Define f(1) in a way that extends (S^3-1)/(S^2-1) to be continuous at S=1

Solve for x : log(3x) + log(x + 4) = log(15).<br><br>Please explain it to me.

zlopas [31]

Answer:

x = 1

Explanation:

$\sf \rightarrow log(3x) + log(x + 4) = log(15)$

Rule: log(a) + log(b) = log(ab)

$\sf \rightarrow log(3x(x + 4)) = log(15)$

cancel out log on both sides

$\sf \rightarrow 3x(x + 4) = 15$

relocate constant variable

$\sf \rightarrow 3x^2 + 12x -15 = 0$

take 3 as a common factor

$\sf \rightarrow 3(x^2 + 4x -5) = 0$

divide both sides by 3

$\sf \rightarrow x^2 + 4x -5 = 0$

middle term split

$\sf \rightarrow x^2 + 5x -x-5 = 0$

factor common terms

$\sf \rightarrow x(x + 5) -1(x+5)= 0$

collect into groups

$\sf \rightarrow (x-1)(x+5)= 0$

set to zero

$\sf \rightarrow x-1 = 0 , \ x+5= 0$

relocate variables

$\sf \rightarrow x = 1, \ x = -5$

There must be a positive solution for log, so the solution is only x = 1

3 0

1 year ago

Read 2 more answers

Which linear function has a negative slope, f(x) or g(x)?

Anit [1.1K]

Answer:

f(x) is negative and g(x) is positive

Step-by-step explanation:

f(x) = 4-x

Rewriting

f(x) = -x+4

We recognize this as

y= mx+b or the representation of a line with slope -1 and y intercept 4

f(x) is linear

g(x) as we increase x by 1 we increase g(x) by 2

The slope is 2, and the y intercept is 1

y = 2x+1

Lets check a point

(2,5)

5 = 2(2)+1

5=5 so we are correct

f(x) is negative and g(x) is positive

8 0

3 years ago

Read 2 more answers

85 Subs Rn from the helpers - Hi guys this is difficult so my friend is super sick and he wants to grow like Mr.Beast and it wou

bagirrra123 [75]

Answer:

sure!

Step-by-step explanation:

8 0

2 years ago

Under his cell phone plan, Xavier pays a flat cost of $44 per month and $3 per

wolverine [178]

Answer:

Answer:

4.8 gigabytes

Step-by-step explanation:

Let the number of gigabytes of data = x

Xavier pays a flat cost of $44 per month and $3 per gigabyte. He wants to keep his bill at $58.40 per month.

The above expression above is represented by the equation:

$44 + $3 × x = $58.40

44 + 3x = 58.40

Solving for x

Subtract 44 from both sides

44 - 44 + 3x = 58.40 - 44

3x = 14.4

x = 14.4/3

x = 4.8 gigabytes

Step-by-step explanation:

6 0

2 years ago

A college football coach has decided to recruit only the heaviest 15% of high school football players. He knows that high school

Alla [95]

Answer:

The coach should start recruiting players with weight 269.55 pounds or more.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 225 pounds

Standard Deviation, σ = 43 pounds

We are given that the distribution of weights is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

We have to find the value of x such that the probability is 0.15

$P( X > x) = P( z > \displaystyle\frac{x - 225}{43})=0.15$

$= 1 -P( z \leq \displaystyle\frac{x - 225}{43})=0.15$

$=P( z \leq \displaystyle\frac{x - 225}{43})=0.85$

Calculation the value from standard normal z table, we have,

$P(z < 1.036) = 0.85$

$\displaystyle\frac{x - 225}{43} = 1.036\\\\x = 269.548 \approx 269.55$

Thus, the coach should start recruiting players with weight 269.55 pounds or more.

3 0

3 years ago