tex] for any real number a.
Given that:
[tex]4^0 = 1[/tex]
[tex](-2)^0 = 1[/tex]
[tex](\frac{1}{3})^0 = 1[/tex]
⇒all the powers have the value of 1 because the exponent is zero
Therefore, the Statement describes what these four powers have in common is, all the powers have the value of 1 because the exponent is zero
Simplify each expression by distributing and combing like terms
-9(m+2)+4(6-7m)
Answers
= -9m - 18 + 24 - 28m
= -37m + 6
Use the figure to complete the sentence.
∠6 and ____ are corresponding angles.
∠2
∠3
∠7
∠8
Answers
Answer:
Its 2
Step-by-step explanation:
i did the test :)
after simpiflying an equation, Juana gets 6=6. explain what this means
Answers
how many 5/16 foot pieces of wood can you cut from a board that is 1 9/16 feet long
Answers
So 5/16 foot pieces from a 1 9/16 feet long piece of wood. OK so this is easy what we do is we do 1 9/16 divided by 5/16 which we switch 1 9/16 to 25/16 divided by 5/16 so we keep 25/16 switch the division symbol to a multiplication symbol and flip the 5/16 so now we have 25/16*16/5 which is 400/80 we can simplify to 5. So a 1 9/16 foot long board can make 5 5/16 pieces of wood.
Hope this helps!
Answer:So 5/16 foot pieces from a 1 9/16 feet long piece of wood. OK so this is easy what we do is we do 1 9/16 divided by 5/16 which we switch 1 9/16 to 25/16 divided by 5/16 so we keep 25/16 switch the division symbol to a multiplication symbol and flip the 5/16 so now we have 25/16*16/5 which is 400/80 we can simplify to 5. So a 1 9/16 foot long board can make 5 5/16 pieces of wood.
Step-by-step explanation:
The formula I = PRT where I = Interest, P = principal, R = rate, and T = time is used to calculate the amount of simple interest earned. Solve this formula for T.
T = I + PR
T = I – PR
T = I divided by the quantity P times R
T = IPR
Answers
I=PRT
(Interest= Principle*Rate*Time)
So, simply divide both sides by PR
T=I/PR
Your answer is C: T = I divided by the quantity P times R
(This should have been represented as: T= I/PR)
~Hope this helps m8
Answer:
C
Step-by-step explanation:
a concrete patio is 5 2/3 feet wide. it has an area of 36 5/6 square feet. Is the concrete slab long enough to fit a 7 foot picnic table without placing the table along the diagonal of the patio? Explain
Answers
Answer:
No
Step-by-step explanation:
W are given that a concrete patio is [tex]5\frac{2}{3}[/tex] feet wide
and area of of concrete patio is [tex]36\frac{5}{6}[/tex]
We have to find out the length of concrete slab is 7 foot or not.
We know that area of rectangle =[tex]l\timesb[/tex]
Let length of concrete patio =x foot
Breadth of concrete patio =[tex]\frac{17}{3}[/tex] feet
Area of concrete patio =[tex]\frac{221}{6}[/tex]
Using formula
[tex]\frac{221}{6}=\frac{17}{3}\times x[/tex]
[tex]\frac{221}{6}\times \frac{3}{17}=x[/tex]
[tex]x=\frac{13}{2}[/tex] foot=6.5 foot
Hence, length of concrete slab is 6.5 foot not 7 foot.Therefore, 7 foot picnic table will no fit.
The concrete slab is not long enough to fit the picnic table.
The concrete patio is in the shape of a rectangle. A rectangle is an object that has four sides. The diagonal is the length from angle of the rectangle to the other angle of the rectangle.
The area of a rectangle = length x width
length = area / width
[tex]36\frac{5}{6}[/tex] ÷ [tex]5\frac{2}{3}[/tex]
Convert to improper fractions
[tex]\frac{221}{6}[/tex] ÷[tex]\frac{17}{3}[/tex]
[tex]\frac{221}{6}[/tex] x [tex]\frac{3}{17}[/tex] = [tex]\frac{13}{2}[/tex]
length = 6.50 feet
The length of the patio is less than the length of the picnic table.
