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3 years ago

What is 2log 9 in simplest form?

Mathematics

1 answer:

Mamont248 [21]3 years ago

5 0

Answer:

1.90

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Please help me asap !!

Natasha2012 [34]

Answer:

3.5

Step-by-step explanation:

(42 - 14)/(12 - 4) = 28/8 = 7/2 = 3.5

5 0

3 years ago

Identify the standard form of the equation by completing the square.

OLEGan [10]

Answer:

$\dfrac{(x-1)^2}{9}-\dfrac{(y-2)^2}{4}=1$

Step-by-step explanation:

Given equation:

$4x^2-9y^2-8x+36y-68=0$

This is an equation for a horizontal hyperbola.

To complete the square for a hyperbola

Arrange the equation so all the terms with variables are on the left side and the constant is on the right side.

$\implies 4x^2-8x-9y^2+36y=68$

Factor out the coefficient of the x² term and the y² term.

$\implies 4(x^2-2x)-9(y^2-4y)=68$

Add the square of half the coefficient of x and y inside the parentheses of the left side, and add the distributed values to the right side:

$\implies 4\left(x^2-2x+\left(\dfrac{-2}{2}\right)^2\right)-9\left(y^2-4y+\left(\dfrac{-4}{2}\right)^2\right)=68+4\left(\dfrac{-2}{2}\right)^2-9\left(\dfrac{-4}{2}\right)^2$

$\implies 4\left(x^2-2x+1\right)-9\left(y^2-4y+4\right)=36$

Factor the two perfect trinomials on the left side:

$\implies 4(x-1)^2-9(y-2)^2=36$

Divide both sides by the number of the right side so the right side equals 1:

$\implies \dfrac{4(x-1)^2}{36}-\dfrac{9(y-2)^2}{36}=\dfrac{36}{36}$

Simplify:

$\implies \dfrac{(x-1)^2}{9}-\dfrac{(y-2)^2}{4}=1$

Therefore, this is the standard equation for a horizontal hyperbola with:

center = (1, 2)
vertices = (-2, 2) and (4, 2)
co-vertices = (1, 0) and (1, 4)
$\textsf{Asymptotes}: \quad y = -\dfrac{2}{3}x+\dfrac{8}{3} \textsf{ and }y=\dfrac{2}{3}x+\dfrac{4}{3}$
$\textsf{Foci}: \quad (1-\sqrt{13}, 2) \textsf{ and }(1+\sqrt{13}, 2)$

4 0

2 years ago

Write a recursive formula for the sequence 10, 6, 2, -2 ..find next term . Make sure to identify first term. Use an&an-1 in

Iteru [2.4K]

hello :
(-2)-(2) =(2)-(6)=(6)-(10)=-4 (common diffrence)of aritmetic sequence
a recursive formula for the sequence is : An+1=An-4
next term is : (-2)+(-4) = -6

4 0

3 years ago

Graph the equation by translating y = |x|.

Tom [10]

It would be graph B since the graph is within the absolute value meaning that the parent graph would have a horizontal shift and since it's + it would move to the left

7 0

3 years ago

The value of a professional basketball player's autograph rose 20% in the last year. It is now worth $336.00. What was it worth

sesenic [268]

Answer:

The value of basketball player's autograph a year ago is $280

Step-by-step explanation:

Given as :

The present value of autograph = $ 336.00

The rate of increase of autograph = 20%

The time period = 1 year

Let The value one year ago = $ x

So ,

The value of autograph after n year = The present value × $(1+\frac{Rate}{100})^{n}$

Or, $ 336.00 = $ x × $(1+\frac{20}{100})^{1}$

Or, $ 336.00 = $x × 1.2

∴ x = $\frac{336.00}{1.2}$ = $280

Hence The value of basketball player's autograph a year ago is $280 Answer

6 0

3 years ago