Answers
The resulting graph of the rational function is the Graph at the top right graph 2.
To depict the rational function f(x) = 2/(x - 1) + 3, we must consider its characteristics. The function has a vertical asymptote at x = 1 because the function is undefined at that point, and it has a horizontal asymptote at y = 3 due to the behavior of the function as x approaches infinity. The graph will approach these asymptotes but never cross them.
For values of x greater than 1, the function will decrease towards the horizontal asymptote because the (x - 1) in the denominator increases, which causes the value of f(x) to decrease.
However, because of the '+3' term in the function, the curve will approach y = 3 as x goes to infinity.
To graph this function, plot several points where x is not equal to 1, then draw the curve that passes through these points while approaching the respective asymptotes.
The portions of the graph should fall above the horizontal line y = 3 for x < 1 and approach y = 3 from below for x > 1.
Therefore, the resulting graph of the rational function is the Graph at the top right graph 2.
The probable question may be:
Which graph represent the rational function f(x)=2/x-1+3
Related Questions
A parking lot space is in the shape of a rectangle. If the space has a length of 23 feet and a width of 12 feet, what is the area of the parking space?
Answers
A=23*12
A=276 <the answer
Given is a parking space in the shape of rectangle with length = 23 feet and width = 12 feet. It says to find the area of parking lot.
We know the formula for area of rectangle is given by :-
Area = Length x Width
We can plug the given values in the above formula and find the answer.
Area = 23 feet x 12 feet
Area = 276 squared feets
So the area of parking space would be 276 squared feets.
Hence, final answer is 276 squared feets.
For each babysitting job, ashley charges $2.50 for bus fare plus $8 per hour for each hour she works. she charged $30.50 for her last babysitting job.
a. write a linear equation to represent the problem. be sure to define the variable you choose. __________
Answers
Variable: h = hours worked
linear equation: 30.50 = 2.50 +8h
What is the solution set of x/4≤9/x?
Answers
Answer:
x≤-6 or 0<x≤6.Option D.
Step-by-step explanation:
Given:
[tex]\frac{x}{4} \leq \frac{9}{x}.[/tex]
Subtract [tex]\frac{9}{x}[/tex] from both sides,
[tex]\frac{x}{4}-\frac{9}{x} \leq[/tex] 0
Simplifying by taking common denominator:
[tex]\frac{x^2-36}{4x}\leq[/tex]0
Factoring numerator:
[tex]\frac{(x+6)(x-6)}{4x}\leq[/tex]0
Computing the signs and selecting that one satisfies ≤ 0:
x≤ -6,0<x≤6.
Option D is the right answer.
A line has a slope of 0 and passes through the point
(7, 7). What is its equation in slope-intercept
form?
Answers
The equation of a line in slope-intercept form is [tex] y=mx+c [/tex].
Where [tex] m [/tex] is slope and [tex] c [/tex] is y-intercept.
Since [tex] m=0 [/tex], the equation of the line is [tex] y=(0)x+c\\ y=c [/tex].
Since this line passes through [tex] (7,7) [/tex]. The equation of the line is
[tex] y=7 [/tex]
The equation of a line in slope-intercept form is y=mx+c .
Where m is slope and c is y-intercept.
Since m=0 , the equation of the line is y=(0)x+c\\ y=c .
Since this line passes through (7,7) . The equation of the line is
y=7
I need help checking my work. MEDALS!!! will be awarded. I chose C.
Kidneys process nitrogenous wastes by
A) seperating water from nitrogenous wastes by passive diffusion.
B) using cells to actively pump water across a membrane.
C) storing the wastes as uric acid until they can be eliminated.
D) pumping ions across membranes to separate water from waste products.
Answers
Find the reduced odds for and the reduced odds against the event of rolling a fair die and getting a 2, 4, or 5 odds for: to odds against: to
Answers
There are 3 ways of getting a 2, 4, or 5. There are also 3 ways of NOT getting a 2, 4, 5 (namely rolling a 1, 3, or 6). That means the odds FOR would be 3:3 = 1:1.
