Suppose that the functions f and g are defined as follows. f(x)= x-6/x+5 g(x)= x/x+5. find f/g. Then, give its domain using an interval or union of intervals. simplify your answers.
Answers
STEP 1:
To find f/g we divide f(x) by g(x)
[tex]\frac{f}{g}=\frac{\frac{x-6}{x+5}}{\frac{x}{x+5}}\text{ = }\frac{x-6}{x+5}\text{ }\times\text{ }\frac{x+5}{x}\text{ =}\frac{x-6}{x}[/tex]Therefore the value of f/g is
[tex]\frac{f}{g}=\frac{x-6}{x}[/tex]STEP 2:
Also, the domain is the set of all possible x-values which will make the function "work", and will output real values.
The domain of this function is
[tex]-\inftyThis implies that the function would exist for all values of x except when x=0The above domain can also be represented as :
[tex](-\infty,0)\text{ and (0,}\infty)[/tex]Related Questions
How many triangles can be formed by joining the vertices of a 10-sided polygon?
Answers
The total number of triangles formed by joining vertices of 10-sided polygon is given by the combination of 10 sides taken at 3, i.e. selection of 3 points from 10 points ( because a triangle has 3 vertices). This gives
[tex]10C3=\frac{10!}{3!(10-3)!}=\frac{10!}{3!\cdot7!}=\frac{10\cdot9\cdot8}{6}=\frac{720}{6}=120[/tex]Then, the answer is the last option: 120
Admission to a state fair is $10, and each ride ticket costs $2.50. Write an en
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EXPLANATION
Let's call t to the number of tickets and c to the total cost, the appropiate relationship would be:
c = 2.5t + 10
The variable in the expression represents the number of tickets.
What is the value of f(-5) in the piecewise function -3x + 1 when x > 1 f(x) = -2x when x = 1 2x - 1 when x < 1
Answers
Answer:
f(-5)=-11
Explanation:
Given the piecewise function:
[tex]f(x)=\begin{cases}{-3x+1,\text{ when }x>1} \\ {-2x,\text{ when }x=1} \\ {2x-1,\text{ when }x<1}\end{cases}[/tex]We want to find the value of f(-5).
When x=-5:
[tex]\begin{gathered} -5<1\implies f(x)=2x-1 \\ \text{ Therefore:} \\ f(-5)=2(-5)-1 \\ =-10-1 \\ =-11 \end{gathered}[/tex]The value of f(-5) is -11.
Show that (3 * 8 * x)⁷ = 6⁷ * 4⁷ * x⁷
Answers
Answer:
Q.E.D.
Explanation:
Given the expression
[tex](3\times8\times x)^7[/tex]We want to show that it is equal to the right-hand side.
Now, we note that: 8 = 2 x 4
Substituting 8 = 2 x 4, we have:
[tex]=(3\times2\times4\times x)^7[/tex]We then go further to get:
[tex]=(6\times4\times x)^7[/tex]Distributing the exponent, we have:
[tex]=6^7\times4^7\times x^7[/tex]This is the given right-hand side of the equation as required.
Order the following from least to greatest: 0.232, 1.2, 1.09, 0, 3, 0.9
Answers
Answer:
0, 0.232 , 0.9 , 1.09, 1.2 , 3
Quantum Logic recently expanded its operations at a cost of $450,000. Management expects that the value of the investment will grow at a rate of 8% per year compounded quarterly for the next 5 years. Find the future value of the investment
Answers
Given:
Quantum Logic recently expanded its operations at a cost of $450,000.
So, P = 450,000
The rate of growth = r = 8% = 0.08
compounded quarterly, n = 4
We will find the future value of the investment (A) after t = 5 years
We will use the following formula:
[tex]A=P\cdot(1+\frac{r}{n})^{nt}[/tex]Substitute with the given values:
[tex]\begin{gathered} A=450,000\cdot(1+\frac{0.08}{4})^{4\cdot5} \\ \\ A=450,000\cdot1.02^{20}\approx668,676.33 \end{gathered}[/tex]So, the answer will be:
The future investment = $668,676.33
In the accompanying diagram of circle O, COA is adiameter, O is the origin, OA = 1, and mLBOA = 30. Whatare the coordinates of B?
