Answers
To find the range of a rational function with a slant asymptote, you first find the asymptote by long division. Then by examining the behavior of the function near the vertical asymptotes by plugging in values, you determine the limits of the range. Generally, the range is all real numbers except where interrupted by the asymptotes.
Explanation:To find the range of a rational function with a slant asymptote, you need to first find the slant asymptote by dividing the numerator by the denominator using long division. When you perform the division, if the degree of the numerator is one more than the degree of the denominator, then the quotient (excluding the remainder) will be the equation for the slant asymptote.
Next, you need to explore the behavior of the function on the left and right of the vertical asymptotes, this is done by substituting values just to the left and right of each vertical asymptote into the function and observing the outputs.
If the function approaches negative infinity, the lower limit of the range will be negative infinity. If the function approaches positive infinity, the upper limit of the range will be positive infinity.
So, the range of the function is typically all real numbers except for the values that are 'cut out' by the asymptotes.
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To determine the range of a rational function with a slant asymptote, graph the function, analyze for vertical and horizontal asymptotes, discontinuities, and observe its long-term behavior relative to the slant asymptote. The range typically includes all real numbers except for values excluded due to vertical asymptotes or holes.
Explanation:To find the range of a rational function with a slant asymptote, follow these steps:
Graph the rational function to observe its behavior and identify the slant asymptote.Analyze the graph to see where the function's output values (y-values) lie as the input (x-values) become very large or very small.Identify any horizontal or vertical asymptotes, as these will also affect the range.Look for any discontinuities such as holes or vertical asymptotes that might create gaps in the range.Combine all this information to determine the set of all possible y-values the function can attain, remembering that the function will approach but not touch the slant asymptote.Considering the slant asymptote, the function will continue to increase or decrease without bound in at least one direction, unless there is another horizontal asymptote. Therefore, the range can often be all real numbers, except possibly excluding specific values or intervals due to vertical asymptotes or holes.
Related Questions
Which symbol can be placed in the box to make this number sentence true?64 (13 – 5) + 8 = 16
a.–
b.÷
c.+
d.×
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Consider the proof.
Given: In △ABC, BD ⊥ AC
Prove: the formula for the law of cosines, a2 = b2 + c2 – 2bccos(A)
Statement
Reason
1. In △ABC, BD ⊥ AC 1. given
2. In △ADB, c2 = x2 + h2 2. Pythagorean thm.
3. In △BDC, a2 = (b – x)2 + h2 3. Pythagorean thm.
4. a2 = b2 – 2bx + x2 + h2 4. prop. of multiplication
5. a2 = b2 – 2bx + c2 5. substitution
6. In △ADB, cos(A) = 6. def. cosine
7. ccos(A) = x 7. mult. prop. of equality
8. a2 = b2 – 2bccos(A) + c2 8. ?
9. a2 = b2 + c2 – 2bccos(A) 9. commutative property
What is the missing reason in Step 8?
a. Pythagorean theorem
b. definition of cosine
c. substitution
d. properties of multiplication
Answers
substituting 2bx for 2bccos(a)
The Law of Cosines is used to find the remaining parts of a triangle when the triangle is not a right triangle and when either the lengths of two sides and the measure of the included angle is known (SAS) or the lengths of the three sides (SSS) are known.
The law of cosine states if a,b,c are the three sides of any triangle then [tex] a^{2} =b^{2} +c^{2} -2bccosA [/tex]
In the above proof in statement 8 the x in statement 5 is replaced by c cos A from statement 6.
Among the given options ,option C holds true as the reason for statement 8.
Melissa and Joey enjoyed dinner at a restaurant. They paid the waiter $100.50 plus a 20% tip. How much did each person pay if they split the total bill in half? $60.30 $70.00 $75.10 $100.10
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the answer is $60.30 because half of 100.50 is 50.25 and the both would pay 10%. 10% of 100.50 is 10.05.
