What of the following is not a vertical asymptote of the function
f(x)= tan(pi x/4) / x^2-8x+15?
2
3
4
5
6
Answers
Rewrite the function as
[tex]f(x) = \dfrac{\tan(\left(\frac{\pi x}4\right)}{x^2 - 8x + 15} = \dfrac{\sin\left(\frac{\pi x}4\right)}{\cos\left(\frac{\pi x}4\right) (x-3) (x-5)}[/tex]
Vertical asymptotes occur wherever the denominator is zero (but not necessarily when the numerator is also zero).
We have
[tex]\cos\left(\dfrac{\pi x}4\right) (x-3) (x-5) = 0[/tex]
[tex]\implies \cos\left(\dfrac{\pi x}4\right) = 0 \text{ or } x - 3 = 0 \text{ or } x - 5 = 0[/tex]
In the first case, we have
[tex]\cos\left(\dfrac{\pi x}4\right) = 0 \implies \dfrac{\pi x}4 = \pm\dfrac\pi2 + 2n\pi \implies x = \pm 2 + 8n[/tex]
where [tex]n[/tex] is an integer. That is, any of [tex]x\in\{\ldots,-10,-2,\boxed{6},14,\ldots\}[/tex] and [tex]x\in\{\ldots,-6,\boxed{2},10,18,\ldots\}[/tex] are asymptotes.
In the latter two cases, we get [tex]x=\boxed{3}[/tex] or [tex]x=\boxed{5}[/tex]. The numerator is finite at these values [tex]\left(\sin\left(\frac{3\pi}4\right)=\frac1{\sqrt2}\text{ and } \sin\left(\frac{5\pi}4\right)=-\frac1{\sqrt2}\right)[/tex].
This means [tex]x=4[/tex] is not an asymptote. (C)
Related Questions
When adding and subtracting numbers in Scientific Notation, the powers of the base 10 must be the same exponent so that you have "like terms". When multiplying and dividing numbers in Scientific Notation, you do not have to have the same power of the base 10. You can simply follow the exponent rules for multiplying and dividing with the like base 10. True or False I NEED HELP NOW
Answers
Answer:
The answer is true!
Step-by-step explanation
can someone please help me with this hw question for pre calc
Answers
Answer: 15. f(1)=3
16. g(3)=1
Step-by-step explanation:
15. (fog)(1)=
f(g(1))=
f(1)=3
16. (gof)(5)=
g(f(5))=
g(3)=1
Why 6:4 and 18:8 are not equivalent ratios?
Answers
The simplest form of the ratios are not the same, hence, the ratios 6:4 and 18:8 are not equivalent ratios
In order to show why the given ratios are not equivalent ratios, we need to express them in their simplest form as shown:
For the ratio of 6:4
6:4 = 6/4
simplify.
= 3/2
= 3×2/2×2
= 3/2
= 3:2
For the ratio of 18:8
18:8 = 18/8
simplify.
= 9/4
= 9×2/4×2
= 9/4
= 9:4
Since the simplest form of the ratios are not the same, hence, the ratios 6:4 and 18:8 are not equivalent ratios.
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a scuba trip costs $80 plus $45 for each diver. write and evaluate an expression to find the total cost for 6 divers
Answers
Answer:
$350.00
Step-by-step explanation:
80 + 6(45) = ?
PLEASE HELP ME I WILL GIVE YOU 100 POINT PLEASE HELP AND MARK BRAINLETS AND STOP REPORTING ME I ALREADY LOST 100 POINTS
Answers
The graphs of the functions and relations gives;
4. The graph of y(x) = x² represents a function and the graph of y² = x represents a relation
5. In equation, y² = x, the value x = 9, gives two y–values y = 3 or -3, therefore y² = x is a relation rather than a function.
6. The domain and range are both [-8, 8]
7. From the equation,x = √(8 - y²), each x– value gives two y–values, therefore x² + y² = 8 is a relation not a function
What are the functions and relations?The given equations of the graphs are;
y(x) = x²y² = xWhere;
x = The input or independent variable
y = The output or dependent variable
In a function each input or value of x can give only one output or value of y, such that a vertical line drawn from each x–value crosses the graph only once.
Therefore;
The graph of y(x) = x², represent a function, given the each x–value has only one y–value, or the value of x determines the y–value.
The graph of y² = x represents a relation given that one x–value can give two y–values (a vertical line drawn at a point, x > 0, crosses the graph twice.
5. Let 9 represent the value chosen from the domain of both y(x) = x² and y² = x, we have;
y(9) = 9² = 81
Therefore, the x–value, x = 9 has only one y–value, which is 89Therefore, the equation, y(x) = x² is a function
In the relation, y² = x, we have;
y² = 9
y = ±3
Therefore, when x = 9, y = 3, or y = -3, which are two outputs or y–value for one input or x–value.
Which makes y² = x a relation rather than a function.
6. The equation of the graph is the equation of a circle, x² + y² = 8
Where;
8 = The square of the radius of the circle
(h, k) = (0, 0), the center of the circle is at the origin.
Therefore;
The coordinates of the edges of the circle on the x–axis are;
(-√8, 0), and (√8, 0)
The domain is therefore [-8, 8]
Similarly, the range, which are the possible y–values is also [-8, 8]
7. The equation x² + y² = 8, and therefore, the graph is not a function given that we have;
x² + y² = 8x = √(8 - y²)Given that y²y(x) = x²is always positive, each x - value gives two y-values, which does not conform with the mapping relationship of a function
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Lauren was trying to approximate the solution to n² = 115. She said that it lies
between √100 and √121. Therefore, it lies between 4 and 5, however a little closer
to 5. She approximated it to be about 4.7. Do you agree or disagree with her
reasoning? Explain.
Answers
What she approximated as 4.7 is not correct because the nearest perfect squares are 10 and 11 which are different from what she got.
How to find the square root of a number?We are told that Lauren is trying to approximate the solution to n² = 115.
Now, she has figured out that it lies between √100 and √121..
Now, √100 = 10 and √121 = 11. Thus, we can say that if she says it is between 4 and 5, then she is wrong because the nearest perfect squares are 10 and 11 which are different from what she got.
Thus, what she approximated as 4.7 is not correct.
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Can you figure out the sequence/progression of the circle?
Answers
Answer:
i the middle
Step-by-step explanation:
A square with side lengths of 4 units is translated on
the coordinate plane. One vertex of the image is at (2,
1).
Which ordered pair could represent another vertex of
the image?
Answers
Please explain how to do this, I have no clue!!!! Literally will give 50 points! Maybe even brainliest, just explain how to do it!!!
Solve the following equation. x/6 + 4 = 20 Then place the correct number in the box provided.
Answers
Answer:
x = 96
Step-by-step explanation:
[tex]\frac{x}{6} +4=20[/tex]
1. Isolate the variable 'x'.
1a. Subtract 4 so the equation becomes [tex]\frac{x}{6} =16[/tex]
2a. Multiply both sides by 6 to turn the fraction into a normal number, which becomes x=96.
Answer:
[tex] \sf \large \: x=96[/tex]
Step-by-step explanation:
Let's solve your equation step-by-step.
x/6+4=20
Step 1: Simplify both sides of the equation.
1/6x+4=20
Step 2: Subtract 4 from both sides.
1/6x+4−4=20−4
1/6x=16
Step 3: Multiply both sides by 6.
6*(1/6x)=(6)*(16)
x=96
i (x)=x² +3
j (x)=4x-3
Find (ij) (-1)
Answers
Brian spent 14 minutes washing the dishes. That was 35% of the total number of minutes he spent doing chores. How many minutes did Brian spend doing chores?
Answers
69
Explanation: none
69 minutes
At a party, a number of guests were served
15 litres of champagne. Each guest had 2
glasses of champagne and each glass held
150 millilitres. Assuming no spillage, how
many guests were at the party?
