what is the pythagorean identity
Answer:
The most common trigonometric identities are those involving the Pythagorean Theorem...
Step-by-step explanation:
The Pythagorean trigonometric identity, also called the fundamental Pythagorean trigonometric identity or simply Pythagorean identity is an identity expressing the Pythagorean theorem in terms of trigonometric functions..
the value of (-1)^500
Answer:
1!!!
Step-by-step explanation:
Sorry late... edge. Use the associative property to create equivalent expressions A + B + (C + D). which statements are true check all that apply. U will get Brainliest.
The associate probably allow us to change grouping terms that are added together.
when changing the grouping, the order of term stays the same only princesses change position.
the expression A + (B + C) + D is an equivalent fraction.
the expression ab(cd) is an equivalent fraction.
the expression (A + B )+ C + D is an equivalent fraction.
the expression A + B (C + D) is an equivalent fraction.
Answer:
is that your shopping list
Step-by-step explanation:
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5. Find the perimeter and area
*Triangle- based prism*
Step-by-step explanation:
for the perimeter you have to say two brackets live plus height plus with plastic
a small college has 500 freshmen, 400 sophomores, 350 juniors, and 300 seniors. administrators wish to conduct a survey of their students, and they find a simple random sample of 50 freshmen, 40 sophomores, 35 juniors, and 30 seniors. the overall sample is:
The overall sample for the survey consists of 50 freshmen, 40 sophomores, 35 juniors, and 30 seniors, totaling 155 students.
To create an overall sample for the survey, the administrators selected a certain number of students from each class level. They randomly sampled 50 freshmen, 40 sophomores, 35 juniors, and 30 seniors. By combining these individual samples from each class, the administrators obtained an overall sample size of 50 + 40 + 35 + 30 = 155 students. This overall sample represents a portion of the student population from each class level and allows for a representation of students from different academic years in the survey.
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answer this attachment pls its upside down btw
The strategies that would eliminate a variable to help solve the system of equations are
B. Multiply the first equation by -2 and add it to the second equation
C. Multiply the first equation by 1/3 and add it to the second equation
D. Multiply the second equation by 3 and add it to the first equation
Determining strategies that would help solve system of equations by eliminationFrom the question we are to determine the strategies that would eliminate a variable to help solve the system of equations.
The given system of equations is
12x + 5y = 7
-4x + 10y = -7
To eliminate y,
Multiply the first equation by -2 and add it to the second equation
-2 × [12x + 5y = 7]
-24x - 10y = -14
Now add to the second equation
-24x - 10y = -14
+ (-4x + 10y = -7
-----------------------------
-28x = -21
To eliminate x
Multiply the first equation by 1/3 and add it to the second equation
1/3 × [12x + 5y = 7
4x + 5/3y = 7/3
Now, add it to the second equation
4x + 5/3y = 7/3
+ (-4x + 10y = -7
------------------------------
5/3y + 10y = 7/3 + (-7)
Also, to eliminate x
Multiply the second equation by 3 and add it to the first equation
3 × [-4x + 10y = -7
-12x + 30y = -21
Now, add to the first equation
-12x + 30y = -21
+ (12x + 5y = 7
----------------------------
35y = -14
Hence, the required strategies are the ones explained above.
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Some one please help
Step-by-step explanation:
a:
g(10) = -3(10)+1
g(10) = -29
b:
g(x) = 16
-3x + 1 = 16
-3x = 15
x = -5
CHECK:
g(-5) = -3(-5) + 1
g(-5) = 15 + 1
g(-5) = 16
Hope that helps
Test Yourself
The divisibility by a prime theorem says that every integer greater than 1 is ________________________________.
The divisibility by a prime theorem states that every integer greater than 1 is either itself a prime number or can be expressed as a product of prime numbers.
In other words, every integer greater than 1 can be factored into a unique product of primes. This is a fundamental result in number theory, and is often used to prove other theorems and results.
The proof of this theorem relies on the fact that any integer greater than 1 can be factored into a product of prime factors. We can then use mathematical induction to show that any integer greater than 1 can be expressed as a product of primes.
The base case is that 2 is a prime number, and the induction step relies on the assumption that any integer less than n can be expressed as a product of primes.
This theorem has many important applications, such as in determining the prime factorization of an integer, finding the greatest common divisor of two integers, and solving Diophantine equations. It is also used in cryptography, where it is essential to factor large numbers into their prime factors in order to break certain encryption algorithms.
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El número de rebanadas de pizza que se comió cada persona en la fiesta de cumpleaños Elian son: 3,4,5,2,1,4,5,3,2,1,0,2,3,4,6. Media: Moda: Mediana:
Respuesta:
Modo = 2, 3, 4
Mediana = 3
Media = 3
Explicación paso a paso:
Dados los datos:
3,4,5,2,1,4,5,3,2,1,0,2,3,4,6
Datos pedidos: 0, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 6
La media = ΣX / n = 45/15 = 3
Donde n = tamaño de la muestra = 15
Mediana = 1/2 * (n + 1) th término
Mediana = 1/2 (16) término
Mediana = octavo término
Mediana = 3
Modo = 2, 3, 4 (el más alto ocurre con una frecuencia de 3 cada uno)
p(x) = 2x2 + 5x - 9
Part A
Evaluate p(1.75).
Answer:
Hi there!
Your answer is:
p(1.75) = 5.875
Step-by-step explanation:
p(1.75) means to plug in 1.75 for x
p(1.75)= 2(1.75)^2 + 5(1.75) - 9
6.125 + 8.75 - 9
SIMPLIFY
5.875
Hope this helps!
Factor the following x^2+3x-108
Answer:3(6+x)(6-x)
Step-by-step explanation:
Used a math app
how would I go about Simplify 2⁵ ÷ 2³
Answer:
2^8
Step-by-step explanation:
A herbalist has 40 oz of herbs costing $4 per ounce. How many ounces of herbs costing $1 per ounce should be mixed with these 40 oz of herbs to produce a mixture costing $2. 20 per ounce?
60 ounces of herbs costing $1 per ounce should be mixed with these 40 oz of herbs to produce a mixture costing $2. 20 per ounce
Let x be the amount of herb that costs $1.00/oz and y be the total amount of the mixture that costs $2.20/oz.
The total weight of the mixture is:
= y=x+40
The total cost of the mixture is:
4(40) + 1x = 2.20y
160 + x = 2.20 (x + 40) .......Substitute y using the expression from the first equation
160 + x = 2.20x + 88 .........Subtract 160 and x from both sides
1.20x = 72 .........Divide both sides by 1.20
x = 60
The herbalist must mix 60 oz of the herb that costs $1.00/oz to the mixture, therefore we can say that:
60 ounces of herbs costing $1 per ounce should be mixed with these 40 oz of herbs to produce a mixture costing $2. 20 per ounce
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Help 6th grade math please help i will give brainliest
Spencer and Lilly are skiing down the same mountain. Spencer is traveling at a speed of 4/5 mile every 1 and 1/3 minutes, and Lilly is traveling at a speed of 3/4 mile every 1 and 1/8 every minute Who is traveling at a faster speed?
A. spencer 36
B lilly 40
C spencer 50
D lilly 64
Lilly is travelling at a faster speed.
What is Speed?Speed is the unit rate in terms of distance travelled by an object and the time taken to travel the distance.
Speed is a scalar quantity as it only has magnitude and no direction.
Given that,
Distance travelled by Spencer = 4/5 mile
Time taken to travel the distance = 1 1/3 minutes = 4/3 minutes
Speed = Distance / Time = (4/5) / (4/3) = 3/5 = 0.60 mile per minute
Distance travelled by Lilly = 3/4 mile
Time taken to travel the distance = 1 1/8 minute = 9/8 minutes
Speed = (3/4) / (9/8) = 2/3 = 0.67 mile per minute
Hence Lilly is travelling at a greater speed of 0.67 mile per minute.
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The length of a rectangular pool is 5 and the width is 5x-2. Which of the following expressions can be used to find the area?'
PLSS HELP NOW PLSSSSSS I WILL GIVE YOU BRAINLEST
Answer:
The answer is c
Step-by-step explanation:
Source: Trust me bro
Prove the theorems below: Let f:(a,b) → R be continuous. Let ce (a,b) and suppose f is differentiable on (a, c) and (c,b). (i) if f'(x) < 0 for x € (a, c) and f'(x) > 0 for xe (c,b), then f has an absolute minimum at c. (ii) if f'(x) > 0 for x € (a, c) and f'(x) < 0 for xe (c, b), then f has an absolute maximum at c.
For function f:(a,b) → R (continuous), and c ∈ (a,b), then
(i) If derivative is negative before c and positive after c, then f has an absolute minimum at c.
(ii) If derivative is positive before c and negative after c, then f has an absolute maximum at c.
Part (i) : If derivative of a function f(x) is negative for values of x between a and c, and positive for values of x between c and b, then the function has an absolute minimum at c.
This means that at point c, function reaches its lowest-value compared to all other points in the interval (a, b). The negative derivative before c indicates a decreasing trend, while the positive derivative after c indicates an increasing trend.
The change from decreasing to increasing at c suggests a minimum point. By the continuity of the function, we can conclude that the minimum value is achieved at c.
