Answers
Given:
[tex]F(x)=\int_2^x(t^3+6t-4)dt[/tex]Find-:
[tex]F(x),F(2),F(5),F(8)[/tex]Sol:
[tex]\begin{gathered} F(x)=\int_2^x(t^3+6t-4)dt \\ \\ \end{gathered}[/tex]Use integration then:
[tex]\begin{gathered} F(x)=\int_2^x(t^3+6t-4)dt \\ \\ F(x)=[\frac{t^4}{4}+\frac{6t^2}{2}-4t]_2^x^ \\ \\ \\ F(x)=\frac{x^4}{4}+3x^2-4x-\frac{2^4}{4}-3(2)^2+4(2) \\ \\ F(x)=\frac{x}{4}^4+3x^2-4x-8 \end{gathered}[/tex]The function value at x = 2 is:
[tex]\begin{gathered} F(x)=\frac{x^4}{4}+3x^2-4x-8 \\ \\ F(2)=\frac{2^4}{4}+3(2)^2-4(2)-8 \\ \\ F(2)=4+12-8-8 \\ \\ F(2)=16-16 \\ \\ F(2)=0 \end{gathered}[/tex]The function value at x = 5
[tex]\begin{gathered} F(x)=\frac{x^4}{4}+3x^2-4x-8 \\ \\ F(5)=\frac{5^4}{4}+3(5)^2-4(5)-8 \\ \\ F(5)=156.25+75-20-8 \\ \\ F(5)=203.25 \end{gathered}[/tex]Function value at x = 8
[tex]\begin{gathered} F(x)=\frac{x^4}{4}+3x^2-4x-8 \\ \\ F(8)=\frac{8^4}{4}+3(8)^2-4(8)-8 \\ \\ F(8)=1024+192-32-8 \\ \\ F(8)=1216-40 \\ \\ F(8)=1176 \end{gathered}[/tex]Related Questions
True or False-Choose "A" for true or "B" for false.40. The inverse property of addition states that a number added to its reciprocal equals one.41. The associative properties state that the way in which numbers are grouped does notaffect the answer.42. The identity property of addition states that zero added to any number equals thenumber.43. The distributive property is the shortened name for the distributive property ofmultiplication over addition.44. The commutative property of addition states that two numbers can be added in anyorder and the sum will be the same.45. is the multiplicative inverse of35346. One is the identity element for addition.
Answers
Given
Statements
Find
Correctness of statements
Explanation
40) False (sum of number and its opposite is 0)
41)True
42) True
43) True
44) True
45) True
46) False (One is Identity Element for multiplication)
Final Answer
40) False
41)True
42) True
43) True
44) True
45) True
46) False
Two wheelchair ramps, each 10 feet long, lead to the two ends of the entrance porch of Mr. Bell's restaurant. The two ends of the porch are at the same height from the ground, and the start of each ramp is the same distance from the base of the porch. The angle of the first ramp to the ground is 24°.Which statement must be true about the angle of the second ramp to the ground?A. It could have any angle less than or equal to 24°.B. It must have an angle of exactly 24°.C. It could have any angle greater than or equal to 24°.D. Nothing is known about the angle of the second ramp.
Answers
Given statement
The ramps have
- the same height
- the same angle measure relative to the ground
- the two ends of the porch are at the same height from the ground
- the start of each ramp is the same distance from the base of the porch
A pictorial description of the problem is shown below:
Since the two ramps have similar descriptions, the angle measure of the second ramp to the ground would be exactly 24 degrees
Answer: Option B
option b your welcome
May I please get help with this. I have tried multiple times but still could not get the correct or at least accurate answers
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step 1
Find out the value of y
we have that
y+75=180 degrees ------> by same side ineterior angle
help meeeeeeeeee pleaseee !!!!!
Answers
The values of the functions are determined as:
a. (f + g)(x) = 3x² + 2x
b. (f - g)(x) = -3x² + 2x
c. (f * g)(x) = 6x³
d. (f/g)(x) = 2/3x
How to Determine the Value of a Given Function?To evaluate a given function, substitute the equation for each of the functions given in the expression that needs to be evaluated.