Answers
50 guests were there at the party
One unit means one thing. A unit rate means the ratio of something. Write this rate as a ratio with a denominator of 1. For example, if you run 70 meters in 10 seconds, on average you walk 7 meters in 1 second. Both reporting 70 meters in 10 seconds and 7 meters in 1 second are rates, but 7 meters in 1 second is the unit price. The unitary method is a method of finding the value of one unit and then finding the value of the required number of units.Suppose you go to the market to buy six apples. The trader tells you that he is selling 10 apples for 100 rupees. In this case the apple is the unit and the price of the apple is the value.
Total champagne available = 15 litres
1 litre = 1000 ml
15 litres = 15000 ml
Total = 15000 ml
Each guest had 2 glasses of 150 ml = 300 ml, which means each guest was served 300 ml of champagne
Total no of guests = Total champagne / champagne served to each
= 15000 / 300
= 50
50 guests were there at the party
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If a car rolled down a 25 meter ramp, continued rolling another 20 meters at the bottom, then reversed and went back to the top of the ramp, what is the car's displacement? What is the car's distance traveled? Explain.
Answers
The car's displacement according to the description given is; 0 meters while it's distance travelled is; 90 meters.
What is the difference between displacement and distance?It follows from definition that, displacement which is a vector quantity is a measure of the change in position of a body after undergoing motion while the distance travelled which is a measure of magnitude only (scalar) is a measure of the space covered over the course of time.
Hence, the displacement is zero as the start position is same as the end position.
Also, the distance is the space covered= 25 +20 +20 +25 = 90 meters.
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Angles ABC and DEF are complementary angles. If m/ABC = 72°, what is m/DEF?
Answers
Answer:
18 degrees
Step-by-step explanation:
If <ABC and <DEF are complementary, m<ABC + m<DEF = 90 degrees. So M<DEF = 90 - 72 = 18 degrees.
Answer: 18
Step-by-step explanation: Complementary angles sum up to 90. (90 - 72 = 18)
a translation of T2, –7(x, y) is applied to ΔABC, what are the coordinates of B'?
Answers
If a translation of T (2, -7) is applied to the triangle ABC as shown in the figure attached hereby for reference, and B (1, 5) gets repositioned to B', then the current coordinates of B' are (3, -2).
As per the question statement, a translation of T (2, -7) is applied to the triangle ABC as shown in the figure attached hereby for reference, and B (1, 5) gets repositioned to B'.
We are required to calculate the coordinates of B'.
To solve this question, we need to know what Translation (a, b) to (x, y) and (-a, -b) to (x, y) means. Translation (a, b) to (x, y) means the abscissa "x" is to be shifted to the right by "a" units while the ordinate "y" is to be shifted to the right by "b" units, i.e., after translation, the new coordinates become [(a + x), (b + x)]. On the other hand, Translation (-a, -b) to (x, y) means the abscissa "x" is to be shifted to the left by "a" units while the ordinate "y" is to be shifted to the left by "b" units, i.e., after translation, the new coordinates become [(a - x), (b - x)].
Here, as per the above mentioned concept, a translation of T (2, -7) if applied to the point B (1, 5), the new point B' will be at [tex][(1+2), (5+(-7)]=[3, (-2)][/tex].
Translation: In Coordinate Geometry, a translation is a repositioning of a point or a figure from one location to another location without changing its size, shape or orientation.Coordinates: The coordinates of a point are a pair of numbers that define its exact location on a two-dimensional coordinate plane by using the horizontal and vertical distances from the two reference axesTo learn more about Translation, click on the link below.
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Answer: D (3,-12)
Step-by-step explanation:
A football team lost 5 yards on each of four plays what was their overall change in position
Answers
Answer: -20 yards
Step-by-step explanation:
Loss in 5 yards ==> -5 yards
-5*4=-20 yards
PLEASE HELP What are the coordinates of point Q?
(0,3)
(0,-3)
(-3,0)
(3,0)
Answers
Answer:
(0, -3)
Step-by-step explanation:
.
A certain state uses the following progressive
tax rate for calculating individual income tax:
Income
Progressive
Range ($)
Tax Rate
0 - 3000
2%
3001 - 5000
3%
5001 - 17,000
5%
17,001 and up
5.75%
Calculate the state income tax owed on an $80,000
per year salary.
tax = $[?]
Round your answer to the nearest whole dollar amount..
Enter
Answers
Answer:
4600
Step-by-step explanation:
80000 is in 17001 and up category so the tax will be 5.75%. 80000/100 *5.75 = 4600
Find the sum..
7/4 − (−1/2)
Please Help! I need it now!
Answers
Answer:
1.25
Step-by-step explanation:
Answer:1.25
Step-by-step explanation:
Which system of inequalities is represented by this graph?
Responses
{y>−2x−4
y≤x+1
{y<−2x−4
y≤x+1
{y<−2x−4
y −2x−4
y
Answers
the graphed system of inequalities is:
y > − 2x − 4
y ≤ x + 1
Which is the first option.
Which system of inequalities is represented by the given graph?
On the image in the quesitonw e cans ee the graph of a system of inequalities. There we can see two lines.
One of the lines has a positive slope and we can see that it is a solid line, and we also can see that the region below that line is shaded, so one of the inequalities is of the form:
y ≤ line with positive slope.
The whole opposite happens for the other line, it has a negative slope, it is dashed (so this time we use the symbols > or <) and the region shaded is above the line, so this time we have an inequality of the form:
y > line with negative slope.
Then the system of inequalities is:
y ≤ line with positive slope.
y > line with negative slope.
By looking at the options, the only one with this form is:
y > − 2x − 4
y ≤ x + 1
Which is the first option
Finally, we conclude that the graphed system of inequalities is:
y > − 2x − 4
y ≤ x + 1
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What is the equation solve it
Answers
Answer:
12x + 9 = 4x + 7
Group likely terms
12x - 4x = 7 - 9
8x = -2
Now we need to isolate x
Therefore; Divide both side by the coefficient of x thus 8
Hence x = -1/4
Answer:
[tex]x = \bf -\frac{1}{4}[/tex]
Step-by-step explanation:
We are given the following equation:
[tex]12x + 9 = 4x + 7[/tex]
In order to solve this equation, we have to rearrange it to make [tex]x[/tex] the subject of the equation:
[tex]12x + 9 = 4x + 7[/tex]
⇒ [tex]12x + 9 - 4x = 4x + 7 - 4x[/tex] [Subtracting [tex]4x[/tex] from both sides]
⇒ [tex]8x + 9 = 7[/tex]
⇒ [tex]8x + 9 - 9 = 7 - 9[/tex] [Subtracting 9 from both sides]
⇒ [tex]8x = -2[/tex]
⇒ [tex]\frac{8}{8} x = -\frac{2}{8}[/tex] [Dividing both sides by 8]
⇒ [tex]x = -\frac{2}{8}[/tex]
⇒ [tex]x = \bf -\frac{1}{4}[/tex] [Simplifying the fraction]
Ahmad is loading a pallet with boxes that each
weighs 45 pounds. The pallet can safely
support no more than 900 pounds. How many
boxes can Ahmad safely load onto the pallet?
Answers
Step by step:
45x = 900
—— ———
45 45
X= 20
what is the common fact or 9 12 15 and 18
Answers
Answer:
3 is the common factor
Step-by-step explanation:
3 x 3 =9
3 x 4= 12
3 x 5 =15
3 x 6 =18
hope it helps
Answer:
Factors for 9: 1, 3, and 9
Factors for 12: 1, 2, 3, 4, 6, and 12
Factors for 15: 1, 3, 5, and 15
Prime Factors for 9: 3 and 3
Prime Factors for 12: 2, 2, and 3
Prime Factors for 15: 3 and 5
GCF = 3
Delcie is asked to rewrite the expression 500 using an exponent. How should Delcie
correctly rewrite the expression?
Answers
Is the line through points (-3,2) and (4, -1) parallel to the line that contains the points (1,3) and (-2, -4)?
Are the two lines parallel?
How do you know?
Answers
Considering the expression of a line, they do not have the same value of m. So, the two lines are not parallel.
