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3 years ago

State the slope-intercept form of the equation for the graph with the points 3,0 and 0,-1

Mathematics

1 answer:

Dvinal [7]3 years ago

6 0

Answer:

The answer is y=1/3x-1

Step-by-step explanation:

m=1/3

y-y=m(x-x1)

y-(-1)=1/3(x-0)

y+1=1/3x-0

-1 -1

y=1/3x-1

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Find x? In 3x - In(x - 4) = ln(2x - 1) +ln3

earnstyle [38]

Answer:

$x = \displaystyle \frac{5 + \sqrt{17}}{2}$ .

Step-by-step explanation:

Because $3\, x$ is found in the input to a logarithm function in the original equation, it must be true that $3\, x > 0$ . Therefore, $x > 0$ .

Similarly, because $(x - 4)$ and $(2\, x - 1)$ are two other inputs to the logarithm function in the original equation, they should also be positive. Therefore, $x > 4$ .

Let $a$ and $b$ represent two positive numbers (that is: $a > 0$ and $b > 0$ .) The following are two properties of logarithm:

$\displaystyle \ln (a) + \ln(b) = \ln\left(a \cdot b\right)$ .

$\displaystyle \ln (a) - \ln(b) = \ln\left(\frac{a}{b}\right)$ .

Apply these two properties to rewrite the original equation.

Left-hand side of this equation:

$\begin{aligned}&\ln(3\, x) - \ln(x - 4)= \ln\left(\frac{3\, x}{x -4}\right)\end{aligned}$

Right-hand side of this equation:

$\ln(2\, x- 1) + \ln(3) = \ln\left(3 \left(2\, x - 1\right)\right)$ .

Equate these two expressions:

$\begin{aligned}\ln\left(\frac{3\, x}{x -4}\right) = \ln(3(2\, x - 1))\end{aligned}$ .

The natural logarithm function $\ln$ is one-to-one for all positive inputs. Therefore, for the equality $\begin{aligned}\ln\left(\frac{3\, x}{x -4}\right) = \ln(3(2\, x - 1))\end{aligned}$ to hold, the two inputs to the logarithm function have to be equal and positive. That is:

$\displaystyle \frac{3\ x}{x - 4} = 3\, (2\, x - 1)$ .

Simplify and solve this equation for $x$ :

$x^2 - 5\, x + 2 = 0$ .

There are two real (but not rational) solutions to this quadratic equation: $\displaystyle \frac{5 + \sqrt{17}}{2}$ and $\displaystyle \frac{5 - \sqrt{17}}{2}$ .

However, the second solution, $\displaystyle \frac{5 - \sqrt{17}}{2}$ , is not suitable. The reason is that if $x = \displaystyle \frac{5 - \sqrt{17}}{2}$ , then $(x - 4)$ , one of the inputs to the logarithm function in the original equation, would be smaller than zero. That is not acceptable because the inputs to logarithm functions should be greater than zero.

The only solution that satisfies the requirements would be $\displaystyle \frac{5 + \sqrt{17}}{2}$ .

Therefore, $x = \displaystyle \frac{5 + \sqrt{17}}{2}$ .

7 0

3 years ago

Solve the inequality. 1/6w≥2.5

Viefleur [7K]

$\dfrac{1}{6}w\geq2.5\qquad\text{multiply both sides by 6}\\\\\not6^1\cdot\dfrac{1}{\not6_1}w\geq6\cdot2.5\\\\\boxed{w\geq15}$

7 0

3 years ago

Read 2 more answers

Assume that instead of conducting experiments, Latané and Darley had used a correlational method to study the relation between t

Len [333]

Answer:

C) a positive correlation

Step-by-step explanation:

More people ⇒ Longer time is a positive correlation between those variables. However, longer time is not the desired outcome.

Rather, shorter time is the desired outcome. The correlation between more people and shorter time is negative. In order to compute that correlation numerically, one would have to define a function that would give a numerical value for "shorter time" that would model the goodness of outcome as time gets shorter.

7 0

3 years ago

What is the probability of a coin landing on

VMariaS [17]

1 /3

On a coin, the probability of heads:

P ( H ) = 1 2/2

ON a die, the probability of getting a number less than 4:

P ( 1 , 2 , 3, 4 ) = 4 /6 P( H and no. less than 4 ) = 1 /2× 4 /6 = 1 /2 × 2/ 6 = 2/6 = 1 /3

if this is wrong im very sorry, not on top on my math at the moment

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3 years ago

8 ft Find the area of the figure.

lina2011 [118]

Answer:

Area of a rectangle is length multiplied by the width. In this case, length is equal to width. So, Area is 8 ft * 8 ft which is 64 ft2.

5 0

2 years ago