An asymptote is a straight line that approaches a curve indefinitely but does not intersect at any point. There are asymptotes at t [tex]\dfrac{3}{2}\rm\ and\ \dfrac{-1}{3}[/tex].
What is an asymptote?An asymptote is a straight line that approaches a curve indefinitely but does not intersect at any point. In other words, when a curve approaches infinity, it approaches an asymptote line.
The function that is given to us is:
[tex]f(x)=\dfrac{x+1}{6x^2-7x-3}[/tex]
As in the function, there is a fraction therefore, the denominator should not be zero in order for the function to be defined. Therefore, there are asymptotes at
[tex]6x^2-7x-3 = 0\\[/tex]
Substituting the value in the formula of the quadratic equation we will get,
[tex]D=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\D = \dfrac{-(-7)\pm\sqrt{(-7)^2-4(6)(-3)}}{2(6)}\\\\D =\dfrac{-(-7)\pm\sqrt{11}}{12} = \dfrac{3}{2}, \dfrac{-1}{3}[/tex]
Thus, there are asymptotes at [tex]\dfrac{3}{2}\rm\ and\ \dfrac{-1}{3}[/tex].
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ANSWER QUICK PLS!!! LOTS OF POINTS!!!
Answer:
x = 8
Step-by-step explanation:
∠M = ∠K7x - 4 = 5x + 122x = 16x = 8Answer:
x = 8
m∠M = 52°
m∠K = 52°
m∠L = 128°
m∠J = 128°
Step-by-step explanation:
If the given shape is a parallelogram, its opposite interior angles are equal.
⇒ m∠M = m∠K
⇒ 7x - 4 = 5x + 12
Subtract 5x from both sides:
⇒ 2x - 4 = 12
Add 4 to both sides:
⇒ 2x = 16
Divide both sides by 2:
⇒ x = 8
Substitute found value of x into the expressions for each angle to find the measures of the angles:
⇒ m∠M = 7(8) - 4 = 52°
⇒ m∠K = 5(8) + 12 = 52°
As the angles on the same side of the transversal in a parallelogram sum to 180°, then
⇒ m∠J + m∠M = 180°
⇒ m∠J = 180° - m∠M
⇒ m∠J = 180° - 52°
⇒ m∠J = 128°
As m∠L = m∠J then m∠L = 128°
A rock is dropped from a height of 100 feet. Calculate the time between when the rock was dropped and when it landed. If we choose "down" as positive and ignore air friction, the
function is h(t) = 16t^2 – 100.
A)t = 2.5 seconds
B)t = 6.25 seconds
C)t = 10 seconds
D)t = 12.5
Answer:
A
Step-by-step explanation:
the rock lands when it reaches height 0.
so, for what t is h(t) = 0 ?
16t² - 100 = 0
16t² = 100
now we pull the square root on both sides (we can ignore the negative solutions, as negative seconds don't make any sense in our scenario)
4t = 10
t = 10/4 = 5/2 = 2.5 seconds
so, A is correct.
I NEED HELP PLEASEEEEEEEEEEE
Devon purchased a new car valued at $16,000 that depreciated continuously at a rate of 35%. Its current value is $2,000. The equation mc025-1. Jpg represents the situation, where t is the age of the car in years and r is the rate of depreciation. About how old is Devon’s car? Use a calculator and round your answer to the nearest whole number. 1 year 2 years 5 years 8 years.
The age of the car that Devon purchased is given by: Option C: 5 years
How to calculate compound interest's amount?If the initial amount (also called as principal amount) is P, and the interest rate is R% per unit time, and it is left for T unit of time for that compound interest, then the interest amount earned is given by:
[tex]CI = P(1 +\dfrac{R}{100})^T - P[/tex]
The final amount becomes:
[tex]A = CI + P\\A = P(1 +\dfrac{R}{100})^T[/tex]
We can use compound interest's formula (with a bit modification if necessary) whenever there is compounding on a base amount on some fixed rate for some time.
For this case, there is decrement happening, so rate can be taken negative. Thus, we take:
R = -35%
Let the car is T years old.
Then, as we have: Initial price of the car = P = $16000, and the final price of the car = A = $2000, thus, we get:
[tex]A = P(1 +\dfrac{R}{100})^T\\\\2000 = 16000(1 + (-35/100) )^T\\1/8 = (1-0.35)^T\\0.125 = 0.65^T\\\\T = log_{0.65}(0.125)\\T \approx 4.827 \approx 5 \text{ (in years) }[/tex]
Thus, the age of the car that Devon purchased is given by: Option C: 5 years
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Answer:
C 5 years
Step-by-step explanation:
Please help I was able to do the hard part but I don’t know how to crack the code
Step-by-step explanation:
what do you mean by "the hard part" ?
anyway,
we need to sum the numbers in every column creating 5 sums.
then we need to multiply these 5 numbers (product) and divide the result by 16 (we need 1/16 of that product).
so, we have
5 + 1 = 6
1 + 6 + 4 + 8 = 19
2 + 1 + 3 = 6
2 + 5 = 7
1 + 0 + 7 = 8
6×19×6×7×8 = 38,304
38,304 / 16 = 2394
that is your code : 2394
find the circumference of circle with radius rcm
Step-by-step explanation:
By definition, pi is equal to c/d, where c is the circumference and d is the diameter.
This means that C = pi(d).
However, since diameter is twice the radius, if we let the radius be r cm, d=2r.
This gives that C=2pi(r).
Please answer this question throughly and with the work you used to answer it and I’ll give brainliest!
With the given budget, the inequality that must be used is:
$5.5*s ≤ $350
Which inequality is the correct one?
We know that the budget is $500.
Then, we know that there is a fixed cost of $150, then the budget left is:
$500 - $150 = $350
With these $350 they pay the food for the students, which costs $5.50 per student.
So the number of students that can go must be such that:
s*$5.50 ≤ $350
There says that the cost in food for the s students must be smaller than or equal to the remaining $350.
So the correct option is the second one.
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1/2(x-1/6)+2/3=5/6+1/3*(1/2-3x)
Answer:
X= 5/18
Step-by-step explanation:
A little help please
Answer:
10
Step-by-step explanation:
2(3)+4 = 10
Please help !!!! I’m desperate people.
Answer:
I believe the answers are a and e.
Step-by-step explanation:
Let me know if you want an explanation.
Hope this helps!!!
A square with side length s has an area of 324 square centimeters. This equation shows the area of the square ^{s^2}is 324
Answer:
s^2 = 324 would mean side length s = 18
Step-by-step explanation:
The square root of 324 would be 18.
A square with side length s has an area of 324 square centimeters. So, the side of the square is 18cm
What is the area of a square?The area of a square can be calculated as the square of the sides of a given figure.
The area of a square = [tex]side^2[/tex]
A square with side length s has an area of 324 square centimeters.
The area of a square = [tex]side^2[/tex]
then s = √324
=18
Thus, the side of the square is 18cm
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3. Use multiplication to find 5% of 180. 5/100 of 180 =…. 180. = ?/100 = ? %5 of 180 is ….
Answer:
9
Step-by-step explanation:
5% of 180 = 5/100 x 180
=> 5/10 x 18
=> 90/10
=> 9
Answer:
9
Step-by-step explanation:
5% of 180 = 5/100 of 180
10% = 18 -----> 5% = 9
180 = ?/1000 -------> 180 = 18000 / 100 = 180
5% of 180 = 9
explain what operation should be used to solve the equation 3.5n= 10.5 what is the value of n?
Answer: n = 3
Step-by-step explanation:
divide 3.5n by 3.5n then divide 10.5 by 3.5 which is
n = 3
Answer:
[tex]\boxed{\sf{n=3}}[/tex]
Step-by-step explanation:
To find the value of n, you have to isolate it on one side of the equation.
3.5n=10.5
First, multiply by 10 from both sides.
[tex]\sf{3.5n*10=10.5*10}[/tex]
Solve.
35n=105
Divide by 35 from both sides.
35n/35=105/35
Solve.
105/35=3
n=3
Therefore, the final answer is n=3.I hope this helps you! Let me know if my answer is wrong or not.
Solve this QUICKLY and explain, please
Answer:
Step-by-step explanation:
c
so you have to combine like terms so subtract 8 - 4 and the 4 disappears so it be like this
8 - 2x = 4 + x
-4 -2x = -4 + x
4 - 2x = x
next combine the like terms of the 2x so
4 - 2x = x
4 + 2x = +2x
4 = 2x
now you divide 4 by 2 so like this
4 = 2x
2 2
and your answer is x = 2 try to solve the other one if you need help ask me
solve pls brainliest
Answer:
No, no, no, yes, yes.
Step-by-step explanation:
A integer is a whole number, 1, 2, 3, etc.
A ball is thrown from the top of a 50-ft building with an upward velocity of 24ft/s. When will it reach its maximum height? How far above the ground will it be?
(Show your work brainliest)
Check the picture below. When will it reach its height? well, at the vertex, so
[tex]~~~~~~\textit{initial velocity in feet} \\\\ h(t) = -16t^2+v_ot+h_o \quad \begin{cases} v_o=\textit{initial velocity}&24\\ \qquad \textit{of the object}\\ h_o=\textit{initial height}&50\\ \qquad \textit{of the object}\\ h=\textit{object's height}\\ \qquad \textit{at "t" seconds} \end{cases} \\\\\\ h(t)=-16t^2+24t+50\implies \\\\[-0.35em] ~\dotfill\\\\ \textit{vertex of a vertical parabola, using coefficients}[/tex]
[tex]h(t)=\stackrel{\stackrel{a}{\downarrow }}{-16}t^2\stackrel{\stackrel{b}{\downarrow }}{+24}t\stackrel{\stackrel{c}{\downarrow }}{+50} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{ 24}{2(-16)}~~~~ ,~~~~ 50-\cfrac{ (24)^2}{4(-16)}\right)\implies \left( \cfrac{3}{4}~~,~~50-\cfrac{576}{64} \right)[/tex]
[tex]\left(\cfrac{3}{4}~~,~~50+9 \right)\implies \stackrel{\underset{\qquad \downarrow }{\textit{how far up it went}}}{\underset{\stackrel{\uparrow \qquad ~~}{\textit{when it reached it}}}{\left( \cfrac{3}{4}~~,~~59 \right)}}[/tex]
Pamela is 6 years younger than Jiri. The sum of their ages is 78 . What is Jiri's age?
Point D has coordinates (8,3). Point G has coordinates (-4,3). What is the length of segment DG?
6 units
12 units
14 units
4 units
Answer: 12 units
Step-by-step explanation:
If you graph them on a graph you count the units between them and that is your anwser.
Answer:
12 units
Step-by-step explanation:
calculate DG using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2 -y_{1} } )^2[/tex]
with (x₁, y₁ ) = D (8, 3 ) and (x₂, y₂ ) = G (- 4, 3 )
DG = [tex]\sqrt{(-4-8)^2+(3-3))^2}[/tex]
= [tex]\sqrt{(-12)^2+0^2}[/tex]
= [tex]\sqrt{144+0}[/tex]
= [tex]\sqrt{144}[/tex]
= 12
In diagram below?FG bisects
Answer: 107 degrees
Step-by-step explanation:
Find in the inverse algebraically y=2(x-3)3+1
Answer:
Step-by-step explanation:
Y=(X-3) 3+1
1. Flip the way the equation is facing
1+3 (3-x)=Y
2. Add or Subtract
4 (3-x)=Y
3. Do the parentheses
4(-3x)=Y
4. Solve for X ( Undo addition or Subtraction)
(4-4)=0
What ever you do to one side you have to do to the other!
Y-4
Your New Equation Looks Like
-3x= -4 + Y
5. Undo Multiplication
-3x/3= x
What ever you do to one side you have to do to the other!
-4/3 y/3
6. Divide Y
y/3= 3
7. New equation
X= -4/3 + 3
8. Plug in X to the Original Equation
Y=2(-4/3+3) -3 +(3+1)
9. Solve accordingly
Write the following as an inequality
X is greater than -9 and less than 9
use x only once in your inequality.
Answer:
-9 < x < 9
Step-by-step explanation: "<" is the symbol for "less than". -9 is less than x, or x is greater than -9. x is less than 9.
Help? im confused plss!
Find the area of the regular polygon with the given radius or apothem
Answer:
50 cm²
Step-by-step explanation:
Given that the regular polygon is a square, there are multiple ways you can jump directly to the answer. Perhaps the simplest is to use the formula for the area of a rhombus:
A = 1/2(d1)(d2)
where d1 and d2 are the lengths of the diagonals. Here, we see that half the diagonal is 5 cm, so the area is ...
A = (1/2)(10 cm)(10 cm) = 50 cm² . . . . area of the polygon
__
Alternate solution
If you want to use the radius and the number of sides in a formula, you can consider the area of each triangle formed by radii and a side. That triangle has area ...
A = 1/2r²sin(α)
where r is the radius and α is the central angle. For an n-sided polygon, the area is the sum of n of these triangles, and the central angle is 360°/n. Then the polygon area is ...
A = n/2·r²·sin(360°/n)
For n = 4 and r = 5 cm, the area is ...
A = (4/2)(5 cm)²(sin(360°/4)) = 2(5 cm)²(1) = 50 cm² . . . . area of square
_____
Additional comment
The formula is somewhat different if you start with the length of the apothem. One way to find the area is using the above formula and the relation between the radius and apothem:
r = a·sec(180°/n)
Another formula uses the apothem directly:
A = n·a²·tan(180°/n)
A sticker company shipped a total of 289,005 stickers last month. This month, the company shipped 338,486 stickers. Estimate the total amount of stickers shipped both months.
Round to the nearest hundred thousand.
Apples cost $1.10 per pound. Darius bought x pounds of apples for a total cost of $2.75.
. In the diagram of collinear points, if AB = 42, AC = 65, then BC = _
Answer:
Bc 23
Step-by-step explanation:
because you muply 42 to 65 and u will get that the same answer
: A group of 28 people bought tickets to a museum. The total cost for the tickets was $315. What was the cost of each ticket?
Answer:
he correct answer is D. 12 adult tickets, 4 child ticket
Step-by-step explanation:
(3a+2b−7)−(4b−10) in standard form
Answer: 3a - 2b + 3
Step-by-step explanation:
(3a + 2b - 7) - (4b - 10)
open the bracket
3a + 2b - 7 - 4b + 10
combine like terms
3a + 2b - 4b - 7 + 10
3a - 2b + 3
solve pls brainliest
Answer:
Step-by-step explanation:
1 1/2 x 4 1/2
2x1=2 2+1=3
3/2
2x4=8 8+1=9
9/2
3/2 x 9/2=
3x9=45
2x2=4
45/4
In this triangle, a = 10 cm, b = 24 cm, and c = 26 cm.
What is the area of this triangle?
312 cm²
240 cm²
130 cm²
120 cm²
120 cm^3
The equation for a triangle: 1/2bh.
1/2(a)(b)
1/2(10)(24)
1/2(240)
120 cm^3
A van can travel 18 miles on each gallon of gasoline. At that rate, how many miles can the van travel on 15 gallons of gasoline?
33 miles
83 miles
120 miles
270 miles
Answer:
270 Miles
Step-by-step explanation:
18 miles per gallon
15 gallons
Basically count 18, 15 times
18*15=270
The van can travel 270 miles