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3 years ago

If g(x-1) = (2-g(x))/8 and g(1) = 3, find the value of g(2).

Mathematics

1 answer:

aniked [119]3 years ago

5 0

Answer:

-22

Step-by-step explanation:

g(2-1)=g(1)=(2-g(2))/8=3

2-g(2)=24

-g(2)=22

g(2)=-22

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Irina18 [472]

Answer:

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2 years ago

Read 2 more answers

2. JI. has coordinates J(-6, 1) and Z(-4, 3). Find the coordinates of the midpoint.

AleksandrR [38]

Answer:

(- 5, 2 )

Step-by-step explanation:

Given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is

( $\frac{x_{1}+x_{2} }{2}$ , $\frac{y_{1}+y_{2} }{2}$ )

Here (x₁, y₁ ) = (- 6, 1) and (x₂, y₂ ) = (- 4, 3) thus

midpoint = $\frac{-6-4}{2}$ , $\frac{1+3}{2}$ ) = ( $\frac{-10}{2}$ , $\frac{4}{2}$ ) = (- 5, 2 )

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2 years ago

Suppose that θ is an acute angle of a right triangle and that sec(θ)=52. Find cos(θ) and csc(θ).

insens350 [35]

Answer:

$\cos{\theta} = \dfrac{1}{52}$

$\csc{\theta} = \dfrac{52}{\sqrt{2703}}$

Step-by-step explanation:

To solve this question we're going to use trigonometric identities and good ol' Pythagoras theorem.

a) Firstly, sec(θ)=52. we're gonna convert this to cos(θ) using:

$\sec{\theta} = \dfrac{1}{\cos{\theta}}$

we can substitute the value of sec(θ) in this equation:

$52 = \dfrac{1}{\cos{\theta}}$

and solve for for cos(θ)

$\cos{\theta} = \dfrac{1}{52}$

side note: just to confirm we can find the value of θ and verify that is indeed an acute angle by $\theta = \arccos{\left(\dfrac{1}{52}\right)} = 88.8^\circ$

b) since right triangle is mentioned in the question. We can use:

$\cos{\theta} = \dfrac{\text{adj}}{\text{hyp}}$

we know the value of cos(θ)=1\52. and by comparing the two. we can say that:

length of the adjacent side = 1
length of the hypotenuse = 52

we can find the third side using the Pythagoras theorem.

$(\text{hyp})^2=(\text{adj})^2+(\text{opp})^2$

$(52)^2=(1)^2+(\text{opp})^2$

$\text{opp}=\sqrt{(52)^2-1}$

$\text{opp}=\sqrt{2703}$

length of the opposite side = √(2703) ≈ 51.9904

we can find the sin(θ) using this side:

$\sin{\theta} = \dfrac{\text{opp}}{\text{hyp}}$

$\sin{\theta} = \dfrac{\sqrt{2703}}{52}}$

and since $\csc{\theta} = \dfrac{1}{\sin{\theta}}$

$\csc{\theta} = \dfrac{52}{\sqrt{2703}}$

4 0

3 years ago

Complete each trinomial such that it can be rewritten in the form a(x+b)^2 or a(x-b)^2

scoundrel [369]

The value of the expression in the form a(x+b)^2 is 1.5(x+2)^2 - 4

<h3>Vertex Form of a quadratic expression</h3>

Given the quadratic expressions

1.5x^2+6x+......

1.5(x^2 + 4x)

Using the completing the square method

The coefficient of x = 4

Half of the coefficient = 4/2 = 2

The square of the result = 2^2 = 4

The equation is expressed as:

f(x) = 1.5(x^2+4x+ 4) - 4

f(x) = 1.5(x+2)^2 - 4

Hence the value of the expression in the form a(x+b)^2 is 1.5(x+2)^2 - 4

Learn more on completing the square method here: brainly.com/question/1596209

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2 years ago

A line passes through the points (2,18) and (8,24). Write a linear function rule in terms of x and y for this line. The linear f

Alinara [238K]

Answer:

Step-by-step explanation:

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3 years ago