Let f(x) = 3x + 5 and g(x) = x^2Find g(x)/f(x) and state it’s domain 3x+5/x^2; domain is the set of real numbers except 0X/8; domain is the set of all real numbersX/3x+5; domain is the set of all real numbers except -5/3 X^2/3x+5; domain is the set of all real numbers except -5/3
Answers
Solution:
Given:
\(\begin{gathered} f(x)=3x+5 \\ g(x)=x^2 \end{gathered}\)\(\frac{g(x)}{f(x)}\frac{}{}=\frac{x^2}{3x+5}\)The domain of a function is the set of input values for which the function is defined.
The function will be undefined when the denominator is 0.
Hence, we test for singularity or undefined points.
\(\begin{gathered} \frac{g(x)}{f(x)}\frac{}{}=\frac{x^2}{3x+5} \\ Equating\text{ the denominator to 0;} \\ 3x+5=0 \\ 3x=-5 \\ x=-\frac{5}{3} \\ \\ Hence,\text{ singularity or undefined point exists at }x=-\frac{5}{3} \end{gathered}\)Thus, the domain will exist at all other values except the singularity or undefined point.
Hence, the domain is;
\(x<-\frac{5}{3}\text{ OR }x>-\frac{5}{3}\)Thus, the final answer is;
\(\frac{x^2}{3x+5};\text{ domain is the set of all real numbers except }-\frac{5}{3}\)OPTION D is correct
Related Questions
si la m<1=35°,la m<4=
Answers
what is the y-intercept of the graph that is shown below? A. (-2, 0) B. (-1, 2) C. (0, 4) D. (4, 0)
Answers
A water balloon is thrown upward from a height of 5 feet with an initial velocity of 35 feet per second. The quadratic function \large h\left(t\right)=-16t^2+35t+5 represents the height of the balloon, h, in feet t seconds after it is thrown. When does the water balloon reach the height of 20 feet? round your answer to the nearest thousandth.
Answers
Since, The equation of the height with the time is provided and the balloon is thrown upwards against gravity from 5 feet, The answer is 0.255 sec.
What do you mean by equation?A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
What is initial and final velocity?When gravity first exerts force on an object, its initial velocity defines how quickly the object moves. The final velocity, on the other hand, is a vector number that gauges a moving body's speed and direction after it has reached its maximum acceleration.
initial height = 5
final height =20
height to travel =20-5 =15
\(15 = 16t^{2}+35t+5\\16t^{2}+35t-10 =0\)
solving we get, t = 0.255 or -2.44
since, -2.44 is not possible,
t = 0.255 seconds.
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Given the exponential equation
Y=1/2 * 1.6 , is it exponential growth or
decay? Why? By what percent?
Answers
The function y = 1/2(1.6)ˣ is an exponential growth function by 60%
How to determine the growth or decay in the functionFrom the question, we have the following parameters that can be used in our computation:
y = 1/2(1.6)ˣ
An exponential function is represented as
y = abˣ
Where
Rate = b
So, we have
b = 1.6
The rate of growth in the function is then calculated as
Rate = 1.6 - 1
So, we have
Rate = 0.6
Rewrite as
Rate = 60%
Hence, the rate of growth in the function is 60%
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CC has the following beginning balances in its stockholders' equity accounts on January 1, 2012: Common Stock, $100,000; Additional Paid-in Capital, $4,100,000; and Retained Earnings, $3,000,000. Net income for the year ended December 31, 2012, is $800,000. Court Casuals has the following transactions affecting stockholders' equity in 2012:
May 18 Issues 25,000 additional shares of $1 par value common stock for $40 per share.
May 31 Repurchases 5,000 shares of treasury stock for $45 per share.
July 1 Declares a cash dividend of $1 per share to all stockholders of record on July 15. Hint: Dividends are not paid on treasury stock.
July 31 Pays the cash dividend declared on July 1.
August 10 Reissues 2,500 shares of treasury stock purchased on May 31 for $48 per share.
Taking into consideration all the entries described above, prepare the statement of stockholders' equity for the year ended December 31, 2012.
