Answers
From the Pythagoras's Theorem, we know that:
(Hypotenuse)² = (base)² + (perpendicular)²
We are Given:
We are given that the 2 legs (Base and Perpendicular) of the triangle are (m²-n² and 2mn)
Solving for the Hypotenuse:
replacing the variables in the Pythagoras's theorem, we get:
Hypotenuse² = (m²-n²)² + (2mn)²
Hypotenuse² = (m⁴ -2m²n² + n⁴) + (4m²n²) [(a-b)² = a² - 2ab - b²]
Hypotenuse² = m⁴ -2m²n² + n⁴ + 4m²n²
Hypotenuse² = m⁴ + 2m²n² + n⁴
Hypotenuse² = (m²)² + 2m²n² + (n²)²
Hypotenuse² = (m² + n²)² [a² + 2ab + b² = (a+b)²]
taking the square root of both the sides
Hypotenuse = m² + n²
Related Questions
Find the midpoint of the segment with the following endpoints.
(-3, 8) and (-8,2)
Answers
Answer:
[tex](\frac{-11}{2},5)[/tex]
General Formulas and Concepts:
Pre-Alg
Order of Operations: BPEMDASAlg I
Midpoint Formula: [tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]Step-by-step explanation:
Step 1: Define
Point (-3, 8)
Point (-8, 2)
Step 2: Solve for midpoint
Substitute: [tex](\frac{-3-8}{2},\frac{8+2}{2})[/tex]Subtract/Add: [tex](\frac{-11}{2},\frac{10}{2})[/tex]Divide: [tex](\frac{-11}{2},5)[/tex]Answer:
The answer is (-5.5, 5)
Enter an Integer to represent the situation.
a $535 profit
Answers
Answer:
67
Step-by-step explanation:
Took a test
12 cookies for 3 students rate and unit rate
Answers
Answer:
3:12 1:4
Step-by-step explanation:
Hope this helps! (^-^)
Answer: 4 cookies per student.
Step-by-step explanation:
his is a fraction equal to
12 cookies ÷ 3 students
We want a unit rate where
1 is in the denominator,
so we divide top and bottom by 3
12 cookies ÷ 3
3 students ÷ 3
=
4 cookies
1 student
=
4 cookies
student
= 4 cookies per student
A pharmacologist measured the concentration of dopamine in the brains of several rats. The mean concentration was 1,269 ng/gm and the standard deviation was 145 ng/gm.4 What was the standard error of the mean if:_______.(a) 8 rats were measured?
(b) 30 rats were measured?
Answers
Answer:
51.265242 ng/gm ; 26.473257 ng/gm
Step-by-step explanation:
The standard error of the mean = standard deviation / √sample size
Given that:
mean concentration = 1,269 ng/gm
Standard deviation (s) = 145 ng/gm
Standard Error if 8 rats were measured :
Sample size (n) = 8
Standard Error = s / √n
Standard Error = 145 / √8
Standard Error = 145 / 2.8284271
Standard Error = 51.265242 ng/gm
If 30 rats were measured :
Standard Error = 145 / √30
Standard Error = 145 / 5.4772255
Standard Error = 26.473257 ng/gm
pls answer this yall
2a-1+8b-12b+7a-12
Answers
solve for the unknown.
4^2x+3=1
what does x equal?
Answers
Answer:
x = -1/8
Step-by-step explanation:
4^2x + 3 = 1 start by simplifying the equation
16x + 3 = 1 now subtract 3 on both sides
16x = -2 isolate the variable by dividing 16 on both sides
x = -1/8
Answer:
x = -1/8
Step-by-step explanation:
4^2x + 3 = 1
You want to try to get the x on one side by itself.
First step subtract 3 from both sides
4^2x + 3 -3 = 1 -3
so now it looks like 4^2x = -2
We know 4^2 is 4x4 which is 16.
16x= -2
Divide 16 by both sides.
x = -2 / 16
Reduce.
x = -1/8
Given 2x+4y=12 what is the x and y int
Answers
8x + 13x
PLEAsE HLEP ME SLOVE THIS PLEASE SHOW WORK TO? THANK YOU
Answers
Answer & Step-by-step explanation:
Since they are like terms (meaning they are in the same form), you can add:
[tex]8x+13x=21x[/tex]
:Done
What the * stands for ?