Thus, we are given the following functions as shown above:
f(x) = 2x
g(x) = 3x²
a. To find the value of the function (f + g)(x), add the equations for the functions f(x) and g(x) together:
(f + g)(x) = 2x + 3x²
(f + g)(x) = 3x² + 2x
b. To find the value of the function (f - g)(x), find the difference of the equations of the functions f(x) and g(x):
(f - g)(x) = 2x - 3x²
(f - g)(x) = -3x² + 2x
c. To find the value of the function (f * g)(x), multiply the equations of the functions f(x) and g(x) together:
(f * g)(x) = 2x * 3x²
(f * g)(x) = 6x³
d. To find the value of the function (f/g)(x), find the quotient of the equations of the functions f(x) and g(x):
(f/g)(x) = 2x/3x²
(f/g)(x) = 2/3x.
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there are 3 members on a hockey team (including all goalie) at the end of a hockey game each member if the team shakes hands with each member of the opposing team. how many handshakes occur?
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Use U-Subscription to solve the following polynomial. Compare the imaginary roots to the code breaker guide. Hi this is a project and this is one of the questions, I have the guide so ignore the code piece part.
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We will substitute the variable x with the variable u using the following relation:
[tex]u=x^2[/tex]Then, we can convert the polynomial as:
[tex]4x^4+2x^2-12=4u^2+2u-12[/tex]We can use the quadratic equation to calculate the roots of u:
[tex]\begin{gathered} u=\frac{-2\pm\sqrt[]{2^2-4\cdot4\cdot(-12)}}{2\cdot4} \\ u=\frac{-2\pm\sqrt[]{4+192}}{8} \\ u=\frac{-2\pm\sqrt[]{196}}{8} \\ u=\frac{-2\pm14}{8} \\ u_1=\frac{-2-14}{8}=-\frac{16}{8}=-2 \\ u_2=\frac{-2+14}{8}=\frac{12}{8}=1.5 \end{gathered}[/tex]We have the root for u: u = -2 and u = 1.5.
As u = x², we have two roots of x for each root of u.
For u = -2, we will have two imaginary roots for x:
[tex]\begin{gathered} u=-2 \\ x^2=-2 \\ x=\pm\sqrt[]{-2} \\ x=\pm\sqrt[]{2}\cdot\sqrt[]{-1} \\ x=\pm\sqrt[]{2}i \end{gathered}[/tex]For u = 1.5, we will have two real roots:
[tex]\begin{gathered} u=1.5 \\ x^2=1.5 \\ x=\pm\sqrt[]{1.5} \end{gathered}[/tex]Then, for x, we have two imaginary roots: x = -√2i and x = √2i, and two real roots: x = -√1.5 and x = √1.5.
Answer:
Let u = x²
Equation using u: 4u² + 2u - 12
Solve for u: u = -2 and u = 1.5
Solve for x: x = -√2i, x = √2i, x = -√1.5 and x = √1.5
Imaginary roots: x = -√2i and x = √2i
Real roots: x = -√1.5 and x = √1.5
I need some help. Could someone explain it to me?
Answers
Problem
We have the following table given:
x y
0 2
1 6
4 -9
8 8
Solution
We know that the domain correspond to the value of x in the relationship and then the correct answer for this case would be:
2
0
Jusrt 2,9 are the values in the domain of the function
What is the equation of the following line written in slope-intercept form? Oy=-3/2x-9/2
Oy=-2/3x+9/2
Oy=3/2x-9/2
Answers
The equation of the line in slope-intercept form is: C. y = -3/2x - 9/2
How to Write the Equation of a Line?If we determine the slope value, m, and the y-intercept value of the line, b, we can write the equation of a line in slope-intercept form as y = mx + b by substituting the values.
Slope of a line (m) = change in y / change in x.
y-intercept of a line is the point on the y-axis where the value of x = 0, and the line cuts the y-axis.
Slope of the line in the diagram, m = -3/2
y-intercept of the line, b = -9/2.
Substitute m = -3/2 and b = -9/2 into y = mx + b:
y = -3/2x - 9/2 [equation in slope-intercept form]
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Needing assistance with question in the photo (more than one answer)
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By definition, the probability of an event has to be between 0 and 1.
Given that definition the options 1.01, -0.9, -5/6 and 6/5 cannot be the probability of an event.
