Answers
Answer:
c)
[tex]f(x)=\frac{1}{x(x+4)}[/tex]
Step-by-step explanation:
Hi there!
This is a Rational Function. The process of graphing it takes a lot more hard work than graphing other functions like linear, quadratic, modulus, and so on.
Here a list on how to proceed
First
1) Find the point of intersections by calculating the zeros of the function on the Numerator. In this case, we just have a 1 on top, so our graph won't intercept x-axis.
2) Calculate the vertical asymptotes by calculating the zeros of the function in the denominator, x²+4x=0 S=(0,-4) on green on the graph below.
3) Construct the table of values for x, and y
4) Trace the graph
By analyzing the asymptotes on the graph, we conclude that the correct option is C.
How to determine the rational function graphed?
To do it, we need to see at which x-values we have asymptotes. These are the values of x where the denominator becomes equal to zero.
Here we can see that we have asymptotes at:
x = 0 and x = -4
Then the denominator must be a polynomial with roots at x = 0 and x = -4, this is written as:
(x - 0)*(x - (-4)) = x*(x + 4)
So the rational function is something like:
[tex]f(x) = \frac{1}{x*(x + 4)}[/tex]
So the correct option is C.
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Related Questions
How many real and complex roots exists for a polynomial?
Answers
Step-by-step explanation:
whenever a complex number is a root of a polynomial with real coefficients, its complex conjugate is also a root of that polynomial. as an example, we'll find the roots of the polynomial..
x^5 - x^4 + x^3 - x^2 - 12x + 12.
the fifth-degree polynomial does indeed have five roots; three real, and two complex.
A savings account was opened with an initial deposit and never touched again. An account that does not meet the minimum
balance requirement is charged a service fee.
Assuming the account was open with an initial deposit below the minimum amount, the current account balance, B, is equal to the
product of the initial deposit, I, and the quantity of the difference of 1 and the monthly service fee, f, raised to the power of n, the
number of months since the account was open.
If an initial deposit of $2,586,00 is made to the account with a monthly service fee of 2% what will be the value of B after
19 months? Round to the nearest cent.
A.
$1,797.62
B. $1,603.32
C. $1,761.67
D. $3,767.31
Answers
Which term describes how the two sides of this figure are related?
O
A. Induction
O
B. Deduction
O
C. Symmetry
O
D. Scientific method
Answers
Answer:
The answer is A - symmetry.
None of the other options really have bearing in relation to the question.
Hope this helps.
Step-by-step explanation:
The given image shows the symmetry of a shape. Both the divided sides are equal halves of the shape. Therefore, option C, symmetry is correct option.
What is symmetry of a figure ?Symmetry is a property of a figure that describes how it looks the same after being transformed in a certain way. In other words, a figure is said to have symmetry if it can be divided into parts that are mirror images or identical to each other.
There are different types of symmetry, such as :reflection symmetry, rotational symmetry, translational symmetry etc.
Symmetry is an important concept in many areas of mathematics and science, such as geometry, crystallography, physics, and chemistry. It is also a fundamental aspect of beauty and aesthetics in art, architecture, and design.
The given figure can be divided into two equal halves. Hence, the two sides are in symmetry. Thus, option C is correct.
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Your complete question is attached below:
How many solutions does the nonlinear system of equations graphed below
have?
A. One
B. Two
C. Four
D. Zero
Answers
Putting two or more equations in a system means to find the set of variables that satisfies all the equations at the same time.
Moreover, the points that satisfy an equation are the points that lay on the graph described by the equation.
So, putting everything together, solving a system means to lay on all the graphs at the same time. In other words, the solutions of a system are the points of intersection between the graphs that represent the functions involved in the system.
In this case, the line and the circumference have two points of intersection, and they are the two solutions of the system.
In the absence of the graph, one can still note that the number of solutions a nonlinear system of equations has depends on the points of intersection of the curves represented by the equations. Each point of intersection represents a solution.
