Find the sum of this infinite geometric series. HELP!!

Determine whether the lines are parallel, perpendicular, or neither. y = 3x - 2 -3x + y = 8

Butoxors [25]

Answer:

they are parallels

Step-by-step explanation:

they have the same slope but different y intercepts so they are parallel

4 0

3 years ago

Read 2 more answers

If AD/DB =AE/EC, then line segment blank is parallel to line segment blank

Marysya12 [62]

Answer:DE and BC

Step-by-step explanation:

5 0

3 years ago

Show your work 4(2x - 6) = 10x - 6

Elden [556K]

4.(2x - 6) = 10x - 6

4.2x - 4.6 = 10x - 6

8x - 24 = 10x - 6

-24 + 6 = 10x - 8x

-18 = 2x

x = -9

4 0

3 years ago

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Analyze the diagram below and complete the instructions that follow.

steposvetlana [31]

Answer:

71°

Step-by-step explanation:

84+(2x-1)+(x+8)+(x+5)=360 [angles in a quadrilateral add to 360°]
4x+96=360 [combine like terms]
4x=264 [subtract 96 from both sides]
x=66 [divide both sides by 4]

So, angle A measures 66+5=71°

5 0

1 year ago

The function y = 58. 7(1. 03)^t gives a country’s population, y (in millions), where t is the number of years since January 1994

GREYUIT [131]

Answer:

Approximate population ≈ 74.36 million.

Step-by-step explanation:

The given problem involves modeling of an exponential growth or decay function of a population.

<h2>Definition:</h2>

Exponential growth ( relative growth ) occurs when a population grows or increases exponentially by the same factor, over the same amount of time.
Exponential decay occurs when a population decreases continuously by a constant factor, over the same amount of time.

We can model the exponential growth of a population using the following Exponential Growth Model:

⇒ $\displaystyle\mathsf{P(t)\:=\:P_0 (1\:+\:r)^t }$

Where:

P( t ) = population after "t" years
P₀ = initial population
r = relative growth rate; positive "r" value means that the population is increasing; negative "r" value implies that the population is decreasing.
t = time (typically in years)

<h2>Solution:</h2>

Based from the given equation, $\displaystyle\mathsf{y\:=\:58.7(1.03)^t }$ , we can infer that:

⇒ $\displaystyle\mathsf{P(t)\:=\:P_0 (1\:+\:r)^t }$ or $\displaystyle\mathsf{y\:=\:P_0 (1\:+\:r)^t }$

Where:

P( t ) or y = population after "t" years
P₀ = initial population = 58.7
r = relative growth rate = 0.03 or 3% = the population is increasing (exponential growth).
t = time (typically in years) = 8 years (difference between January 2002 and January 1994).

Step 1: Substitute the given values into the Exponential Growth Model formula, and solve for P( t ) :

$\displaystyle\mathsf{P(t)\:=\:P_0 (1\:+\:r)^t }$

⇒ $\displaystyle\mathsf{P(8)\:=\:58.7 (1\:+\:.03)^8 }$

Step 2: Follow the order of operations, addition inside the parenthesis:

⇒ $\displaystyle\mathsf{P(8)\:=\:58.7 (1.03)^8 }$

Step 3: Follow the order of operations, applying the exponent into the parenthesis (do not round off the digits inside the parenthesis):

⇒ $\displaystyle\mathsf{P(8)\:=\:58.7 (1.266770081) }$

Step 4: Follow the order of operations, multiplying 58.7 (P₀) into the parenthesis:

⇒ $\displaystyle\mathsf{P(8)\:\approx \:74.35940378\quad or \quad 74.36\:\:million}$

<h2>Final Answer:</h2>

Therefore, the approximate population of the country in January 2002 is 74.36 million.

<h3>________________________</h3><h3>Keywords:</h3>

Exponential functions

Exponential growth

Exponential decay

Exponential growth model

____________________________

Learn more about exponential functions here:

brainly.com/question/25802424

7 0

2 years ago