Answers
Total stockholders’ equity 7,800,000
Statement of stockholders’ equity for CC for the year ended December 31, 2012:Particulars Amount ($)
Common Stock 100,000
Additional Paid-in Capital 4,100,000
Retained Earnings (Opening Balance) 3,000,000
Add: Net Income for the year ended December 31, 2012 800,000
Total retained earnings 3,800,000
Less: Cash Dividend Declared on July 1 and paid on July 31 (200,000)
Retained earnings (Closing balance) 3,600,000
Total stockholders’ equity 7,800,000
Explanation:The given information is as follows:Common Stock on January 1, 2012 = $100,000Additional Paid-in Capital on January 1, 2012 = $4,100,000
Retained Earnings on January 1, 2012 = $3,000,000Net Income for the year ended December 31, 2012 = $800,000Cash Dividend Declared on July 1 and paid on July 31 = $200,000
To prepare the statement of stockholders’ equity for the year ended December 31, 2012, we will begin by preparing the opening balances of each of the equity accounts. We will then add the net income to the retained earnings account.
The closing balance for retained earnings is then computed by subtracting the cash dividend declared and paid from the total retained earnings. Finally, the total stockholders' equity is calculated by adding the balances of all the equity accounts.
Calculations:Opening balance of common stock = $100,000
Opening balance of additional paid-in capital = $4,100,000
Opening balance of retained earnings = $3,000,000
Net Income for the year ended December 31, 2012 = $800,000
Retained earnings (Opening Balance) = $3,000,000
Add: Net Income for the year ended December 31, 2012 = $800,000
Total retained earnings = $3,800,000Less: Cash Dividend Declared on July 1 and paid on July 31 = $200,000Retained earnings (Closing balance) = $3,600,000
Total stockholders’ equity = Common Stock + Additional Paid-in Capital + Retained Earnings (Closing balance) = $100,000 + $4,100,000 + $3,600,000 = $7,800,000
Therefore, the statement of stockholders’ equity for CC for the year ended December 31, 2012, is as follows:Particulars Amount ($)
Common Stock 100,000
Additional Paid-in Capital 4,100,000
Retained Earnings (Opening Balance) 3,000,000
Add: Net Income for the year ended December 31, 2012 800,000
Total retained earnings 3,800,000
Less: Cash Dividend Declared on July 1 and paid on July 31 (200,000)
Retained earnings (Closing balance) 3,600,000
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L is the circle with the equation x²+y²=9
full question in photo :)
Answers
The values of the variables, a, b, and c obtained from the equation of the circle and the coordinates of the point P are;
a) a = 2
b = -2
c = 4
What is the general equation of a circle?The general equation of a circle is; (x - h)² + (y - k)² = r²
Where;
(h, k) = The coordinates of the center of the circle
r = The coordinates of the radius of the circle
The specified equation of a circle is; x² + y² = 9
The coordinates of the center of the circle, is therefore, O = (0, 0)
a) The coordinates of the points P and O indicates that the gradient of OP, obtained using the slope formula is; ((3·√3)/4 - 0)/(3/2 - 0) = ((3·√3)/4)/(3/2)
((3·√3)/4)/(3/2) = (√3)/2
The specified form of the gradient is; (√3)/a, therefore;
(√3)/a = (√3)/2
a = 2
The value of a is 2
b) The gradient of the tangent to a line that has a gradient of m is -1/m
The gradient of OP is; (√3)/2, therefore, the gradient of the tangent at P is -2/(√3)
The form of the gradient of the tangent at P is b/(√3), therefore;
-2/(√3) = b/(√3)
b = -2
The value of b is; -2
c) The coordinate of the point on the tangent, (0, (7·√3)/c) indicates
Slope of the tangent = -2/(√3)
((7·√3)/c - ((3·√3)/4))/(0 - (3/2)) = -2/(√3)
((7·√3)/c - ((3·√3)/4)) = (3/2) × 2/(√3) = √3
(7·√3)/c = √3 + ((3·√3)/4) = 7·√3/4
Therefore; c = 4
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A cube has sides of length 2 cm. Find its surface area.