Answers
Given:
COA is a diameter
O is the origin
OA = 1
m< BOA = 30
Re-drawing the diagram to show the coordinates of the B:
Let the coordinates of B be (x,y)
Using trigonometric ratio, we can find the length of side AB
From trigonometric ratio, we have:
[tex]tan\text{ }\theta\text{ = }\frac{opposite}{adjacent}[/tex]Substituting we have:
[tex]\begin{gathered} tan\text{ 30 = }\frac{y}{1} \\ Cross-Multiply \\ y\text{ = tan30 }\times\text{ 1} \\ y\text{ = 0.577} \\ y\text{ }\approx\text{ 0.58} \end{gathered}[/tex]Hence, the coordinates of B is (1, 0.58)
Just give me the answer please, my device is at 10%
Answers
Solve for x
We can use sine
[tex]\begin{gathered} \sin 48^0=\frac{x}{17} \\ \text{Cross multiply} \\ x=17\times\sin 48^0 \\ x\text{ =17}\times0.7431448 \\ x=12.6\text{ } \end{gathered}[/tex]Based on the two data sets represented below, complete the following sentences.Options: "greater" or "less"
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We can check that the median of the dataset T is 14, and its mean is also close to 14, while the median of the dataset U is 17 and its mean is close also close to 17. We can also check that the range of the dataset T is 14 and the data is more concentrated at its center, while the range of the dataset U is 20 and the data is more dispersed.
Therefore, we can state that The center of Data Set T is less than the center of Data Set U, and the spread of Data Set T is less than the spread of Data Set U.
question In photograph
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The equation that represents the relationship between x and y in the table is (L.) y = -5x + 3.
What is an Equation in Math?In mathematics, an equation is a relationship between two expressions that are expressed as equality on each side of the equal to sign.
Given in the table is the relationship between x and y respectively.
Substitute the values of x in the respective equations to find the value of y, the resulting value which matches the value of y in the table determines the correct equation.
J. y = -5x -27
⇒ For x = -3, y = -5(-3) - 27 = 15 -27 = -12 ≠ 18
K. y = -5x + 18
⇒ For x = -3, y = -5(-3) + 18 = 15 + 18 = 33 ≠ 18
L. y = -5x + 3
⇒ For x = -3, y = -5(-3) + 3 = 15 + 3 = 18 ≈ 18
For x = -1, y = -5(-1) + 3 = 5 + 3 = 8
For x = 2, y = -5(2) + 3 = -10 + 3 = -7
For x = 6, y = -5(6) + 3 = -30 + 3 = -27
All the values of x and y in the table satisfy the equation y = -5x + 3. Hence this is the required equation that represents the relationship.
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Solve for x. Write the reasons next to each step.Submit723x+10
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x = 26/3
Explanation:We would apply the mid-segment theorem:
The base of the smaller triangle = 1/2 (the base of the bigger triangle)
The base of the smaller triangle = 3x + 10
the base of the bigger triangle = 72
3x + 10 = 1/2(72)
Reason: Mid segment is parallel to the base of the large triangle. And it is equal to half the length of the base of the large triangle
simplifying:
3x + 10 = 72/2
3x + 10= 36
subtract 10 from both sides:
3x + 10 - 10 = 36 - 10
3x = 26
DIvide both sides by 3:
3x/3 = 26/3
x = 26/3
or x = 8 2/3
use the half angle identity to find the exact value of the trigonomic expression. given 0
Answers
Given a right angle triangle:
we need to find the measure of the angle θ
As shown:
The opposite side to the angle θ = 24
The adjacent side to the angle θ = 45
So,
[tex]\begin{gathered} \tan \theta=\frac{opposite}{adjacent}=\frac{24}{45} \\ \\ \theta=\tan ^{-1}\frac{24}{45}=28.0725 \\ \\ \sin \frac{\theta}{2}=\sin \frac{28.0725}{2}=\sin 14.036=0.2425 \end{gathered}[/tex]so, the answer will be sin θ/2 = 0.2425
Brianna's teacher asks her if these two expressions 3x + 5 and 4x are equivalent.Brianna says the expressions are equivalent because the value of each expression is 20 when x = 5.Is Brianna correct synlainthink ASAP please
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Step 1
Given data
Expression 1 = 3x + 5
Expression 2 =
Consider the following relation: (1,12) ,(3, 8) , (3, 11) , (6, 9) , (7, 11) . Whichordered pair could be removed so thatthe relation is a function?Group of answer choices
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Answer: Rajesh Kumar
Step-by-step explanation I took the wok to poland
Estimate the time it would take you to drive 278 miles at38 miles per hour. Round to the nearest hour
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Speed formula:
[tex]s=\frac{d}{t}[/tex]d is the distance
t is the time
As you need to find a time having the distance and speed, solve the equation above for t:
[tex]\begin{gathered} t\cdot s=d \\ t=\frac{d}{s} \end{gathered}[/tex]Use the given data to find the time:
[tex]\begin{gathered} t=\frac{278mi}{38mi/h} \\ \\ t=7.31h \\ \\ t=7h \end{gathered}[/tex]Then, it would take you 7 hours to drive 278 mi at 38mi/hwhich of the following describes the two spheres A congruentB similarC both congruent and similarD neither congruent nor similar
Answers
The two spheres are similar since they have a proportion of their radius. This proportion is 9/6 (3/2) or 6/9 (2/3).
They are not congruent. They do not have the same radius.
Therefore, the spheres are similar.
Jason provided the following work when asked to convert 0.105 to its
simplest fraction form.
1. Why did Jason get the problem wrong?
2. Provide the work for properly writing the decimal in its simplest fraction
form.
Jason's Work:
0.105=
105/1000
21/200
Answers
Jason provided the work when asked to convert 0.105 to its simplest fraction form which is; 21/200
How to convert from decimal to fraction?For conversion from decimal to fraction, we write it in the form a/b such that the result of the fraction comes as the given decimal. To get the decimal of the form a.bcd, we will count the digits that are there after the decimal point; then we write 10 raised to that many power as the denominator and the considered number without any decimal point as the numerator.
Given that Jason's Work:
0.105
Jason provided the work when asked to convert 0.105 to its simplest fraction form which could be;
0.105 = 105/1000
= 21/200
Hence, Jason provided the work when asked to convert 0.105 to its simplest fraction form which is; 21/200
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(−1/2x+7/10)−(−3/4x−1/5)
Answers
The expression (−1/2x + 7/10) − (−3/4x − 1/5) has a value of 1/4x + 9/10 when simplified
How to evaluate the expression?From the question, the expression is given as
(−1/2x+7/10)−(−3/4x−1/5)
Rewrite the expression properly to make it legible
So, we have
(−1/2x + 7/10) − (−3/4x − 1/5)
Expression the above parameter as an equation
This is represented as
(−1/2x + 7/10) − (−3/4x − 1/5) = (−1/2x + 7/10) − (−3/4x − 1/5)
Open the brackets
So, we have the following equation
(−1/2x + 7/10) − (−3/4x − 1/5) = −1/2x + 7/10 + 3/4x + 1/5
Collect the like terms in the equation
(−1/2x + 7/10) − (−3/4x − 1/5) = 3/4x − 1/2x + 7/10 + 1/5
Evaluate
(−1/2x + 7/10) − (−3/4x − 1/5) = 1/4x + 9/10
The expression cannot be further simplified
Hence, the solution to the expression (−1/2x + 7/10) − (−3/4x − 1/5) is 1/4x + 9/10
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Angel Corporation produces calculators selling for $25.99. Its unit cost is $18.95. Assuming a fixed cost of $80,960, what is the breakeven point in units?
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The breakeven point of Angel Corporation equals to 11,500 units.
How do we get the breakeven point?Given that the unit price is $25.99, so if they sell a x units, then, the revenue is: R(x) = $25.99*x
Given that the cost per unit is $18.95, plus a fixed cost of $80,960, then, the cost of x units is: C(x) = $80,960 + $18.95*x
Now, the breakeven point is a value of x such that the cost is equal to the revenue, so we need to solve:
$25.99*x = $80,960 + $18.95*x
$25.99*x - $18.95*x = $80,960
$7.04*x = $80,960
x = $80,960/$7.04
x = 11,500 units
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the length of a rectangle is 13 centimeters less then four times it’s width it’s area is 35 centimeters find the dimensions of the rectangle
Answers
Solution:
The area of a recatngle is expressed as
[tex]\begin{gathered} \text{Area of rectangle = L}\times W \\ \text{where} \\ L\Rightarrow\text{length of the rectangle} \\ W\Rightarrow\text{ width of the rectangle } \end{gathered}[/tex]Given that the length of the rectangle is 13 centimeters less than four times its width, this implies that
[tex]L=4W-13\text{ ---- equation 1}[/tex]Tha area of the rectangle is 35 square centimeters. This implies that
[tex]36=L\times W\text{ --- equation 2}[/tex]Substitute equation 1 into equation 2. Thus,
[tex]\begin{gathered} 36=L\times W \\ \text{where} \\ L=4W-13 \\ \text{thus,} \\ 36=W(4W-13) \\ open\text{ parentheses} \\ 36=4W^2-13W \\ \Rightarrow4W^2-13W-36=0\text{ ---- equation 3} \\ \end{gathered}[/tex]Solve equation 3 by using the quadratic formula expressed as
[tex]\begin{gathered} W=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}_{} \\ \text{where} \\ a=4 \\ b=-13 \\ c=-36 \end{gathered}[/tex]thus, we have
[tex]\begin{gathered} W=\frac{-(-13)\pm\sqrt[]{(-13)^2-(4\times4\times-36)}}{2\times4}_{} \\ =\frac{13\pm\sqrt[]{169+576}}{8} \\ =\frac{13\pm\sqrt[]{745}}{8} \\ =\frac{13}{8}\pm\frac{\sqrt[]{745}}{8} \\ =1.625\pm3.411836016 \\ \text{thus,} \\ W=5.036836016\text{ or W=}-1.786836016 \end{gathered}[/tex]but the width cannot be negative. thus, the width of the recangle is
[tex]W=5.036836016[/tex]From equation 1,
[tex]\begin{gathered} L=4W-13 \\ \end{gathered}[/tex]substitute the obtained value of W into equation 1.
Thus, we have
[tex]\begin{gathered} L=4W-13 \\ =4(5.036836016)-13 \\ =20.14734-13 \\ \Rightarrow L=7.14734 \end{gathered}[/tex]Hence:
The width is
[tex]5.036836016cm[/tex]The length is
[tex]7.14734cm[/tex]why is 10'15 equal to 10'11? explain ur thinking. ___ 10'4
Answers
Exponent rule is the following:
[tex]\frac{x^a}{x^b}=x^{a-b}[/tex][tex]\text{Therefore, if for }\frac{10^{15}}{10^4}\text{ a is 15 and b is 4, therefore:}[/tex][tex]\frac{10^{15}}{10^4}=10^{15-4}[/tex][tex]So,\text{ }10^{\mleft\{15-4\mright\}}=10^{11}[/tex]Quadratic Factoring: Demonstrate solving some quadraticequations using the following methods: factoring, taking theroot, and completing the square.
Answers
The Solution:
Let's solve with the Factoring Method:
[tex]x^2-x-6=0[/tex][tex]\begin{gathered} x^2-3x+2x-6=0 \\ x(x-3)+2(x-3)=0 \\ (x+2)(x-3)=0 \end{gathered}[/tex][tex]\begin{gathered} x+2=0\text{ or }x-3=0 \\ x=-2\text{ or }x=3 \end{gathered}[/tex]Solving by the Completing the Square:
[tex]\begin{gathered} x^2-x=6 \\ x^2-x+(\frac{1}{2})^2=6+\frac{1}{4} \\ \\ (x-\frac{1}{2})^2=\frac{25}{4} \end{gathered}[/tex]Take the square root of both sides.
[tex]\begin{gathered} x-\frac{1}{2}=\sqrt{(\frac{25}{4})} \\ \\ x=\frac{1}{2}\pm\frac{5}{2}=\frac{1\pm5}{2} \end{gathered}[/tex][tex]\begin{gathered} x=\frac{1+5}{2}=\frac{6}{2}=3 \\ \\ \\ x=\frac{1-5}{2}=\frac{-4}{2}=-2 \end{gathered}[/tex]Therefore, the answers is:
[tex]x=-2\text{ or }x=3[/tex]16 1 point
Triangle congruence SSS is being shown?
True
False
|||
+||
Answers
Answer:
True
Step-by-step explanation:
SSS is being shown because the two sides are known by congruence marks, and the third side is known because it is equal--the two triangles are sharing it.
A couple of friends decide to race each other. Emmet can run 6 yards per second, whereas Ayana can run 9 yards per second. Because he is slower, Emmet also gets a head start of 30 yards. Shortly after they start running, Ayana will catch up to Emmet. How far will Ayana have to run?Write a system of equations, graph them, and type the solution.
Answers
We know the formula d=rt where d is distance, r is rate and t is time
Emmet:
d = 6 yd/s * t
Ayana:
d = 9 yd/s * t
We give Emmet 30 less yards to run
Emmet:
d - 30 = 6 yd/s * t
d = 6t + 30
Setting the equations equal to each other
9 * t = 6t + 30
Subtract 6t from each side
9t-6t = 30
3t = 30
Divide by 3
3t/3 = 30/3
t = 10 seconds
It will take 10 seconds for Ayana to catch up
Ayana:
d = 9 yd/s * t
d = 8 * 10 = 90 yds
how do we do this one there two parts to i t
Answers
Given:
[tex]8\sqrt{y}=x-5y[/tex]Find: differentiation
Explanation: on differentitaion with respect to x
[tex]\begin{gathered} 8\sqrt{y}=x-5y \\ \frac{8}{2}y^{\frac{-1}{2}}\frac{dy}{dx}=1-5\frac{dy}{dx} \\ 4y^{\frac{-1}{2}}\frac{dy}{dx}+5\frac{dy}{dx}=1 \\ (4y^{\frac{-1}{2}}+5)\frac{dy}{dx}=1 \\ \frac{dy}{dx}=\frac{1}{4y^{\frac{-1}{2}}+5} \end{gathered}[/tex][tex]\begin{gathered} \frac{-4}{2}y^{\frac{-3}{2}}\frac{dy}{dx}\frac{d^2y}{dx^2}+5\frac{d^2y}{dx^2} \\ 0=(-2y^{\frac{-3}{2}}\frac{dy}{dx}+5)\frac{d^2y}{dx^2} \\ \frac{d^2y}{dx^2}=0 \end{gathered}[/tex]put the value of
[tex]\frac{dy}{dx}[/tex]we get,
[tex]\begin{gathered} (-2\frac{y^{\frac{-3}{2}}}{4y^{\frac{-1}{2}}+5}+5)\frac{d^2y}{dx^2}=0 \\ \frac{d^2y}{dx^2}=0 \end{gathered}[/tex]Y=1/3x+2 standard form
Answers
3y - x = 6 is standard form for the given equation
What is standard form of linear equation ?The typical form for linear equations with two variables is Ax+By=C.For instance, the linear equation 2x+3y=5 is in standard form. Finding both intercepts of an equation in this style is quite easy (x and y).This form is also very useful when trying to solve systems of two linear equations.Calculationy = 1/3x + 2
3y = x + 6
3y - x = 6 is standard form
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I really need help solving thisIt’s from my trig prep bookIt asks to answer (a) and (b)
Answers
The sum in summation notation is:
[tex]\sum ^4_{r\mathop{=}0}(-1)^r(4Crx^{4-r}y^r)[/tex]The expansion is:
[tex]81x^{20}-12x^{15}y^3+\frac{2}{3}x^{10}y^6-\frac{4}{243}x^5y^9+\frac{1}{6561}y^{12}[/tex]Explanation:Given the expression:
[tex](3x^5-\frac{1}{9}x^3)^4[/tex]In summation notation, this can be written as:
[tex]\sum ^4_{r\mathop=0}(-1)^r(4Crx^{4-r}y^r)[/tex]The simplified terms of the expression is:
[tex]\begin{gathered} 4C0(3x^5)^{\mleft\{4-0\mright\}}(\frac{1}{9}y^3)^0-4C1(3x^5)^{\mleft\{4-1\mright\}}(\frac{1}{9}y^3)^1+4C2(3x^5)^{\mleft\{4-2\mright\}}(\frac{1}{9}y^3)^2-4C3(3x^5)^{\mleft\{4-3\mright\}}(\frac{1}{9}y^3)^3+4C4(3x^5)^{\mleft\{4-4\mright\}}(\frac{1}{9}y^3)^4 \\ \\ =(3x^5)^4-4(3x^5)^3(\frac{1}{9}y^3)+6(3x^5)^2(\frac{1}{9}y^3)^2-4(3x^5)^{}(\frac{1}{9}y^3)^3+(\frac{1}{9}y^3)^4 \\ \\ =81x^{20}-12x^{15}y^3+\frac{2}{3}x^{10}y^6-\frac{4}{243}x^5y^9+\frac{1}{6561}y^{12} \end{gathered}[/tex]Hello, may I please have some help with this question. Thank you.
Answers
The total distance that Kim walked in 3 days is 6 2/3 miles. We would convert this distance to mixed numbers. To do this, we would multiply 6 by 3 and add 2. The denominator would still be 3. It becomes
20/3 miles
If she walked 20/3 miles in 3 days, the number of miles that she walked per day would be
total distance/number of days
It becomes
(20/3) / 3
If we change the division sign to multiplication, it means that we would flip 3 such that it becomes 1/3. Thus, we have
20/3 * 1/3 = 20/9
= By converting to mixed numbers, we would find how many 9's are in 20. It is 2. The remainder is 20 - 18 = 2
Thus, the answer is
2 2/9 miles per day
for each of the following polynomial functions, write the equation of a different polynomial function that has the same key characteristic. explain your thinking.
Answers
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Draw the given graph.
STEP 2: Get the function plotted on the graph.
[tex]undefined[/tex]What is the gcf of 16 and 28
Answers
Answer:
4
Step-by-step explanation:
