Answer:
Step-by-step explanation:
[tex]Z_1=3+i\\Z_2=6\\Z_3=4+4i\\\\||Z_2\ Z_1||^2=||-3+i||^2=9+1=10\\\\||Z_1\ Z_3||^2=||1+3i||^2=10\\\\||Z_2\ Z_3||^2=||-2+4i||^2=20\\\\And\ 10+10=20[/tex]
Using the converse of the Pythagorean's theorem, the triangle is right.
Using Pythagorean theorem, the points 3 + i, 6, and 4 + 4i indeed form the vertices of a right triangle.
The Pythagorean theorem states that in a right triangle, the sum of the squares of the lengths of the two shorter sides (legs) is equal to the square of the length of the longest side (hypotenuse).
Let's calculate the distances between the points and then check if the Pythagorean theorem holds for them.
Distance between points A (3 + i) and B (6):
Distance AB = |6 - (3 + i)|
= |6 - 3 - i|
= |3 - i|
= [tex]\sqrt{(3^2 + (-1)^2)[/tex]
= √10
Distance between points A (3 + i) and C (4 + 4i):
Distance AC = |4 + 4i - (3 + i)|
= |1 + 3i|
= [tex]\sqrt{(1^2 + 3^2)[/tex]
= √10
Distance between points B (6) and C (4 + 4i):
Distance BC = |4 + 4i - 6|
= |-2 + 4i|
= [tex]\sqrt{((-2)^2 + 4^2)[/tex]
= √20
Now let's check if the Pythagorean theorem holds for these distances:
Longest side: [tex]BC^2 = (\sqrt20)^2 = 20[/tex]
Sum of squares of shorter sides:
[tex]AB^2 + AC^2 = (\sqrt10)^2 + (\sqrt10)^2[/tex] = 10 + 10 = 20
Since the sum of the squares of the shorter sides is equal to the square of the longest side.
So, the points 3 + i, 6, and 4 + 4i are vertices of a right triangle.
Learn more about Pythagorean theorem here:
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In which situation would it make the most sense to use a sample? 1)to find the number of members Of the lions club that are over 50 years old. 2) to find the percent of all voters that are over 50 years old.
3) to find the median age of members of a bowling league. 4) To find the mean age of 25 people in a yoga class.
Answer:
999
Step-by-step explanation:
hhhh7
Will mark brainless for first response!!!
Instructions
Consider the polynomials numbered 1 through 4, and the binomials A through F. For each
polynomial, find a binomial that can be used as a denominator to create an expression
without a remainder, and find a binomial that can be used as a denominator to create an
expression with a remainder. Feel free to use the same binomials multiple times. Show your
work.
1. 2x2 – 13x - 7
2. 3x2 - x - 10
3. 3x3 + 8x2 – 31x - 60
4. 6x3 + 37x2 + 57x + 20
A.X-2
B. X-3
C. x - 7
D. x + 4
E. 2x + 1
F. 3x + 5
if image of a point (4,6) under enlargement with centre (0,0) and scale factor 'k' is (2,3) find value of k
Answer:
k = 2
Step-by-step explanation:
2 x 2 = 4
3 x 2 = 6
so (2,3) multiplied by 2 will be (4,6)
1. Can the numbers 12, 6, 6 be used to form the sides of a triangle? Why or why not?
Answer: No, a triangle is not possible in this case
Why not? Because the two sides 6 and 6 add to 6+6 = 12, which does not exceed the remaining side.
Refer to the triangle inequality theorem. This theorem says that for a triangle to be possible, we need these three facts to be true
a+b > cb+c > aa+c > bwhere a,b,c are the three sides of the triangle. In short: adding any two sides must be larger than the third side.
I recommend cutting out slips of paper to try making a triangle with sides 12,6, and 6. You'll find its not possible. The two smaller sides combine to perfectly line up with the larger side. The three sides form a line and not a triangle.
Calculate 20% of 3 3/4 years in months.
Answer:
It is 9 months
Step-by-step explanation:
[tex] = 20\% \times 3 \frac{3}{4} \\ \\ = \frac{20}{100} \times \frac{15}{4} \\ \\ = \frac{300}{400} \\ \\ = \frac{3}{4} \: \: { \sf{years}}[/tex]
convert them to months by multiplying by 12:
[tex]{ \sf{ = \frac{3}{4} \times 12}} \\ \\ = { \sf{9 \: months}}[/tex]
The length of a rectangle is 22 meters. This is 8 more than twice of the width. Find the width of the rectangle
Answer:
w = 7
Step-by-step explanation:
L = 22
L = 2*w + 8
Since the Ls are the same thing, you can equate them
2w + 8 = 22 Subtract 8 from both sides
2w = 22 - 8 Combine
2w = 14 divide by 2
w = 14/2
w = 7
What is the fraction or mixed number and write in its simplest form.
3.8416
3.8416=—- (type an integer,proper fraction, or mixed number.)
Answer:
38416/10000
plss mark me brainliestt
Step-by-step explanation:
3.8416=38416/10000
La chispa de un relámpago artificial de 10.0 MV libera una energia de 0.125 MW .s ¿Cuántos coulombs de
carga fluyen?
Answer:
nzbzbzZnzbznzbzbzhzhsbsjs
simplify. (3st)^2
a.6s^2t*2
b. 9s^2t^2
c. 3st^2
d. 2s^2t^2
Answer:
b. 9s^2 t^2
Step-by-step explanation:
If (x*y) ^ 2 = multiple of x and y then power 2
(x * y) ^2 is equal to (x^2 * y^2)
That makes 9s^2t^2
Answer:
Option B. 9s^2t^2 is the correct answer.
Step-by-step explanation:
I just completed it.
On solving equation 3*1/5b+5=50, the value of b will be?
Answer:
Step-by-step explanation:
14 1⁄16
State the transformations of the following function in order: = − 3|6 − 2| + 1
Answer:
6
Step-by-step explanation:
-3 | 6 - 2| + 1
-3 + 6 + 2 + 1
-3 + 9 = 6
27 devided by 1234 chunking method
Answer:
45
Step-by-step explanation:
Do you guys know this because I was trying to submit but it don’t let me I put 7/6 but it say I need different Way
Answer:
is 5
Step-by-step explanation:
Hope it is helful...Answer:
5
Step-by-step explanation:
So first when dividing fractions you need to invert and multiply. Thus the fraction becomes:
1/4 * 20/1.
When simplified it becomes 20/4 which is 5.
HOPE THIS HELPED
Please help due tomorrow
The scaled factor is 3 for all of them.
F(x) =∛2x g(x)=3x+1 Find (f/g) (x) Include any restrictions on the domain
Answer:
x ≠ -1/3
Step-by-step explanation:
(f/g)(x) = f(x)/g(x) = ∛2x/(3x+1)
since division by zero is undefined,
Answer:
Step-by-step explanation:
x = - 1/2
Need answers in 2 minutes ASAP
Step-by-step explanation:
f(10)=10
f(-2)=-2
f(a)=a
f(a+b)=a+b
g(10)=5×10-12=3
g(-2)=5×(-2)-12=-10-12=-22
g(a)=5×a-12=5a-12
g(a+b)=5×(a+b)-12=5a+5b-12
h(10)=(10)^2 +4(10)-7=100+40-7=133
h(-2)=(-2)^2 +4(-2)-7=4-8-7=-11
h(a)=a^2 +4a -7
h(a+b)=(a+b)^2 +4a+4b-7=a^2+2ab+b^2+4b-7
Given that f(x) = 2x³-7x²+7ax+ 16 is divisible by x-a, find
(i) the value of the constant a
(ii) the remainder when f(x) is divided by 2x+1.
Answer:
a = - 2, remainder = 21
Step-by-step explanation:
The Remainder theorem states that if f(x) is divided by (x - a) the remainder is f(a)
Since f(x) is divisible by (x - a) then remainder is zero , then
f(a) = 2a³ - 7a² + 7a² + 16 = 0 , that is
2a³ + 16 = 0 ( subtract 16 from both sides )
2a³ = - 16 ( divide both sides by 2 )
a³ = - 8 ( take the cube root of both sides )
a = [tex]\sqrt[3]{-8}[/tex] = - 2
Then
f(x) = 2x³ - 7x² - 14x + 16
Evaluate f(- [tex]\frac{1}{2}[/tex] ) for remainder on division by (2x + 1)
f(- [tex]\frac{1}{2}[/tex] ) = 2(- [tex]\frac{1}{2}[/tex] )³ - 7(- [tex]\frac{1}{2}[/tex] )² - 14(- [tex]\frac{1}{2}[/tex] ) + 16
= 2(- [tex]\frac{1}{8}[/tex] ) - 7([tex]\frac{1}{4}[/tex] ) + 7 + 16
= - [tex]\frac{1}{4}[/tex] - [tex]\frac{7}{4}[/tex] + 23
= - [tex]\frac{8}{4}[/tex] + 23
= - 2 + 23
= 21
Perform the operation and reduce the answer fully. Make sure to express your answer as a simplified fraction. 4/3 divided 7/4
Answer:
so we have 4/3 divided by 7/4
= 4/3 * 4/7
= 4*4/3*7
= 16/21
Step-by-step explanation:
answer from gauth math
Which statement describes the graph?
Answer:
the graph crosses the y-axis at -5 and x-axis at -6
Determine the sum by suitable re arrangement .
a) 6254 + 1297 + 446 + 103 Ans:
b) 1983 + 647 + 217 + 353 2.
Answer:
a.8100
b.3200
Step-by-step explanation:
hope you're okay
derivative : y=[(1+x^2)arctgx-x]/2
Answer:
s,-8*2-`±_'682-¥´owhsi
The sum of a rational number and an irrational number is always rational,
A.True
B.False
Answer:
True
Step-by-step explanation:
The sum of any rational number and any irrational number will always be an irrational number
Determine the quotient of 1 and 2 over 3 divided by 4 over 5.
A 1 and 1 over 3
B 1 and 8 over 15
C 2 and 1 over 12
D 2 and 5 over 6
Answer:
D
Step-by-step explanation:
1 2/3÷4/5
=5/3×5/4
=25/12
2 and 1 over 12
which graph represents the following system of inequalities?
a
b
c
d
Answer:
A
Step-by-step explanation:
Mark me brainliest.
A bag contains 3 red balls and 5 green balls. What is the probability of picking a red ball from the bag AND getting heads upon flipping a fair coin
Answer:
the probability would be 3/8
Step-by-step explanation:
Since there are 3 red and 5 green, there is a total of 8 balls in the bag making it a chance of 3/8 to get a red ball. You're Welcome :) <3
Probability of picking a red ball is [tex]\frac{3}{8}[/tex]
Probability of getting head coin is [tex]\frac{1}{2}[/tex]
What is probability?"Probability is the possibility or chance of an event to occur." Ratio of number of favorable outcomes and total number of favorable outcomes is called probability.
We have,
Red balls = 3
Green balls =5
Formula for probability
[tex]\frac{Number of Favorable Outcomes}{Total Number of Favorable Outcomes}[/tex]
Total number of outcomes n(S) = 8
Number of favorable outcomes for getting a red ball n(E) = 3
Probability of picking a red ball
= [tex]\frac{Number of Favorable Outcomes}{Total number of Favorable Outcomes}[/tex]
= [tex]\frac{3}{8}[/tex]
We have a fair coin,
Total number of outcomes n(S) = 2
Number of favorable outcomes for getting head n(E) = 1
Probability of getting head coin
= [tex]\frac{Number of Favorable Outcomes}{Total Number of Favorable Outcomes}[/tex]
= [tex]\frac{1}{2}[/tex]
Hence, Probability of picking a red ball is [tex]\frac{3}{8}[/tex]
Probability of getting head coin is [tex]\frac{1}{2}[/tex].
Learn more about probability here
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Draw an equilateral triangle PQR with sides of length 6 cm.
Answer:
the answer is attached herewith
ps.hv a great day ahead! :)
express 3x-x^2 as m-(x-n)^2. Ill give brainliest to correct answer!
(Also please see the picture since you might mistake x having a square as a 2x)
This is simply done by Method of Completing the Square.
3x - x²
Add and subtract half the coefficient of x and square it.
( This is done so there'd be no alterations to the quadractic Expression)
So To start
We'd like x² to be positive...(So factor out a negative).
–(x² - 3x )
Now In this case
You see there's a Negative Outside the the bracket
Instead of adding and Subtracting squared values of half the coefficient of X... We'd Add Twice and do not subtract.
Reason: If you add outside the bracket and subtract the other inside the bracket... This will be wrong because there's a negative patiently waiting outside the bracket to Interact with the negative you subtracted to make it Positive.
See what I mean.
Let's say you added 2² and subtracted 2² in this problem
2² – ( x² - 3x - 2²)
If you decide to open the bracket
You'll have
2² – x² + 3x + 2²
NOW THIS IS WRONG BECAUSE WE ALTERED THIS EXPRESSION. WHERE'D 2² + 2² COME FROM?
THIS IS WHY YOU'LL ADD THE SQUARED COEFFICIENT OF X TWICE IN CASES LIKE THESE.
SO GOING BACK TO THE ORIGINAL QUESTION.
– (x² - 3x )
Adding the half the coefficient of x twice and squaring them...
Coefficient of x = 3
Half of 3 = 3/2
Squaring it gives (3/2)²
NOW PROCEEDING
(3/2)² – [ x² - 3x + (3/2)²]
If you open this bracket... (3/2)² will cancel out with —(3/2)²
Meaning that we haven't altered the expression in any way
Moving On...
Applying basic factorizing principle
9/4 – ( x - 3/2)².
Answer = 9/4 – ( x - 3/2)² Which is in the Form m – ( x - n )²
Therefore m = 9/4 and n = 3/2.
Hope This Helps
GIVING BRAINLIEST PLS HELP
Solve using substitution.
6x + y = 7
8x + 9y = 17
(_,_)
Please help me I really need it
Select the correct answer.
Based on these segment lengths, which group of segments cannot form a triangle?
OA 12,7,8
OB. 8, 7, 13
OC. 1,2,3
OD. 80,140, 70
Reset
Next
2021 EdimentumAll rights
Answer:
C
Step-by-step explanation:
If you add up the length of two sides, the sum must be greater than the third side of the triangle.
If you add 1 and 2, it equals 3
But that means it will be equal to the length of the third side, 3
It will be impossible to make a triangle with those lengths of sides no matter how the sides or angles are set.
It's sort of difficult to explain this without any visual
You can look up "triangle inequality" to find out more about this