Answers
Answer:
24 cm^2
Step-by-step explanation:
There are 6 sides on a cube.
If the length of a side is 2, then the area of a face is 4 because it is a square.
4 x 6 = 24.
log b x= y
Which variable can be negative???
Answers
Answer:
last one
Step-by-step explanation:
give explanation please, thank
you.
(b) Let S = {x|x = 1 - 1, n = 1,2,3,... ..}.. i) What is the set of boundary points of S? ii) What is the set of interior points of S. iii) Is S an open set? Briefly explain. iv) Is S a closed set? Br
Answers
(i) The set of boundary points of S is {1}.
(ii) There are no interior points in S.
(iii) S is not an open set because it does not contain any interior points.
(iv) S is a closed set because it contains all of its boundary points.
Let's analyze the set S step by step:
(i) Boundary points of S:
A boundary point of a set is a point that is neither an interior point nor an exterior point. In this case, since S consists of the elements x = 1 - 1/n for n = 1, 2, 3, ..., we can see that as n approaches infinity, x approaches 1. So, the set of boundary points of S is {1}.
(ii) Interior points of S:
An interior point of a set is a point that has an open neighborhood contained entirely within the set.
In this case, since S is defined as x = 1 - 1/n for n = 1, 2, 3, ..., we can see that as n increases, x approaches 1.
However, for any n, we can always find another n' greater than n such that 1 - 1/n' is closer to 1.
Therefore, there are no interior points in S.
(iii) S as an open set:
An open set is a set that contains all of its interior points.
Since S has no interior points (as discussed in part ii), it cannot contain all of its interior points.
Therefore, S is not an open set.
(iv) S as a closed set:
A closed set is a set that contains all of its boundary points.
In this case, the set of boundary points of S is {1}, and this set is contained within S itself.
Therefore, S contains all of its boundary points and is considered a closed set.
In summary, the set S has a single boundary point {1}, no interior points, is not an open set, and is a closed set.
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please help me i really need it
Answers
Answer:
Step-by-step explanation:
From the given information, we know that 14 boys chose German and 10 boys chose French. However, we don't have data on the number of girls choosing German or French.
Let's assume x girls chose German and y girls chose French.
Therefore, the completed two-way table would look like this:
French German Total
-----------------------------------
Boys 10 14 24
Girls y x x+y
Total 10+x 14+y 50
As for calculating the probability of picking a boy who chose German, we can use the formula:
P(Boy and German) = Number of boys who chose German / Total number of students
= 14 / 50
= 0.28 or 28%
Please note that without information about the number of girls choosing German or French, we cannot determine the specific values for boys and girls in each category.
Find the surface area of the composite figure.
Answers
The surface area of the composite figure shown in the image is 952 ft²
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Surface area of composite is the sum of the individual areas of the surface.
Hence:
Surface area of composite = 2(14 * 9) + 2(0.5 * 10 * 8) + 2(10 * 10) + 2(10 * 14) + (10 * 14) = 952 ft²
The surface area of the composite figure shown in the image is 952 ft²
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6 multiplied by 3, then increased by 10
Answers
(6 * 3) + 10
Simplifying the expression:
18 + 10
Which equals:
28
Answer:28
Step-by-step explanation:
Break it up! 6x3 is 18. Then 18 + 10 is 28 :P
Hope this helps :D
Customers at a large department store rated their satisfaction with their purchases, on a scale from 1 (least satisfied) to 10 (most satisfied). The cost of their purchases was also recorded. To three decimal places, determine the correlation coefficient between rating and purchase amount spent. Then describe the strength and direction of the relationship.
Rating,x 6 8 2 9 1 5
Amount Spent, y $90 $83 $42 $110 $27 $31
show all work
Answers
About 0.623 is the correlation coefficient between the rating and the price of the purchase.
To determine the correlation coefficient between the rating and purchase amount spent, we can use the formula for the Pearson correlation coefficient. Let's calculate it step by step:
First, we'll calculate the mean values for the rating (x) and amount spent (y):
x1 = (6 + 8 + 2 + 9 + 1 + 5) / 6 = 31/6 ≈ 5.167
y1 = (90 + 83 + 42 + 110 + 27 + 31) / 6 = 383/6 ≈ 63.833
Next, we'll calculate the deviations from the mean for both x and y:
x - x1: 0.833, 2.833, -3.167, 3.833, -4.167, -0.167
y - y1: 26.167, 19.167, -21.833, 46.167, -36.833, -32.833
Now, we'll calculate the product of the deviations for each pair of data points:
(x - x1)(y - y1): 21.723, 54.347, 69.289, 177.389, 153.555, 5.500
Next, we'll calculate the sum of the products of the deviations:
Σ[(x - x1)(y - y1)] = 481.803
We'll also calculate the sum of the squared deviations for x and y:
Σ(x - x1)² = 66.833
Σ(y - y1)² = 21255.167
Finally, we can use the formula for the correlation coefficient:
r = Σ[(x - x1)(y - y1)] / √[Σ(x - x1)² * Σ(y - y1)²]
Plugging in the values we calculated:
r = 481.803 / √(66.833 * 21255.167) ≈ 0.623
The correlation coefficient between rating and purchase amount spent is approximately 0.623.
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03. Determine side length BC. Round your
answer to the nearest tenth.
A
√11 cm
17°
C
B
4
Answers
The length of the side of the triangle BC is 0. 97 cm
How to determine the valueIt is important to note that their are different trigonometric identities. These identities are;
sinetangentcotangentcosecantsecantcosineFrom the information given, we have that;
cos θ = adjacent/hypotenuse
sin θ = opposite/hypotenuse
tan θ = opposite/adjacent
Then, we have;
sin 17 = BC/√11
cross multiply the values, we have;
BC = sin 17 (√11)
BC = 0. 97 cm
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find the time in which a train of length 132 M will cross and electric post if the speed of the train be to 6.4 km /hour
Answers
Answer:
It will take the train 1.2375 minutes to pass the tunnel
Step-by-step explanation:
Mathematically, we know that ;
time = distance/ speed
The distance here is the length of the train which is 132 m ; we can convert this to km by dividing by 1000
We have this as 132/1000 = 0.132 km
So, we have the time as;
0.132 km/6.4 km/hr = 0.020625 hr
Mathematically, we know that 60 minutes make an hour;
so we have
0.020625 * 60 = 1.2375 minutes
Spiral work
Solve the system of linear
equations for problems 6.
6) A used book store also started selling used CDs and videos. In the first week, the store
sold a combination of 45 CDs and videos. They charged $3 per CD and $7 per video and the
total sales were $187. Determine the total number of CDs and videos sold.
I
Answers
Answer:
32 CDs, 13 Videos
Step-by-step explanation:
You can represent this question using variables.
Let x = #CDs sold, Let y = #videos sold.
You can formula two equations with the information given:
3x + 7y = 187
x + y = 45
Substitute x into the equation above by reducing the equation below:
x + y = 45 -> x = 45 -y
Since we are now able to remove x from the equation, plug in your new value into the equation above.
3(45-y) + 7y =187
135 - 3y +7y = 187
135 + 4y = 187
4y = 52
y = 13
Knowing the value of y, simply plug in this y value to solve for x:
x + 13 = 45
x = 32
in 2009 a total of R36 000 was invested in two accounts. One account earned 7% annual interest and the other earned 9% .The total annual earned was R2 920 .How much was invested in each accounts?
Answers
a = amount invested at 7%
b = amount invested at 9%
we know the amount invested was ₹36000, thus we know that whatever "a" and "b" are, a + b = 36000. We can also say that
\(\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{7\% of a}}{\left( \cfrac{7}{100} \right)a}\implies 0.07a~\hfill \stackrel{\textit{9\% of b}}{\left( \cfrac{7}{100} \right)b}\implies 0.09b\)
since we know the interest earned from the invested was ₹2920, then we say that 0.07a + 0.09b = 2920.
