Find a formula for a function f that satisfies the following conditions. lim x→±∞ f(x) = 0, lim x→0 f(x) = −∞, f(2) = 0 lim x→7− f(x) = ∞, lim x→7+ f(x) = −∞
Answers
9514 1404 393
Answer:
f(x) = (x -2)/(x²(7-x))
Step-by-step explanation:
The horizontal asymptotes of zero mean the denominator degree needs to be greater than the numerator degree. The zero at x=2 means (x-2) will be a factor in the numerator. The limit at x=0 means there will be a factor of x² in the denominator. Since the numerator term is negative at x=0, the signs of the terms so far do not need modification.
The vertical asymptote at x=7 means there will be a factor of (x-7) in the denominator. In order for the limits to be correct, it must have a negative sign:
-(x -7) = (7 -x)
Then the function with these characteristics can be written ...
f(x) = (x -2)/(x²(7 -x))
Related Questions
what is 5(2x - 2y) - (4x + 3y)
Answers
Answer:
6x - 13y
Step-by-step explanation:
5(2x - 2y) - (4x + 3y)
10x - 10y - 4x - 3y
10x - 4x - 10y - 3y
6x - 13y
A number is equal to twice a smaller number plus 3. The same number is equal to twice the sum of the smaller number and 1. How many solutions are possible for this situation?
* Infinitely many solutions exist because the two situations describe the same line.
* Exactly one solution exists because the situation describes two lines that have different slopes and different y-intercepts.
* No solutions exist because the situation describes two lines that have the same slope and different y-intercepts.
* Exactly one solution exists because the situation describes two lines with different slopes and the same y-intercept.
Answers
Answer:
There is no solution to this.
Explanation :
We have a double system of equation to solve. Let x be the big number and let y be the smaller number, such that y < x.
x is equal to twice a smaller number plus 3, which translates into : x = 2y + 3
and x is equal to twice the sum of the smaller number and 1 : x = 2 * (y + 1)
We get this system to solve : [tex]\left \{{{x=2y+3} \atop {x=2(y+1)}} \right. \left \{{{x-2y=3} \atop {x-2y=2}} \right.[/tex]
It's either x minus 2y equals 3, or x minus 2y = 2 but it can't be both. No solutions exist because the situation describes two lines that have the same slope and different y-intercepts
303 million, 90 thousand write it in digits
Answers
There you go!
PLEASE HELP :'))
Point R is a centroid of the triangle SQU. If VR = 18 cm, what is UV?
A) 12 cm
B) 36 cm
C) 27 cm
D) 54 cm
Answers
Answer:
D) 54 cm
Step-by-step explanation:
We can use the Centroid Theorem to solve this problem, which states that the centroid of a triangle is [tex]\frac{2}{3}[/tex] of the distance from each of the triangle's vertices to the midpoint of the opposite side.
Therefore, [tex]R[/tex] is [tex]\frac{2}{3}[/tex] of the distance from [tex]U[/tex] to [tex]V[/tex], since the latter is the midpoint of the side opposite to [tex]U[/tex]. We know this because [tex]R[/tex] belongs to [tex]UV[/tex], so [tex]R[/tex] must be [tex]QS[/tex]'s midpoint due to the fact that by definition, the centroid of a triangle is the intersection of a triangle's three medians (segments which connect a vertex of a triangle to the midpoint of the side opposite to it).
We can then write the following equation:
[tex]VR=\frac{1}{3} UV[/tex]
Substituting [tex]VR = 18[/tex] into the equation gives us:
[tex]18=\frac{1}{3} UV[/tex]
Solving for [tex]UV[/tex], we get:
[tex]18=\frac{1}{3} UV[/tex]
[tex]3 *18=3*\frac{1}{3}UV[/tex] (Multiply both sides of the equation by [tex]3[/tex] to get rid of [tex]UV[/tex]'s coefficient)
[tex]54=UV[/tex] (Simplify)
[tex]UV=54[/tex] (Symmetric Property of Equality)
Therefore, the answer is D. Hope this helps!
Sociologists say that 90% of married women claim that their husband's mother is the biggest bone of contention in their marriages (sex and money are lower-rated areas of contention). Suppose that seven married women are having coffee together one morning. Find the following probabilities. (For each answer, enter a number. Round your answers to three decimal places.) (a) All of them dislike their mother-in-law. (b) None of them dislike their mother-in-law. (c) At least five of them dislike their mother-in-law. (d) No more than four of them dislike their mother-in-law.
Answers
For each married women, there are only two possible outcomes. Either they dislike their mother in law, or they do not. The probability of a women disliking their mother in law is independent of any other women, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
90% of married women claim that their husband's mother is the biggest bone of contention in their marriages (sex and money are lower-rated areas of contention).
