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
Help please!!!!!!!!!!!
Answer:
ok give me a min
Step-by-step explanation:
Simplify (7ty)(3t)
(answer fast please)
Answer:
I think they are correct
If spring A has a spring constant which is 8 times spring B's spring constant, what is the ratio of their periods? Which is the stiffer spring?
If spring A has a spring constant which is 8 times spring B's spring constant then the ratio of their periods is = 9K and \(\frac{9K}{8}\)
Spring stiffness is a characteristic that describes the relationship between load and deflection. If k is stiffness, P is load, and x is deflection, P = kx. The smaller the deflection at a constant load, the stiffer the spring, k.
Given that,
If spring A has a spring constant which is 8 times spring B's spring constant,
Let us assume,
A spring is cut into two parts of length La and Lb
Also given that La : Lb
La : Lb = 1 : 8
The total of spring constant is = 1 + 8 = 9
If the length of spring is L , then La
La = \(\frac{L}{9}\)
And length of B , Lb
Lb = \(\frac{8L}{9}\)
We know, for spring force , spring constant or stiffness of spring is inversely proportional to length of spring .
K ∝ 1 / L
If initial spring constant is k then,
kL= KaLa = KbLb
Then,
Ka = \(\frac{K}{\frac{1}{9} }\)
Ka = 9K
And Kb = \(\frac{K}{\frac{8}{9} }\)
Kb = \(\frac{9K}{8}\)
Hence, stiffness of A is given by, 9K
Stiffness of B is given by \(\frac{9K}{8}\)
Therefore,
If spring A has a spring constant which is 8 times spring B's spring constant then the ratio of their periods is = 9K and \(\frac{9K}{8}\)
To learn more about Stiffer spring ratio problems visit :
brainly.com/question/14944249
#SPJ4
Which statement about 5(1 + 3x) is true?
A. 5(1 + 3x) is a quotient.
B. 5(1 + 3x) has two variables.
C. 5(1 + 3x) has one variable.
D. 5(1 + 3x) is a product of three factors.
well well here it has only one variable that is x
hence option c is correct
Answer:
it is c since it only has one variable
Eduardo buys a sandwich and a drink.
Use mental math to find the amount of
change he gets from $10.00
Answer:
Eduardo will get $4.03
Step-by-step explanation:
To solve this problem, first add 4.99 and 0.98 together, remember to line up the decimals
4.99
+ 0.98
-------------
5.97
Now take 5.97 from 10.00
first you can't take 7 from 0 so you take 1 from the tens place making 10.00 into 9.9 10, now you can take 7 from 10 which equals 3. Into the tenths place you can take 9 from 9 which is a 0. Lastly 9 - 5 is 4, adding the decimal back you get
10.00
- 05.97
--------------
$ 4.03
plz help i need helpplz help i need helpplz help i need helpplz help i need helpplz help i need helpplz help i need helpplz help i need helpplz help i need helpplz help i need help
Answer:
the answer should be 9
Step-by-step explanation:
\((256 * 3^{-5} * 6^{0} )^{-2} * (\frac{3^{-2}}{2^{3}} )^{4} * 2^{28}\)
\((256*\frac{1}{3^{5}} *6^{0})^{-2}*(\frac{3^{-2}}{2^{3}})^{4}*2^{28}\)
\((256*\frac{1}{243} *6^{0})^{-2}*(\frac{3^{-2}}{2^{3}})^{4}*2^{28}\)
\((\frac{256}{243} *6^{0})^{-2}*(\frac{3^{-2}}{2^{3}})^{4}*2^{28}\)
\((\frac{256}{243})^{-2}*(\frac{3^{-2}}{2^{3}})^{4}*2^{28}\)
\((\frac{243}{256})^{2}*(\frac{3^{-2}}{2^{3}})^{4}*2^{28}\)
\(\frac{59049}{65536}*(\frac{1}{2^{3}*3^{2}})^{4}*2^{28}\)
\(\frac{59049}{65536}*(\frac{1}{8*9})^{4}*2^{28}\)
\(\frac{59049}{65536}*(\frac{1}{72})^{4}*2^{28}\)
\(\frac{59049}{65536}*\frac{1}{26873856}*2^{28}\)
\(\frac{9}{65536}*\frac{1}{4096}*2^{28}\)
\(\frac{9}{65536*4096}*2^{28}\)
\(\frac{9}{268435456}*268435456\)
\(9\)
Answer:
the answer should be 9
Step-by-step explanation:
please mark me brainliest thanks so much i really appreciate it!
hope you have an amazing rest of your day and thanks for your time!
Is 4y+9+3 and 3y+9+4y equivalent
B.6 Based on Activity B, define phrase, clause and sentence.
Phrase:
Clause:
Sentence:
Answer:
Phrase:they are small groups standing together as a conceptual unit
Clause:it is a unit of grammatical organization next below the sentence in rank
Sentence: it is a set of words that is complete in itself
I may be asking a lot but these questions are due for tomorrow’s so please bare with me:)
Answer:
He jogged 4/15 of a mile farther.
Step-by-step explanation:
To find the difference between Monday and Tuesday, you have to subtract \(\frac{3}{5} - \frac{2}{6}\).
You can simplify this equation and make it \(\frac{3}{5} - \frac{1}{3}\).
Then you have to turn them into equivalent fractions with the same denominator. They can share a common denominator of 15, so the equation becomes \(\frac{9}{15} -\frac{5}{15}\).
Then you subtract and get \(\frac{4}{15}\).
Hope this helps!
The volume of a right cylinder is 277 cubic centimeters, and the
height is 3 centimeters (cm). What is the radius of the cylinder?
Answer:
3cm
use the formula for the volume of a cylinder
and substitute
Please help me with number 2?
Answer:
y= 2× +4
Step-by-step explanation:
Slope intercept form y = mx +b
4x -2y = -8
-2y = -4x-8
y = 2x +4
slope = 2x
y intercept = 4
1.
(03.03 MC)
A biologist is studying the growth of a particular species of algae. She writes the following equation to show the radius of the algae, f(d), in mm, after d days:
f(d) = 11(1.01)d
Part A: When the biologist concluded her study, the radius of the algae was approximately 11.79 mm. What is a reasonable domain to plot the growth function? (4 points)
Part B: What does the y-intercept of the graph of the function f(d) represent? (2 points)
Part C: What is the average rate of change of the function f(d) from d = 2 to d = 7, and what does it represent? (4 points)
Answer:
sept one
Step-by-step explanation:
20 characters just for you brainly
Answer:
first and last option
Step-by-step explanation:
the first and the last are increasing from left to right since the slope is positive.
Use the distributive property and combine like terms: 8(p + 4) - 6p
Answer:
2p+32
Step-by-step explanation:
8(p+4)-6p
8(p)+8(4)-6p
8p+32-6p
8p-6p+32
2p+32
Hopes this helps please mark brainliest
In a system of equations, WHAT
lines would have the same slope and thus there would be no solution for the system.
Answer:
Parallel Lines: If the two linear equations have the same slope (and different y-intercepts), the lines will be parallel. Since parallel lines never intersect, a system composed of two parallel lines will have NO solution (no intersection of the lines.)
Step-by-step explanation:
Hank made payments of $219 per month at the end of each month for 30 years to purchase a piece of property. He promptly sold it for $195,258. What interest rate, compounded monthly, would he need to earn on an ordinary annuity for a comparable rate of return?
To achieve a comparable rate of return, Hank would need to earn an interest rate of approximately 0.86% per month, compounded monthly on his ordinary annuity.
To find the interest rate, compounded monthly, that Hank would need to earn on an ordinary annuity for a comparable rate of return, we can use the present value formula for an ordinary annuity.
First, let's calculate the present value of Hank's payments. He made payments of $219 per month for 30 years, so the total payments amount to $219 * 12 * 30 = $78840.
Now, we need to find the interest rate that would make this present value equal to the selling price of the property, which is $195,258.
Using the formula for the present value of an ordinary annuity, we have:
PV = P * (1 - (1+r)\(^{(-n)})\)/r,
where PV is the present value, P is the payment per period, r is the interest rate per period, and n is the number of periods.
Plugging in the values we have, we get:
$78840 = $219 * (1 - (1+r)\({(-360)}\))/r.
Solving this equation for r, we find that Hank would need to earn an interest rate of approximately 0.86% per month, compounded monthly, in order to have a comparable rate of return.
For more questions on interest rates
https://brainly.com/question/31261623
#SPJ8
pls help asap i will give brainliest!!!
Answer:
K=-13/5
Step-by-step explanation:
Ok so this equation is exactly like a point-slope formula
Y=Mx+b
Think of that k as m
You have b=4 and b is the y-intercept! So that means the coordinates are (0,4)
Now you use slope formula to figure out the slope:
Using (0,4) and (5,-9)
-9-4/5-0 = -13/5
K=-13/5
WILL GIVE BRAINLIEST + MAX POINTS!!!
Sara is working on a Geometry problem in her Algebra class. The problem requires Sara to use the two quadrilaterals below to answer a list of questions. Part A: For what one value of are the perimeters of the quadrilaterals the same? (Hint: The perimeter of a quadrilateral is the sum of its sides.) Part B: For what one value of are the areas of the quadrilaterals the same? (Hint: The area of a quadrilateral is the product of its base and height.) Please help me outtt!
HELLO
I NEEDED HELP WITH THE SAME QUESTION SO I PUT IT UP WITH A PIC SO U CAN ALSO GET AN ANSWER FROM THERE
HERE YA GO <3
https://brainly.com/question/24188218?referrer=searchResults
Answer:
heyy i did this problem a while ago and got kinda stuck on it
A camper leaves her cabin and hikes 6 miles due south. She then turns and hikes 7 miles due east how many miles is the camper from her cabin?
Answer:
9.22 miles
Step-by-step explanation:
Right triangle
6^2 + 7^2 = x^2
36 + 49 = x^2
Sqrt 85 = x
X = 9.22 miles
A firm makes two products X and Y, and has a total production capacity of 9 tones per day, X and Y requiring the same production capacity. The firm has a permanent contract to supply at least 2 tones of X and at least 3 tones of Y per day to another company. Each tone of X requires 20 machine hours of production time and each tone of Y requires 50 machine hours of production time. The daily maximum possible number of machine hour is 360. All the firm’s output can be sold, and the profit made is birr 80 per tone of X and birr 20 per tone of Y. it is required to determine the production schedule for maximum profit.
The production schedule for maximum profit is; X = 3 and Y = 6 with a maximum profit of $960
How to solve Linear Programming problems?We are told that two products X and Y, has a total production capacity of 9 tones per day, X and Y requiring the same production capacity
The firm has a permanent contract to supply at least 2 tones of X and at least 3 tones of Y per day to another company.
Let product A be x and product B be y. Therefore we have the following inequalities and constraints as;
x + y ≤ 9
x ≥ 2
y ≥ 3
Now, we are told that each tonne of A requires 20 machine hours of production time and each tonne of B requires 50 machine hours of production time. The daily maximum possible number of machine hours is 360. Thus, we have;
20x + 50y ≤ 360
Wea re told that all the firm's output can be sold and the profit made is $80 per tonne of A and $120 per tonne of B. Thus, we have the inequality as;
Z = 80x + 120y maximize
The solution from the graph attached is;
x = 3, y = 6
Thus, the maximum profit is;
Z = 80(3) + 120(6)
Z = 960
Read more about Linear Programming at; https://brainly.com/question/14309521
#SPJ1
Two math students were asked to write an exeponential growth equations that had a starting value of 300 and a growth rate of 2%. Pierre thinks the answer is y=300(1.02)^x and Scott thinks that the answer is y=300(1.2)^x. Are either of them right and why?
Answer:
Pierre is right.
Step-by-step explanation:
A growth rate of 2% means that the values is increasing by 0.02 each year so the multiplying factor is 1.02.
Pierre is correct y = 300(1.02)^x.
Scotts answer 1.2 = a growth rate of 20%.
Find F-1(x), the inverse of F(x), for 3 and 4
Solving for number 3:
Step 1. Define the function.
The original function we have is:
\(F(x)=x-10\)Step 2. To find the inverse function, the first thing we need to do is to change F(x) for y:
\(y=x-10\)Step 3. Now, we are going to interchange the letters x and y (swap x and y):
\(x=y-10\)Step 4. Finally, the last step is to solve for y:
\(y=x+10\)change y for F-1(x), and the inverse function is:
\(F^{-1}(x)=x+10^{}\)Answer:
\(F^{-1}(x)=x+10\)Answer:
Solving for number 3:
Step 1. Define the function.
The original function we have is:
Step 2. To find the inverse function, the first thing we need to do is to change F(x) for y:
Step 3. Now, we are going to interchange the letters x and y (swap x and y):
Step 4. Finally, the last step is to solve for y:
Change y for F-1(x), and the inverse function is:
Answer:
Step-by-step explanation:
A portfolio manager generates a 5% return in Year 1, a 12% return in Year 2, a negative 6% return in Year 3, and a return of 2% (nonannualized) in the first quarter in Year 4. The annualized return for the entire period is the closest to __________.
The annualized return for the entire period is the closest to 10.5%.
To calculate the annualized return for the entire period, we need to consider the returns for each year and the return in the first quarter of Year 4. Since the returns are given for each period, we can use the geometric mean to calculate the annualized return.
The formula for calculating the geometric mean return is:
Geometric Mean Return = [(1 + R1) * (1 + R2) * (1 + R3) * (1 + R4)]^(1/n) - 1
Where R1, R2, R3, and R4 are the returns for each respective period, and n is the number of periods.
Given the returns:
Year 1 return: 5% or 0.05
Year 2 return: 12% or 0.12
Year 3 return: -6% or -0.06
First quarter of Year 4 return: 2% or 0.02
Using the formula, we can calculate the annualized return:
Annualized Return = [(1 + 0.05) * (1 + 0.12) * (1 - 0.06) * (1 + 0.02)]^(1/3) - 1
Annualized Return = (1.05 * 1.12 * 0.94 * 1.02)^(1/3) - 1
Annualized Return = 1.121485^(1/3) - 1
Annualized Return ≈ 0.105 or 10.5%
Therefore, the annualized return for the entire period is approximately 10.5%.
For more question on return visit:
https://brainly.com/question/30761579
#SPJ8
Is (1, 2) a solution to the equation y = 8x?
Answer:
no it is not
Step-by-step explanation:
8 × 1 does not equal 2
What is the greatest common divisor of 1665, 4554, 1683, and 4050?
Answer:
9
Step-by-step explanation:
I checked it, you can too
Find RS.
R
S
22
X
Q
T
26
I don’t know how to do this one.
Answer:
RS is about 18.615
Step-by-step explanation:
since XY is the midsegment, it is parallel to the other 2 lines. That also makes the lines proportional
\(\frac{22}{26} =\frac{x}{22}\)
cross multiple
484=26x
x= 18.615
Were the Cubans happy being a Spanish colony? What happened that allowed for the Cubans to gain more freedom? (social studies)
The mean, median, and mode are all measures of central tendency. The mean is usually the preferred measure of central tendency, but there are specific situations in which it is Aa Aa impossible to compute a mean or in which the mean is not particularly representative of the distribution
Which of the following statements about the mean are true? Check all that apply. □
It is commonly referred to as the arithmetic average
It is algebraically defined (that is, there is an equation you can use to calculate its value)
It is easily influenced by extreme scores.
It can be used for data that are measured on a nominal scale.
Which of the following statements about the median are true? Check all that apply.
It is appropriate for ordinal data.
It is algebraically defined (that is, there is an equation you can use to calculate its value).
There can be more than one.
It can be found when there are undetermined scores.
Which of the following statements about the mode are true? Check all that apply.
It is also referred to as the arithmetic average.
It corresponds to an actual score in the data.
It is the score at the 50th percentile.
There can be more than one.
The statements that are true are:
Regarding the mean: It is commonly referred to as the arithmetic average, it is algebraically defined, and it is easily influenced by extreme scores.
Regarding the median: It is appropriate for ordinal data, it is algebraically defined, and there can be more than one.
Regarding the mode: It corresponds to an actual score in the data, and there can be more than one.
Regarding the mean:
It is commonly referred to as the arithmetic average.
It is algebraically defined, and there is an equation (sum of values divided by the number of values) to calculate its value.
It is easily influenced by extreme scores, as it takes into account the value of each data point.
It cannot be used for data that are measured on a nominal scale since the values in a nominal scale have no quantitative relationship.
Regarding the median:
It is appropriate for ordinal data, which have a ranking or order.
It is algebraically defined as the middle value when the data is arranged in order.
There can be more than one median if the data set has an even number of values.
It can be found when there are undetermined scores, as it only requires the order of the data.
Regarding the mode:
It is not referred to as the arithmetic average, as the mode represents the most frequently occurring value(s) in the data.
It corresponds to an actual score in the data.
It is not necessarily the score at the 50th percentile; it is the most frequent value(s).
There can be more than one mode if multiple values occur with the same highest frequency.
In summary, the statements that are true are:
Regarding the mean: It is commonly referred to as the arithmetic average, it is algebraically defined, and it is easily influenced by extreme scores.
Regarding the median: It is appropriate for ordinal data, it is algebraically defined, and there can be more than one.
Regarding the mode: It corresponds to an actual score in the data, and there can be more than one.
For more such questions on mean
https://brainly.com/question/20118982
#SPJ8
solve for y 3x-7y=21
A. y=-3/7x+21
B. y=3/7x-21
C. y=3/7x-3
D. y=-3/7x+3
Answer:
Y = 3/7x-3
Step-by-step explanation:
I don't have an explanation other than the fact I put this into a calculator and this is what it gave me.
Given: 1; -5; -13 ; -23 ; ...
Derive a formula for the nth term in the pattern.
Answer:
f(n) = -n^2 -3n +5
Step-by-step explanation:
Suppose the formula is ...
f(n) = an^2 +bn +c
Then we have ...
f(1) = 1 = a(1^2) +b(1) +c
f(2) = -5 = a(2^2) +b(2) +c
f(3) = -13 = a(3^2) +b(3) +c
__
Here's a way to solve these equations.
Subtract the first equation from the second:
-6 = 3a +b . . . . . 4th equation
Subtract the second equation from the third:
-8 = 5a +b . . . . . 5th equation
Subtract the fourth equation from the fifth:
-2 = 2a
a = -1
Then substituting into the 4th equation to find b, we have ...
-6 = 3(-1) +b
-3 = b
and ...
1 = -1 +(-3) +c . . . . . substituting "a" and "b" into the first equation
5 = c
The formula is ...
f(n) = -n^2 -3n +5