There are 3 ways of NOT getting a 2, 4, or 5 (again rolling a 1, 3, or 6). There are also 3 ways of getting a 2, 4, 5. That means the odds AGAINST would be 3:3 = 1:1.
Reduced odds for rolling a 2, 4, or 5: 1:1
Reduced odds against rolling a 2, 4, or 5: 1:1
To determine the reduced odds for and against rolling a 2, 4, or 5 on a fair six-sided die, we need to calculate the probabilities of these events.
Step 1: Calculate the probability of rolling a 2, 4, or 5.
There are three favorable outcomes (rolling a 2, 4, or 5) out of a total of six possible outcomes.
[tex]\[ P(\text{rolling a 2, 4, or 5}) = \frac{3}{6} = \frac{1}{2} \][/tex]
Step 2: Calculate the probability of not rolling a 2, 4, or 5.
There are three unfavorable outcomes (rolling a 1, 3, or 6) out of a total of six possible outcomes.
[tex]\[ P(\text{not rolling a 2, 4, or 5}) = \frac{3}{6} = \frac{1}{2} \][/tex]
Step 3: Calculate the odds for rolling a 2, 4, or 5.
Odds for an event are given by the ratio of the number of favorable outcomes to the number of unfavorable outcomes.
[tex]\[ \text{Odds for rolling a 2, 4, or 5} = \frac{\text{Number of favorable outcomes}}{\text{Number of unfavorable outcomes}} = \frac{3}{3} = 1:1 \][/tex]
Step 4: Calculate the odds against rolling a 2, 4, or 5.
Odds against an event are given by the ratio of the number of unfavorable outcomes to the number of favorable outcomes.
[tex]\[ \text{Odds against rolling a 2, 4, or 5} = \frac{\text{Number of unfavorable outcomes}}{\text{Number of favorable outcomes}} = \frac{3}{3} = 1:1 \][/tex]
Therefore, The reduced odds for and the reduced odds against the event of rolling a fair die and getting a 2, 4, or 5
Reduced odds for rolling a 2, 4, or 5: 1:1
Reduced odds against rolling a 2, 4, or 5: 1:1
Quadrilateral ABCD is inscribed in a circle.
What is the measure of angle A?
Enter your answer in the box.
m∠A=
°
Answers
x + 2 + 3x + 6 = 180
4x + 8 = 180
4x = 172
x = 43
Now solve for A
3(43) + 6 = A
129 + 6 = A
135 = A
The measure of angle A is 135 degrees.
Hope this helps =)
The answer is m∠A= 135°
Write a real world problem that you would represent with the equation 4x+5=37.
Answers
x=8
37-5=32
32/4=8.
factor this polynomial 3y-6x+4xy-2y^2
Answers
= 4xy -6x -2y^2 +3y
= 2x(2y -3) -y(2y -3)
= (2x -y)(2y -3)
= 4xy - 2y^2 - 6x + 3y
= (4xy - 2y^2) - (6x - 3y)
= 2y(2x - y) - 3(2x - y)
= (2x - y)(2y - 3)
The graph of y = 12x2 will be more narrow than the graph of the parent function, y = x².
Question 2 options:
True
False
The quadratic function shown can be written in the form y = ax². Determine the equation of the quadratic function.
Question 4 options:
y = x²
y = -x²
y = 2x²
y = -2x²
Answers
Based on the graph attached, we know a will not be a negative number, since the graph is open upward instead of downward. A negative coefficient "flips" the graph. Since it goes through the point (1, 2) it will not be the parent function y = x²; if you substitute 1 in for x you would get a value of 1, not 2. Therefore the choice must be y = 2x².
Solve this problem. Find the number of gallons of paint needed to cover all four sides four sides) of the building shown with two coats of paint if one gallon covers 350 square feet. Disregard windows and doors. Round to the nearest gallon.
Answers
1) calculate the area all four sides
A=[12+9+12+9]*8=336 ft²
if 1 gallons---------------------------- > covers 350 ft²
X------------------------------------ > 336 ft²
X=336/350=0.96 gallons
but remember
that there are two coats of paint
therefore
0.96*2----------- > 1.92------- > 2 gallons
the answer is 2 gallons
Answer: the answer is 3 gallons of paint is required to paint the building.
Step-by-step explanation:
The area to be painted is:
= 2× [Area of Rectangle with dimensions 20 ft.×10 ft.+Area of triangle with height 5 ft. and base 20 ft.+Area of rectangle with dimensions 24 ft. and 10 ft.]
=2×[20×10+(1/2)×5×20+24×10]
=2×[200+50+240]
=2×490
=980 square ft.
Hence, the area to be painted=980 square feet.
Now, amount of paint require to cover 350 square feet=1 gallon.
i.e. 1 square feet requires=1/350 gallon of paint.
⇒ 980 square feet requires=980/350=2.8 gallons of paint.
Hence, to the nearest gallon we could say that:
3 gallons of paint is required to paint the building.
A lamp manufacturer has daily production costs of C = 0.25n2 – 10n + 800, where C is the total cost in dollars for n lamps produced.
What is a reasonable domain for this function, given the problem's context?
A) all integers
B) all real numbers
C) all positive integers
D) all positive real numbers
Answers
The reasonable domain for the given cost function, considering the context of lamp production, is all positive integers (C) because lamps can only be produced in whole, positive quantities.
The lamp manufacturer's daily production costs are given by the function C = 0.25n2 - 10n + 800, where C represents the total cost in dollars and n is the number of lamps produced. Considering the context of the problem, where production numbers must be whole and non-negative, the reasonable domain for this function is all positive integers, which represents the count of lamps that can be produced. This is because the manufacturer cannot produce a fraction of a lamp, nor can they produce a negative number of lamps. Hence, the correct choice for the domain is (C) all positive integers.
Each interior angle of a regular hexagon is 4x+24°. What is x?
Answers
.. 4x +24° = 120°
.. 4x = 96° . . . . . . . subtract 24°
.. x = 24° . . . . . . . . divide by 4
Convert 302 inches to yards
Answers
Hope this helps!
302inches/36 inches=8 yards 14 inches or
About 8.38 yards
What is the vertex form of y=-2x^2-8x+10? Give the coordinates of the vertex, state if there is a minimum or maximum, and find the equation of the line of symmetry.
This is for Algebra 2 regular.
Answers
notice the leading term's coefficient, is -2, is negative, that means the parabola is opening downwards, is facing down, so it goes up up up, reaches the U-turn and then down down down, is a "hump" or a maximum point.
[tex]\bf \textit{vertex of a vertical parabola, using coefficients} \\\\ \begin{array}{lcccl} y = & -2x^2& -8x& +10\\ &\uparrow &\uparrow &\uparrow \\ &a&b&c \end{array} \qquad \left(-\cfrac{ b}{2 a}\quad ,\quad c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left( -\cfrac{-8}{2(-2)}~~,~~10-\cfrac{(-8)^2}{4(-2)} \right)\implies \left( \cfrac{8}{-4}~~,~~10-\cfrac{64}{-8} \right) \\\\\\ \left( -2~~,~~10+8 \right)\implies (-2~~,~~18)[/tex]
and the line of symmetry, well is a vertical parabola, mirroring itself at the line x = -2, which is the x-coordinate of the vertex.
A standard number cube is rolled two times. What is the probability that the sum of the two rolls is 13?
Answers
The volume of right circular cylinder a is 22 cubic centimeters. what is the volume, in cubic centimeters with twice the radius and half the height?
Answers
[volume of right circular cylinder]=pi*r²*h
Vo=pi*r²*h--------------> original volume
Vo= 22 cm³
if twice the radius and half the height
r1=2*r
h1=h/2
then
V1=pi*ri²*h1
substituting
V1=pi*(2*r)² *(h/2)----------->V1= pi*4*r² *h/2-----------> V1=2*pi*r² *h
V1=2*[pi*r² *h]------------> V1=2Vo
V1=2*22=44 cm³
the answer is 44 cm³
To find the volume of the new cylinder with twice the radius and half the height, use the formula for the volume of a cylinder and substitute the new values. The volume of the new cylinder is also 22 cubic centimeters.
Explanation:To find the volume of the new cylinder with twice the radius and half the height, we can use the formula for the volume of a cylinder: V = πr2h.
First, we double the radius of the original cylinder. Let's say the original radius is r. The new radius would be 2r.
Next, we halve the height of the original cylinder. Let's say the original height is h. The new height would be h/2.
Substituting these values into the volume formula, we get the volume of the new cylinder as V = π(2r)2(h/2)=4πr2(h/2)=2πr2h.
So, the volume of the new cylinder is also 22 cubic centimeters.
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Red and gray bricks were used to build a decorative wall. The number of red bricks number of gray bricks was Start Fraction 5 over 2 End Fraction . There were 175 bricks used in all. How many red bricks were used?
Answers
Red = 5x
Gray = 2x
The total is 175 bricks, right?
5x+2x=7x
7x=175
x=25
The value of x is 25. Now, substitute that into the expression for red bricks, or 5x
5x=5(25)=125
There were 125 red bricks used. Hope this helps!
Final answer:
To find the number of red bricks used, the ratio 5:2 is represented as 5x:2x. Solving the equation 7x = 175 gives x = 25. Multiplying this by 5, there were 125 red bricks used.
Explanation:
The question asks us to find the number of red bricks used to build a wall when the ratio of red bricks to gray bricks is 5:2 and there were 175 bricks used in total. To solve this, we set up the ratio 5x:2x where 'x' represents the multiplier for the number of bricks, and the sum of red and gray bricks which is 5x + 2x equals the total number of bricks, 175.
First, we combine like terms: 5x + 2x = 7x. Next, we solve for 'x' by dividing both sides of the equation by 7.
7x = 175
x = 175 / 7
x = 25
We then multiply this value by 5 to find the number of red bricks: 5 * 25 = 125.
Therefore, 125 red bricks were used to build the wall.
Marta is making 3 servings of fruit salad.she adds 3/8 cup blueberries for each serving.her measuring cup holds 1/8 cup.how many times must Marta measure 1/8 cup of blueberry to have enough for the fruit salad?
Answers
1. You have the following information given in the problem above:
- Marta is making 3 servings of fruit salad.
- Marta adds 3/8 cups blueberries for each serving.
- Her measuring cup holds 1/8 cup.
2. Then, you have:
1 time----1/8 cup
x----3/8 cups
x=(3/8)/(1/8)
x= 3x8/1x8
x=24/8
x=3 times
How many times must Marta measure 1/8 cup of blueberry to have enough for the fruit salad?
The answer is: 3 times
Paul has a coupon for $2.50 off a box of name brand cereal that normally costs $12.78 the store brand cereal costs $10.98 how much will Paul save if he uses his coupon and buys the name brand cereal instead of the store brand cerial
Answers
1.Name brand cereal: $12.78 and Store brand cereal: $10.98.
2. Coupon for $2.50 off on the name brand.
What the question is asking is how much would he save if he used the coupon. So you would need to know how much it will be after the coupon is used. Here is the following steps to this question:
Step1 find out the price after coupon:
Regular price 12.78－Coupon worth 2.50 = 10.28
Now after knowing the price after coupon we need to find how much she saved
Step2 finding how much Pual saved after using to coupon and buy the named brand
Store brand price 10.98 －The price after discount 10.28 = $0.70
So Pual saved $0.70 by using the coupon and buying the named brand cereal.
Hope it helps!
an elephant in an african wildlife perserve is 59.3 years old the table shows some students estimates for the elephants age who correctly rounded the age of the elephants to the nearest year
Answers
Hope i helped:)
Have a nice day!
~Luis~
In July 2010 there were approximately 500 million Facebook users. In July 2011 there were approximately 750 million Facebook users. How many more users were there in 2011. Write your answer in scientific notation
Answers
Match the reasons with the statements in the proof.
Given: c | | d, m 4 = m 5
Prove: m 7 = m 8
1. c||d, m∠4=m∠5
Substitution
2. m∠4 = m∠7
Vertical angles are equal.
3. m∠5 = m∠8
If lines ||, alternate interior angles are equal.
4. m∠7 = m∠8
Given
Answers
Prove: m 7 = m 8
1. c||d, m∠4=m∠5
GIVEN
2. m∠4 = m∠7
If lines ||, alternate interior angles are equal.
3. m∠5 = m∠8
Vertical angles are equal.
4. m∠7 = m∠8
Substitution
Answer:
Step-by-step explanation:
Given: c is parallel to d and ∠4=∠5.
To prove: ∠7=∠8
Proof:
Statement Reason
1. c║d, ∠4=∠5 Given
2.∠4=∠7 If lines ||, alternate interior angles are equal.
3.∠5=∠8 Vertical angles are equal
Since, ∠4=∠5, therefore ∠7=∠8
4.∠7=∠8 Substitution
An isosceles triangle with angles measuring 50°, 50°, and 80° undergoes a translation, rotation, and reflection.
Determine whether the angle measures of the image of the triangle are 50°, 50°, and 80° after each transformation.
Select Yes or No for each transformation.
{Translation}
Yes?
or
No?
{Rotation]
Yes?
or
No?
{Reflection}
Yes?
or
No?
Answers
Translation will be the similar as that of the pre image, that means they will retain the same value of 50, 50 and 80.
The answer is yes.
Rotation will be similar to that of the preimage. This is because rotation of the figure will only affect the position of the original figure and not the size of the figure. Therefore the size of the angles will be 50, 50 and 80.
Reflection will be the same as that of the preimage, reason being the reflected figure always has the same size as the object and it is always same distance as the preimage is in front of the mirror.
For the isosceles triangle undergoing transformations, the angle measures will change for translation but remain the same for rotation and reflection.
No for Translation because translations do not change angle measures.
Yes for Rotation because rotations preserve angle measures.
Yes for Reflection because reflections preserve angle measures.
What is the value of x? Enter your answer in the box. x = A triangle with midsegment parallel to the base. the left side is labeled 72 cm below the midsegment and 9 cm above the midsegment. the right side is labeled 56 cm below the midsegment and 3 x minus 20 above the midsegment.
Answers
72/9 = 56/(3x -20)
We can multiply by (3x -20)/8 to get
3x -20 = 7
3x = 27
x = 9
72/9 = 56/(3x -20)
We can multiply by (3x -20)/8 to get
3x -20 = 7
3x = 27
x = 9
Jerry solved the system of equations.
X-3y= 1
7x+2y=7 As the first step, he decided to solve for y in the second equation because it had the smallest number as a coefficient. Max told him that there was a more efficient way. What reason can Max give for his statement?
Answers
Answer:
A: The variable x in the first equation has a coefficient of one so there will be fewer steps to the solution.
Step-by-step explanation:
I got it right on Edge
The value of x and y is 1 and 0 for the given system of equations.
And, the reason Max gives for his statement that " the variable x in the first equation has coefficient of one so there will be fewer steps to the solution".
What is system of equations?A system of equations is a set of two or more equations with the same variables. A solution to a system of equations is a set of values for the variable that satisfy all the equations simultaneously.
