How can you tell from the equation of a rational function if the function has a hole in the graph ( a removable discontinuity) at x, rather than a vertical asymptote? Give an example
Answers
Consider that,
x^2+4x+4 = (x+2)(x+2)
x^2+7x+10 = (x+2)(x+5)
Dividing those expressions leads to
(x^2+4x+4)/(x^2+7x+10) = (x+2)/(x+5)
The intermediate step that happened is that we have (x+2)(x+2) all over (x+2)(x+5), then we have a pair of (x+2) terms cancel as the diagram indicates (see below). This is where the removable discontinuity happens. Specifically when x = -2. Plugging x = -2 into (x+2)/(x+5) produces an output, but it doesn't do the same for the original ratio of quadratics. So we must remove x = -2 from the domain.
Related Questions
Triangle EFG is dilated by a scale factor of one half centered at (1, 1) to create triangle E'F'G'. Which statement is true about the dilation?
Answers
Answer:
A triangle is dilated by scale factor of 1/5
Step-by-step explanation:
A triangle has three sides. All the corresponding angles of triangle must be congruent. When the triangle is dilated it is rotated 90 degrees clockwise about its origin. The shape of the triangle will not change due to rotation of dilation.
A jug contains 1560 no of Apple juice in it. How many will each child get if 12 children share juice equally?
Answers
Answer:
130
Step-by-step explanation:
total apple juice= 1560
if 12 children share juice equally
they get
=1560/12
= 130
You are going to take a 10-question True/False test. How many ways can this test be answered if leaving questions blank is a viable option for each question?
Answers
Answer:
There are 59,049 different ways of answering the exam.
Step-by-step explanation:
The first thing we need to count is the total number of selections, then we need to count the number of options for each one of these selections. The total number of combinations will be equal to the product between all the numbers of options.
Here, the selections are each one of the 10 questions, so we have 10 selections.
And each one of these selections has 3 options (true, false, blank)
So, we have 10 selections with 3 options each, then the total number of combinations will be:
C = 3*3*3*3*3*3*3*3*3*3 = 3^10
C = 59,049
There are 59,049 different ways of answering the exam.
X + 2x - 7/4=1 - x/2 -x ayudaaaaa
Answers
Answer:
|x| - |-x| = 0
Step-by-step explanation:
Answer:
no se
Step-by-step explanation:
no se
BRAIN TO CORRECT ANSWER!!
A clothing store conducts a survey to determine customer satisfaction.
Which of these methods will produce the most representative sample of the population of store customers?
A. Survey all customers as they arrive at the store on a Monday.
B. Survey all customers who purchase shoes
C. Survey every 10th customer to enter the store.
D. Survey all customers who leave the store without making a purchase
Answers
Answer:
C
Step-by-step explanation:
This method is the best because it will survey the customers under one condition : every 10. If the store gets a lot of customers, then this should be easier to do. The rest are mostly dependent on what they do and that influences the survey. However, C makes it so that every 10 people are surveyed.
Answer:
A isnt the correct answer. B doesnt seem reasonable because its one specific item. D means they arent exactly a customer since they didnt buy anything therefore the answer would be C
C is your answer.
not sure about it tho but its what i would put
DUS is a 30°-60°-90° triangle with short leg SU. If SU = x, determine the
length of the long leg and the length of the hypotenuse.
Answers
Answer:
SD = 2x
UD = x[tex]\sqrt{3}[/tex]
Step-by-step explanation:
The hypotenuse of a 30-60-90 triangle is 2 times the length of the shorter leg.
SU is the shorter leg = x
So, SD = 2x
The longer leg of a 30-60-90 triangle is [tex]\sqrt{3}[/tex] times the shorter leg.
So, UD = x[tex]\sqrt{3}[/tex]
Answer:
Below in bold.
Step-by-step explanation:
In a 30-60-90 triangle the sides are in the ratio 1:√3:2 so if the shortest side SU = x then the long leg = √3x and the hypotenuse = 2x.
Simplify: (-7x - 5) - (-9x2 + 8x + 7). Choose the standard form of the answer.
Answers
Answer:
-15x - 12 + 9x^2
Step-by-step explanation:
(-7x - 5) - (-9x^2 + 8x + 7)
-7x - 5 + 9x^2 - 8x -7
-15x - 12 +9x^2
what is that 2 by the 9x
We will simplify the given expression to get:
9x^2 - 15x - 12
How to simplify the given expression?
Here we have the expression:
(-7x - 5) - (-9x^2 + 8x + 7)
To simplify it, we just perform the difference between the polynomials:
-7x - 5 + 9x^2 - 8x - 7
Now we group terms with correspondent powers of x:
9x^2 + (-7x - 8x) + (-5 - 7)
Now we simplify this:
9x^2 - 15x - 12
This is the quadratic equation simplified.
If you want to know more about simplification, you can read:
https://brainly.com/question/723406
list the planets in order from least to greatest
Only give me an answer if you know the answer please
Answers
Answer:
Uranus, Neptune, Saturn, Jupiter
Step-by-step explanation:
l
How would I be able to solve for m
Answers
Answer:
131
Step-by-step explanation:
180-49= 131 therefore the answer is 131
Phillip helps his neighbors with various jobs. The table shows some jobs he did, the number
of hours he worked, and the amount he was paid. Is Phillip's pay proportional to the number
of hours he works?
Use the drop-down menus to explain your answer.
Job
Fixing a Fence
Pulling Weeds
Painting a Garage
Mowing a Yard
Hours Worked
5
4.5
6
1.5
Amount Paid ($)
75
54
78
18
Answers
Answer:
Is and his pay is always a multiple of 3
Step-by-step explanation:
I did the i-Ready
Answer: his pay is always a multiple of 3
Step-by-step explanation:
Help need help cause I don’t understand stand
Answers
Answer:
A
Step-by-step explanation:
just cut off one side and add it to the other thats how you solve paralellograms
Answer: 6 x 7?
Step-by-step explanation: To find the area of a parallelogram it's base times height.
find the length of CD.
Answers
5. Subtract using the zero principle.
b) (2y- * - 3y) - (-2x + y)
Answers
Answer:
4x + 2y
Step-by-step explanation:
( 2x - - 3y ) - ( - 2x + y )
→ Simplify
2x + 3y + 2x - y
→ Collect x and y terms
4x + 2y
Alan and Margot each drive from City A to City B, a distance of 147 miles. They take the same route and drive at constant speeds. Alan begins driving at 1:40 p.m. and arrives at City B at 4:15 p.m. Margot’s trip from City A to City B can be described with the equation y = 64x, where y is the distance traveled in miles and x is the time in minutes spent traveling. Who gets from City A to City B faster?
Answers
Answer:
Margot gets from A to B faster
Step-by-step explanation:
Alan takes 2 hr and 35 min = 2. 58... hr
Margot takes 147/64 hr = 2.296.. hr
3x+5(2+x)=4x-7 help me out here?
Answers
Answer:
x = -17/4
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightDistributive Property
Equality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
Terms/CoefficientsStep-by-step explanation:
Step 1: Define
Identify
3x + 5(2 + x) = 4x - 7
Step 2: Solve for x
[Distributive Property] Distribute 5: 3x + 10 + 5x = 4x - 7[Addition] Combine like terms: 8x + 10 = 4x - 7[Subtraction Property of Equality] Subtract 4x on both sides: 4x + 10 = -7[Subtraction Property of Equality] Subtract 10 on both sides: 4x = -17[Division Property of Equality] Divide 4 on both sides: x = -17/4Answer:
x=[tex]\frac{-17}{4}[/tex]
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
3x+5(2+x)=4x−7
3x+(5)(2)+(5)(x)=4x+−7(Distribute)
3x+10+5x=4x+−7
(3x+5x)+(10)=4x−7(Combine Like Terms)
8x+10=4x−7
8x+10=4x−7
Step 2: Subtract 4x from both sides.
8x+10−4x=4x−7−4x
4x+10=−7
Step 3: Subtract 10 from both sides.
4x+10−10=−7−10
4x=−17
Step 4: Divide both sides by 4.
[tex]\frac{4x}{4}[/tex]=[tex]\frac{-17}{4}[/tex]
x=[tex]\frac{-17}{4}[/tex]
PLEASE HELP!!!
The club will base its decision about whether to increase the budget for the indoor rock climbing facility on
the analysis of its usage. The decision to increase the budget will depend on whether members are using
the indoor facility at least two times a week. Use the best measure of center for both of the original data
sets to determine whether the club should increase the budget. Assume there are four weeks in a month.
If you think the data is inconclusive, explain why.
Answers
Answer:
Yes, they should increase the budget, because both 8 (Manuel) and 9 (Gretchen) are at least 8. 8 times per month is equivalent to 2 times per week.
Step-by-step explanation:
Answer from Plato
Hence, the answer is Plato.
What is the measurement?
Measurement is the process of finding a number that shows the amount of something. Time the ongoing sequence of events is time. We can measure time in seconds, minutes, hours, days, weeks, months, and years.
Here given that,
The club will base its decision about whether to increase the budget for the indoor rock climbing facility on
the analysis of its usage. The decision to increase the budget will depend on whether members are using
the indoor facility at least two times a week. Use the best measure of center for both of the original data
sets to determine whether the club should increase the budget.
As per this we get that,
Yes, they can increase the budget, because both Manuel has [tex]8[/tex] and Gretchen [tex]9[/tex] are at least [tex]8[/tex] and [tex]8[/tex] times per month is equivalent to the two times per week.
Hence, the answer is Plato.
To know more about the measurement
https://brainly.com/question/18076822
#SPJ2
PLS HELPP GUYS !!!! in a hurry !!!!!!!
Answers
Answer:
A because it uses all of domains
Step-by-step explanation:
(1, -3) and (0,-1)
Equation: y=-2x-1
Slope:-2
Y-intercept:___?
Answers
Answer:
-1
Step-by-step explanation:
Solve 10^(x + 2) = 34
Answers
Answer:
-.4685
Step-by-step explanation:
[tex]x^y=z\\y=log_zy\\10^{x+2}=34\\x+2=log_{10}34\\x+2=log34\\x+2=1.531478917\\x=-.468521083[/tex]
What is simplifying? I honestly know what it is, but I forgot the definition.
Answers
Guys I need help on all three please
Answers
Answer:
graph 1 proportional
graph 2&3 is non proportional
i think
An example for my question before
Answers
Answer:
angle c is 82 degree because 82 degree and angle c are corresponding angles.
Step-by-step explanation:
note :corredponding angles are always equal.
the sum of co interior angle id 180 degree.alternate angle are equalthe sum of co exterior angle is 180 degreethe sum of alternate exterior angle is 180 degree………………………………………………….
Answers
Answer:
Tan(Ф) = [tex]\frac{12}{5}[/tex]
Step-by-step explanation:
Tan(Ф) = [tex]\frac{opposite}{adjacent}[/tex]
Tan(Ф) = [tex]\frac{12}{5}[/tex]
Hope this helps!
?????????????????????????????????????????????????
Answers
Answer:
a) 0
b) -5
Step-by-step explanation:
We want to find f(x) = -4
This means find the value of x where y=-4
The value of x where y=-4 is x=0
Then find f(2)
This means find the value of y when x =2
The value of y when x=2 is -5
NO LINKS PLEASE
EXPLANATION REQUIRED
I WILL GIVE BRAINLIEST
DONT MINF MY PRO CROPPING. DEFF.
ALSO ITS NOT C
Answers
Answer:
B is the correct answer
Step-by-step explanation:
Subtract area of triangle from total area: 30 - 14 = 16Since the figure is a square, all the sides are equal. Therefore, we need to find the square root of 16: √16 = 4All the sides of the square are 4 cm longTo check, reverse application:4 x 4 = 1616 + 14 = 30What is the quotient of 6.58* 10^6 and 4.7×10^3
expressed in scientific notation?
Answers
Answer:
1.4 · 10³
Step-by-step explanation:
6.58 · [tex]10^{6}[/tex] ÷ 4.7 · 10³
6.58 ÷ 4.7 = 1.4
[tex]10^{6}[/tex] - 10³ = 10³
1.4 · 10³
Answer:
3.0926 x 10^10
Step-by-step explanation:
If the data represented by the graph is normally distributed, what are the endpoints of the middle 68% of the data?
Answers
Answer: -1.8 and 11.4
Step-by-step explanation:
Trust me or don’t lol
Answer:
D. 2.6 and 7
Step-by-step explanation:
Plato course, did the test
28.
If 30% of a number is 15, what is the number?
No links!!
I will report if say something wrong.
Will give brainlest
Answers
Answer:
50
Step-by-step explanation:
30% * n = 15
Change to decimal form
.30 *n = 15
Divide each side by .30
.30n/.30 = 15/.30
n =50
The number is 50
A school pays $1,825 for 150 shirts. This includes the $25 flat-rate shipping cost.
a. What equation models the total cost as a function of the number of T-shirts
ordered?
b. What does each variable represent?
c. What are the initial value and rate of change of the function? What does each
one represent?
Answers
Answer:
a)
We know that the total cost for the 150 shirts (plus a flat-rate of $25) is $1,825.
First, let's find how much costs each shirt.
First, the total cost of the shirts alone (neglecting the flat-rate) is:
$1,825 - $25 = $1,800
Then each shirt costs equal to the quotient of the cost and the number of shirts:
$1,800/150 = $12
Each shirt costs $12.
Then if you order T shirts, the total cost will be the flat-rate of $25 plus T times $12. The equation is:
C(T) = $25 + T*$12
b) C represents the cost
T represents the number of shirts ordered.
c) The initial value is the constant value, in this case, is $25
The rate of change is the coefficient that multiplies the independent variable (T), in the equation the rate of change is $12.
Enter an estimate. Round each mixed number to the nearest whole in your estimate
Answers
Answer:
1. 4-2=2
2.2 10/21
Step-by-step explanation: