What is the vertical asymptote for the function f(x) = ln(x + 4) - 2? Be sure to write your answer as an equation for a line.

Answers

Answer 1

Answer: f(x) = ln (x+4) -2
Change f(x) to y
y=ln (x+4) -2
Inverse x and y
x=ln(y+4) -2
Solve for y, result will be inverse.
x+2=ln(y+4)
convert to exponential form
e^(x+2) = y+4
y=e^(x+2) -4
This is the inverse.
f^-1(x) = e^(x+2) -4

Looking at the above function, it is (e^x) shifted to the left by two unit, being brought down (4) units. The only important part of this function is the down-shift of (4), because this represents the horizontal asymptote.

y = -4 is the horizontal asymptote, which means

for f(x) =ln(x+4) -2
x=-4 is a vertical asymptotes.

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Given a mean of 9 and a standard deviation of 2.8, what is the z-score of the value 11 rounded to the nearest tenth?–0.9

–0.7

0.9

0.7

Answers

The answer is 0.7. Since the formula of the z-score is the difference of the score (x) and the mean divided by the standard deviation (SD)...

z= [ (x-mean)/SD ]

You simply substitute the values given.

z = (11-9)/2.8
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z- = 0.7

Both the leftmost digit and the rightmost digit of a four-digit numberN are equal to 1. When these digits are removed, the two-digit number
thus obtained is N ÷ 21. Find N.

Answers

$N=1000w+100x+10y+z\nw=z=1\nx,y\in\{0,1,2,\ldots,7,8,9\}\n10x+y=(N)/(21)\n10x+y=(1000w+100x+10y+z)/(21)\n10x+y=(1000+100x+10y+1)/(21)\n10x+y=(100x+10y+1001)/(21)\n210x+21y=100x+10y+1001\n110x+11y-1001=0\n10x+y-91=0\ny=-10x+91\n\n\hbox{The above equation meets the condition }x,y\in\{0,1,2,\ldots,7,8,9\}\n\hbox{only for } x=9:\ny=-10\cdot9+91\ny=-90+91\ny=1\n\n\hbox{Therefore:}\nN=1000\cdot1+100\cdot9+10\cdot1+1\nN=1000+900+10+1\nN=\boxed{1911}$

Find the equation of the line parallel to y = 1/3x + 4 that passes through (-9, 4).

Answers

For a line to be parallel, the slope has to be the same(1/3) only its coordonate on the y axis (b) changes. Therefore the new equation will be y=1/3x+b To find be, tou have to isolate it after inputting the new coordinates (-9,4) (4)=1/3(-9)+b 4=-3+b 7=b Therefore, the new equation is y=1/3x+7

Pls help me on this!

Answers

Answer:

The answer is A

Step-by-step explanation:

You would measure earth's mass is kg and not in g , mg or mcg

Blair's garden is four feet shorter than double its width. The perimeter of the garden is 64 feet. The width of the garden is ___ feet.

The length of the garden is ____ feet.

Answers

Answer:

The width of the garden is 12 feet.

The length of the garden is 20 feet.

Step-by-step explanation:

Let l be the length and w be the width

Then according to given statements

$l = 2w-4\ \ \ Eqn\ 1$

Second equation is:

$2l+2w = 64\ \ \ \ Eqn\ 2$

Putting l = 2w -4 in equation 2

$2(2w-4)+2w = 64\n4w-8+2w = 64\n6w -8 = 64\n6w = 64+8\n6w = 72\n(6w)/(6) = (72)/(6)\nw = 12$

Putting w = 12 in equation 1

$l = 2(12)-4 = 24-4 = 20$

Hence,

The width of the garden is 12 feet.

The length of the garden is 20 feet.

A charity fair raised $6,000 by selling 500 lottery tickets. There were two types of lottery tickets: A tickets cost $10 each, and B tickets cost $60 each. How many tickets of each type were sold?

Answers

Let a be the tickets that cost 10 each and b the tickets that cost 60 each. So therefore, a + b = 500 and 10a + 60b = 6000. By substituting the given numbers, a will be equals to 480. So the tickets sold are: 480 tickets for 10 each and 20 tickets for 60 each. Thank you for posting your question. I hope this answer helped you. Let me know if you need more help.

Answer:

on plato E. 480,20

Step-by-step explanation:

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