A similar question was answered here: https://brainly.com/question/6636974?referrer=searchResults
Team Tool Bella canoed 15 3/4 miles in 5 1/4 hours. What was their average speed in miles per hour
Answers
we know that
To find the average speed divide the total distance by the time
In this problem we have
[tex]total\ distance=15\frac{3}{4}\ miles[/tex]
[tex]time=5\frac{1}{4}\ hours[/tex]
Convert mixed numbers to an improper fractions
[tex]total\ distance=15\frac{3}{4}\ miles=\frac{15*4+3}{4} =\frac{63}{4}\ miles[/tex]
[tex]time=5\frac{1}{4}\ hours=\frac{5*4+1}{4} =\frac{21}{4}\ hours[/tex]
Divide the total distance by the time
[tex]\frac{(63/4)}{(21/4)} =\frac{63}{21} =3\frac{miles}{hours}[/tex]
therefore
the answer is
the average speed is [tex]3\frac{miles}{hours}[/tex]
All of the following expressions are equivalent except _____.
2 - x
x - 2
-2 + x
x + (-2)
Answers
2 - 4 = -2
4 - 2 = 2
-2 + 4 = 2
4 + (-2) = 2
Hello! Your answer would be A. 2 - x.
God bless! :)
Hey principal evenly distribute six copies of paper to eat fifth grade teachers. How many copies of paper does the fifth graders teachers receive.
Answers
6/8= 0.75
each teacher would get 0.75 (3/4) of a ream of paper
What is the cost of the bill if a drink costs $3, a meal costs $20
Answers
The triangle below has a total perimeter of 450 cm:
picture of a triangle with sides 128 and 150. Third side unknown
Write an equation and solve it to find the length of the longest side of the triangle.
Answers
So the longest side is 172 cm
HELP ASSAPP WITH THIS QUESTION
Answers
the number of students enrolled at a college is 15,000 and grows 4% each year
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The words regarding growth factor for the given blanks are a) 15000, b) 0.04, 1.04, c) 15000 × 1.04 and d) y = 15000(1.04)ˣ
What is growth factor?The growth factor refers to a specific part of an exponential function. This is the base of an exponential function.
Given is a black statement, we need to find the words to be filled in them,
a) The number of students enrolled at a college is 15,000 and grows 4% each year,
Since, the number of students at time of enrollment is 15000, therefore, the initial amount = 15000
b) The percent rate of change is 4%, so the growth factor b is 1 + ______ = ______
Here, the percent rate of change is for growth, therefore,
the growth factor = 1 + 0.04 = 1.04
c) To find the number of students enrolled after one year, you calculate
15,000....
To find the number of students after one year = 15000 × 1.04
d) Complete the equation y = ?
The equation for the same will be =
y = 15000(1.04)ˣ
Hence, the words regarding growth factor for the blanks are a) 15000, b) 0.04, 1.04, c) 15000 × 1.04 and d) y = 15000(1.04)ˣ
Learn more about growth factor, click;
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What is the length of AC¯¯¯¯¯ ?
Enter your answer in the box.
Answers
so
AB = BC
x + 4 = 3x - 8
3x - x = 4 + 8
2x = 12
x = 6
AC = x = 6
The length of [tex]AC[/tex] is [tex]6[/tex].
Given:
In triangle [tex]ABC, \angle A\cong \angle C,AB=x+4,BC=3x-8,AC=x[/tex].
To find:
The length of [tex]AC[/tex].
Explanation:
In the given triangle, two angles are congruent and we know that the base angles of an isosceles triangle are congruent. It means the triangle [tex]ABC[/tex] is an isosceles triangle with [tex]AB=BC[/tex].
[tex]x+4=3x-8[/tex]
[tex]x-3x=-4-8[/tex]
[tex]-2x=-12[/tex]
Divide both sides by [tex]-2[/tex].
[tex]x=6[/tex]
Now,
[tex]AC=x[/tex]
[tex]AC=6[/tex]
Therefore, the length of [tex]AC[/tex] is [tex]6[/tex].
Learn more:
https://brainly.com/question/24262350
For f(x) = 5x +1 , find f(-4)
Answers
This means 5(-4)+1
Which is equal to -19
= -20+1
= -19
option A is correct
find the next three terms in this sequence 1,4,9,16,25
Answers
3 5 7 9 ...
The next 3 terms are 36, 49, and 64.
Hope this helps!
1,4,9,16,25,36,49,64,81,100...