Explanation:Unfortunately, without the graph, it is rather difficult to directly answer how many solutions the nonlinear system of equations has. In general, the number of solutions for a nonlinear system of equations can be determined by where the curves represented by the equations intersect. The point of intersection is considered a solution. This is because at this point both equations hold true. If the curves intersect once, then there is one solution. If they intersect twice, then there are two solutions. If they never intersect, there are zero solutions.
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What is the length of cord AB
Answers
Answer:
CE = 16
Step-by-step explanation:
From my understanding, the length of cord AB is given. According to the question in the picture attached, you need to find CE.
Triangle ABD and triangle ACE are similar.
Therefore, AB/AC = BD/CE
AB = 6, AC = 8, BD = 12, CE = ?
6/8 = 12/CE
CE = 12x8/6
CE = 16
Therefore, CE is equal to 16.
!!
What is the mean of 108,305,252,113,191
Answers
Answer:
193.8
Step-by-step explanation:
Mean is the average. Find the average by dividing the sum of all numbers by the amount of numbers.
108+305+252+113+191
divided by 5
108+305+252+113+191= 969
969/5= 193.8
Final answer:
The mean of 108, 305, 252, 113, and 191 is 193.8.
Explanation:
To find the mean of a set of numbers, you need to add up all the numbers in the set and then divide the sum by the total number of values.
In this case, we have the numbers 108, 305, 252, 113, and 191.
To find the sum, you add these numbers together:
108 + 305 + 252 + 113 + 191 = 969.
Next, you divide this sum by the total number of values, which is 5 in this case.
So, the mean is 969 ÷ 5 = 193.8.
This is the average value of the set of numbers provided.
the slope in decimal form ?
Answers
Answer:
2
Step-by-step explanation:
Look at two points on the graph that are easy to read.
(0, 0) and (1, 2) are on the graph and are easy to read.
slope = (y2 - y1)/(x2 - x1) = (2 - 0)/(1 - 0) = 2/1 = 2
Answer:
-2
Step-by-step explanation:
Let's get two coordinate points and plug into the slope equation.
(1,2) and (.5,1)
[tex](y_{2} - y_{1}) / (x_{2} - x_{1} )[/tex]
(1-2) / (.5 - 1)
1 / (-.5)
-2
Violet was carrying around the steps to solve square root of 3x plus 1 = 4. On her way through the Math Factory, Violet dropped them and they mixed with other steps. Put the correct steps in order to solve square root of 3x plus 1 = 4.
A. Subtract 1 from both sides B. Subtract 4 from both sides C. Square root both sides
D. Square both sides E. Divide by 3 from both sides F. Divide by 4 from both sides
Answers
Answer:
D
Step-by-step explanation:
solve square root of 3x plus 1 = 4:
D is correct and results in 3x + 1 = 16; after this we subtract 1 from both sides and end up with 3x = 15, or x = 5.
Answer:
To solve this equation we have to first remove the square root from LHS and to remove the square we have to square both sides.
Step-by-step explanation:
The quadratic equation which violet has to solve is given as
[tex]\sqrt{3x+1}=4[/tex]................(1)
Step 1
To solve this equation we have to first remove the square root from LHS and to remove the square we have to square both sides.
After squaring both the sides we got following equation
[tex]3x+1=16[/tex]....(2)
Step 2
now subtract 1 from both sides to remove 1 from LHS
so we will get the following equation
[tex]3x=15[/tex]....(3)
Step 3
Now divide by 3 from both sides to remove 3 from LHS
Therefore,
[tex]x=\frac{15}{3}[/tex]
[tex]x=5[/tex]
if Q(-3,4), R(-2,-1),T(3,1),W(3,5) is a quadrilateral and Q'(-27,36) is the image of Q under a dilation centered at the origin, find W'
Answers
Answer:
W'(27,45)
Step-by-step explanation:
First we must fnd the scale factor of the dilation and then multiply the coordinates of W(3,5) by the scale factor.
Let k be the scale factor of the dilation centered at the origin.
The mapping for a dilation by a scale factor k is
[tex](x,y)\to (kx,ky)[/tex]
[tex]Q( - 3,4)\to Q'( - 3k,4k)[/tex]
But we were given the coordinates of the image, which is
Q'(-27,36)
Comparing coordinates:
[tex]4k = 36[/tex]
[tex] \implies \: k = 9[/tex]
We could compare the first coordinates too and get the same result.
The image of W(3,5) is given by:
[tex]W(3,5) \to \: W'(3 \times 9,5 \times 9)[/tex]
[tex]W(3,5) \to \: W'(27,45)[/tex]
The variable z is directly proportional to x, and inversely proportional to y. When x is 16 and y is 5, z has the value 16. What is the value of z when x= 21, and y= 14 Round to at least the thousandths place if needed.
Answers
Answer:
z = 7.5
Step-by-step explanation:
Given that z is directly proportional to x and inversely proportional to y then the equation relating them is
z = [tex]\frac{kx}{y}[/tex] ← k is the constant of proportionality
To find k use the condition when x = 16, y = 5, z = 16, then
k = [tex]\frac{zy}{x}[/tex] = [tex]\frac{16(5)}{16}[/tex] = 5
z = [tex]\frac{5x}{y}[/tex] ← equation of proportionality
When x = 21, y = 14, then
z = [tex]\frac{5(21)}{14}[/tex] = 7.5
Hey scale rounds the weight of object to the nearest 10th of a pound what amount would it around the following wait to
Round to the nearest 10th :
A) 53.864 pound ————
B) 14.62 pounds ————-
C) 608.97 pounds ———-
Please answer fast
Answers
B: 14.60
C: 609.00 (zeros are optional)
A hummingbird lives in a nest that is 3 meters high in a tree. The hummingbird flies 5 meters to get from the nest to a flower on the ground. How far is the flower from the base of the tree
Answers
Imagine a right triangle. The right angle is formed by the line from the nest to the ground, and the line from the tree to the flower. The hypotenuse is the direct distance from the nest to the flower. The hypotenuse is 5 meters, and the height of the nest is 3 meters. If the distance from the flower to the base of the tree is X, then 3^2 + x^2 = 5^2. So, x = 4.
Answer: 4 meters.
Step-by-step explanation: You need to set up the Pythagorean Theorem, which is a^2 + b^2 = c^2. The c is the hypotenuse. A is 3 because it is the height. We are trying to find b, the distance from the flower to the tree. C is 5.
Plug in the numbers.
3^2 + b^2 = 5^2.
Simplify.
9 + b^2 = 25.
Isolate b by subtracting 9 from each side.
B^2 =16.
Square root each side.
B = 4.
The flower is 4 meters away from the base of the tree.
the slope of the line below is -5/-7. write a point slope equation of the line using coordinates of the labeled point
Answers
Answer:
B
Step-by-step explanation:
Point slope equation is y-y₁=m(x-x₁) so as long as the x or y is not negative you have to subtract the number hence y-2=-5/7(x-6)
Answer:
B
Step-by-step explanation:
just did it
Simplify the expression below.
3 · -8 + 5 - 4 ÷ 2
A-11.5
B-21
C-12.5
S-27
Answers
3 · -8 + 5 - 4 ÷ 2
Use PEMDAS
P=parenthesis
E=exponents
M= multiplication
A= addition
S=subtraction
-24+5- 4÷ 2
-19-2
=-21
Answer is B-21
Answer:
B. -21
Step-by-step explanation:
You have to follow PEMDAS
3*-8=-24
So, -24+5-4÷2
-4÷2=-2
So, -24+5-2
Then add and subtract from left to right
-24+5=-19
-19-2=-21
mike is 7.5 miles ahead of julia running at 5.5 miles per hour and julia is running at the speed of 6 miles per hour.How long does it take julia to catch mike.
The answer is 15 hours but I am unsure as to why,can someone explain?
Answers
Answer:
15 hours.
Step-by-step explanation:
Suppose the time taken to catch Mike is t hours and the distance ran by Mike is x miles then
5.5 = x/ t (Mike) --- ...(1)
6 = (x +7.5 )/ t (Julia ).......(2)
From equation (1):
x = 5.5t ..............(3).
From equation (2):
x + 7.5 = 6t
x = 6t - 7.5............(4).
Eliminating x from equations 3 and 4:
6t - 7.5 = 5.5t
0.5t = 7.5
t = 15 hours.
