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3 years ago

Solve for x. Please show your work. 2x + 6 = 3x - 2

Mathematics

1 answer:

Valentin [98]3 years ago

6 0

Answer:

x=8

Step-by-step explanation:

$2x + 6 = 3x - 2$

then subtract the 6 from both sides of the equation

$2x = 3x - 8$

then subtract the 3x from both sides of the equation

$- 1x = - 8$

then divide each side by -1

$x = 8$

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Question 16 (Essay Worth 7 points) Verify the identity. tan (x + π/2) = -cot x

Rus_ich [418]

Step-by-step explanation:

We know that tan=sin/cos, so tan(x+π/2)=

$\frac{sin(x+pi/2)}{cos(x+pi/2)}$

Then, we know that sin(u+v)=sin(u)cos(v)+cos(u)sin(v),

so our equation is then

$\frac{sin(x)cos(\pi/2)+cos(x)sin(\pi/2)}{cos(x+\pi/2)} = \frac{cos(x)}{cos(x+\pi/2) }$

Then, cos(u+v)=cos(u)cos(v)-sin(u)sin(v), so our expression is then

$\frac{cos(x)}{cos(x)cos(\pi/2)-sin(x)sin(\pi/2)} = \frac{cos(x)}{-sin(x)} = -cot(x)$

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3 years ago

In 3 apples cost 48¢ , how many dozen apples can be bougth for $3.84?

Law Incorporation [45]

1 dozen = 12 apples.

3 apples cost 0.48, multiply that by 4 to get the price of 1 dozen.

0.48 x 4 = $1.92 per dozen.

Divide the total you can spend ( 3.84) by cost per dozen:

3.48 / 1.92 = 2

You can buy 2 dozen.

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3 years ago

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What is the answer to (-3b^4)^2/-12b^-9

ladessa [460]

Answer:

(−3b4)2

−12

b−9

−3

Step-by-step explanation:

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3 years ago

The smallest to largest 0.354 0.4 0.35 0.345

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Answer:0.345, 0.35, 0.354, 0.4

Step-by-step explanation:

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3 years ago

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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

3 years ago