\(\begin{cases} a + b = 36000\\\\ 0.07a+0.09b=2920 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{using the 1st equation}}{a + b = 36000\implies \underline{b = 36000-a}}~\hfill \stackrel{\textit{substituting on the 2nd equation}}{0.07a~~ + ~~0.09(\underline{36000-a})~~ = ~~2920} \\\\\\ 0.07a+3240-0.09a=2920\implies 3240-0.02a=2920\implies -0.02a=-320 \\\\\\ a=\cfrac{-320}{-0.02}\implies \boxed{a=16000}~\hfill \boxed{\stackrel{36000~~ - ~~16000}{20000=b}}\)
WILL GIVE BRAINLEST (GEOMETRY BASICS)
How would I find the measurement of 116th street and Park street and what is the measurement
Answers
Answer:
i think that the answer 90 degrees
Step-by-step explanation:
i really hope this helped
Select all ratios that are in their simplest form.
A 4:23 B 11:17 C 30:23 D 18:26 E 26:13
Answers
hope this helps
m² - 5m – 14 = 0
Please help me to solve this quadratic equation.
Don't answer if you don't know.
Answers
Answer:
The answer is m=-2 or m=7.
Step-by-step explanation:
The steps to solve this equation are below:
Factor: to get (m+2)(m−7)=0.
m+2=0 or m−7=0
m=−2 or m=7. So, your answer is m=-2 or m=7.
Answer:
m = 7
m = -2
Step-by-step explanation:
ax^2 + bx + c
1m^2 - 5m - 14
a = 1
b = -5
c = -14
-b ± √b^2 - 4ac/2a
-(-5) ± √(-5)^2 - 4(1)(-14)/2(1)
5 ± √25 + 56/2
5 ± √81/2
5 ± 9/2
5 + 9/2
14/2 = 7
5 - 9/2
-4/2 = -2
find the cofactors of each entry in the first row of matrix.
Answers
Answer:
Ac_11 = -13
Ac_12 = 44
Ac_13 = 27
Step-by-step explanation:
Plato
The cofactors of each entry in the first row of the matrix are
Ac_11 = -13
Ac_12 = 44
Ac_13 = 27
We have to determine the cofactors of each entry in the first row of the matrix.
What is the matrix?
A set of numbers is arranged in rows and columns so as to form a rectangular array. The numbers are called the elements, or entries, of the matrix.
Therefore the cofactors of each entry in the first row of the matrix is
Ac_11 = -13
Ac_12 = 44
Ac_13 = 27
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Fractional distance send help
Answers
Bro please someone help me
Answers
Answer:
A
Step-by-step explanation:
because y=one over four and one over four is a fuction
Are the ratios 9:14 and 1:2 equivalent?
yes
Submit
no
Answers
Answer:
No
Step-by-step explanation:
Solve for x. Round to nearest tenth
SOMEONE PLEASE HELP ME WITH THIS ILL GIVE YOU BRAINLIST ANSWER
Image above
Answers
Answer:
x ≈ 0.5
Step-by-step explanation:
using the tangent ratio in the right triangle
tan63° = \(\frac{opposite}{adjacent}\) = \(\frac{IJ}{JK}\) = \(\frac{1}{x}\) ( multiply both sides by x )
x × tan63° = 1 ( divide both sides by tan63° )
x = \(\frac{1}{tan63}\) ≈ 0.5 ( to the nearest tenth )
Answer:
x = 0.5
Step-by-step explanation:
We can use tan Θ to find the value of x.
tan Θ = Opposite ÷ Adjacent
Let us solve it now
tan 63 = 1 ÷ x
1.9626 = 1 ÷ x
x = 1 ÷ 1.9626
x = 0.5095
x ≈ 0.5 ( nearest 10th )
Solve the system of equations:
y = 2x - 3
y= x2 – 2x-8
A. (-1, -3) and (5, 4)
B. (0, -3) and (3, 3)
C. (4,0) and (-2,0)
D.(-1,-5) and (5,7)
Answers
Answer:
D.(-1,-5) and (5,7)
Step-by-step explanation:
I used a graphing tool to graph the two equations together. When graphed, the equations intercept (5,7) and (-1,-5). Therefore, they are the solutions to the system.
Option D should be the correct answer.
Supppose that we want to solve the Travelling Salesman Problem
(TSP) which is represented as a weighted graph G. Given a vertex
v, we can nd the 1-tree lower bound for the TSP by computing
a minimum spanning tree T on the graph G n v, then adding the
two shortest edges from v to T. Explain why the 1-tree lower
bound is indeed a lower bound on the solution to the TSP.
Answers
The 1-tree lower bound is a valid lower bound on the solution to the Traveling Salesman Problem (TSP) because it provides a lower limit on the optimal solution's cost.
To understand why the 1-tree lower bound is valid, let's consider the definition of the TSP. In the TSP, we are given a complete graph with vertices representing cities and edges representing the distances between the cities. The goal is to find the shortest Hamiltonian cycle that visits each city exactly once and returns to the starting city.
In the context of the 1-tree lower bound, we start with a given vertex v and compute a minimum spanning tree (MST) T on the graph G excluding the vertex v. An MST is a tree that spans all the vertices with the minimum total edge weight. It ensures that we have a connected subgraph that visits each vertex exactly once.
Adding the two shortest edges from v to T creates a 1-tree. This 1-tree connects the vertex v to the MST T. By construction, the 1-tree includes all the vertices of the original graph G and has a total weight that is at least as large as the weight of the optimal solution.
Now, let's consider the Hamiltonian cycle of the TSP. Any Hamiltonian cycle must contain an edge that connects the vertex v to the MST T because we need to return to the starting vertex after visiting all other cities. Therefore, the optimal solution must have a cost that is at least as large as the cost of the 1-tree.
By using the 1-tree lower bound, we have effectively obtained a lower limit on the optimal solution's cost. If we find a better solution with a smaller cost, it means that the 1-tree lower bound was not tight for that particular instance of the TSP.
In summary, the 1-tree lower bound is a valid lower bound on the TSP because it constructs a subgraph that includes all the vertices and has a cost that is at least as large as the optimal solution. It provides a useful estimate for evaluating the quality of potential solutions and can guide the search for an optimal solution in solving the TSP.
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The formula d = rt gives the distance, d, traveled in time, t, at rate, r. A motorcycle traveled 67.2 mi in 1.2 h. What was its average speed (rate)? 30 mph 56 mph 66 mph 80 mph
Answers
Answer:
56mph
Step-by-step explanation:
If d=rt,
then s=d/t,
so if d=67.2 and t=1.2,
then 67.2/1.2=56
Evaluate the expression. Will choose brainliest
Answers
Answer:
-213
Step-by-step explanation:
3|3-5|^2-(-15)^2
3(4)-225
=12-225= -213
Answer:
-213
Step-by-step explanation:
=3|x+y|²-(xy)²
Subtitute value of x and y above:
=3(|3+-5|)²-(3×-5)²
=3(|-2|)²-(-15)²
=3(2)²-(225)
=3(4)-225
=12-225
=-213
Note: If you need to ask question,I'll gladly give you answee.Thanks
The temperature fell by 18 degrees Fahrenheit today.
Write a signed number to represent this temperature change.
___
Ali received 5 dollars.
Write a signed number to represent this change.
____
Answers
Answer:
The temperature fell by 18 degrees Fahrenheit today.
Write a signed number to represent this
temperature change:
-18
Ali received 5 dollars.
Write a signed number to represent this change:
5
The signed number to represent both situations are - 18 and + 5 respectively.
What is an equation?An equation is written in the form of variables and constants separated by the operation of multiplication and division,
An equation states that terms in different forms on both sides of the equality sign are equal.
Multiplication and division do not separate the terms of an equation.
Given, The temperature fell by 18 degrees Fahrenheit today.
Assuming the change in temperature is \(T_f\) and initial temperature is \(T_i\).
The tem[parature change can be represented by,
\(T_f = T_i - 18.\)
Or - 18°F
Ali received 5 dollars, Assuming he had x dollars and after receiving he has now y dollars,
∴ The signed number represents this change.
y = x + 5.
Or + 5.
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