A group of college students is volunteering for Homes for the Community during their spring break. They are putting the finishing touches on a house they built. Working alone, Wade can paint a certain room in 5 hours. Rhonda can paint the same room in 6 hours. How long will it take them working together to paint the room? Round your answer to the nearest hundredth if necessary.
Answers
Answer: 2.72 hours
Step-by-step explanation:
Let's call [tex]t_1[/tex] while it takes Wade to paint the room
Let's call [tex]t_2[/tex] while it takes Rhonda to paint the same room.
Then we know that:
[tex]t_1 = 5\ hours\\t_2 = 6\ hours[/tex].
Let's call it t as it takes Rhonda and Wade to paint the same room working together.
Now we use the following formula to calculate t.
[tex]\frac{1}{t}=\frac{1}{t_1}+\frac{1}{t_2}[/tex]
[tex]\frac{1}{t}=\frac{1}{5}+\frac{1}{6}[/tex]
[tex]\frac{1}{t}=\frac{11}{30}[/tex]
[tex]t=\frac{30}{11}[/tex]
[tex]t=2.72\ hours[/tex]
If they work together they will be able to paint the room in 2.72 hours
Answer: 2.73 hours
Step-by-step explanation:
What is the value of x in the equation 2(x−3)+9=3(x+1)+x?
x = −3
x = −1
x = 0
x = 3
Answers
Answer : 0
Step-by-step explanation:
2(x−3)+9=3(x+1)+x
2x-6+9=3x+3+x
3-3=4x-2x
0=2x
x=0
The value of x in the equation 2(x−3)+9=3(x+1)+x is 0 option third x = 0 is correct.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
We have a linear equation in one variable:
2(x−3)+9=3(x+1)+x
2x - 6 + 9 = 3x + 3 + x
Combine like terms
2x + 3 = 4x + 3
x = 0
Thus, the value of x in the equation 2(x−3)+9=3(x+1)+x is 0 option third x = 0 is correct.
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Turkey sandwiches cost $2.50 and veggie wraps cost $3.50 at a snack stand. Ben has sold no more than $30 worth of turkey sandwiches and veggie wraps in the first hour of business. Let x represent the number of turkey sandwiches and y represent the number of veggie wraps. The inequality represents the food sales in the first hour. If Ben has sold 4 veggie wraps, what is the maximum value of turkey sandwiches Ben could have sold? 5 6 7 10
Answers
Answer:
The maximum number of turkey sandwiches Ben could have sold is 6.
Step-by-step explanation:
We are given that turkey sandwiches cost $2.50 and veggie wraps cost $3.50 at a snack stand.
Given the information, we are to find the maximum value of turkey sandwiches Ben could have sold.
[tex] 2 . 5 0 x + 3 . 5 0 y \leq 3 0 [/tex]
Number of veggie wraps sold (y) = 4
2.50x + 3.50(4) < 30
2.50x + 14 < 30
- 14 -14
2.50x < 16
[tex]x<\frac{16}{2.50}[/tex]
[tex]x <6.4[/tex]
The maximum number of turkey sandwiches Ben could have sold is 6.
The maximum value of turkey sandwiches Ben could have sold is;
Option B; 6
Let number of turkey sandwiches be x
Let number of veggie wraps be y.
We are told that Turkey sandwiches cost $2.50 and veggie wraps cost $3.50.
Thus, for x number of Turkey sandwiches, the cost will be; 2.5x
For y number of veggie wraps, the cost will be 3.5y.
We are told he sold no more than $30 worth of turkey sandwiches and veggie wraps in the first hour of business. Thus, inequality to represent this scenario is;
2.5x + 3.5y ≤ 30
Now, he has sold 4 veggie wraps. Thus;
2.5x + 3.5(4) ≤ 30
2.5x + 14 ≤ 30
2.5x ≤ 30 - 14
2.5x ≤ 16
x ≤ 16/2.5
x ≤ 6.4
Since the number can't be decimal, we approximate to a whole number to get; x = 6
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For Cynthia's third lab report, she calculated the mass of an object as it slid down an inclined plane. She got the following three masses.
1.20 kg
0.91 kg
1.08 kg
The true mass of the object is 1 kg.
Cynthia's percent error was [blank]−−−−−−%.
Enter your answer as the number that correctly fills in the blank, rounded to two decimal places, like this: 42.53
Answers
Answer:
Percent error: 6.00%
Step-by-step explanation:
We find the mean of the three masses
Mean = 1.20 + 0.91 + 1.08 / 3
Mean = 1.06 kg
The experimental value of mass is = 1.06 kg
The actual value of mass = 1 kg
The percent error is: (experimental value - actual value/actual value)*100
Percent error : (1.06 - 1 / 1)*100
Percent error: 6.00%
Answer:
6.33
Step-by-step explanation:
1. Find the average:
1.20+0.91+1.08 = 3.19
3.19/3 = 1.06333... (aka the Average)
2. Subtract the average by the True mass:
1.06333... - 1 (the True Mass) = 0.06333...
3. Divide answer by the True mass:
[Because when you divide it by the True Mass it's still 0.06333...]
4. Multiply by 100 (to get the percentage)
0.06333 * 100 = 6.333...
5. In result 6.33% is the correct answer.
Square root of 4/(7-3i)+(2+5i)
Answers
you can do it ans is above
Quadrilateral ABCD is similiar to quadrilateral EFGH. The lengths of the three longest sides in quadrilateral ABCD are 20 feet, 18 feet, and 14 feet long. If the two shortest sides of quadrilateral EFGH are 6 feet long and 5 feet long, how long is the 4th side on quadrilateral ABCD
Answers
Answer:
35/3 ft = 11 2/3 ft
Step-by-step explanation:
We make a table of the lengths of the sides in descending order of side length. Each line contains two corresponding sides.
Quadrilateral Quadrilateral
ABCD EFGH
Side 1 20 ft ?
Side 2 18 ft ?
Side 3 14 ft 6 ft
Side 4 ? 5 ft
The line corresponding to side 3 is the only line that has the lengths of both corresponding sides.
The ratio of the length of sides in ABCD to EFGH is 14/6 = 7/3.
To find the length of the 4th sides of ABCD, we multiply the length of the 4th side of EFGH by the ratio.
7/3 * 5 ft = 35/3 ft = 11 2/3 ft
Which is the standard form of the equation of the parabola that has a vertex of (3,1) and a directrix of x= -2?
Answers
Answer:
(y-1)^2=20(x-3)
Step-by-step explanation:
The parabola is sideways so the squared part will be on the y.
The equation will be using is (y-k)^2=4p(x-h)
where (h,k) is the vertex.
p tells us which way the parabola opens by the sign.
p also tells us how far the directrix is from the vertex or the vertex from the focus.
Anyways if you graph the vertex and the directrix you will see the parabola opens to the right so p is going to be positive.
Now since the directrix is at x=-2 and the vertex is at (3,1) then p=3-(-2)=5. 5 means that the directrix and vertex are 5 units apart.
The vertex was given as (3,1) so h=3 and k=1.
Let's plug this information in:
(y-1)^2=4*5(x-3)
Let's simplify just a little.
(y-1)^2=20(x-3)
Answer:
C
Step-by-step explanation:
on edge
3 units
V13 units
2 units
In this right triangle, the length of the hypotenuse, BC, is units:
Answers
Answer:
[tex]\large\boxed{BC=\sqrt{13}}[/tex]
Step-by-step explanation:
[tex]\text{If}\ a\leq b\leq c\ \text{are lengths of sides of a right triangle, then}\\\\a^2+b^2=c^2.\\\\\text{We have:}\ 2<3<\sqrt{13}\\\\\text{Substitute:}\\\\2^2+3^2=(\sqrt{13})^2\qquad\text{use}\ (\sqrt{a})^2=a\\4+9=13\\13=13\qquad\bold{CORRECT}\\\\\text{The hypotenuse is the longest side of a right triangle.}\\\text{Therefore}\ BC=\sqrt{13}[/tex]
what is 4/2 ÷ 2 +(3^2 - 1)
Answers
Answer:
9
Step-by-step explanation:
Good ol' PEMDAS
First things first, we simplify what is in the parentheses.
4/2 ÷ 2 + (3² - 1)
4/2 ÷ 2 + (9 - 1)
4/2 ÷ 2 + 8
Next we do division. Because there are two instances of division, we work left-to-right. Note that a fraction such as 4/2 is division itself.
4/2 ÷ 2 + 8
2 ÷ 2 + 8
1 + 8
Lastly, it just solving the addition.
1 + 8 = 9
the answer would be 9
Solve |y-2|<10
——————————
Answers
[tex]|y-2|<10\\y-2<10 \wedge y-2>-10\\y<12 \wedge y>-8\\y\in(-8,12)[/tex]
Which of the following is the equation of
the line passing through the points (1, 1)
and (-3,5)?
(A) y=x
(B) y= -x
(C) y= -1x – 2
(D) y= -1x + 2
Which of the following is the equation of a
line with a slope of 0 passing through (2,5)?
(A) x = 2
(B) x= -2
(C) y=5
(D) y= -5
Answers
Answer:
a) Option A is correct.
b) Option C is correct.
Step-by-step explanation:
a) Which of the following is the equation of the line passing through the points (1, 1) and (-3,5)?
We will use the equation
(y-y₁)=m(x-x₁)
m= (y₂-y₁)/(x₂-x₁)
m= (5-1)/(-3-1)
m= 4/-4
m= -1
Consider point (1,1) and Putting value of m
(y-y₁)=m(x-x₁)
(y-1)=1(x-1)
y-1=x-1
y=x-1+1
y=x
So, Option A is correct.
b) Which of the following is the equation of a line with a slope of 0 passing through (2,5)?
The formula used is:
y= mx+b
Finding b:
5=0(2)+b
=> b = 5
So, equation is:
y = mx+b
y=0x+5
y=5
So, Option C is correct.
Which similarity postulate or theorem can be used to verify that the two
triangles shown below are similar?
Answers
What number comes next in the series? 31, 1031, 402, 16, ____
Answers
Answer:
Another person already answered this question. Their name is writersparadise. I give all credit to him/her for this answer.
Step-by-step explanation:
There could be many answers for this question. In general, the number that comes after 16 is a number with 8 as the sum of its digits.
Explanation:
1st number 31 – Sum of digits is 3 + 1 = 4
2nd number 1031 – Sum of digits is 1 + 0 + 3 + 1 = 5
3rd number 402 – Sum of digits is 4 + 0 + 2 = 6
4th number 16 – Sum of digits is 1 + 6 = 7
Therefore, the missing number could be the single digit number 8 or any of the two-digit numbers 17, 26, 35, 44, 53, 62, 71 or 80. It could also be a bigger number with the digits of any of the given two-digit numbers and 0 for the other digits such as 260 or 7001.
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Which statement best describes triangles UWW and
XYZ?
Answers
Answer:
Similar but not congruent
Step-by-step explanation:
For them to be congruent, they have to have same everything but not necessarily the same orientation. They are not congruent because their corresponding sides aren't the same measurement.
You can tell if two triangles are similar if each pair of corresponding are congruent.
They will also have corresponding sides are proportional.
That is 50/40=60/48=40/32 in this case? Well does it? It does, because each one of them is equal to 1.25.
Answer:
The correct answer is second option
They are similar, but not congruent
Step-by-step explanation:
From the given diagram we can see two triangles.
ΔUVW and ΔXYZ
m<X = m<U,
m<Y = m<V and
m<Z = m<W
Therefore two triangles are similar
The sides of these two triangles are not congruent, therefore these two triangles are not congruent.
The correct answer is second option
They are similar, but not congruent
Complete the equation of the line through (6,-6) and (8,8).
Use exact numbers.
y=?
Answers
use slope formula so, y2 - y1 over x2 - x1 to get your m value or your slope which is 7. then plug in the slope and a random set of point so I used (6, -6). -6 = 6(7) + b, simplify.
-6 = 42 + b, subtract 42 which leaves you with b= -48. hope this helps :)
Answer:
7x-48
Step-by-step explanation: