can somebody help me please?
Answer:
Domain = [tex](-\infty,6)\;\cup\;(6,\infty)[/tex]
Range = [tex](-\infty,1)\;\cup\;(1,\infty)[/tex]
vertical asymptote is at [tex]x=6[/tex]
Step-by-step explanation:
Domain is all the x values, with an asymptote, it is just a line that approaches a number but never reaches it. The vertical asymptote if you look at x, the lines look like the come from infinity on the left and right, try to reach 6 but can't.
So the interval notation for this is the union of all the numbers from negative infinity up to 6 but not including 6, and all the numbers from positive infinity up to 6 but not including 6.Range is all the y values, with an asymptote, it approaches a number but never reaches it. The horizontal asymptote if you look at y, the lines look like the come from infinity on the top and bottom, try to reach 1 but can't.
So the interval notation for this is the union of all the numbers from negative infinity up to 1 but not including 1, and all the numbers from positive infinity up to 1 but not including 1.Which of the following equations could be th equation to represent the given graph? Make sure you explain your answer thoroughly.
Answer:
Option (C) is correct.
Step-by-step explanation:
The given options of the possible equation for the graph are as follows:
[tex](A) y=2\left(\frac{3}{2}\right)^x \\\\(B) y=-2\left(\frac{3}{2}\right)^{-x} \\\\(C) y=2\left(\frac{2}{3}\right)^x \\\\(D) y=-2\left(\frac{2}{3}\right)^{-x} \\\\[/tex]
The given graph is decreasing and at x=0, y=2.
So, first checking the value of the given options for x=0
[tex](A) y=2\left(\frac{3}{2}\right)^0=2\times 1= 2 \\\\(B) y=--2\left(\frac{3}{2}\right)^{-0}= -2\times 1= -2 \; (not\; possible) \\\\(C) y=2\left(\frac{2}{3}\right)^0= 2\times 1= 2 \\\\(D) y=2\left(\frac{2}{3}\right)^{-0} = -2\times 1= -2 \; (not\; possible)[/tex]
As, for x=0, y=2, so options (C) and (D) are not possible, so rejected.
Now, checking the nature (increasing or decreasing) of the given equation by differentiating it.
For option (A),
[tex]\frac{dy}{dx}=2\left(\frac{3}{2}\right)^{x}\times \ln\left(\frac{3}{2}\right)[/tex]
As [tex]\ln \left(\frac{3}{2}\right)=\ln(1.5)>0 \;and\; \left(\frac{3}{2}\right)^{x} >0[/tex]
So, [tex]\frac{dy}{dx}>0[/tex]
Therefore, the function in option (A) is increasing function.
Similarly, for option (C),
[tex]\frac{dy}{dx}=2\left(\frac{2}{3}\right)^{x}\times \ln\left(\frac{2}{3}\right)[/tex]
As [tex]\ln \left(\frac{2}{3}\right)=\ln(0.67)<0 \;and\; \left(\frac{3}{2}\right)^{x} >0[/tex]
So, [tex]\frac{dy}{dx}<0[/tex]
Therefore, the function in option (C) is decreasing function.
As the given graph is decreasing, so, (C) represents[tex]y=2\left(\frac{2}{3}\right)^x[/tex] the given graph.
Hence, option (C) is correct.
The equation [tex](C) y = 2(\dfrac{2}{3})^{x[/tex] could be the equation to represent the given graph is decreasing.
We have to determine, Which of the following equations could be the equation to represent the given graph.
According to the question,
The given options of the possible equation for the graph are as follows:
[tex](A)y = 2(\frac{3}{2})^x[/tex] [tex](B)y = -2(\frac{3}{2})^{-x}[/tex] [tex](C)y = 2(\frac{2}{3})^{x}[/tex] [tex](D)y = -2(\frac{2}{3})^{-x}[/tex]The given graph is decreasing and at x = 0, y = 2.
Then,
First checking the value of the given options for x = 0.
[tex](A)y = 2(\frac{3}{2})^x = 2(\frac{3}{2})^0 = 2 \times1 = 2[/tex] [tex](B)y = -2(\frac{3}{2})^{-x} = (A)y = -2(\frac{3}{2})^{-0} = -2 \times 1 = -2 (not \ possible)[/tex][tex](C)y = 2(\frac{2}{3})^x = 2(\frac{2}{3})^0 = 2 \times1 = 2[/tex] [tex](D)y = -2(\frac{2}{3})^{-x} = -2(\frac{2}{3})^{-0} = -2 \times1 = -2 (not \ possible)[/tex]For x = 0, y = 2, so options (C) and (D) are not possible, so the options are rejected.
Therefore,
To check the nature (increasing or decreasing) of the given equation by differentiating it.
For function A;[tex]\dfrac{dy}{dx} = 2(\dfrac{2}{3})^x \times ln(\dfrac{3}{2})\\\\ln(\dfrac{3}{2}) = ln(1.5) >0 \ and\ (\dfrac{3}{2})^{x} >0\\\\So, \dfrac{dy}{dx}>0\\\\[/tex]
Therefore, The function in option A is increasing function.
For function c;
[tex]\dfrac{dy}{dx} = 2(\dfrac{2}{3})^x \times ln(\dfrac{2}{3})\\\\ln(\dfrac{3}{2}) = ln(0.67) <0 \ and\ (\dfrac{3}{2})^{x} >0\\\\So, \dfrac{dy}{dx}<0\\\\[/tex]
Therefore, The function in option c is decreasing function.
The given graph is decreasing, so, the function c represents the given graph decreasing.
Hence, option (C) is correct.
To know more about the Graphs click the link given below.
https://brainly.com/question/16351335
HELP ASAP!!
geometry
Answer:
Step-by-step explanation:
Y+6=3y-30
Subtract y from the left
6=2y-30
Add 30 to both sides
36=2y
Divide by 2
18=y
2x+29=4x-47
Subtract 2x
29=2x-47
Add 47
76=2x
Divide by 2
38=x
Plz help I’m getting timed
Answer:
10
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
Answer:
10 meters
Step-by-step explanation:
You can count each unit since each unit equals 1 meter
Which of the following functions is quadratic?
Answer:
A
Step-by-step explanation:
Answer:
a.
Step-by-step explanation:
Sandra wants to buy some t-shirts online that cost $14 each, and the shipping cost is $23. She has $65 to spend.
How many t-shirts did Sandra purchase?
(this is two-step equation math)
Answer:3
Step-by-step explanation: it’s exactly 3
Sandra purchased three t-shirts
65-23=42
42/3=14
Brainliest for the correct answer 20 points!!!
Answer:
y = -3/2x + 3
Step-by-step explanation:
Answer:
y= 3 - 2x
Step-by-step explanation:
A number increased by fifteen is nineteen. A number increased by fifteen is nineteen.
Answer:
the number is 4
Step-by-step explanation:
we can write this as
x + 15 = 19
now we transpose
x= 19-15
x= 4
I NEED HELP!!!!
A sports team has won 21 out of the 40 games it has played. About what percent of games has the team won?
Answer:
About 50% percent
Step-by-step explanation:
20 is 50 percent of 40, so 21 is about 50 percent (52.5 %)
~theLocoCoco
Answer:
52.5%
Step-by-step explanation:
21/40 = 52.5/100
52.5/100= 52.5%
im not sure but you can try :<
Find the equation of a line that passes through (1,12) and is parallel to the graph of y=3x+3 Write the equation in slope-intercept form, if possible.
Answer:
The equation of the parallel line is
y = 3x + 9
Step-by-step explanation:
The general equation of a straight line is given as;
y = mx + c
where m is the slope and c is the intercept
If two lines are parallel, their slopes are equal
So the slope of the new line too is 3
Using the point-slope formula
y-y1 = m(x-x1)
y-12 = 3(x-1)
y-12 = 3x-3
y = 3x-3 + 12
y = 3x + 9
What is the answer to 1/2 divided by 8/7
7/16
Steps:
[tex]\frac{1}{2} /\frac{8}{7} =\frac{1}{2} *\frac{7}{8} =\frac{7}{16}[/tex]
Baxter Tree Service charges $42 per tree to trim them, and an additional $75.50 to remove the trimmings from the property. His competitor, Barron and Son, charges $37 per tree to trim them but charges $95.50 to remove trimmings. How many trees, t, must be trimmed to make the two companies cost the same amount?
Answer:
[tex]t = 4[/tex]
Step-by-step explanation:
Baxter Tree Service:
Per tree trimming charges = $42
Additional charges for removing the trimmings from the property = $75.50
Number of trees trimmed = [tex]t[/tex]
Total charges = Additional charges + cost of trimming [tex]t[/tex] trees
Total charges = $75.50 + $42[tex]t[/tex]
Barron and Son:
Per tree trimming charges = $37
Additional charges for removing the trimmings from the property = $95.50
Number of trees trimmed = [tex]t[/tex]
Total charges = Additional charges + cost of trimming [tex]t[/tex] trees
Total charges = $95.50 + $37[tex]t[/tex]
Now, the total charges need to be same and we have to find the value of [tex]t[/tex].
[tex]75.50+42t = 95.50+37t\\\Rightarrow 42t-37t=95.50-75.50\\\Rightarrow 5t=20\\\Rightarrow \bold{t =4}[/tex]
[tex]t = 4[/tex] number of trees must be trimmed.
Bobby and Gautham each save the same amount of money from each lawn they mow. What must be true for Gautham to have more money than Bobby after they have each mowed 18 lawns?
Answer:
I don't have any favorites. There is a reason for this, i don't read a lot of books but when i do, i usually like a mashup of different types of text styles. I guess i do have a favorite of a mashup. When i do read i usually pick a book that has an argument between different characters, a type of fiction memoir? And autobiography.
This mashup usually leads up to Wonder which is one of my all-time favorites. But there is another one i like and it is Diary of a Wimpy Kid. The only thing about that one is that doesn't have the whole autobiography part.
I like these styles because most of the books that i read have either funny traits or intense traits which, i love both of them.
Step-by-step explanation:
A rectangular carpet has a perimeter of 194 inches. The length of the carpet is 67 inches more than the width. What are the dimensions of the carpet?
Answer:
The dimensions of the carpet are 15 inches and 82 inches
Step-by-step explanation:
Assume that the width of the carpet is x inches
∵ The width of the carpet is x inches
∵ The length of the carpet is 67 inches more than the width
∴ The length of the carpet is (x + 67) inches
∵ The perimeter of the rectangle = 2(length + width)
∵ The perimeter of the carpet = 194 inches
→ Equate the two right sides of the perimeter
∴ 2(length + width) = 194
→ Divide both sides by 2
∴ length + width = 97
→ Substitute the value of the length and width in the equation above
∵ x + 67 + x = 97
→ Add the like terms in the left side
∴ (x + x) + 67 = 97
∴ 2x + 67 = 97
→ Subtract 67 from both sides
∵ 2x + 67 - 67 = 97 - 67
∴ 2x = 30
→ Divide both sides by 2
∴ x = 15
∵ x represents the width of the carpet
∴ The width of the carpet is 15 inches
∵ The length of the carpet = 15 + 67
∴ The length of the carpet is 82 inches
∴ The dimensions of the carpet are 15 inches and 82 inches
There are 12 books on a shelf. 7of these books are new.
(a) What is the ratio of new books to used books?
(b) What is the ratio of all books to used books?
Answer:
(a) 7 : 5
(b) 19 : 5
Hope this helps :)
Answer:
(a) 5:7 ( 5 new to 7 used). (B) 12:7 (12 books to 7 used ones). You are welcome :)
Step-by-step explanation:
What is (x+234)(x+8)=10x+2
Solve for x and justify your answer
First one will get brainless if right
Answer:
x = -8.4 and -223.6
Step-by-step explanation:
I 'foiled' and simplied, then graphed; x-intercepts (listed above) were the x-intercepts
evaluate (log) PLS HELP ASAP!!!! thank you!!! *will give brainliest*
Answer:
-3 ( D )
Step-by-step explanation:
Logarithm base 3 of 1/27 is -3.
A rectangular prism with a volume of 4 cubic units is filled with cubes with side lengths of 1/3 unit. How many 1/3 unit cubes does it take to fill the prism?
A - 108
B - 36
C - 12
D - 112
Answer:
your answer would be c hope this helps and if its wrong lmk
Step-by-step explanation:
HURRY I NEED HELP ASAP question: The name used to represent 1,000 liters is the
Answers : kiloliter, centiliter, or milliliter.
Answer:
KILOLITER
Step-by-step explanation:
Answer milliletres
Step-by-step explanation:
1. Find the percent of the given quantity using any method: 40% of 320
Answer:
128
Step-by-step explanation
Turn 40% into a decimal by placing a decimal point 2 places to the left making it 0.40. Then, calculate using 320 multiplied by 0.40 which is 128.
Answer:
the answer is 128.
40% of 320 = 128 :)
Given the arithmetic sequence below, write the general formula in simplified terms and
find the 110th term.
-3,2, 7, 12...
Answer:
542
Step-by-step explanation:
-3, 2, 7, 12
-3 + x = 2 x = 5
2 + x = 7 x = 5
7 + x = 12 x = 5
If you want to find the 3rd term in the sequence and you start with the first number, then you do this:
-3 + (2 * 5) = -3 + (10) = 7
The same goes for the 110th term:
-3 + (109 * 5) = -3 + (545) = 542
The formula to find the nth term is:
f(n) = n(0) + (n-1) * 5
Suppose n(0) = -3 then
f(110) = -3 + {(110-1) * 5}
f(110) = -3 + {(109) * 5}
f(110) = -3 + (545) = 542
You can simplyfy f(n) = n(0) + (n-1) * 5
f(n) = n(0) + (n-1) * 5
f(n) = n(0) + (5n-5)
f(n) = n(0) + 5n - 5
f(110) = -3 + (5 * 110) - 5
f(110) = -3 -5 + (550)
f(110) = - 8 + 550
f(110) = 542
Given f(x) = x^2 + 1 with domain: {-2, -1, 0, 1, 3}. What is the range, R?
a) {-1, -2, 0, 1, 3}
b) {4, 1, 0, 1, 9}
c) {5, 2, 1, 2, 10}
d) {3, 0, -1, 0, 8}
can someone please help me
Answer:
see explanation
Step-by-step explanation:
(a)
9n = [tex]\frac{15}{7}[/tex] - 2 ( multiply through by 7 to clear the fraction )
63n = 15 - 14 = 1 ( divide both sides by 63 )
n = [tex]\frac{1}{63}[/tex]
(b)
[tex]\frac{1}{3}[/tex] = k - 4 ( multiply through by 3 to clear the fraction )
1 = 3k - 12 ( add 12 to both sides )
13 = 3k ( divide both sides by 3 )
[tex]\frac{13}{3}[/tex] = k
(c)
g - [tex]\frac{2}{5}[/tex] g = 3 ( multiply through by 5 to clear the fraction )
5g - 2g = 15
3g = 15 ( divide both sides by 3 )
g = 5
(d)
[tex]\frac{3}{7}[/tex] w + 2w = 3 ( multiply through by 7 to clear the fraction )
3w + 14w = 21
17w = 21 ( divide both sides by 17 )
w = [tex]\frac{21}{17}[/tex]
Luke cut down a tree that was 25.8 feet tall. Then he cut the tree into 6 equal pieces to take it away.
What is the length of each piece?
Answer:
the length of each piece is 4.8 feet
Step-by-step explanation:
please help its math!!! will give brainly and more points if correct please I need help
The equations of four lines are given. Identify which lines are perpendicular.
Line 1: y+8x=−5
Line 2: x+16y=−5
Line 3: y=−6x−7
Line 4: y+3=18(x−1)
Lines 2 and 3 are perpendicular.
Lines 1 and 2 are perpendicular.
All four lines are perpendicular.
Lines 1 and 4 are perpendicular.
Answer:
None of the options match
Step-by-step explanation:
First let's check option 1: lines 2 and 3.
line 2 in mx+b form: y=-1/16x -5
line 3, already in mx+b form: y=-6x-7
if it was perpendicular, the slopes should have been -1/16 and 16 or -6 and 1/6.
now for the 2nd option: lines 1 and 2.
line 1 in mx+b form: y=-8x-5
line 2 in mx+b form: y=-1/16x-5
Again, the slopes do not match, they should have been -8 and 1/8 or -1/16 and 16.
For the 3rd option: all lines
this is obviously wrong since lines 1, 2 and 2, 3 are not perpendicular themselves. No need to bother checking this option.
Lastly, 1 and 4.
line 1 in mx+b form: y=-8x-5
line 4 --> y+3=18x-18 --> y=18x-21
This is also wrong since the slopes should have been -8 and 1/8 or 18 and -1/18.
To conclude, I think the answer is none. None of the combinations on here are perpendicular anyways...
Answer:
D
Step-by-step explanation:
We have the four lines:
[tex]\displaystyle\text{Line 1: }y+8x&=-5 \\\\ \text{Line 2: } x+\frac{1}{6}y&=-5\\\\\text{Line 3: } y&=-6x-7 \\\\\text{Line 4: } y+3&=\frac{1}{8}(x-1)[/tex]
Remember that for two lines to be perpendicular, their slopes are negative reciprocals of each other.
So, let’s determine the slope of each line.
For Line 1, we can rewrite our equation as:
[tex]y=-8x-5[/tex]
So, the slope of Line 1 is -8.
We can rewrite Line 2 as:
[tex]\displaystyle \begin{aligned} \frac{1}{6}y&=-x-5\\y&=-6x-30\end{aligned}[/tex]
So, the slope of Line 2 is -6.
The slope of Line 3 is also -6.
And the slope of Line 4 is 1/8.
So, the slopes of perpendicular lines must be negative reciprocals.
The negative reciprocal of -8 (slope of Line 1) is 1/8. We multiply by a negative and then take the reciprocal.
Since the slope of Line 4 is 1/8, this means that Lines 1 and 4 are perpendicular.
For Lines 2 and 3, they have the same slope, not negative reciprocals of each other.
So, they will instead of parallel instead of perpendicular.
And Line 1 is perpendicular only to Line 4, and no other line.
Therefore, our answer is D.
find the surface area of this cylinder using pie.
Answer:
Thus the surface area of this cylinder involving pie is:
[tex]A=750\pi[/tex] ft²
or
[tex]A\approx 2356.19[/tex] ft²
Step-by-step explanation:
Given
radius = r = 10 ft
height = h = 15 ft
The surface area of a cylinder formula is:
[tex]A=2\pi rh+2\pi r^2[/tex]
substituting the value = r = 10 ft and h = 15 ft
[tex]\:A=\left(2\times \:\pi \:\times \:15\times 10\right)+\left(2\times \pi \:\times \:15^2\right)\:[/tex]
[tex]A=750\pi[/tex] ft²
Thus the surface area of this cylinder involving pie is:
[tex]A=750\pi[/tex] ft²
or
[tex]A\approx 2356.19[/tex] ft²
Write a recursive formula for the following arithmetic sequence.
-6, -9, -12, -15, ...
Answer:
[tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] - 3
Step-by-step explanation:
The recursive formula lets us find a term in the sequence by adding the common difference d to the previous term.
Here d = a₂ - a₁ = - 9 - (- 6) = - 9 + 6 = - 3 , thus
[tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] - 3 with a₁ = - 6
Six increased by 1-3 of a number is 11 . Find the number
Answer:
7 is the answer
Step-by-step explanation:
6 + 1 - 3 of a number = 11
1 - 3 = -2
6 - 2 = 4
so 4 + 7 is 11
Hope it helps!
Charlie weighs 5 times his little sister Tali. If the total weight of both children is at 132 pounds, how much does each child weigh?
Answer:
5x+x=132
Step-by-step explanation:
132/6=22
22*5=110
Charlie weighs 110 pounds and Tali weighs 22 pounds.
e owner of a skatepark wants to increase her entry fee of $5 Buy in increments of $0.50 currently the skate park has an average of 500 paying customers per week the equation (500 - 25x)( $5 + $0.50x) give me the estimated weekly income where X is the number of $0.50 entry fee price increases if the entry fee is increased to $7.50 what will be the expected average number of paying customers each week
Answer:
375 paying customers
Step-by-step explanation:
First you need to find how much the fee was increased from $5.00 to $7.50
7.5 - 5 = 2.5
Then how many times the pay increase goes into that number to find your X value
2.5/.5 = 5
Now that we have found our x value lets plug it into the equation to find the money the park will make in increments of 1
500 - 25(1) = 475
500 - 25(2) = 450
500 - 25(3) = 425
500 - 25(4) = 400
500 - 25 (5) = 375
Answer:
375
Step-by-step explanation: