Given:
The function is
[tex]f(x)=\dfrac{x^2-2x-2}{x-2}[/tex]
To find:
The vertical asymptote and oblique asymptote.
Solution:
We have,
[tex]f(x)=\dfrac{x^2-2x-2}{x-2}[/tex]
To find vertical asymptote, equate denominator equal to 0.
[tex]x-2=0[/tex]
[tex]x=2[/tex]
So, the vertical asymptote is [tex]x=2[/tex].
In the given function degree of numerator is greater than denominator so, their is an oblique asymptote. To find oblique asymptote divide the numerator by denominator.
Dividing [tex]x^2-2x-2[/tex] by [tex]x-2[/tex] using synthetic division, we get
2 | 1 -2 -2
2 0
--------------------------
1 0 -2
-------------------------
Here, starting elements of bottom row represent coefficient of quotient and last element of bottom row represents the remainder.
[tex]Quotient=x, Remainder=-2[/tex]
Since, quotient is x, therefore, the oblique asymptote is [tex]y=x[/tex].
Therefore, the correct option is B.
Choose a value for B so that the relation below is not a function
Answer:2
Step-by-step explanation:
plz leave a like
ANSWER URGENTLY !!!
f(1) =
Answer:
f(1) = 1
General Formulas and Concepts:
Algebra I
Reading a Cartesian PlaneFunction NotationStep-by-step explanation:
f(1) is asking for the y-value when x = 1. According to the graph of f, when x = 1, y = 1. Therefore, f(1) = 1.
AB= 17 cm and BC= 12.75cm Find DB.
Twice the sum of x and 3 is decreased by 13
Given:
Twice the sum of x and 3 is decreased by 13.
To find:
The expression for the given statement.
Solution:
The sum of x and 3 is (x+3).
Twice the sum of x and 3 is two times of (x+3), i.e., 2(x+3)
Negative sign is used of decrease.
Decreased by 13 is represented by -13.
Using these representation, we get
Twice the sum of x and 3 is decreased by 13: [tex]2(x+3)-13[/tex]
Therefore, the required expression is [tex]2(x+3)-13[/tex].
Miguel took 7 hours to read a 259-page book and Julissa took 5 hours to read a 175-page book. Who read more pages per hour?
39 points!
Draw a right triangle and label the legs 15 cm and 17 cm. Use the Pythagorean theorem to find the length of the
hypotenuse. Show all of your work
Answer:
a^2+b^2=c^2
15+17=32cm
Step-by-step explanation:
Answer:
57.59cm
Step-by-step explanation:
Use the Pythagorean theorem to calculate the hypotenuse from right triangle sides. Take a square root of sum of squares:
c = √(a² + b²)
Right triangle with law of sines formulas. a over sin(α) equals b over sin(β) equals c, because sin(90°) = 1
Given angle and one leg
c = a / sin(α) = b / sin(β), from the law of sines
Given area and one leg
As area of a right triangle is equal to a * b / 2, then
c = √(a² + b²) = √(a² + (area * 2 / a)²) = √((area * 2 / b)² + b²)
If you’re correct you’ll get brainliest answer!
Factor out the coefficient of the variable term.
The expression 6s - 3/4 factored is
Answer:
[tex]6s - \frac{3}{4}=3(2s - \frac{1}{4})[/tex]
Step-by-step explanation:
Given
[tex]6s - \frac{3}{4}[/tex]
Required
Factorize
[tex]6s - \frac{3}{4}[/tex]
Express 6s as 3 * 2s
[tex]3 * 2s - \frac{3}{4}[/tex]
Express 3/4 as 3 * 1/4
[tex]3 * 2s - 3 * \frac{1}{4}[/tex]
Factorize:
[tex]3(2s - \frac{1}{4})[/tex]
Hence:
[tex]6s - \frac{3}{4}=3(2s - \frac{1}{4})[/tex]
Pls tell me the answer
Answer:
1/4
Step-by-step explanation:
1. The zeros of a quadratic relation are 3 and The second differences are positive
a) Will the optimal value be a maximum or minimum? Justify your answer.