This means that [tex]p = 0.9[/tex]
Suppose that seven married women are having coffee together one morning.
This means that [tex]n = 7[/tex]
Question a:
This is P(X = 7), so:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 7) = C_{7,7}.(0.9)^{7}.(0.1)^{0} = 0.4783[/tex]
Thus, 0.4783 = 47.83% probability that all of them dislike their mother-in-law.
Question b:
This is P(X = 0), so:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{7,0}.(0.9)^{0}.(0.1)^{7} = 10^{-7}[/tex]
Thus, [tex]10^{-7}[/tex] probability that none of them dislike their mother-in-law.
Question c:
This is:
[tex]P(X \geq 5) = P(X = 5) + P(X = 6) + P(X = 7)[/tex], so:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 5) = C_{7,5}.(0.9)^{5}.(0.1)^{2} = 0.1240[/tex]
[tex]P(X = 6) = C_{7,6}.(0.9)^{6}.(0.1)^{1} = 0.3720[/tex]
[tex]P(X = 7) = C_{7,7}.(0.9)^{7}.(0.1)^{0} = 0.4783[/tex]
Then
[tex]P(X \geq 5) = P(X = 5) + P(X = 6) + P(X = 7) = 0.1240 + 0.3720 + 0.4783 = 0.9743[/tex]
0.9743 = 97.43% probability that at least five of them dislike their mother-in-law.
Question d:
This is:
[tex]P(X \leq 4) = 1 - P(X > 4)[/tex]
Considering [tex]P(X > 4) = P(X \geq 5) = 0.9743[/tex]:
[tex]P(X \leq 4) = 1 - P(X > 4) = 1 - 0.9743 = 0.0257[/tex]
Thus, 0.0257 = 2.57% probability that no more than four of them dislike their mother-in-law.
For another example of the binomial distribution, you can check https://brainly.com/question/15557838
-5 + 3 and also what is 1/4 of 24
What is the answer i am struggling
Answers
Answer:
-5+3=-2
1/4 of 24 = 6
Step-by-step explanation:
What is the slope of the linear function that passes through the points (-2, 3) and (3, -4)?
Answers
Answer:
-7/5
Step-by-step explanation:
Slope,
(-4-3)/(3-(-2))
= -7/5
[tex]\boxed{\sf Slope(m)=\dfrac{y_2-y_1}{x_2-x_1}}[/tex]
[tex]\\ \sf\longmapsto m=\dfrac{-4-3}{3+2}[/tex]
[tex]\\ \sf\longmapsto m=\dfrac{-7}{5}[/tex]
The recipe for gelatin uses 2 cups of water with 4 packages of the gelatin mix. ? How many cups of water will be used with 12 packages of gelatin mix?
Answers
Step-by-step explanation:
2 cups of water used with 4 packs
therefore for 12 we use x cups of water
2:4
X :12
therefore 6'cups of water?
Write a linear(y =mx + b) quadratic (y = ax exponent 2) or exponential (y = a(b) x) function that models the data HELP
Answers
Answer:
y = 48x + 36
Step-by-step explanation:
m = 48
y = 48x +36
tan inverse X + tan inverse Y + tan inverse z=pie prove that X+Y+Z=xyz
Answers
Answer:
see explanation
Step-by-step explanation:
Given
[tex]tan^{-1}[/tex]x + [tex]tan^{-1}[/tex]y + [tex]tan^{-1}[/tex] z = π
let
[tex]tan^{-1}[/tex]x = A , [tex]tan^{-1}[/tex]y = B , [tex]tan^{-1}[/tex]z = C , so
x = tanA, y = tanB , z = tanC
Substituting values
A + B + C = π ( subtract C from both sides )
A + B = π - C ( take tan of both sides )
tan(A + B) = tan(π - C) = - tanC ( expand left side using addition identity for tan )
[tex]\frac{tanA+tanB}{1-tanAtanB}[/tex] = - tanC ( multiply both sides by 1 - tanAtanB )
tanA + tanB = - tanC( 1 - tanAtanB) ← distribute
tanA+ tanB = - tanC + tanAtanBtanC ( add tanC to both sides )
tanA + tanB + tanC = tanAtanBtanC , that is
x + y + z = xyz
8x( 5 x 2 ) Pls give answer
Answers
Answer:
80x
Step-by-step explanation:
Bracket first
5 x 2 = 10
8x x 10 = 80x
(Unless the 'x' next to the 8 is the term for multiplying:
8 x 10 = 80)
Answer:
80
Step-by-step explanation:
8 x (5 x 2)
8 x 10
Answer = 80
What is the equation of this graph
Answers
Answer:
y-1=x^2
Step-by-step explanation:
That is the equation of a parabola with vertex at (0,1). The equation is y-1=x^2.
–21:(–2 – 5) + ( –14) + 6.(8 – 4.3)
Answers
If that, the answer is 155.2:)) im sorry if im wrong:((
...For each of the following numbers, find the smallest number by which it should be multiplied so as to get a perfect square number. Also find the square root of the square number so obtained.
(i) 252
(ii) 180
(iii) 1008
(iv) 2028
(v) 1458
(vi) 768
Answers
Answer:
BELOW
Step-by-step explanation:
252 : multiply it by 7 to get 1764 and its square root is 42.
180: multiply it by 5 to get 900 and its square root is 30.
1008: multiply it by 7 to get 7056 and its square root is 84.
2028: multiply it by 3 to get 6084 and its square root is 78.
1458: multiply it by 2 to get 2916 and its square root is 54.
768: multiply it by 3 to get 2304 and its square root is 48.
A number should be a perfect square if its square root is a whole number. The square roots should be integers.
HOPE THIS HELPED
6) Frazer cycles the first 20 miles at an average speed of 21mph. The second
part is more uphill, and he only manages 13mph. By what percentage did his
speed decrease?
How to solve
Answers
9514 1404 393
Answer:
38.1% decrease
Step-by-step explanation:
A percentage change is found from ...
% change = (change)/(original amount) × 100%
= (new value - original amount)/(original amount) × 100%
= (13 -21)/21 × 100% = -8/21 × 100% ≈ -38.1%
Frazer's speed decreased by 38.1% during the second part.
_____
Additional comment
A negative % change represents a decrease; a positive % change represents an increase.
A circle is centered at (7, 8) and has a radius of 11. Which of the following is the equation for this circle? (x − 7)2 + (y − 8)2 = 121 (x − 7)2 + (y − 8)2 = 11 (x + 7)2 + (y + 8)2 = 121 (x + 7)2 + (y + 8)2 = 11
Answers
Answer:
(x − 7)2 + (y − 8)2 = 11
Step-by-step explanation:
I took the test
The equation of the circle with center at (7, 8) and radius of 11 is
(x - 7)² + (y - 8)² =121
The equation of a circle with center at (a, b) and radius of r is:
(x - a)² + (y - b)² = r²
The center of the circle, (a, b) = (7, 8)
That is, a = 7, b = 8
The radius, r = 11
Substitute a = 7, b = 8, and r = 11 into the equation (x - a)² + (y - b)² = r²:
(x - 7)² + (y - 8)² = 11²
(x - 7)² + (y - 8)² = 121
Therefore, the equation of the circle with center at (7, 8) and radius of 11 is
(x - 7)² + (y - 8)² =121
Learn more here: https://brainly.com/question/23226948
find the measure of a
Answers
Answer:
C
Step-by-step explanation:
e = 20 ° angles subtended by the same arc are equal
d = 20° opp base angles of an isosceles are equal
a+d =90° angles subtended by a diameter = 90°
a+20=90°
a=70°
solve the equation -x^2+5x+9=0
Answers
-x² + 5x + 9 = 0
On comparing this equation to: ax²+bx+c= 0
We get, a = -1; b = 5; c = 9
Solving by quadratic formula,
x = [-b ± √(b²-4ac)]/2a
=> x = [-5 ± √{5²-4(-1)(9)}]/2(-1)
=> x = [-5 ± √(25-(-36)]/-2
=> x = [-5 ± √(25+36)]/-2
=> x = [-5 ± √61]/-2
=> x = [-5 + √61]/-2 or [-5 - √61]/-2
=> x = (-5/-2) + (√61/-2) or (-5/-2) + (-√61/-2)
=> x = (5/2) + (-√61/2) or (5/2) + (√61/2)
So, x = (5/2) + (-√61/2) or (5/2) + (√61/2)
Look at the image to see the question
Answers
Answer:
Does the answer help you
Solve equation for the given variable
Answers
Answer:
p=30
Step-by-step explanation:
First, you need to subtract 10 from both sides to get 1/2p=25. You do this just because simplifying is much easier.
Then, you need to isolate p, so you divide 1/2 by both sides, which is the same thing as multiplying by 2. 1/2*2p=15*2.
Simplifying, you get p=30.
Answer:
2. x = 2
3. p = 30
4. n = 1/10 ---> less than 1 whole
5. r = 5/2 ----> greater than 1 whole
Step-by-step explanation:
See the images attached below for better understanding. If you don't understand the steps I've composed, please comment down below and I will help you! :)
A fruit production company has three packaging facilities, each of which uses different-sized boxes as follows: 20 pieces/box, 28 pieces/box, and 36 pieces/box. Step 1 of 2: Assuming that the truck provides the same quantity of uniformly-sized pieces of fruit to all three packaging facilities, what is the minimum number of pieces of fruit that will be delivered so that no fruit will be left over
Answers
9514 1404 393
Answer:
1260
Step-by-step explanation:
The required number is the Least Common Multiple of the box sizes:
LCM(20, 28, 36) = 4·5·7·9 = 1260
1260 pieces of fruit will be delivered so that none is left over.