10.05+50.25= 60.30
In the question it is already given that Melissa and Joey would have to share the total bill along with the tips at the resturant during their dinner. The paid the water an amount of $100.50 and additional 20% tip.Firstly we have to find the amount of the tip and then add with the total amount to calculate the total amount paid by both of them.
Amount of tips paid to the waiter = (20/100) * 100.50 dollars
= 2010/100 dollars
= 20.10 dollars
So Melissa and Joey paid $20.10 as tips to the waiter.
Then the total amount paid by both of them = (100.50 + 20.10) dollars
= 120.60 dollars
Then the amount paid by Melissa and Joey = 120.60/2 dollars
= 60.3 dollars.
So Melissa and Joey will individually pay $60.3 each.
Use the Law of Sines to find the missing angle of the triangle. Find measure of angle b given that c=83 , a=44 and that measure of angle a =31 . A=76.3 degrees B= 15.8 degrees C= 72.7 degrees,
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(sinC)/c = (sinA)/a
sincC = c(sinA)/a
C = sin⁻¹(c·sinA / a)
Plugging in numbers:
C = sin⁻¹(83·sin(31) / 44)
= sin⁻¹(0.97155)
= 76.3°
- We know that the sum of the internal angles of a triangle is 180°, therefore:
B = 180 - (A + C)
= 180 - (31 + 76.3)
= 180 - 107.3
= 72.7°
- Therefore the corret answer is C: angle B is 72.7°
Answer:
C : angle B is 72.7°
Step-by-step explanation:
I did the same Assingnment
1.The graph shows the distance a car travels at a constant speed. What is the speed of the car?
2.Write an equation that represents the speed of the car.Question 2 options:
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speed = 40/1 = 40 miles per hour
2)
y = 40x
Why would ww2 make it easier for African nations to gain independence
Answers
After the WW2, Britain had become weaker and its powers had started to decrease. It had lost many of its soldiers and revenues in the world war. Also it needed to focus on the development of its own country now.
so, the rebels in the colonial Africa became stronger than Britishers. So Africans were able to fight back for their freedom and land. Hence, after a while colonial powers left completely from certain parts of Africa.
Sally left a $12.24 tip that represented 17% of her bill. What was the original cost of the meal?
Answers
Answer:
72 is the og
Step-by-step explanation:
72*.17=12.24
The original cost of the meal is $72.
What is percentage?In mathematics →
a percentage is a number or ratio expressed as a fraction of 100.it is often denoted using the percent sign "%".Given is that Sally left a $12.24 tip that represented 17% of her bill.
Assume that the original cost of the meal is $[x]. So, we can write -
12.24 = 17% of {x}
12.24 = (17/100) × {x}
{x} = (12.24 x 100)/17
{x} = 1224/17
{x} = 72
Therefore, the original cost of the meal eaten by Sally is $72.
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What is the perimeter of this tile.
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4 x4 = 16
However this only works if the 2D shape is an equilateral. So this trick only works in certain situations.
Express the polynomial −g + 3g + 2g2 in standard form and then classify it.
Answers plz?
Answers
The first part of the question wants us to put this polynomial in standard form. This means that we put the terms in order of descending degrees and we add like terms...
-g+3g+2g^2
2g+2g^2
2g^2+2g
Because the highest exponent is 2, this is a quadratic polynomial.
I really hope this helps!
Best wishes :)
5. The two trapezoids are similar. Which is a correct proportion for corresponding sides?
A. BA FG
— = —
FE BC
B. BA CD
— = —
FE GD
C. BA AD
— = —
FE GD
D. BA AD
— = —
FE FG
Answers
Answer B
Sara bought a soft drink for 4 dollors and 9 candy bars. she spent a total of 49 dollors. how much did each candy bar cost
Answers
what is the approximate area of a rectangle that is 5ft in length and 15 feet in width
Answers
15*5=75
area is 75 square feet
A = 5 * 15 = 75 in²
Hope this helps :)
Jamie rode her bike home for 5 blocks before realizing she forgot her math book at school and would need it for her homework. She rode back to school, found her math book, and then rode home.
Which graph best represents the scenario described?
Answers
Answer:
Its B
Step-by-step explanation:
I just took the test
Which is a possible number of real roots for a cubic function? Select all that apply.
0
1
2
3
4
what even is this,
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Whatever the highest exponent of the variable is tells us the highest number of roots it can have. It can have that many or fewer but no less than 0.
A machine is made of two parts, gizmos and widgets. the probability that a gizmo is defective is 0.20, and the probability that a widget is defective is .25. if a machine is assembled with one gizmo and one widget, what is the probability that the machine will not have any defective parts?
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Gizmo is defective is 0.20
widget is defective is 0.25
The probability that:
Gizmo is not defective is 1-0.2=0.8
Widget is not defective is 1-0.25=0.75
If the machine is assembled with only one gizmo and one widget, the probability that the will not have any defective part is:
P(Widget is not defective)*P(Gizmo is not defective)
=0.8*0.75
=0.6
The length of a rectangle is 4 cm more than 3 times it’s width. If the area of the rectangle is 15 cm^2, find the width. Use quadratic equations.
Answers
I have another Brainliest
Answers
I need help on the bottom problem
Answers
[tex]\sf\dfrac{96x^3+36x^2+4x-1}{4x}[/tex]
[tex]\sf\dfrac{96x^3}{4x}+\dfrac{36x^2}{4x}+\dfrac{4x}{4x}-\dfrac{1}{4x}[/tex]
Just divide them separately.
96/4 = 24
x^3/x = x^2
So our first term is 24x^2.
36/4 = 9
x^2/x = x
So our second term is 9x.
4x/4x = 1
Anything divided by itself is 1. This is our 3rd term.
-1/4x, we can't simplify this any further, so this is our last term.
So we have:
[tex]\boxed{\sf 24x^2+9x+1-\dfrac{1}{4x}}[/tex]
You only have an error in the last term. It's actually a very good start.
24x^2 + 9x + 1 - 0.25/x is one way to do it. Or you could leave it as 1/4x. It depends on how this is marked. If it is a machine, take your best shot. If you get it wrong, there must be a person somewhere that understands what you meant. Appeal it.
How many odd integers are there between 101 and 199?
Answers
98/2 49
49+ 1=50
there are 50 odd numbers
Answer:
49 odd numbers are there between 101 and 199.
Step-by-step explanation:
Given : 101 and 199.
To find : How many odd integers are there between 101 and 199.
Solution : We have given 101 and 199.
Total number(N) between 101 and 199
N = 199 - 101 = 98
N = 98 .
We can see 98 is even number so, there are half numbers are odd and half numbers are even .
Odd number = [tex]\frac{N}{2}[/tex].
Odd number = [tex]\frac{98}{2}[/tex].
Odd number = 49.
Therefore, 49 odd numbers are there between 101 and 199.
The quality-control department of Starr Communications, a manufacturer of video-game DVDs, has determined from records that 1.5% of DVDs sold have video defects, 0.8% have audio defects, and 0.4% have both audio and video defects. What is the probability that a DVD purchased by a customer a. will have a video or audio defect? b. Will not have a video or audio defect?
Answers
So,
P(A) = 1.5 %
Let B represents the event that DVD has a audio defect.
So,
P(B) = 0.8 %
A ∩ B represents that DVD has both audio and video defect.
So,
P(A∩B) = 0.4%
Part a)
A ∪ B represents that DVD has a video or audio defect.
P(A∪B) = P(A)+P(B)-P(A∩B) = 1.5 + 0.8 - 0.4 = 1.9%
Thus the probability that the DVD purchased by the customer has a video or audio defect is 1.9%.
Part b)
The complement of P(A∩B) will represent the probability that the DVD does not have video or audio defect.
So, the probability that DVD purchased by customer does not have video or audio defect is 1 - 0.4 = 0.96%
Final answer:
The probability that a DVD will have a video or audio defect is 1.9%, calculated using the principle of inclusion-exclusion. The probability that a DVD will not have any defect is 98.1%, obtained by subtracting the probability of having a defect from 100%.
Explanation:
To solve the probability that a DVD purchased by a customer will have a video or audio defect or not, we can use the principle of inclusion-exclusion for probabilities.
According to the given data:
P(video defect) = 1.5%P(audio defect) = 0.8%P(both video and audio defects) = 0.4%Part a: The probability that a DVD will have a video or audio defect (at least one type of defect) is calculated by adding the probabilities of each defect and subtracting the probability of both defects occurring, as these are counted twice.
P(either type of defect) = P(video defect) + P(audio defect) - P(both defects)
P(either type of defect) = 1.5% + 0.8% - 0.4% = 1.9%
Part b: To find the probability that a DVD will not have any defect, we subtract the probability of either defect from 100%.
P(no defect) = 100% - P(either type of defect)
P(no defect) = 100% - 1.9% = 98.1%
Therefore, the probability that a DVD will have a video or audio defect is 1.9%, and the probability that a DVD will not have any defect is 98.1%.
What is the next fraction in each of the following patterns? a. 1⁄40, 4⁄40, 9⁄40, 16⁄40, 25⁄40 . . .? b. 3⁄101, 4⁄101, 7⁄101, 11⁄101, 18⁄101, 29⁄101. . .? c. 5⁄1, 10⁄2, 9⁄2, 18⁄4, 17⁄8, 34⁄32, 33⁄256. . .? PLEASE HELP ME, ALSO CAN YOU EXPLAIN HOW YOU GOT THE ANSWER SO I CAN FIGURE IT OUT ON MY OWN THE NEXT TIME.
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you are adding by odd numbers example 1+3=4. 4+5=9 .9+7=16. 16+9=25 and so on.
b. 47/101, 76/101, 123/101
you are adding by the answers
example. 3+1=4. 4+3=7. 7+4=11. 11+7= 18. 18+11= 29. 29+18=47. 47+29=76. 76+47=124.
Imagine if you wrapped a rope tightly around the earth at the equator. how much longer would you have to make the rope if you wanted it to be exactly one foot above the surface all the way around?
Answers
In your problem, you didn't give any measurements to use, so we can't determine an exact answer. However, the given formula above would work.
The first term calculates the extended length of rope. The second term calculates the original length of rope. All you need to do is subtract them.
Online, you can find the radius of the Earth if you need an exact value. 3,959 miles
Help me on this please
Answers
.. (16 cm)*(34 cm) = 544 cm^2
A circle of diameter 16 cm has been removed. The area of that circle is
.. π*(d/2)^2 = 3.14*(16 cm/2)^2 = 200.96 cm^2
Then the area of the paper that remains is
.. 544 cm^2 -200.96 cm^2
.. = 343.04 cm^2
Verify each identity:
(tanx+tany)/(1-tanxtany)=(sinxcosy+cosxsiny)/(cosxcosy-sinxsiny),
Answers
Final answer:
The trigonometric identity (tan(x) + tan(y)) / (1 - tan(x)tan(y)) = (sin(x)cos(y) + cos(x)sin(y)) / (cos(x)cos(y) - sin(x)sin(y)) can be verified by using the angle addition formulas for sine and cosine, and by applying the tangent sum formula. Both sides reduce to tan(x + y), confirming the identity.
Explanation:
The given trigonometric identity to verify is:
(tan(x) + tan(y)) / (1 - tan(x)tan(y)) = (sin(x)cos(y) + cos(x)sin(y)) / (cos(x)cos(y) - sin(x)sin(y)).
Trigonometric identities are equations involving trigonometric functions that are true for all values of the occurring variables where both sides of the equation are defined.
Let's verify the given identity step by step. First, rewrite the right-hand side using the angle addition formulas for sine and cosine:
sin(x + y) = sin(x)cos(y) + cos(x)sin(y)cos(x + y) = cos(x)cos(y) - sin(x)sin(y)So, the right-hand side can be written as sin(x + y) / cos(x + y). This is equivalent to tan(x + y).
Now, let's examine the left-hand side and apply the tangent sum formula:
tan(x + y) = (tan(x) + tan(y)) / (1 - tan(x)tan(y))As we can see, the left-hand side is exactly the tangent sum formula; therefore it also simplifies to tan(x + y).
Since tan(x + y) is a common form for both sides of the identity, we can conclude that the identity is verified:
(tan(x) + tan(y)) / (1 - tan(x)tan(y)) = sin(x + y) / cos(x + y)
The first terms of (x + y)5 is y5.
TRUE
FALSE
Answers
(x+y)^5 = x^5 + 5x^4y + 10x^3y^2+10x^2y^3+ 5xy^4+ y^5
PLEASE HELP ASAAAPPPPPP
Answers
f(3) = 3375
The answer is 3375
What is the sum of the series?
4+12+36+108+...+8748
8908
10,204
13,120
17,816
Answers
Final answer:
The sum of the series 4+12+36+108+...+8748 is found by observing that it is a geometric progression with a common ratio of 3. By comparing the last term to the options, and understanding the rapidly increasing nature of geometric series, the sum is slightly larger than the last term, which only matches the option 8908.
Explanation:
To find the sum of the geometric series 4+12+36+108+...+8748, we first need to identify the common ratio (r) of the series. Each term is obtained by multiplying the previous term by the constant r. In this case, r = 12 / 4 = 36 / 12 = 108 / 36 = 3. The series is therefore a geometric progression with the first term a = 4 and common ratio r = 3.
We can then use the formula for the sum of the first n terms of a geometric series, which is Sn = a(1-rn) / (1-r), where r ≠ 1. However, we need the number of terms (n). To find n, we use the formula for the nth term of a geometric sequence, which is an = a * rn-1. We can solve for n considering the last term given: 8748 = 4 * 3n-1.
However, instead of manually finding the value of n and then the sum, let us approach the problem with the available options. The sum of a geometric series increases very rapidly due to the exponential nature of each subsequent term. Comparing the last term with the provided options, we can infer that the sum has to be a little bit greater than the last term of the series, 8748.
By inspection of the options, the only number that is slightly greater than 8748 is 8908. Therefore, to the quickest approximation and without going through detailed calculations, the sum of the series is 8908.
What is the difference between log(x/y) and log(x)/log(y)?
Answers
The difference between log(x/y) and log(x)/log(y) is that the first expression can be written as log x - log y, which is not equal to the second term.
What is a logarithm function?The opposite of exponentiation is the logarithm. This indicates that the exponent to which b must be raised in order to obtain a number x is the logarithm of x to the base b. For instance, because 1000 = 10³, the logarithm of 1000 in base 10 is 3, or log₁₀ = 3.
Given:
log(x/y) and log(x) / log(y),
The formula for log(x / y) can be written as shown below,
log(x / y) = log x - log y
As you can see the term is not equal to log(x) / log(y), hence they are different,
The values of the function would differ as in this expression log(x/y) you would first divide x by y and then will take the log of the result,
In the expression log(x) / log(y), you will take the log first individually and then divide the answer.
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Matthew ran 3/8 mile and then walked 7/10 mile. Which pair of fractions can he use to find how far he went in all? (A 15/40 and 28/40 (B 35/40 and 21/40 (C 35/40 and 37/40 (D 30/80 and 70/80 *Please Help*
Answers
8 goes into 40 five times
3/8= (3*5)/40 = 15/40
10 goes into 40 four times
7/10= (7*4)/40= 28/40
ANSWER: A) 15/40 and 28/40
Hope this helps! :)
Answer:
Before we could add these numbers, 3/8 and 7/10 need a common denominator. Both 8 and 10 go into 40.
8 goes into 40 five times
3/8= (3*5)/40 = 15/40
10 goes into 40 four times
7/10= (7*4)/40= 28/40
ANSWER: A) 15/40 and 28/40
Hope this helps! :)
Step-by-step explanation:
find the area of the triange with the given vertices A(0,4), B(0,0), C(2,0)
Answers
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Hope this helps!