Answers
Answer:
Given that 1 and 4 are vertical asymtotes we have;
(a) -∞
(b) +∞
(c) +∞
(d) -∞
Step-by-step explanation:
(a) For the function;
[tex]\lim_{x\rightarrow 4^{-}}\left (\dfrac{2\cdot x^{2}+13\cdot x+20}{x^{2}-5\cdot x+4} \right )[/tex]
We have the denominator given by the expression, x² - 5·x + 4 which can be factorized as (x - 4)(x - 1)
Therefore, as the function approaches 4 from the left [lim (x → 4⁻)] gives;
[tex]\lim_{x\rightarrow 4^{-}}\left (\dfrac{2\cdot x^{2}+13\cdot x+20}{(x - 1)\cdot (x - 4)} \right )[/tex] [tex]\lim_{x\rightarrow 4^{-}}\left (\dfrac{2\cdot x^{2}+13\cdot x+20}{(3.999 - 1)\cdot (3.999 - 4)} \right )[/tex] [tex]\lim_{x\rightarrow 4^{-}}\left (\dfrac{2\cdot x^{2}+13\cdot x+20}{(2.999)\cdot (-0.001)} \right )[/tex][tex]=- \infty[/tex]
(b) Similarly, we have;
[tex]\lim_{x\rightarrow 4^{+}}\left (\dfrac{2\cdot x^{2}+13\cdot x+20}{x^{2}-5\cdot x+4} \right )[/tex]
We have the denominator given by the expression, x² - 5·x + 4 which can be factorized as (x - 4)(x - 1)
Therefore, as the function approaches 4 from the right [lim (x → 4⁺)] gives;
[tex]\lim_{x\rightarrow 4^{+}}\left (\dfrac{2\cdot x^{2}+13\cdot x+20}{(x - 1)\cdot (x - 4)} \right )[/tex] [tex]\lim_{x\rightarrow 4^{+}}\left (\dfrac{2\cdot x^{2}+13\cdot x+20}{(4.0001 - 1)\cdot (4.0001 - 4)} \right )[/tex] [tex]\lim_{x\rightarrow 4^{+}}\left (\dfrac{2\cdot x^{2}+13\cdot x+20}{(3.0001)\cdot (0.0001)} \right )[/tex][tex]= +\infty[/tex]
(c)
[tex]\lim_{x\rightarrow 1^{-}}\left (\dfrac{2\cdot x^{2}+13\cdot x+20}{x^{2}-5\cdot x+4} \right )[/tex]
We have the denominator given by the expression, x² - 5·x + 4 which can be factorized as (x - 4)(x - 1)
Therefore, as the function approaches 1 from the left [lim (x → 1⁻)] gives;
[tex]\lim_{x\rightarrow 1 ^{-}}\left (\dfrac{2\cdot x^{2}+13\cdot x+20}{(x - 1)\cdot (x - 4)} \right )[/tex] [tex]\lim_{x\rightarrow 1^{-}}\left (\dfrac{2\cdot x^{2}+13\cdot x+20}{(0.999 - 1)\cdot (0.999 - 4)} \right )[/tex] [tex]\lim_{x\rightarrow 4^{+}}\left (\dfrac{2\cdot x^{2}+13\cdot x+20}{(-0.001)\cdot (-3.001)} \right )[/tex][tex]=+ \infty[/tex]
(d) As the function approaches 1 from the right [lim (x → 1⁺)]
We have;
[tex]\lim_{x\rightarrow 1^{+}}\left (\dfrac{2\cdot x^{2}+13\cdot x+20}{(1.0001 - 1)\cdot (1.0001 - 4)} \right )[/tex]= [tex]\lim_{x\rightarrow 1^{+}}\left (\dfrac{2\cdot x^{2}+13\cdot x+20}{(0.0001)\cdot (-2.999)} \right ) =- \infty[/tex]
Related Questions
Based on these data, is it better to describe the centers of distribution in terms of the mean or the median? Explain. Mean for both bakeries because the data is symmetric PLEASE ANSWER THIS IS MY 4TH TIME ASKING BRAINLIEST AND 43 POINTS Mean for Bakery B because the data is symmetric; median for Bakery A because the data is not symmetric Mean for Bakery A because the data is symmetric; median for Bakery B because the data is not symmetric Median for both bakeries because the data is not symmetric
Answers
Answer:
Mean
Step-by-step explanation:
The numbers have a very large range. So you should use the mean(or average) to get more accurate data.
Which represents the inverse of the function f(x) = 4x?
h(x) = x + 4
h(x) = x -4
h(x) = 3
h(x) =
77 X
Answers
This is the same as h(x) = x/4
In decimal form, it would be h(x) = 0.25x
=============================================
Explanation:
Inverses undo the original function. The original function tells us to take any input (x) and multiply by 4 to get the output y = f(x) = 4x
To get the inverse, we reverse the operation applied here. The opposite of multiplication is division. So we'll divide by 4 instead of multiply by 4. This is why the answer is x/4 or (1/4)x
-----------
Another approach is to do the following: Replace f(x) with y. Swap x and y. Solve for y
f(x) = 4x
y = 4x
x = 4y
4y = x
y = x/4
h(x) = x/4
We end up with the same result as before.
-----------
Extra info:
For any real number x, the following two equations are true
h( f(x) ) = x
f( h(x) ) = x
in the figure below, BCA ~ STR. Find cos C, sin C, and tan C. Round your answers to the nearest hundredth.
Answers
Answer:
[tex]\sin C\approx0.85\\\\\cos C \approx0.52\\\\\tan C\approx1.63[/tex]
Step-by-step explanation:
According to the trigonometric ratios in aright triangle :
[tex]\sin x =\dfrac{\text{Side opposite to x}}{\text{Hypotenuse}}\\\\\cos x =\dfrac{\text{Side adjacent to x}}{\text{Hypotenuse}}\\\\\tan x=\dfrac{\sin x}{\cos x}[/tex]
Given: ΔBCA ~ ΔSTR
Since , corresponding angles of two similar triangles are equal.
So, ∠C = ∠T ...(i) [Middle letter]
In triangle STR
[tex]\sin T=\dfrac{\text{Side opposite to T}}{\text{Hypotenuse}}\\\\=\dfrac{26.4}{30.9}\approx0.85\\\\\cos x =\dfrac{\text{Side adjacent to T}}{\text{Hypotenuse}}\\\\=\dfrac{16.2}{30.9}\approx0.52\\\\\tan T=\dfrac{\sin T}{\cos T}\\\\=\dfrac{0.85}{0.52}\approx1.63[/tex] ...(ii)
From (i) and (ii), we have
[tex]\sin C\approx0.85\\\\\cos C \approx0.52\\\\\tan C\approx1.63[/tex]
Multiply and simplify
(x +1)3 x (x+1)4
Answers
Answer:
12x^2+24x+12
Step-by-step explanation:
(3x+3) * (4x+4)
12x^2+24x+12
Answer:
( x+1)^7
Step-by-step explanation:
(x +1)^3 * (x+1)^4
Replace x+1 with m
m^3 * m^4
The bases are the same so we can add the exponents
m^ (3+4)
m^7
Replace m with x+1
( x+1)^7
Simplify the inequalities and match them with the graphs that represent them. x + 1 15 7x 12 arrowRight arrowRight arrowRight arrowRight Reset Next
Answers
Answer:
I dont quite understand the inequalities, I think it might be the way is shows up, bit the first graph represents x equals all numbers less than 6. The second graph is all numbers greater than 6. Third graph is all numbers less than 7. forth graph is all numbers greater than 7.
Step-by-step explanation:
If you want to give me a better representation of the inequalities, I would be more than happy to help you more!! :)
Hope this helps!!
PLEASE READ BEFORE PROCEEDING! I want you all to get the answer without wasting money so you can still answer with something but I will still place the answer at the end of the question. What are two factors of the composite number 46 other than 1 and 46? A. 3 and 7 B. 2 and 13 C. 2 and 23 D. 3 and 33 ANSWER : C. 2 and 23
Answers
Answer:
The answer is C:2 and 23
Step-by-step explanation:
Answer:
U have told the answer in the ques. then why r u asking question.
U know the answer already...
4) Kevin and his team do not know what direction Mike went when he left the trail. This means that they will have
to search a circular area based on how fast Mike walks. He has been missing for 12 hours and his estimated
speed is 4 km per hour. Determine the surface area of the circle to be searched.
Answers
Answer:
Step-by-step explanation:
Distance traveled by Mike in 12 hours = 4 * 12 = 48 km
This will become the radius of the circle
r = 48 km
Area of the circle to be searched = πr²
= 3.14 * 48 * 48
= 7234.56 square km
Jacqueline. Harry, and Stanley bought a pizza pie to share for dinner. Harry ate
of the pie, and then Jacqueline ate of what was left. After Jacqueline
finished, Stanley ate of what was left of the pic. What fractional part of the
pizza pie was left after Stanley finished eating?
Answers
Answer:
1/6
Step-by-step explanation:
Harry 1x1/2=1/2
Jacqueline 1/2x1/2=1/4
Stanley 1/3x1/4=1/12
1-1/2-1/4-1/12=
12/12-6/12-3/12-1/12=
2/12 or 1/6
A number is no more than five. How would you graph this inequality?
Answers
Answer:
X<=5 and you would graph it with a closed dot on five and an arrow going left of it.
Step-by-step explanation:
Answer:
[tex]a<5\\\\a\in R[/tex]
Step-by-step explanation:
In several ways, for example, let:
[tex]a[/tex], an arbitrary constant, where:
[tex]a\in R[/tex]
Besides:
[tex]a< 5[/tex]
Because the number can be greater than five.
Therefore, the graph, would be all number over the interval:
[tex](-\infty, 5)[/tex]
As you can see, all numbers bellow the line [tex]y=5[/tex].
......................................
Answers
Answer:
Towards the left
Step-by-step explanation:
Which point is the image of R? Choose one answer: A B C D
Answers
Answer:
point D
Step-by-step explanation:
moving 270 degrees clockwise from point R would result in the point being in quadrant I
point D is the only point in quadrant I
order the following values from least to greatest: 22.4, -28, 27, -17
Answers
Answer:
asDawas
Step-by-step explanation:
sadasda
Answer: -28, -17, 22.4, 27
hope this helps
What is the slope of the line shown on the graph? A)3 B)1/3 C)−3 D)−1/3
Answers
Answer:
1/3
Step-by-step explanation:
The slope of the line is found by
m = (y2-y1)/(x2-x1)
we have two point ( 0,0) and ( 3,1)
= ( 1-0)/( 3-0)
= 1/3
Please help..........
Answers
See the attached picture:
Which of the following equations is of a parabola with a vertex at (0, 6)?
O y= (x - 6)2
O y= (x + 6)2
O y=x2-6
Oy= x2 + 6
Answers
Answer:
y= x^2 + 6
Step-by-step explanation:
y= x2 + 6 (which should be written as y= x^2 + 6) has the form y - k = a(x - h)^2. For y= x^2 + 6, h = 0 and k = 6. Thus the vertex is (0, 6)
I need help doing this can anyone help?
Answers
You posted a lot of questions. I'll do the first four problems to get you started.
============================
Problem 1
This sequence is arithmetic because we add the same amount (4) each time to get the next term. The first term is -2. The first five terms are: -2, 2, 6, 10, 14
============================
Problem 2
This sequence is geometric. We multiply each term by 1/4 to get the next term. We start with 8 as the first term. The first five terms are 8, 2, 1/2, 1/8, 1/32.
============================
Problem 3
Similar to problem 1. This time we're adding -19 to each term to get the next one. The starting term is -6. This sequence is arithmetic and the first five terms are -6, -25, -44, -63, -82
============================
Problem 4
Similar to problem 2. This sequence is geometric with common ratio 2/3. First term is 6. The first five terms are 6, 4, 8/3, 16/9, 32/27
is this right?? please help!
Answers
Answer:
6 < x < 8
Step-by-step explanation:
The compound inequality in this instance represent the "and" condition, not the "or" condition.* We might solve it like this.
-47 > 1 -8x > -63 . . . . given
Multiply by -1:
47 < -1 +8x < 63
Add 1:
48 < 8x < 64
Divide by 8:
6 < x < 8
______
* You can tell this is the case by looking at the ends of the given statement:
-47 > -63 . . . . a true statement, so the solution set will be an intersection, not a union.
Line
A.
C.
D.
B.
Defined
Postulates
Theorems
Undefined
Terms
Answers
Answer: Undefined
Step-by-step explanation:
In geometry there are three undefined terms that we use to define other terms:
Point → In geometry a point has a location but no dimension.Plane → A plane extends is a 2-dimensional surface that extends infinitely on both sides. Line → A line is a one-dimensional undefined figure that extends infinitely in both the directions. It has length but has no width.Hence, the correct option is "Undefined".
Put the steps of storm formation in the correct order.
Ice and water droplets fall
The Sun heats the
Water vapor condenses
Water droplets freeze.
Warm air rises into the
to the surface
surface
upper atmosphere.
Answers
Answer:
The Sun heats the surface
Warm air rises into the upper atmosphere
Water Vapors condenses to the surface
Water droplets freeze
Ice and water droplets fall.
Step-by-step explanation:
Clouds are formed when invisible water vapors condenses into air and droplets or ice crystals are formed. Water enters into the air through evaporation process. The are few necessary steps for storm formation. The sun heats the surface of the earth and warm air rises into the upper most atmosphere where temperature is lowered. Water vapors condenses from the surface and rises to the upper atmosphere water droplets freeze in upper atmosphere because of reduce temperature and then ice or water droplets fall.
Answer:
The Sun heats the surface
Warm air rises into the upper atmosphere
Water Vapors condenses to the surface
Water droplets freeze
Step-by-step explanation:
Trust me on this, also can I have brainiest please?
Hope you do well! :D
Terry bought some gum and candy. The number of packages of chewing gum was one more than the number of mints. The number of mints was three times the number of candy bars. If gum was 6 cents a package, mints were 3 cents each, and candy bars were 10 cents each, how many of each did he get for 80 cents?
Answers
Answer:
2 Candy bars
6 Mints
7 Gum
Step-by-step explanation:
Candy bars=x
mints=3x
gum=3x+1
10(x)+3(3x)+6(3x+1)=80
10x+9x+18x+6=80
37x=80-6
37x=74
x=2
SO:
cand bars = x = 2
mints = 3x = 6
gum = 3x+1 = 7
Answer:
2 candy bars, 6 mints, and 7 packages of gumm
Step-by-step explanation:
Mandy works construction. Shes knows that a 5 meter long metal bar has a mass of 40 kg.Mandy wants to figure out the mass (w) of a bar made out of the same metal that is 3 meters long and the same thickness.
Answers
Answer:
24 kg
Step-by-step explanation:
40/5 = 8 and 3x8 = 24
Answer:
24 kg
Step-by-step explanation:
[tex]\frac{5}{40} =\frac{3}{w} \\5w=120\\w=\frac{120}{5}=24[/tex]
AssAssessment captures blank growth
Answers
What value, written as a decimal, should Lena use as the common ratio?
Answers
Answer:
an=1*2.5^(n-1)
=2.5^(n-1)
Step-by-step explanation:
Complete question below:
What value, written as a decimal, should Lena use as the common ratio? Lena is asked to write an explicit formula for the graphed geometric sequence. On a coordinate plane, 3 points are plotted. The points are (1, 1), (2, 2.5), (3, 6.25).
Solution
Point (1, 1), (2, 2.5), (3, 6.25).
a=1
ar=2.5
ar^2=6.25
From ar and ar^2
r=6.25/2.5
=2.5
r=2.5
an=ar^(n-1)
Therefore, the explicit formula is
an=1*2.5^(n-1)
=2.5^(n-1)
Alice is building a caterpillar habitat for some caterpillars she found in her back yard. She plans to cover all sides of the habitat with screen so the caterpillars get plenty of fresh air. What is the total amount of screen that Alice will need for her habitat? Give an exact answer (do not round).
Answers
Answer:
SA = 3.04m²
Step-by-step explanation:
SA = 2 x ( Length x Width + Width x Height + Length x Height )
SA = 2 x ( 0.4 x 1 + 0.4 x 0.8 + 1 x 0.8 )
SA = 2 x ( 0.4 + 0.32 +0.8)
SA = 2 x 1.52
SA = 3.04 m²
I wish this could help you !
Answer:
3.04 is the correct answer =)
Step-by-step explanation:
In Mr. Rojo’s art class, students are asked to create an orange background for their new painting. They mixed red paint and yellow paint to create a shade of orange. The table shows the number of pints of red paint, y, and yellow paint, x, different students used to create the orange color. Pints of Yellow (x) Pints of Red (y) 2 3 3 4.5 4 6 6 9 Identify the equation that relates the number of pints of red and yellow paint used. x=1.5y y=1.5x y=4.5x x=4.5y
Answers
Answer:
y = 1.5x.
Step-by-step explanation:
2 yellow (x) 3 red (y) (3 /2 = 1.5)
3 yellow 4.5 red (1.5)
4 yellow 6 red (1.5)
6 yellow 9 red (1.5)
So the equation is
y = 1.5x
Find the path of the numbers from the upper left corner to the bottom right corner. The sum of the numbers must be equal to the number at the exit arrow. You are allowed to move either down or to the right only.
Answers
Answer:
8, 11, 19, 1, 6, 18, 3
Step-by-step explanation:
8+11+19+1+6+18+3=66
Translate the following into an algebraic expression: A number is 30% of 20% of the number x.
Answers
Answer:
.06x
Step-by-step explanation:
So 20 percent of x has to first be represented. So would do .2x. So then we have to find 30% of that number. So we multiply .2x*.3 and we get 0.06x.
I believe this is correct but tell me if I'm wrong
Answer:
0.06x
Step-by-step explanation:
.2x*.3=0.06x
solve as many as you can please
Answers
Answer:
1. 5²
2. 6p⁵
3. y⁶
4. 1/5w²
5. n⁶/9p⁷
7. 12²
8. 2/5
30. Three apples plus twice as many pears add up to one-half the number of grapes in a fruit basket. How many grapes are
in the basket?
(A) 8
(B) 18
c.28
d.38
Answers
Answer:
3 + 6 = 1/2(#grapes)
3 + 6 = 9
9 = 1/2(#grapes)
2(9) = 1(#grapes)
18 = # of grapes
Step-by-step explanation:
-p + 3/5a -1/10q + 1/9-1/9p+2 1/3p
Answers
Step-by-step explanation:
1.) first simplify or combine like terms.[tex]\frac{3a}{5} -p-\frac{p}{9}+\frac{7p}{3} -\frac{q}{10}+\frac{1}{9}[/tex]
2.) then condense. [tex]\frac{3a}{5} +\frac{11p}{9}-\frac{q}{10}+\frac{1}{9}[/tex].