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3 years ago

Solve the equation below

Mathematics

2 answers:

Bingel [31]3 years ago

8 0

(1/3)(12+x)=(-8)(6-x)
(1/3)*12 + (1/3)*x = -8*6 - (-8)*x
4 + 1/3x = -48 + 8x
1/3x - 8x = -48 - 4
-23/3x = -52
x = 156/23

kotykmax [81]3 years ago

6 0

1/3(12+x) = -8 (6-x)

Distribute the 1/3 and the -8 through their parentheses

4 + 1/3x = -48 + 8x

subtract 4 from each side

1/3x = -52 + 8x

subtract 8x from each side

1/3x - 8x = -52

combine like terms

1/3x - 24/3x = -52
-23/3x = -52

divide each side by -23/3 (multiply the reciprocal of the divisor)

x = -52 × -3/23
x = 156/23

x = 6 18/23 or 6.78

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3 years ago

The population of bacteria can be modeled by the function below, where t represents the time since the population started decayi

Oksana_A [137]

Answer:

See Explanation

Step-by-step explanation:

The question is incomplete. I will assume the function is:

$f(t) = 15(0.86)^t$

Required

Determine the rate of decay

In an exponential function $f(x) = ab^x$ ,

The decay rate of the function is calculated as:

$1 - r = b$

By comparison:

$b = 0.86$

So, the equation becomes:

$1 - r = 0.86$

Make r the subject

$r = 1 - 0.86$

$r = 0.14$

<em>The rate of decay is 0.14</em>

3 0

3 years ago

Consider the functions f and g defined by \[f(x) = \sqrt{\dfrac{x+1}{x-1}}\qquad\qquad\text{and}\qquad\qquad g(x) = \dfrac{\sqrt

tino4ka555 [31]

Answer:

The given functions are not same because the domain of both functions are different.

Step-by-step explanation:

The given functions are

$f(x)= \sqrt{\dfrac{x+1}{x-1}}$

$g(x) = \dfrac{\sqrt{x+1}}{\sqrt{x-1}}$

First find the domain of both functions. Radicand can not be negative.

Domain of f(x):

$\dfrac{x+1}{x-1}>0$

This is possible if both numerator or denominator are either positive or negative.

Case 1: Both numerator or denominator are positive.

$x+1\geq 0\Rightarrow x\geq -1$

$x-1\geq 0\Rightarrow x\geq 1$

So, the function is defined for x≥1.

Case 2: Both numerator or denominator are negative.

$x+1\leq 0\Rightarrow x\leq -1$

$x-1\leq 0\Rightarrow x\leq 1$

So, the function is defined for x≤-1.

From case 1 and 2 the domain of the function f(x) is (-∞,-1]∪[1,∞).

Domain of g(x):

$x+1\geq 0\Rightarrow x\geq -1$

$x-1\geq 0\Rightarrow x\geq 1$

So, the function is defined for x≥1.

So, domain of g(x) is [1,∞).

Therefore, the given functions are not same because the domain of both functions are different.

4 0

3 years ago

What do we do to both sides of this equation to solve?

anzhelika [568]

Add 10 to both sides

Step-by-step explanation:

x-10 = 8

x - 10 + 10 = 8+ 10

x = 18

8 0

2 years ago

Read 2 more answers

5. Patricia is on the edge of the top of a mountain and notices that a kayak on the lake is 30 meters

zhuklara [117]

The distance from the kayak to the mountain to the nearest whole number is 43 meters.

The situation will form a right angle triangle as shown below in the diagram.

<h3>Properties of a right angle triangle:</h3>

One of its angle is 90 degrees.
The sides and angle can be found by using trigonometric ratios.

The height(opposite side) of the triangle is the kayak distance from the mountain to the lake below. The distance from the kayak to the mountain is the adjacent side of the triangle.

Therefore, using trigonometric ratios,

tan 35 = opposite / adjacent

tan 35° = 30 / a

a = 30 / tan 35°

a = 30 / 0.70020753821

a = 42.8444402023

a = 42.84 meters

a ≈ 43 meters

learn more on the angle of depression: brainly.com/question/13969247?referrer=searchResults

8 0

3 years ago