Using the graph as your guide, complete the following statement.

Solve the equation below Explain your steps . Show your math work 2(3x + 4) = 4x + 2

lisabon 2012 [21]

Answer:

x = -3

Step-by-step explanation:

4 0

3 years ago

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Amanda is 4 year older than Caroline. David is 2 years less than double Amanda’s age. Kene is 12 years younger than David. Toget

Sloan [31]

A is 34
C is 17
D is 66
K is 54

3 0

3 years ago

Verify that each equation is an identity (1 - sin^(2)((x)/(2)))/(1+sin^(2)((x)/(2)))= (1+cosx)/(3-cosX)

Allisa [31]

Answer:

Given that we have;

$sin \left (\dfrac{x}{2} \right ) = \sqrt{\dfrac{1 - cos (x)}{2} }$

By the application of the law of indices and algebraic process of adding a and subtracting a fraction from a whole number, we have;

$\therefore \dfrac{\left ( 1 - sin^2 \left (\dfrac{x}{2} \right ) \right )}{\left ( 1 + sin^2 \left (\dfrac{x}{2} \right ) \right )} =\dfrac{\left ( \dfrac{1 + cos (x)}{2} \right)}{\left (\dfrac{3 - cos (x)}{2} \right ) } =\dfrac{\left ( 1 + cos (x))}{(3 - cos (x))}$

Step-by-step explanation:

An identity is a valid or true equation for all variable values

The given equation is presented as follows;

$\dfrac{\left ( 1 - sin^2 \left (\dfrac{x}{2} \right ) \right )}{\left ( 1 + sin^2 \left (\dfrac{x}{2} \right ) \right )} =\dfrac{\left ( 1 + cos (x))}{(3 - cos (x))}$

From trigonometric identities, we have;

$sin \left (\dfrac{x}{2} \right ) = \sqrt{\dfrac{1 - cos (x)}{2} }$

$\therefore sin^2 \left (\dfrac{x}{2} \right ) = \dfrac{1 - cos (x)}{2}$

$1 - sin^2 \left (\dfrac{x}{2} \right ) = 1 - \dfrac{1 - cos (x)}{2} = \dfrac{2 - (1 - cos (x))}{2} = \dfrac{1 + cos (x))}{2}$

$1 + sin^2 \left (\dfrac{x}{2} \right ) = 1 + \dfrac{1 - cos (x)}{2} = \dfrac{2 + 1 - cos (x))}{2} = \dfrac{3 - cos (x))}{2}$

$\therefore \dfrac{\left ( 1 - sin^2 \left (\dfrac{x}{2} \right ) \right )}{\left ( 1 + sin^2 \left (\dfrac{x}{2} \right ) \right )} =\dfrac{\left ( \dfrac{1 + cos (x)}{2} \right)}{\left (\dfrac{3 - cos (x)}{2} \right ) } =\dfrac{\left ( 1 + cos (x))}{(3 - cos (x))}$

$\therefore \dfrac{\left ( 1 - sin^2 \left (\dfrac{x}{2} \right ) \right )}{\left ( 1 + sin^2 \left (\dfrac{x}{2} \right ) \right )} =\dfrac{\left ( 1 + cos (x))}{(3 - cos (x))}$

3 0

3 years ago

2 Points

saw5 [17]

There’s no shape so I think it’s D

3 0

3 years ago

Please help!!!!! The graph of function f is shown on the coordinate plane. Graph the line representing function g, if g is defin

dedylja [7]

Answer:

g(x) = - x + 1

Step-by-step explanation:

Lets get the equation for the graphed function

Using two points:

(0, -6) and (3, 0)

Y-intercept is known, it is -6 as per the first point

Slope is:

m = (y2 - y1)/(x2 - x1)
m = (0+6)/(3-0) = 6/3= 2

So the function f is:

f(x) = 2x - 6

g(x) is going to be

g(x) = -1/2f(x + 2) = -1/2 (2(x+2) - 6) = -1/2(2x + 4 - 6) = -1/2(2x - 2) = - x + 1

So

g(x) = -x + 1

The graph is attached

7 0

3 years ago

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