Answers
In math it’s used for multiplying.
So 5*5= 25
g The average work week in Los Angeles was 40.1 hours in the first quarter of 2019. It is believed that the pandemic has led to a reduction in the average work week. To test the validity of this belief, the hypotheses are
Answers
Answer:
b. Hо : μ ≥ 40.1; Ha : μ > 40.1
Step-by-step explanation:
Note: The complete options to the question is attached as picture below
The alternative hypothesis is focusing on "the recession has led to a reduction in the average work week".
So, it will be less than the past average. i.e, 40.1.. so, we will use a less than (<) sign to write the alternative hypothesis.
The hypotheses are as below:
Hо : μ ≥ 40.1 (Null hypothesis)
Ha : μ > 40.1 (Alternative hypothesis)
Which recursive formula defines the sequence?
f(1) = 6, f(4) = 12, f(7) = 18
Answers
Step-by-step explanation:
HELP PLEASE NO FOOLISH ANSWERS
QUESTION: When we apply a force to something, it moves! Mass is important for calculating how fast things accelerate (change speed) when we apply a force to them. What determines how fast a car can speed up? You probably know that your car accelerates slower if it has five adults in it than if it only has one. IDEK WHY THIS IS A MATH PROBLEM-
Answers
Answer:
Mass determines how fast a car can accelerate. Since a car accelerates slower with more adults, and faster with less adults, this means that the mass has a big impact on acceleration. Therefore, we can conclude that the mass determines how fast a car can accelerate.
How many ways can you arrange the word HOCKEY using only 5 letters
if each letter can only be used once?
Answers
Answer:
Total arrangement = 720
Step-by-step explanation:
Given:
Total letter n = 6
Using letter r = 5
Computation:
Total arrangement = nPr
Total arrangement = !n / !(n-r)
Total arrangement = !6 / !(6-5)
Total arrangement = 6 x 5 x 4 x 3 x 2
Total arrangement = 720
Factors of 121 what do you think ???
Answers
Step-by-step explanation:
[tex]121 = 11 \times 11[/tex]
1, 11 and 121
if receiver travels 54 yards in 9 seconds whats the average speed
Answers
Answer:
Step-by-step explanation:
The average speed is 6 yards in 1 second!
GO CHEIFS!
Hope it helps
Answer:
6
Step-by-step explanation:
To find the average speed which is also the unit rate you simply need to divide the two numbers.
54 ÷ 9 = 6
So, 6 yards is your average speed.
Make me brainliest
How do you solve 5(N+4)/3 = N-8
Answers
Answer:
n=-22
Step-by-step explanation:
rewrite the equation as 5(n+4) = n-8
3
now distribute the 5 through the parentheses 5n+20 = n-8
3
multiply each side by 3 5n+20=3n - 24
subrtact 3n from both sides 5n+20=3n - 24
-3n -3n
2n+20=-24
then subtract 20 from each side 2n +20=-24
-20 -20
Giving you 2n=-44 then divide both sides by 2
2n=-44 Giving you n=-22
2 2
Lisa takes a night walk after dinner every night. She walks 1/4 mile in 2 minutes. How how does she walk in 10 minutes? (write-in decimal form)
Answers
Answer:
1.25 miles
Step-by-step explanation:
Lisa takes a night walk after dinner every night.
She walks 1/4 mile in 2 minutes.
Distance = 1/4 mile
Time, t = 2 minutes
For covering 1 mile,
1/4 mile = 2 minutes
In 1 minute she will cover [tex]\dfrac{1}{8}\ \text{mile}[/tex]
For 10 minutes, she will cover [tex]\dfrac{10}{8}\ \text{mile}\ or\ 1.25\ \text{miles}[/tex]
So, she will cover 1.25 miles.
In which pair do both decimals represent rational numbers?
O A. 0.296 and 0.9888...
B. 4.462837305718274... and 0.9888
O C. 6.32891237302554... and 0.9888...
D. 6.32891237302554... and 0.296
Answers
Answer:
Step-by-step explanation:
Option A. 0.296 and 0.9888 is correct because rational no are terminating and repeating ..