What is substitution method?The substitution method can be defined as a way to solve a linear system algebraically. In this method we substitute one y-value with the other. To put it simply, the method involves finding the value of the x-variable in terms of the y-variable.
According to the given question.
We have system of equations.
x - 3y = 1
and 7x + 2y = 7
To solve the above system of equations we use substitution method.
Since, the first the corffeficient of x in first equation is 1. So we will use the value of x of equation x -3y = 1 to substitute in second equation. Because it require fewer steps to get the solution.
So,
From x - 3y = 1
We cay say that
x = 1 + 3y
Substitute the value of x in 7x + 2y = 7.
⇒ 7(1 + 3y) + 2y = 7
⇒ 7 + 21y +2y = 7
⇒ 7 + 23y = 7
⇒ 23y = 7-7
⇒ 23y = 0
⇒ y = 0
Again susbstitute the value of y in x =1 + 3y.
⇒ x = 1 + 3(0)
⇒ x = 1
Hence, the value of x and y is 1 and 0 for the given system of equations.
Therefore, the reason Max gives for his statement that " the variable x in the first equation has coefficient of one so there will be fewer steps to the solution".
Find out more information about system of equations and substitution method here:
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HELP HELP HELP PLEASE!!!!!
What is the area of this polygon?
Answers
Answer: 35.5 [tex]unit^2[/tex]
Step-by-step explanation:
For finding the area of this polygon we can divide it into triangles and rectangle,
By the below diagram,
The area of this polygon = Area of rectangle having dimension 4× 3 + Area of triangle having base 4 unit and height 3 unit +Area of triangle having base 7 unit and height 3 unit + Area of triangle having base 7 unit and height 2 unit,
=[tex]12 + \frac{1}{2}\times 4\times 3 + \frac{1}{2}\times 7\times 3 + \frac{1}{2}\times 7\times 2[/tex]
= [tex]12 + 6 + 10.5 + 7[/tex]
= [tex]35.5\text{ square unit}[/tex]
Which type of transformation maps trapezoid PQRS onto trapezoid P'Q'R'S'?
reflection
rotation
translation
dilation
Answers
Answer is DILATION
Answer: Dilation.
Step-by-step explanation:
From the given picture , it can be seen that the size of trapezoid P'Q'R'S' is decreased from trapezoid PQRS .
Reflection , rotation and translation are rigid motions that produces congruent images and do not change the size of the shapes.
But dilation is not a rigid motion because it changes the size of the shape by using a scale factor.
Hence, the transformation maps trapezoid PQRS onto trapezoid P'Q'R'S' is "Dilation".
Donnie is solving the equation 2x2=27+3x with the quadratic formula. Which values could he use for a, b, and c? a = 2, b = −3 , c = −27 a = 2, b = −27, c = −3 a = 2, b = 3, c = 27 a = 2, b = 27, c = 3
Answers
a= 2
b= -3
c= -27
The given equation is :
[tex] 2x^{2} =27+3x [/tex]
Now let us write it in standard form:
[tex] 2x^{2} -3x-27=0 [/tex]
Comparing it with general standard form:
[tex] ax^{2} +bx+c=0 [/tex]
So we have a=2, b=-3 and c=-27
First option is correct answer .
Which of the following is a radical equation?
Answers
Answer:
D) [tex]7\sqrt{x} = 14[/tex]
Step-by-step explanation:
If x is under a radical symbol, then it is called radical equation.
For example, [tex]\sqrt{x} = 2[/tex]
[tex]\sqrt{x-2} = 5[/tex]
From the given equations, we have to find in which equation x under radical.
x + [tex]\sqrt{5} = 12[/tex], here x is not under radical.
[tex]x^{2} = 16[/tex], here also x is not under radical.
3 + x√7 =13, here x is not under radical
7[tex]\sqrt{x} = 14[/tex]
Here x is under the radical symbol.
Therefore, the answer is [tex]7\sqrt{x} = 14[/tex]