Linear equation o lineA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.Knowing two points (x1, y1) and (x2, y2) of a line, the slope m of said line can be calculated using the following expression:
m= (y2 - y1)÷ (x2 - x1)
Substituting the value of the slope m and the value of one of the points in the expression of a linear equation, y = mx + b, the value of the ordinate to the origin b can be obtained.
Parallel lineParallel lines are two lines that are always at the same distance from each other and that prolonged towards infinity never touch.
Two lines are parallel if they have the same slope and different y-intercepts. That is, they have the same value of m and different value of b.
Lines in this caseIn this case, you can calculated the slope of the two lines as:
Being (x1,y1)= (-3,2) and (x2,y2)= (4, -1), the slope m can be calculated as:
m= (-1 -2)÷ (4 - (-3))
Solving:
m= (-3)÷ 7
m= -3/7
Being (x1,y1)= (1,3) and (x2,y2)= (-2,-4), the slope m can be calculated as:
m= (-4 -3)÷ (-2 -1)
Solving:
m= (-7)÷ (-3)
m= 7/3
You can observe that they do not have the same value of m. Finally, the two lines are not parallel.
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A clothing store sells 300 skirts in January of the number of skirt it sells in February is 40% higher how many skirts will it sell
Answers
In February, it will sell 420 skirts.
What is a percentage?A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.
Given:
A clothing store sells 300 skirts in January.
The number of skirts it sells in February is 40%,
that means,
the number of skirts,
= 300 x 1.4
= 420 skirts.
Therefore, It will sell 420 skirts.
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Graph the inequality.
y < −x + 3
Answers
The graph is attached below.
The given inequality is:y < -x + 3On rearranging,x + y < 3To graph the inequality, first of all, we need to draw the corresponding equation of line on the graph.The corresponding equation of a line for an inequality can be found by replacing the less than or greater than sign with an equal to sign.The corresponding equation for the given inequality is:x + y = 3The two points which satisfy the above equation of line are (0, 3) and (3, 0).Plot the line on the graph.Now, put the coordinates of the origin into the inequality.If the inequality holds true, then shade the area from the line towards the origin and vice versa.Thus, the graph of the inequality is obtained.To learn more about equations, visit :
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Select the Correct answer: Josh rents a kayak at a nearby state park. He pays a flat rate of $12.99 plus $3.75 for each hour that he spends in the water. How much did Josh spend if he was on the river for 4 1/2 hours? $16.88, $29.87, $16.74, $28.74
Answers
Answer:12.99+ 3.75x= total. therefore, 12.99+3.75(4)= 27.99
Step-by-step explanation:
tho
Find the circumference and area of the figure If each unit on the graph measures 1 centimeter. Round answers to the nearest tenth, If necessary.
Answers
The circumference and area of the circular figure as given in the task content are; 31.4 and 78.5 respectively.
What is the circumference and area of the figure?Since each unit on the graph measures one centimeter, it follows that the radius of the circle which is described by line PQ can be determined as; 5units = 5 centimetres.
On this note, the circumference of the figure; 2πr = 2 × 3.14 × 5
Circumference = 31.4 cm.
Also, the area of the circle in discuss can be determined from; πr² = 3.14 × 5²
Area = 3.14 × 25
Area = 78.5cm²
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Mariam took a taxi from her house to the airport. The taxi company charged a pick-
up fee of $2.90 plus $1.25 per mile. The total fare was $6.65, not including the tip.
Write and solve an equation which can be used to determine m, the number of miles
in the taxi ride.
Answers
The equation is 2.90 + 1.25m= 6.65
The number of miles in the taxi ride is 3 miles
How to calculate the number of miles in the taxi ride ?
The airport charged a pick up fee of $2.90
$1.24 was charged per mile
The total fare was $6.65
The equation can be expressed as
2.90 + 1.25m= 6.65
collect the like terms
1.25m= 6.65 - 2.90
1.25m= 3.75
divide by the coefficient of m which is 1.25
m= 3.75/1.25
m= 3
Hence the number of miles of the taxi ride is 3
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