Part (ii) : Conversely, if derivative of a function f(x) is positive for values of x between a and c, and negative for values of x between c and b, then the function has an absolute maximum at c.
This means that at point c, the function reaches its highest-value compared to all other points in the interval (a, b). The positive derivative before c indicates an increasing trend, while the negative derivative after c indicates a decreasing trend.
The change from increasing to decreasing at c suggests a maximum point. By the continuity of the function, we can conclude that the maximum value is achieved at c.
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Prove the theorems below: Let f:(a,b) → R be continuous. Let c ∈ (a,b) and suppose f is differentiable on (a, c) and (c, b).
(i) if f'(x) < 0 for x ∈ (a, c) and f'(x) > 0 for x ∈ (c, b), then f has an absolute minimum at c.
(ii) if f'(x) > 0 for x € (a, c) and f'(x) < 0 for x ∈ (c, b), then f has an absolute maximum at c.
Actually 100 points check for yourself (Easiest 100 points) Match each ordered pair on the left with the functions on the right.
Answer:
(-4, 40) y = -9x + 4
(8, 50) y = 6x + 2
(9, -36) y = -3x - 9
(5, 38) y = 8x - 2
Do you want an explanation?
#1
y=-9x+4Put (-4,40)
40=-9(-4)+440=40Verified
#2
y=-3x-9put (9,-36)
-36=-3(9)-9-36=-36Verified
#3
y=8x-2Put (5,38)
38=8(5)-238=38Verified
#4
y=6x+2Put (8,50)
50=6(8)+250=50Hence verifiedl
Write two equivalent ratios to 4:10.
Answer:
2:5
Step-by-step explanation:
divide / simplify the ratio
Answer:
2:5 8:20
Because 2:5 is equivalent to 4:10 and so it 8:20
Take the first 4 digits of your student number as the first number and the last 3 digits as the second number. Write the matlab code to find the greatest common divisor of these numbers using the Euclidean algorithm.
The required Matlab code to find the greatest common divisor of a number using the Euclidean algorithm is shown.
To find the greatest common divisor (GCD) of two numbers using the Euclidean algorithm in MATLAB, you can use the following code:
% Replace '12345678' with your actual student number
studentNumber = '12345678';
% Extract the first 4 digits as the first number
firstNumber = str2double(studentNumber(1:4));
% Extract the last 3 digits as the second number
secondNumber = str2double(studentNumber(end-2:end));
% Find the GCD using the Euclidean algorithm
gcdValue = gcd(firstNumber, secondNumber);
% Display the result
disp(['The GCD of ' num2str(firstNumber) ' and ' num2str(secondNumber) ' is ' num2str(gcdValue) '.']);
Make sure to replace '12345678' with your actual student number. The code extracts the first 4 digits as the first number and the last 3 digits as the second number using string indexing. Then, the gcd function in MATLAB is used to calculate the GCD of the two numbers. Finally, the result is displayed using the disp function.
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Write the next thee numbers in each number pattern. Describe the pattern.
a) 2, 4, 3, 6, 5, 10, 9, 16, …
b) 7, 5, 8, 6, 9, 7, 10, …
Answer:
a) 2, 4, 3, 6, 5, 10, 9, 16, ...
Step-by-step explanation:
A stone is tossed in the air from ground level with an initial velocity of 20 m/s. Its
height at time t seconds is h(t) = 20t − 4.9t
2 meters. Compute the average velocity of
the stone over the time interval [1, 3].
The average velocity of the stone over the time interval [1,3] is given by:Average velocity = distance/time = (-19.6 meters)/(2 seconds) = -9.8 meters/second.Therefore, the average velocity of the stone over the time interval [1,3] is -9.8 meters/second.
The average velocity of the stone over the time interval [1,3] when a stone is tossed in the air from the ground level with an initial velocity of 20 m/s can be computed as follows: Given,Height at time t seconds, h(t) = 20t - 4.9t^2 meters.We are to find the average velocity of the stone over the time interval [1,3].The velocity of the stone at time t seconds is given as:v(t) = h'(t)where h'(t) is the derivative of the height function h(t).The velocity of the stone at time t seconds, v(t) = h'(t) = 20 - 9.8t.We need to find the average velocity of the stone over the time interval [1,3].So, we need to find the distance travelled by the stone during this time interval.We can find the distance travelled by the stone during this time interval using the height function h(t) as follows:Distance travelled by the stone during the time interval [1,3] = h(3) - h(1)Using the height function h(t), h(3) = 20(3) - 4.9(3)^2 = -4.5 metersand h(1) = 20(1) - 4.9(1)^2 = 15.1 meters.Distance travelled by the stone during the time interval [1,3] = -4.5 - 15.1 = -19.6 meters.The average velocity of the stone over the time interval [1,3] is given as:Average velocity = distance/timeTaken together, the time interval [1,3] corresponds to a time interval of 3 - 1 = 2 seconds.
So, the average velocity of the stone over the time interval [1,3] is given by:Average velocity = distance/time = (-19.6 meters)/(2 seconds) = -9.8 meters/second. Therefore, the average velocity of the stone over the time interval [1,3] is -9.8 meters/second.
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can i get some help on this question please? ASAP!!
Answer:
left is a very good approximately .9 POSITIVE correlation
right is a very good approximately -.9 NEGATIVE correlation
Step-by-step explanation:
If F(x) = 5x-7 and G(x)=√x +13, what is F(G(x)) ?
Answer:
5x - 7 ( √ x + 13)
5x√x + 65x - 7√x -91
√3 (5x - 7) +13 (5x - 7)
(5x - 7) (√3 + 13)
5x(√3 + 13) -7
Encuentren dos números cuyo cociente sea -1 y que la resta del primero menos el segundo sea -3/2
Answer:
\(\dfrac{3}{4}\ \text{and}\ \dfrac{-3}{4}\)
Step-by-step explanation:
Find two numbers whose quotient is -1 and the subtraction of the first minus the second is -3/2
Let two numbers are x and y. When they are divided the quotient is -1. So,
\(\dfrac{x}{y}=-1\)
It can also be written as :
x = -y ....(1)
The subtraction of first minus the second is -3/2 .
\(x-y=\dfrac{-3}{2}\ .....(2)\)
Use equation (1) in (2),
\(-y-y=\dfrac{-3}{2}\\\\-2y=\dfrac{-3}{2}\\\\y=\dfrac{3}{4}\)
From equation (1) : \(x=\dfrac{-3}{4}\)
Hence, two numbers are \(\dfrac{3}{4}\ \text{and}\ \dfrac{-3}{4}\).
Nina can stitch 2/3 of dress in 4 hours. If represents the number of dresses and the represents the number of hours, which equation represents this proportional relationship?
Answer:
d :4h
Step-by-step explanation:
hope this helps (;
In Richmond, Virginia, the average daily high temperature was 90°F for July. The average daily low temperature for the same month was 69°F. If a day's temperature change is measured by comparing the morning/low temperature to the afternoon/high temperature, what is the percent of increase between the average low and high temperatures in July? Round your answer to the tenths place.
Answer:
To find the percent increase between the average low and high temperatures in July, we need to calculate the difference between the average high and low temperatures and then divide that difference by the average low temperature. Finally, we multiply the result by 100 to get the percentage increase.
The difference between the average high and low temperatures is:
90°F - 69°F = 21°F
To find the percentage increase, we need to divide the difference by the average low temperature and multiply by 100:
Percentage increase = (21°F / 69°F) × 100%
≈ 30.4%
Therefore, the percent of increase between the average low and high temperatures in July is approximately 30.4%, rounded to the tenths place.
i need help someone help pls and thx
Answer:
Two
Step-by-step explanation:
hope this helps tell me if I'm wrong though
In which quadrant does an angle of 1523° terminate? Assume the vertex of the angle is at the origin and one leg of the angle is in the positive x-axis. Find the quadrant of the other leg of the angle.
Check the picture below.
1523° = 360° + 360° + 360° + 360° + 83°.
The population of grizzly bears in a remote area is modeled by the function P(t)=200t−120t+0.5 , where t=1 represents the year 2001, t=2 represents the year 2002, and so on. Use the model to complete the table below.
By answering the presented question, we may conclude that Therefore, function the completed table is as shown below. To complete the table, we need to substitute each value of t into the formula \(P(t) = 200t - 120t^2 + 0.5\) and calculate the corresponding value of P(t).
What is function?In mathematics, a function seems to be a link between two sets of numbers in which each member of the first set (known as the domain) corresponds to a specific member of the second set (called the range). In other words, a function takes input from one collection and creates output from another. The variable x has frequently been used to represent inputs, whereas the variable y has been used to represent outputs. A formula or a graph can be used to represent a function. For example, the formula y = 2x + 1 depicts a functional form in which each value of x generates a unique value of y.
To complete the table, we need to substitute each value of t into the formula \(P(t) = 200t - 120t^2 + 0.5\) and calculate the corresponding value of P(t).
Year t P(t)
2001 1 80.5
2002 2 162.5
2003 3 214.5
2004 4 236.5
2005 5 228.5
2006 6 190.5
Therefore, the completed table is as shown above.
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