I need help with this question plz
Answers
Answer:
slope = 6
tangent line y=6x-5
Step-by-step explanation:
Circle O has secants GEY and MTY meeting at Point Y. Use the given information to solve for the missing angle or arc. If the measure of arc GM is 142degree and the measure of angleY = 58.5, find the measure of arc ET.
Answers
Answer:
Hello,
answer: m∠arc ET=25°
Y is out the circle .
y is a exterior angle of the circle.
Step-by-step explanation:
m∠y=58.5°
m∠arc GM=142°
m∠arc ET=x°
m∠arc ET=25°
Stephanie went to the shoe store and bought two pairs of flip-flops. One pair was $19.95, and the other was $23.55. If she has $50.00, how much will she have left after buying the shoes?
Answers
Answer:
$6.50
Step-by-step explanation:
First start by adding the prices of the pairs of shoes combined.
19.95+23.55=43.50
subtract the total price of both pairs of shoes from her total
50-43.50 = 6.50
Which of the following graphs represents a one-to-one function? On a coordinate plane, a function has two curves connected to a straight line. The first curve has a maximum of (negative 6, 4) and a minimum of (negative 4.5, negative 1). The second curve has a maximum of (negative 3.5, 2) and a minimum of (negative 2.5, 0.5). The straight line has a positive slope and starts at (negative 2, 1) and goes through (1, 2). On a coordinate plane, a circle intersects the x=axis at (negative 2, 0) and (2, 0) and intercepts the y-axis at (0, 4) and (0, negative 4). On a coordinate plane, a v-shaped graph is facing up. The vertex is at (0,0) and the function goes through (negative 4, 4) and (4, 4). A coordinate plane has 7 points. The points are (negative 4, 1), (negative 3, 4), (negative 1, 3), (1, negative 3), (3, negative 4), (4, negative 2), (5, 3). Mark this and return
Answers
Answer:
d. this graph
Step-by-step explanation:
Please help meeee
Find the value of d.
A. 47
B. 56
C. 75
D. 30
Answers
Answer:
56
Step-by-step explanation:
Angle Formed by Two Chords= 1/2(sum of Intercepted Arcs)
75 = 1/2 (94+d)
Multiply by 2
75*2 = 94+d
150 = 94+d
Subtract 94 from each side
150-94 = d
56=d
A garden plot turned out to be a trapezoid whose parallel sides
measured 18 feet and 42 feet respectively. The garden is 12 feet wide.
What is the area of the garden plot?
Select one:
n
O a. 720 ft?
b. 9,072 ft2
O c. 42 ft?
O d. 360 ft
Answers
Answer:
Step-by-step explanation:
Trapezoid area is the Average of the parallel lines times the width
A = ½(18 + 42)(12) = 360 ft²
The area of the garden plot is 360 ft².
What is Trapezoid?
A trapezoid is a four-sided closed 2D figure which has an area and its perimeter. Two sides of the shape are parallel to each other and they are termed as the bases of the trapezoid.
Here, the length of parallel sides = 18ft. and 42 ft.
Width of plot = 12 ft.
Area of Trapezoid = 1/2 X (b₁+b₂) X h
= 1/2 X (18 + 42) X 12
= 6 X 60
= 360 sq. ft.
Thus, the area of the garden plot is 360 ft².
Learn more about trapezoid from:
https://brainly.com/question/11908553
#SPJ2
Please answer due tonight!!!
Answers
Answer:
Step-by-step explanation:
Factored form: (x - 8)(x + 1)
x-int: (8, 0) and (-1, 0)
Axis of symmetry: -(-7)/2 = 7/2
Vertex: (7/2, -81/4)
Domain: all real numbers
Range: y>= -81/4
In the xy -plane above, point C has coordinates (6,9).
Which of the following is an equation of the line that
contains points O and C
Answers
increased from 1432 to 2219. Which of the following is the approximate percent of increase
22. Between the years 2000 and 2010, the number of births in the town of Daneville
in the number of births during those ten years?
a. 55%
b. 36%
c. 64%
d. 42%
Answers
9514 1404 393
Answer:
a. 55%
Step-by-step explanation:
The percentage increase is calculated from ...
% increase = (amount of increase)/(original amount) × 100%
= (2219 -1432)/1432 × 100% = 787/1432 × 100% ≈ 54.96%
The number of births increased by about 55% during those 10 years.
Answer:
Step-by-step explanation:
2219-1432/1432 x 100% = 787/1432 x 100 = 54.9581~~ 55%