Please turn the sentence into an expression
3. twelve more than the sum of ten and a
number
Answers
Answer:
Do U-Turn
Step-by-step explanation:
Step-by-step explanation:
12+(10+x)
I hope this helps
A city holds an election for mayor every 2 years and an election for treasurer every 6 years. It held elections for both mayor and treasurer this year. How many years will
it be before the elections for mayor and treasurer both happen in the same year again?
Answers
Answer:
3years
Step-by-step explanation:
Answer:
It will take for about 6 six years for the election for both positions be taken
A laboratory scale is known to have a standard deviation of Ï = 0.001 gram in repeated weighings. Scale readings in repeated weighings are Normally distributed, with mean equal to the true weight of the specimen. A particular specimen is weighed 8 times on this scale. The average weight is x ¯ = 4.1602 grams. A 99% confidence interval for the true weight of the specimen is:_______
Answers
Answer:
the confidence interval for the true weight of the specimen is;
4.1593 ≤ μ ≤ 4.1611
Step-by-step explanation:
We are given;
Standard deviation; σ = 0.001
Sample size; n = 8
Average weight; x¯ = 4.1602
We are given a 99% confidence interval and the z-value at this interval is 2.576
Formula for confidence interval is;
CI = x¯ ± (zσ/√n)
Plugging in the relevant values, we have;
CI = 4.1602 ± (2.576 × 0.001/√8)
CI = 4.1602 ± 0.000911
CI = (4.1602 - 0.000911), (4.1602 + 0.000911)
CI ≈ (4.1593, 4.1611)
Thus, the confidence interval for the true weight will be expressed as;
4.1593 ≤ μ ≤ 4.1611
Where μ represents the true weight
200 people watched a movie. 55% of the people liked the movie. How many
people did not like the movie?
Answers
Answer:
115
Step-by-step explanation:
Answer:
90 people
Step-by-step explanation:
So, all you have to do is put the equation as a proportional rate. First, you should subtract 55% from 100% to get you 45%, since that's the percentage of the people who didn't like it. Now, put that percentage in a fraction, so 45/100. Next to it, put the fraction x/200, since the denominator should be the total amount of people and x for the people who didn't like the movie. To solve this, you must take the numerator from 45/100 with the denominator from x/200 and multiply it, getting you 9000. Now divide this from the denominator in the fraction 45/100, getting you to 45/100 = 90/200. So x=90.
If that was confusing, just think about it like this... 200 is a multiple of 100, right? So, to get your answer you could just multiply 45/100 by 2 on both sides getting you to 90/200 = 90/200.
Hope that helps ;D
Rewrite 4x − 2y = 10 in slope-intercept form. Give the slope and y-intercept.
y =
m =
b =
Answers
2y = 4x - 10
Divide by 2
Y = 2x - 5
m= 2, b= -5
Answer:
y=2x-5
slope is 2 and y intercept is -5
Step-by-step explanation:
this is because you put y by itself and the equation becomes -2y=-4x+10. Multiply by -1 to make these positive and get 2y=4x-10. Divide both sides by 2 and make the equation y=2x-5. Hope this helps
Please Note: IMAGE BELOW IS NOT DRAWN TO SCALE!
Given: Point E is the midpoint of AC and DF
Prove: ADEA AFEC
C
F
А
B
B
Answers
Answer:
more imformation?
Step-by-step explanation:
Set up a proportion and solve. Round answers to the nearest tenth.
What is 20% of 72?
Answers
What is the Magnitude of 6.8
Answers
Santiago Chile (AP)
♥plz give me brain list it would help a lot! ♥
♥ お力になれて、嬉しいです ！♥a number plus the sum of the number
and seven.
Answers
Answer:
x+(x+7)
Step-by-step explanation:
sum=add all together
A carpenter needs to cut two pieces of trim around a window at 34 3/8 inches each. If the saw blade will remove 1/8 of an inch of wood, what is the smallest piece of wood that can be used to produce both pieces?
Answers
Answer:
It is so ez, it is of course 2
Step-by-step explanation:
If ll m, find the value of each missing variable(s) .
Answers
Answer:
1. m=5
2. 2(8x+11)
3.m=7
Step-by-step explanation:
What are the different ways to write multiplication?
Answers
Answer:
Distribution, equal groups, skip counting, repeated addition, and array.
Step-by-step explanation: