The graph has no vertical asymptote
===========================================================
Explanation:
Let's simplify the function by factoring each piece.
[tex]f(x) = \frac{x^2-64}{8x-64}\\\\f(x) = \frac{(x-8)(x+8)}{8x-64}\\\\f(x) = \frac{(x-8)(x+8)}{8(x-8)}\\\\f(x) = \frac{x+8}{8}\\\\[/tex]
In the 2nd step, I used the difference of squares rule to factor the numerator. In the 4th step, the (x-8) terms cancel.
The simplified version doesn't have any variables in the denominator. This indicates the denominator is always 8, and never 0. So it's impossible to divide by zero in this simplified form. Consequently it means this graph has no vertical asymptotes.
However, there is a hole at x = 8 because this input causes a division by zero error in the original non-simplified function. Why? Because the calculator will use PEMDAS to evaluate the expression after replacing every copy of x with 8. It likely won't attempt to simplify like shown in the steps above. This is what causes the hole at x = 8.
The value x = -8 is perfectly fine in either the original function or the simplified one. It doesn't cause the denominator to be zero.
A stainless steel patio heater is a square pyramid. The length of one side of the base is 23.4 in. The
slant height of the pyramid is 93.2 in. What is the height of the pyramid?
The height of the pyramid is aboutin.
(Round to one decimal place as needed.)
The height of the square-based pyramid is 91.72 in if the length of one side of the base is 23.4 in.
What is a square pyramid?In geometry, it is defined as the shape having a square base with equal sides length and all the vertex of the square's joints at the top, which is perpendicular to the center of the square.
We have a square pyramid.
Length of the pyramid = 23.4 in
The slant height of the pyramid = 93.2 in
From the figure:
Base length CB = DC = 23.4 in
In a right-angled triangle, BCD
Applying Pythagoras theorem:
DC² + CB² = DB²
23.4² + 23.4² = DB²
DB = 33.092 in
OB = (1/2)DB
OB = (1/2)33.092 = 16.546 in
In the right-angle triangle AOB, again applying Pythagoras theorem:
AO² + OB² = AB²
h² + 16.546² = 93.2²
AO = h (height of the square pyramid)
AB = slant height = 93.2 in
After calculating, we get:
h = 91.719 ≈ 91.72 in
Thus, the height of the square-based pyramid is 91.72 in if the length of one side of the base is 23.4 in.
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HELP FOR BRAINLIEST & 100
please
Answer:
Hi,
Step-by-step explanation:
1) PC=PD since PC*PA=PD*PB
2)25 since PO²=PA²+r² PO=14.5, PB=14.5+10.5=25
3)
6²=3*x==> x=12
What is the conditional probability that you will randomly select a green box if there are 6,000 boxes. Of those boxes 2,000 are green.
Select one:
a.
1/6
b.
1/5
c.
2/6
d.
1/3
The conditional probability that you will randomly select a green box is 1 / 3.
What is the probability?Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
Probability of selecting a green box = number of green boxes / total number of boxes
2000 / 6000 = 1/3
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For the function f(x) = 3x + 7, find the following:
a) f(2)=
c) f(x) = 8
b) f(-3) =
d) f(x) = 10
Answer:
a) 13
b) 1/3
c) -2
d) 1
Step-by-step explanation:
This is quite simple if you look at it from a different perspective. Imagine that when it says "f(2)" That you are plugging the number 2 in for every x on the right side of the equation:
For example:
f(x) = 3x + 7
f(2) = 3(2) + 7
f(2) = 6 + 7
f(2) = 13
________
f(-3) = 3x + 7
f(-3) = 3(-3) + 7
f(-3) = -9 + 7
f(-3) = 7 - 9 (This is just for those that hate negative values. You can rearrange the values as long as their sign is the same when you do move them. Ex: -14 + 6 - 4 + 9 == 9 + 6 - 14 - 4. I hope that makes sense.
f(-3) = -2
The other way is quite simple as well, if you look at it from a different perspective. Imagine that when it says "f(x) = 8" that you are changing the f(x) to the number 8:
For example:
f(x) = 8
f(x) = 3x + 7
8 = 3x + 7
8 - 7 = 3x
1 = 3x
x = 1/3
f(x)= 10
f(x) = 3x + 7
10 = 3x + 7
10 - 7 = 3x
3 = 3x
3/3 = x
1 = x
I hope this helps!
2. Find the area and the perimeter of these figures.
Answer:
A = 16.78 km squared
P = 14.28 km
Step-by-step explanation:
Area of triangle: (5*4)/2 = 10
Area of Semi-circle: (πr2)/2 = 6.28
Area of figure: 10 + 6.28 = 16.78
Perimeter: 5 + 3 + (2πr)/2 = 8 + (2π) = 8 + 6.28 = 14.28
Hope this helps!
Answer:
i don't know the perimeter but I do know the area hope this helps if it doesn't I am sorry
Ok for area for a triangle is 1/2 ×base×height and for a semi circle it is pi (π)or 3.14 or 22/7×rsquare with is radius x radius
Step-by-step explanation:
lets start with the triangle so it is 1/2×3/1×5/1×4/1 =30/1 =30sqkm
now for the semi circle it is 22/7×2/1×2/1=88/7=12.5÷2=6.2 why is 4/1 turned into 2/1 it is because you are finding area and 4 is the diameter but we need radius so the radius is half of the diameter
so 30+6.2=36.2kmsq
help me pleaseeeeeeeeeeeeeee
Answer:
C
Step-by-step explanation:
Evaluating the options :
Option A
⇒ 5/2x + 7/2 = 3/4x + 14
⇒ 2.5x - 0.75x = 14 - 3.5
⇒ 1.75x = 10.5
⇒ x = 6
⇒ No ×
===========================================================
Option B
⇒ 5/4x - 9 = 3/2x - 12
⇒ 1.5x - 1.25x = -9 + 12
⇒ 0.25x = 3
⇒ x = 12
⇒ No ×
=========================================================
Option C
⇒ 5/4x - 2 = 3/2x - 4
⇒ 1.5x - 1.25x = -2 + 4
⇒ 0.25x = 2
⇒ x = 8
⇒ Yes √
C is the right answer.
PLEASE HELP ILL LIKE AND ITS WORTH 20 points !!
Answer:
EG=
[tex] \frac{28 }{ \sqrt{3} } [/tex]
EF=
[tex] \frac{56}{ \sqrt{3} } [/tex]
Step-by-step explanation:
You have to memories Trigonometric ratios of 60
HELPP PLEASE ASAP Use the Pythagorean theorem to find the missing length in the right triangle
Answer:
c = 10
Step-by-step explanation:
The pythagoras theorem :
a² + b² = c²
a = 6 and b = 8
6² + 8² = c²
36+64 = c²
100 = c²
c = √100
c= 10
Hope this helped and brainliest please
The graph shows the probability distribution of a random variable.
What is the value of P(4≤X≤8)?
0.40
0.45
0.50
0.55
who was regarded as the father of geomotry
Answer:Euclid
Step-by-step explanation:
Euclid was an ancient Greek mathematician in Alexandria, Egypt. Due to his groundbreaking work in math, he is often referred to as the 'Father of Geometry'. Euclid's most well-known collection of works, called Elements, outlines some of the most fundamental principles of geometry.
Answer:
Euclid
I hope this helps you!
calculate the area of this trapezium:
b = 15cm
h = 6cm
top part = 9cm
PLEASE I NEED THIS ASAP !!!
Answer:
72
Step-by-step explanation:
hopefully you dont need work since you need it asap :(
Answer:
Step-by-step explanation:
1/2 (a+b) x h
a+b = 9+15= 24 / 2 = 12
12 x 6 = 72cm2
The hour and minute hand of a clock form an angle that constantly changes. During each hour of the day,the clock hands will form right, acute and obtuse angles. Assume the hour hand points directly at the hour.Write a time of day when the two clock hands form each tyep of angle
The each type of angle are discussed below
What is angle?An angle is formed when two straight lines or rays meet at a common endpoint. The common point of contact is called the vertex of an angle.
If the hours hand point to the hour 1 and minute hand at 12 then
angle will be acute.
If the hours hand point to the hour 2 and minute hand at 12 then
angle will be acute.
If the hours hand point to the hour 3 and minute hand at 12 then
angle will be right angle .
If the hours hand point to the hour 4 and minute hand at 12 then
angle will be obtuse.
If the hours hand point to the hour 5 and minute hand at 12 then
angle will be obtuse.
If the hours hand point to the hour 6 and minute hand at 12 then
angle will be straight angle .
If the hours hand point to the hour 7 and minute hand at 12 then
angle will be reflex.
If the hours hand point to the hour 8 and minute hand at 12 then
angle will be reflex.
If the hours hand point to the hour 9 and minute hand at 12 then
angle will be reflex.
If the hours hand point to the hour 10 and minute hand at 12 then
angle will be reflex.
If the hours hand point to the hour 11 and minute hand at 12 then
angle will be reflex.
If the hours hand point to the hour 12 and minute hand at 12 then
angle will be Complete angle.
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What does X= please help
Answer:
27
Step-by-step explanation:
The first angle you get with 180-61 = 119
The second angle you get by the rules of the circle which is 68/2 = 32
And finally X= 180 - 119 - 32 = 27
There are 760 calculators,6 were defective what is the probability that a calculator chosen at random will be defective
Answer:
Unlikely
Step-by-step explanation:
well if you want the chance it’s unlikely. This is because you only have 6 defective calculators and the rest or majority are not defective.
The arm span and foot length were both measured (in centimeters) for each of 20 students in a biology class. The computer output displays the regression analysis.
Which of the following is the best interpretation of the standard deviation of the residuals?
The typical arm span is 161 centimeters.
The typical foot length is 16.1 centimeters.
The typical distance between the observed and predicted arm spans is 1.61 centimeters.
The typical distance between the observed and predicted foot lengths is 1.61 centimeters.
Answer:
D
Step-by-step explanation:
The correct answer should have a 63%.
It's probably D. The terminology is a little confusing.
The equation of the output looks like:
-7.611 + .186(x) = y
x --> Arm span
y --> Foot span
The linear relationship is formed with the armspan.
which of the following demonstrates how the 20 is calculated using the combination pattern
The combination expression that demonstrates how the 20 is calculated using the combination pattern is 6C3
Permutation and CombinationWhile combination has to do with selection, permutation has to do with arrangement.
According to the combination rule
nCr = n!/(n-r)!r!
The expression that gives the result of 20 is expressed below;
6C3 = 6!/(6-3)!3!
6C3 = 6!/3!3!
6C3 = 6!/6*6
6C3 = 720/36
6C3 =20
Hence the combination expression that demonstrates how the 20 is calculated using the combination pattern is 6C3
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Sam Whittington was the fastest cyclist on record (in 2009) with a speed of 37.5 m/s. Calculate the time taken in hours to cycle 53.2 km.
Answer:
39.407 hour
Step-by-step explanation:
T = D/S
37.5 m/s in km/h
=375×18/10×5
=135 km/h
T = ABCDEFGHIOJKLMNOPQRSTUVWXYZ
If f(x) = x³ +7x²-x and g(x)=x²-3, What is the degree of g(f(x))?
a)2
b)3
c)6
d)8
Answer:
c) 6
Step-by-step explanation:
Given :
⇒ f(x) = x³ + 7x² - x
⇒ g(x) = x² - 3
===============================================================
Finding the degree of g(f(x)) :
⇒ Degree of f(x) = 3
⇒ Degree of g(x) = 2
⇒ Therefore, degree of g(f(x)) = degree of f(x) × degree of g(x)
⇒ Degree of g(f(x)) = 3 × 2
⇒ Degree of g(f(x)) = 6
Degree of g(f(x))
Use Pascal's law
3×26Option C
10 identical spheres of radius 7cm are to be painted. What is the total area of surface to be painted
Answer:
Surface area = 4 π r2 square units
Step-by-step explanation:
35. the set, s consists of 900,000,000 whole numbers, each being the same number of digits long. howmany digits long is a number from s? (hint: use the fact that a whole number cannot start with the digit 0.)
Answer:
9 digit longLet the number of digits be n and the number of elements in set be s.
When n = 1The set contains 1-digit numbers, 1 through 9,The set consists of 10 - 1 = 9 numbers.When n = 2The set contains 2-digit numbers, 10 through 99,The set contains 100 - 10 = 90 numbers.When n = 3The set contains 3-digit numbers, 100 through 999,The set contains 1000 - 100 = 900 numbers.The pattern we see helps us determine the relationship between s and n as follows.
When set contains n-digit numbers, the set contains:
s = 10ⁿ - 10ⁿ⁻¹ = 10ⁿ⁻¹(10 - 1) = 9*10ⁿ⁻¹ elementsWe have s known, substitute it into equation above and solve for n:
900000000 = 9*10ⁿ¹100000000 = 10ⁿ⁻¹10⁸ = 10ⁿ⁻¹n - 1 = 8n = 9The numbers in the set s are 9-digit long.
0.75x + 0.8(x + 10) = 101
what is x
Step-by-step explanation:
0.75x + 0.8(x + 10) = 101
0.75x + 0.8x + 8 = 101
1.55x = 101 - 8
1.55x = 93
x = 93 ÷ 1.55
x = 60
The ratio of the number of squares to the number of triangles in simplest form is
added to make the ratlo of the number of squares to the number of triangles 1: 1 Is
The ratio of the number of squares to the number of triangles is 5 : 2
The number of triangles that should be added to make the ratio is 6
What are the ratios?
Ratio expresses the relationship between two or more numbers. It is the number of times that one value is contained in another number.
Ratio of the number of squares to the number of triangles = number of squares : number of triangles
10 : 4
5 : 2
The number of triangles that should be added to make the ratio 1 : 1 - 10 - 4 = 6
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please explain how to do this
find the angle of this sector.
on the image
Answer:
[tex]\alpha =107.4^{o}[/tex]
Step-by-step explanation:
[tex]15=\frac{\pi (8)\alpha }{180}[/tex]
[tex]\alpha =\frac{(15)(180)}{8\pi } =\frac{2700}{25.13}=107.4[/tex]
Hope this helps
[tex]\textit{arc's length}\\\\ s = \cfrac{\theta \pi r}{180} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ s=15\\ r=8 \end{cases}\implies 15=\cfrac{\theta \pi (8)}{180}\implies 15=\cfrac{2\pi \theta }{45} \\\\\\ 675=2\pi \theta \implies \cfrac{657}{2\pi }=\theta \implies 104.56^o\approx \theta =a[/tex]
Find (fog)(0).
f(x)
=
6x
g(x) = 3x + 6
(fog)(0)
Answer:
12
Step-by-step explanation:
The functions f(x) and g(x) are defined as f(x) = 6x and g(x) = 3x + 6
fog(x) = f(g(x))
= f(3x + 6)
= 6(4x +2)
6 x 4x = 24x
6 x 2 = 12
fog(x) = 24x + 12
(fog)(0) where x = 0
= 24(0) + 12
= 0 + 12
(fog)(0) = 12
Fawzia has an action figure collection of 500 action figures. She keeps 58% of the action figures on her wall. How many action figures does she keep on her wall?
Answer:
290
Step-by-step explanation:
Formula :
Number of action figures on wall = Total number of figures × % of figures on wall
=============================================================
Given :
⇒ Total number of action figures = 500
⇒ % of action figures on wall = 58%
=============================================================
Solving :
⇒ Action figures on wall = 500 × 58%
⇒ Action figures on wall = 500 × 58/100 (all % are ratios of 100%)
⇒ Action figures on wall = 5 × 58
⇒ Action figures on wall = 290
Total action figures
58% of 5000.58(500)2.9(100)290action figuresDone!
What is the (LCD) 1/6and 1/3
Answer:
The LCD of 1/6 and 1/3 is 6.
Step-by-step explanation:
Rewriting input as fractions if necessary:
1/6, 1/3
For the denominators (6, 3) the least common multiple (LCM) is 6.
LCM(6, 3)
Therefore, the least common denominator (LCD) is 6.
Calculations to rewrite the original inputs as equivalent fractions with the LCD:
1/6 = 1/6 × 1/1 = 1/6
1/3 = 1/3 × 2/2 = 2/6
What is Oiler's Number and what equations can you do with it?
The first few digits are: 2.7182818284590452353602874713527 (and more ...) It is often called Euler's number after Leonhard Euler (pronounced "Oiler"). e is an irrational number (it cannot be written as a simple fraction).
can someone help me asap !!
Answer:
The answer is negative. Answer choice B
Step-by-step explanation:
Here is the question:
-3^40(5.6/2.1)
According to order of operations, we must do -3^40 first.
Its important to note that -3^40 is different than (-3)^40. In the problem you specified, the ^40 only applies to the 3, not -3. So, first we do 3^40 which is a huge number. And then, we need to add a negative symbol to that huge number. So now we have a massive negative number multiplied by 5.6/2.1, which is obviously positive. Obviously, a negative number multiplied by a positive number is still negative. Therfore, the answer is negative.
I hope my answer helped you :)
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Write the equation 2x - 4y = 14 in slope-intercept form, and then find the slope and y-intercept.
Answer:
y = 1/2x - 7/2
Slope: 1/2
Y-intercept: (0, -7/2)
Step-by-step explanation:
We know the slope-intercept form of an equation of a line is y = mx + c where slope is m and y-intercept is c.
So, -4y = (-2)x + 14 [divide both sides by -4]
-4/-4 = -2/-4 + 14/-4
y = 1/2 -7/2
Hence the slope = 1/2 and y-intercept = -7/2.