Answer:
The optimal, vertex, value will be a minimum
Step-by-step explanation:
The given zeros of the quadratic relation are 3 and 3
The sign of the second differences of the quadratic relation = Positive
Whereby the two zeros are the same as x = 3, we have that the point 3 is the optimal value or vertex (the repeated point in the graph of the quadratic relation) of the quadratic relation
Whereby, the table of values for the quadratic relation from which the second difference is found starts from x = 3, we have;
To the right of the coordinate points of the zeros of the quadratic relation, the positive second difference in y-values gives as x increases, y increases which gives a positive slope
By the nature of the quadratic graph, the slope of the line to the left of the coordinate point of the zeros of the quadratic relation will be of opposite sign (or negative). The quadratic relation is cup shaped and the zeros, therefore, the optimal value will be a minimum of the quadratic relation
tickets to a concert went on sale at 10 a.m. by 12 p.m. 208 tickets have already been sold at this rate how many tickets will be sold in the first 5 hours of the tickets go on sale
A. 520
B. 1,040
C. 41.6
D.728
Answer:
We conclude that 520 tickets will be sold in the first 5 hours of the tickets go on sale.
Hence, option A is true.
Step-by-step explanation:
Given that the tickets to a concert went on sale at 10 a.m. by 12 p.m.
10 a.m. by 12 p.m means the total number of hours = 2 hoursGiven that the tickets sold in 2 hours = 208
Thus,
Unit rate = 208 tickets / 2 hours
= 104 tickets per hour
Therefore,
Tickets sold in the first 5 hours of the tickets go on sale:
104 × 5 = 520 tickets
Therefore, we conclude that 520 tickets will be sold in the first 5 hours of the tickets go on sale.
Hence, option A is true.
how is per capita gross domestic product calculated "total market value of goods and services produced within a year divided by total population"?
Answer: See explanation
Step-by-step explanation:
You didn't really say what you want to know but let me explain.
The gross domestic product of an economy is the value of the goods and.d services that are being produced in such an economy. The gross domestic Product is used to know how well an economy is doing
Per capita gross domestic product (GDP) is a used to know the economic output of a particular country per person. It is calculated by dividing the GDP of such an economy by the population.
For example, let us say the GDP of a country is $800,000,000 and the population is 3,500,254. Therefore, the per capita GDP would be:
= $800,000,000 / 3,500,254
= $228.56 per person
Answer:total market value of goods and services produced within a year divided by total population
Step-by-step explanation:
basic defenition
What is the value of x in the equation -x = 2 - 3x + 6?
a) 8
b) -4
c) 4
d) -8
Answer: x = 4
Step-by-step explanation:
first, we calculate it.
-x = 8 - 3x
then, we move the variable to the left.
-x + 3x = 8
then, we collect like terms.
2x = 8
finally, we divide both sides.
x = 4
s=ut+1/2at²
u=3 a=-12 t=1/3
work out the value of s
Step-by-step explanation:
s = ut + 0.5at²
= (3)(1/3) + 0.5(-12)(1/3)²
= 1 - 2/3
= 1/3
The value of s is 1/3.
Answer:
[tex]s = ut + \frac{1}{2} a {t}^{2} \\ s = (3 \times \frac{1}{3} ) + ( \frac{1}{2} \times -12 \times {( \frac{1}{3}) }^{2} ) \\ s = (1) + ( -\frac{2}{3} ) \\ s = - \frac{1}{3} \\ s = -\frac{1}{3} \: metres[/tex]
Write the word sentence as an inequality. Then solve the inequality.
Six times a number x is at least −24.
An inequality is
.
The solution of this inequality is
.
Answer:
The inequality is 6x ≥ -24
The solution of this inequality is {x : x ∈ R, x ≥ -4} ⇒ [-4, ∞)
Step-by-step explanation:
In the inequality not more than means ≤In the inequality at least means ≥Let us solve the question
∵ Six times a number x means 6 × x = 6x
∵ At least means ≥
∴ Six times a number x is at least -24 is 6x ≥ -24
∴ The inequality is 6x ≥ -24
Now we will find the solution of the inequality
∵ 6x ≥ -24
→ Divide both sides by 6
∵ [tex]\frac{6x}{6}[/tex] ≥ [tex]\frac{-24}{6}[/tex]
∴ x ≥ -4
∴ The solution of this inequality is {x : x ∈ R, x ≥ -4} ⇒ [-4, ∞)
Answer:
The inequality is 6x ≥ -24
The solution is x ≥ -4
Step-by-step explanation:
To solve this you have to divide both sides by 6, so 6 ÷ 6 cancels out and -24 ÷ 6 = -4
So, the solution is x ≥ -4
65 effing points, will mark brainliest! here we go again
Jeremy has heard a lot of people in the club talking about tackling a 950-foot rock formation. Jeremy has set a limit that they won’t climb anything that takes longer than 7 hours, so they have enough time to travel to and from the place. Will it be possible to climb a 950-foot rock formation within Jeremy’s time constraint? Explain why or why not.
Answer:
No
Step-by-step explanation:
The amount of minutes to climb up 1 foot of height would take around 2 to 3 minutes. if you divide 950 with 2, you get 475 which would be the time in minutes it takes to climb, if we convert 475 minutes to hours, it would be an estimate of 7.92 hours. So as we see they would need an extra 92 minutes to climb the full 950 feet. If you were able to climb it at an average rate of 135.7 ft/hr, you could make it.
(this was someone elses explanation)
HELP FAST!! WILL GIVEV BRAINLIEST
Answer:
-2, -4, -1.5
Step-by-step explanation:
-6x+10>16
-6x>6
x<-1
(anything less than -1)
Answer:-4, -2, -1.5
Step-by-step explanation: First, simplify the equation. You should get -6x+10>16
Then, substitute the values into the place of x. If they are greater than 16, they are solutions. -4, -2, and -1.5 work. Hope this helps you!
Find the missing number to make a unit rate 6/2=3/?
Answer:
yes
Step-by-step explanation:
Answer:
i think its 6/2=3/1
Step-by-step explanation:
What is 4cos2(165°) – 2 expressed as a single trigonometric function? 4cos(330°) 2cos(330°) 4cos(82.5°) 2cos(82.5°)
Answer:
2cos(330º)
Step-by-step explanation:
both equal to √3
Expressing 4cos2(165°) – 2 as a single trignometric function, it will be written as : 2cos(330º)
Meaning of trigonometric functionTrigonometric function can be defined as real functions in mathematics that forms a relationship between an angle of a right-angled triangle to the ratio of the length of two sides.
Trigonometric function is very important as it is mostly concerned with functions of angles and their application in calculation
In conclusion, to express 4cos2(165°) – 2 as a single trignometric function, it will be written as : 2cos(330º)
Learn more about trigonometric function: https://brainly.com/question/24349828
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A man has to drive 40 more miles to a meeting in Indianapolis compared to Chicago,
which is 160 miles away. What is the percent increase in the number of miles to
Indianapolis?
Answer:
25% i believe
Step-by-step explanation:
40 is 1/4 (or 25%) of 160
Colton is taking a long bike ride where he rides at a constant speed. The distance he bikes is proportional to the amount of time he has been biking. After 3.5 hours, he has traveled a distance of 49 miles.(b) Colton travels at the same rate as in (a) for 6 hours. Let d be the distance he biked. Set up and solve a proportion for d. (c) Colton would like to bike 200 miles. Let h be the number of hours it will take Colton to bike this distance. Solve a proportion for h. Round to the nearest tenth of an hour.
Answer:
b) [tex]d[/tex] = 84 miles
c) [tex]h[/tex] = 14.3 hours
Step-by-step explanation:
Given that:
The speed of Colton is constant while riding a bike.
Formula for speed is given as:
[tex]Speed = \dfrac{Distance}{Time}[/tex]
If speed is constant, then we can deduct that:
[tex]Distance \propto Time[/tex]
Time = 3.5 hours
Distance = 49 miles
Therefore, the speed will be equal to:
Speed = [tex]\frac{49}{3.5}[/tex] = 14 miles/hr
b) Given that:
Time = 6 hours, then we have to find the distance to be hiked if the speed is same.
[tex]14 = \dfrac{d}{6}\\\Rightarrow d = \bold{84}\ miles/hr[/tex]
c) Given that:
Distance = 200 miles
Number of hours = [tex]h[/tex]
To find, the value of [tex]h[/tex].
[tex]14 = \dfrac{200}{h}\\\Rightarrow h = \dfrac{200}{14}\\\Rightarrow h = \bold{14.3}\ hours[/tex]
2x^3=128
work out the value of x
Step-by-step explanation:
2x^3=128
or,x^3=128/2
or,x^3=64
or,x=3√64
or,x=4
Jodie spent 25% less buying her English reading books thank Claudia. .Gianna spent 9% less than Claudia. Gianna spent more than Jodie by what percent? If your using decimal round to the nearest tenth
Answer:
21.3%
Step-by-step explanation:
Given that:
Money spent by Jodie for buying English reading books = 25% lesser than that of Claudia
and
Money spent by Gianna is 9% lesser than that of Claudia.
To find:
By what percent, Gianna spent more than Jodie ?
Solution:
Let the money spent by Claudia on her English books = 100
Now, as per question statement:
Money spent by Jodie = 100 - [tex]\frac{9}{100}\times 100[/tex] = 75
Money spent by Gianna = 100 - [tex]\frac{25}{100}\times 100[/tex] = 91
Now, to find the answer:
[tex]\dfrac{\text{Difference between money spent by Gianna and Jodie}}{\text{Money spent by Jodie}}\times 100[/tex]
[tex]\Rightarrow \dfrac{91-75}{75}\times 100\\\Rightarrow \dfrac{16}{75}\times 100\\\Rightarrow \bold{21.3\%}[/tex]
Therefore, Gianna spent 21.3% more than the amount that was spent by Jodie.
Where is the midpoint of AB if A(6,4) and B(5,-2)?
A (11,2)
B) (11,6)
C) (5.5,3)
D (5.5,1)
Answer:
Midpoint={5.5,1}
Step-by-step explanation:
M={x1+x2/2,y1+y2/2}
M={6+5/2,-2+4/2}
M={11/2,2/2}
M={5.5,1}
Charles needs to mix 6 tablespoons of water with 5 tablespoons of vinegar to make a cleaning solution. How many tablespoons of water are needed for each tablespoon of vinegar?
Answer:
The answer is 1.2
Step-by-step explanation:
Can someone help I think it’s a, b, d but I would like to see what everyone else’s opinion is:)
Answer:
D
Step-by-step explanation:
There are 5 ways to prove congruence:
1. SSS (3 sides)
Not applicable here
2. SAS (side-angle-side)
This requires a side, then an angle in between, and another side. This cannot be met with angles (as we currently have side-angle) so none of these are possible
3. ASA (angle-side-angle)
This is a side between angles, so if we squished line AC between angles C and A, and angle A=angle O, this would be true -- B is one answer
4. AAS (angle-angle-side)
Similar to option 3, but would be with angles T and G instead,
D is another answer
5. hypotenuse leg (only in right triangles)
The reason T and G fit AAS is because we hit angle T, then angle C, then side CA, all congruent with G, D, and DO in that order.
Please help!!!! Select all the intervals where g is increasing.
Answer:
-3 < x < -2
Step-by-step explanation:
Here, we want the interval in which g is increasing
The interval are the point in which we have an upward curve
From the given graph, we can see an upward curve at -3 < x < -2
And that is our answer
Which transformation of the parent square root function will result in the given domain and range? domain : [2,∞) range : [3,∞)
Answer:
B. g(x) = (x - 2)^(1/2) + 3Step-by-step explanation:
This is B
(x - 2) is not negative and defined when x≥0g(x) gets minimum value of 3 at minimum value of x = 2Maria planted 6 pots of flowers each pot holds 8 flowers. Explain how to use the bar model to solve for the total number of flowers. Include the total number of flowers in your answer
Answer:
[tex]48[/tex]
Step-by-step explanation:
There are [tex]6[/tex] pots each of which contains [tex]8[/tex] flowers.
In the bar model it can be seen that one unit of the bar represents a pot with [tex]8[/tex] flowers. The entire bar represents [tex]6[/tex] pots. We will need to add [tex]8[/tex] six times or multiply [tex]8[/tex] with [tex]6[/tex] to find the total number of flowers.
So total number of flowers is
[tex]8+8+8+8+8+8=48[/tex]
or
[tex]8\times 6=48[/tex].
So, the total number of flower is [tex]48[/tex].
What is 843,623 rounded to the nearest hundred thousand
Answer:
800,00
Step-by-step explanation:
It's simple math
Answer:
800,000
Step-by-step explanation:
Because the ten thousand's place is not 5 or more than that!
What is 2 ÷ 1/6 ?
Please Help 100 Points
Answer:
6
Step-by-step explanation:
2/ 1/3=6
The reason why is because, when you divide a fraction it will become a multiplication and depending on the numerator and the denominator it changes the number. For example, 2/ 2/3 would be 3. Therefore, your answer to this question would be 6.