For the compound inequalities below (5-7), determine whether the inequality results in an overlapping region or a combined region. Then determine whether the circles are open are closed. Finally, graph the compound inequality. Simplify if needed. x-1>_5 and 2x<14
Answers
The inequalities are:
[tex]x-1\ge5\text{ and }2x<14[/tex]So, we need to solve for x on both inequalities as:
[tex]\begin{gathered} x-1\ge5 \\ x-1+1\ge5+1 \\ x\ge6 \end{gathered}[/tex][tex]\begin{gathered} 2x<14 \\ \frac{2x}{2}<\frac{14}{2} \\ x<7 \end{gathered}[/tex]Now, we can model the inequalities as:
So, the region that results is an overlapping region and it is written as:
6 ≤ x < 7
So, the lower limit 6 is closed and the upper limit 7 is open.
Answer: The region is overlaping and it is 6 ≤ x < 7
Hi, can you help me to solve thisexercise, please!!For cach polynomial, LIST all POSSIBLE RATIONAL ROOTS•Find all factors of the leading coefficient andconstant value of polynonnal.•ANY RATIONAL ROOTS =‡ (Constant Factor over Leading Coefficient Factor)6x^3+7x^2-3x-1
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1) We can do this by listing all the factors of -1, and the leading coefficient 6. So, we can write them as a ratio this way:
[tex]\frac{p}{q}=\pm\frac{1}{1,\:2,\:3,\:6}[/tex]Note that p stands for the constant and q the factors of that leading coefficient
2) Now, let's test them by plugging them into the polynomial. If it is a rational root it must yield zero:
[tex]\begin{gathered} 6x^3+7x^2-3x+1=0 \\ 6(\pm1)^3+7(\pm1)^2-3(\pm1)+1=0 \\ 71\ne0,5\ne0 \\ \frac{1}{2},-\frac{1}{2} \\ 6(\pm\frac{1}{2})^3+7(\pm\frac{1}{2})^2-3(\pm\frac{1}{2})+1=0 \\ 2\ne0,\frac{7}{2}\ne0 \\ \\ 6(\pm\frac{1}{3})^3+7(\pm\frac{1}{3})^2-3(\pm\frac{1}{3})+1=0 \\ 1\ne0,\frac{23}{9}\ne0 \\ \frac{1}{6},-\frac{1}{6} \\ 6(\frac{1}{6})^3+7(\frac{1}{6})^2-3(\frac{1}{6})+1=0 \\ \frac{13}{18}\ne0,-\frac{5}{3}\ne0 \end{gathered}[/tex]3) So the possible roots are:
[tex]\pm1,\pm\frac{1}{2},\pm\frac{1}{3},\pm\frac{1}{6}[/tex]But there are no actual rational roots.
Choose an equation that models the verbal scenario. The cost of a phone call is 7 cents to connect and an additional 6 cents per minute (m).
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"The cost of a phone call is 7 cents to connect and an additional 6 cents per minute (m)"
If "C" indicates the total cost of a phone call and "m" corresponds to the number of minutes the phone call lasted.
The phone call costs 7 cents to connect, this means that regardless of the duration of the call, you will always pay this fee. This value corresponds to the y-intercept of the equation.
Then, the phone call costs 6 cents per minute, you can express this as "6m"
The total cost of the call can be calculated by adding the cost per minute and the fixed cost:
[tex]C=6m+7[/tex]Which of the following is not a correct way to name the plane.
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For this case the first option is correct Plane P
the marketing department of a company has determined that the profit for selling x units of a product is appropriated by function f(x)= 15× -600
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You have the following function for the profit for selling x units of a product:
f(x) = 15x - 600
in order to determine the profit for 15,600 units, replace x = 15,600 into the previous function and simplify:
f(15,600) = 15(15,600) - 600 = 233,400
Hence, the profit for 15,600 units is $233,400
Identity two angles that are marked congruent to each other on the diagram below.(Diagram is not to scale.)Mthth& congruent toSub Arwwer
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Congruency in this context is a term that describes a pair of angles as being identical.
In our shape, we have a parallelogram and
could you please help me answer this please and thank you it's about the rectangular prism....
