Use the Pythagorean identity sin^2 Θ + cos^2 Θ = 1 to derive the other Pythagorean identities, 1 + tan^2 Θ = sec^2 Θ and 1 + cot^2 Θ = csc^2 Θ. Discuss how to remember these identities and other fundamental identities.

Answers

Answer 1

Answer: 1 ) 1 + tan² t = sec² t
1 + sin² t / cos² t = 1 / cos² t
( This is because we know that tan x = sin x / cos x and csc x = 1 / cos x )
Then we will multiply both sides of an equation by cos² t
1 * cos² t + sin² t * cos² t / cos² t = 1
cos² t + sin² t = 1 ( and we know that it is the identity - true )
2 ) 1 + cot ² t = csc² t
1 + cos² t / sin² t = 1 / sin² t / · sin² t ( multiply both sides by sin² t )
sin² t + cos² t = 1 ( true )

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PLEASE HELP ! ALGABRA 1

Answers

Answer: No solutions (C)

Explanation: The two lines have the same slope but different Y intercept this means they will increase/decrease at the same rate but since they start at different locations on a graph, they will never touch making it parallel

In a certain manufacturing plant, the first operation can be done on any one of five machines, the second operation on only one machine, the third operation on any one of six machines, and the fourth operation on either of two machines. Over how many routes can the raw material be processed?14
56
60

Answers

Let's see all the steps:
1) operation : 5 options
2) only one option: we ignore it
3) the third operation: 6 options
4): 2 options.

So we have 5 options, 6 options and 2 options: and they are independent of each other. This means that we multiply the numbers, and 5*6*2=60 So the answer is 60!

Answer:

Step-by-step explanation:

Does anyone know the pattern to this? Does anyone also know the slope to it and where the line intersects at the y-axis and the equation of the line?

Answers

Answer:

see explanation

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = $(y_(2)-y_(1) )/(x_(2)-x_(1) )$

with (x₁, y₁ ) = (1, 3) and (x₂, y₂ ) = (3, 7) ← 2 ordered pairs from the table

m = $(7-3)/(3-1)$ = $(4)/(2)$ = 2

The line crosses the y- axis at (0, 1 ) ← from table

Then c = 1

y = 2x + 1 ← equation of line

The scatter plot shows the ages of children and how many stuffed animals they own.What is the range of ages for the cluster?

Answers

the answer is 8 to 10 that is the range of ages for the cluster

One of the factors of the polynomial x3 − 5x2 is x + 3. What is the other factor?a. x2-8x+24+(72/x+3)
b. x2-8x+24
c. x2-8x+24-(72/x+3)
d. x3-8x2+24x-72

Answers

The answer is letter c. x2-8x+24-[72/(x+3)]. If you do not know how to solve this using the long division method, you can always evaluate the options through the process of elimination first. Since the degree of the other factor is already 1 (x to the power of 1), you know that option d. is not the correct answer because you know that the other factor must be raised to the power of 2. That leaves us with a, b and c. Working backwards and multiplying the given factor (x+3) with the factor in b, gives us x3-5x2+72. So from there, you know that you have to eliminate 72, which can be removed when it is subtracted by itself. Letter c does just that. Try multiplying (x+3) and option c for yourself :).

Answer:

Option C is correct.

Step-by-step explanation:

Given polynomial : x³ - 5x²

Factors of given polynomial = x + 3

Let, p(x) = x³ - 5x²

To get other factor of p(x), we divide p(x) by given factor.

On division we get,

Quotient = x² - 8x + 24

Remainder = -72

So another factor is $x^2-8x+24-(72)/(x+3)$

Therefore, Option C is correct.

Which of the following is a solution of y - x < -3?

Answers

If you would like to find the solution for the inequation y - x < - 3, you can do this using the following steps:

y - x < - 3
y - x + x < - 3 + x
y < - 3 + x
y < x - 3

The correct result would be y < x - 3.

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