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ANSWER:
[tex]A_T=8+8+20+20+40+40[/tex]STEP-BY-STEP EXPLANATION:
In this case, what we must do is calculate the face area and then add each face, like this:
The area of each area is the product between its length and its width, therefore
[tex]\begin{gathered} A_1=2\cdot4=8 \\ A_2=10\cdot4=40 \\ A_3=10\cdot2=20_{} \\ A_4=10\cdot4=40 \\ A_5=10\cdot2=20_{} \\ A_6=2\cdot4=8 \end{gathered}[/tex]The total area would be the sum of all the areas, if we organize it would be like this:
[tex]A_T=8+8+20+20+40+40[/tex]A lab assistant needs to create a 1000 ML mixture that is 5% hydroelectric acid. The assistant has solutions of 3.5% and 6% in supply at the lab. Using the variables x and y to represent the number of milliliters of the 3.5% solution and the number of milliliters of the 6% solution respectively, determine a system of equation that describes the situation the situation.Enter the equations below separated by a comma How many milliliters of the 3.5% solution should be used?How many milliliters of 6% solution should be used?
Answers
Given:
A lab assistant needs to create a 1000 ML mixture that is 5% hydroelectric acid.
The assistant has solutions of 3.5% and 6% in supply at the lab.
let the number of milliliters from the solution of 3.5% = x
And the number of milliliters from the solution of 6% = y
so, we can write the following equations:
The first equation, the sum of the two solutions = 1000 ml
So, x + y = 1000
The second equation, the mixture has a concentration of 5%
so, 3.5x + 6y = 5 * 1000
So, the system of equations will be as follows:
[tex]\begin{gathered} x+y=1000\rightarrow(1) \\ 3.5x+6y=5000\rightarrow(2) \end{gathered}[/tex]Now, we will find the solution to the system using the substitution method:
From equation (1)
[tex]x=1000-y\rightarrow(3)[/tex]substitute with (x) from equation (3) into equation (2):
[tex]3.5\cdot(1000-y)+6y=5000[/tex]Solve the equation to find (y):
[tex]\begin{gathered} 3500-3.5y+6y=5000 \\ -3.5y+6y=5000-3500 \\ 2.5y=1500 \\ y=\frac{1500}{2.5}=600 \end{gathered}[/tex]substitute with (y) into equation (3) to find x:
[tex]x=1000-600=400[/tex]So, the answer will be:
Enter the equations below separated by a comma
[tex]x+y=1000,3.5x+6y=5000[/tex]How many milliliters of the 3.5% solution should be used?
400 milliliters
How many milliliters of 6% solution should be used?
600 milliliters
I need help with some problems on my assignment please help
Answers
The circumcenter of a triangle is the center of a circumference where the three vertex are included. So basically we must find the circumference that passes through points O, V and W. The equation of a circumference of a radius r and a central point (a,b) is:
[tex](x-a)^2+(y-b)^2=r^2[/tex]We have three points which give us three pairs of (x,y) values that we can use to build three equations for a, b and r. Using point O=(6,5) we get:
[tex](6-a)^2+(5-b)^2=r^2[/tex]Using V=(0,13) we get:
[tex](0-a)^2+(13-b)^2=r^2[/tex]And using W=(-3,0) we get:
[tex](-3-a)^2+(0-b)^2=r^2[/tex]So we have a system of three equations and we must find three variables: a, b and r. All equations have r^2 at their right side. This means that we can take the left sides and equalize them. Let's do this with the second and third equation:
[tex]\begin{gathered} (0-a)^2+(13-b)^2=(-3-a)^2+(0-b)^2 \\ a^2+(13-b)^2=(-3-a)^2+b^2 \end{gathered}[/tex]If we develop the squared terms:
[tex]a^2+b^2-26b+169=a^2+6a+9+b^2[/tex]Then we substract a^2 and b^2 from both sides:
[tex]\begin{gathered} a^2+b^2-26b+169-a^2-b^2=a^2+6a+9+b^2-a^2-b^2 \\ -26b+169=6a+9 \end{gathered}[/tex]We substract 9 from both sides:
[tex]\begin{gathered} -26b+169-9=6a+9-9 \\ -26b+160=6a \end{gathered}[/tex]And we divide by 6:
[tex]\begin{gathered} \frac{-26b+160}{6}=\frac{6a}{6} \\ a=-\frac{13}{3}b+\frac{80}{3} \end{gathered}[/tex]Now we can replace a with this expression in the first equation:
[tex]\begin{gathered} (6-a)^2+(5-b)^2=r^2 \\ (6-(-\frac{13}{3}b+\frac{80}{3}))^2+(5-b)^2=r^2 \\ (\frac{13}{3}b-\frac{62}{3})^2+(5-b)^2=r^2 \end{gathered}[/tex]We develop the squares:
[tex]\begin{gathered} (\frac{13}{3}b-\frac{62}{3})^2+(5-b)^2=r^2 \\ \frac{169}{9}b^2-\frac{1612}{9}b+\frac{3844}{9}+b^2-10b+25=r^2 \\ \frac{178}{9}b^2-\frac{1702}{9}b+\frac{4069}{9}=r^2 \end{gathered}[/tex]So this expression is equal to r^2. This means that is equal
How many ones are between 1 and 1,000,000 (inclusive)?
Answers
There are 600,001 ones are between 1 and 1,000,000.
By using the below process we can find the number of ones between 1 and 1,000,000.
The number of times a digit 2 to 9 digit appears in numbers 1 to [tex]10^n = n(10^(^n^-^1^))[/tex].
The number of times the digit 1 appears in numbers in numbers 1 to [tex]10^n = n(10^(^n^-^1^)) + 1[/tex]
Therefore, the number of times a digit 1 appears in numbers 1 to 1,000,000 [tex]= 6(10^(^6^-^1^)) + 1\\= 6(10^5) + 1\\= 600,000 + 1\\= 600,001[/tex]
Therefore, there are 600,001 ones are between 1 and 1,000,000.
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Knowledge CheckUse the distributive property to remove the parentheses.--7(-5w+x-3)X 5
Answers
The distributive property states that:
[tex]k\cdot\left(a+b+c\right?=k\cdot a+k\cdot b+k\cdot c.[/tex]In this problem, we have the expression:
[tex]-7\cdot(-5w+x-3)=(-7)\cdot(-5w+x-3).[/tex]Comparing this expression with the general expression of the distributive property, we identify:
• k = (-7),
,• a = -5w,
,• b = x,
,• c = -3.
Using the general expression for the distributive property with these values, we have:
[tex]\left(-7\right)\cdot(-5w)+\left(-7\right)\cdot x+\left(-7\right)\cdot(-3).[/tex]Simplifying the last expression, we get:
[tex]35w-7x+21.[/tex]AnswerApplying the distributive property to eliminate the parenthesis we get:
[tex]35w-7x+21[/tex]hey there mr or ms could you please help me out here?
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The two triangles have a common side, RQ.
Also, given the two sides (left and right) are equal.
Also, the angle between the two sides (one side given and bottom side) is given as 90 degrees.
Thus,
we have
2 sides AND 1 angle congruent in each triangle
That is:
Side-Angle-Side, which is
SAS
THe triangles are congruent according to SAS, option B
A box contains six red pens, four blue pens, eight green pens, and some black pens. Leslie picks a pen and returns it to the box each time. The outcomes are recorded in the table.a. what is the experimental probability of drawing a green pen?b. if the theoretical probability of drawing a black pen is 1/10, how many black pens are in the box
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given the follwing parameters,
number of times a Red Pen is picked is 8
numbr o f times the Blue Pen is picked is 5
Number of times the Green Pen is picked is 14
Number of times the Black Pen is picked is 3
so,
(a) to get the experimental probability of drawing a Green Pen is,
P = favoured results/all obtained
then,
14/(8+5+14+3)
= 14/30 that is a
(
Use the binomial expression (p+q)^n to calculate abinomial distribution with n = 5 and p = 0.3.
Answers
ANSWER :
The binomial distributions are :
0.16807
0.36015
0.3087
0.1323
0.02835
0.00243
EXPLANATION :
In a binomial distribution of (p + q)^n :
n = 5
p = 0.3 and
q = 1 - p = 1 - 0.3 = 0.7
[tex]_nC_x(p)^x(q)^{n-x}[/tex]We are going to get the values from x = 0 to 5
[tex]\begin{gathered} _5C_0(0.3)^5(0.7)^{5-0}=0.16807 \\ _5C_1(0.3)^5(0.7)^{5-1}=0.36015 \\ _5C_2(0.3)^5(0.7)^{5-2}=0.3087 \\ _5C_3(0.3)^5(0.7)^{5-3}=0.1323 \\ _5C_4(0.3)^5(0.7)^{5-4}=0.02835 \\ _5C_5(0.3)^5(0.7)^{5-5}=0.00243 \end{gathered}[/tex]Which statement best reflects the solution(s) of the equation? X/ x-1 - 1/ x-2 = 2x-5/x^2-3x+2 There is only one solution: x=4. The solution x=1 is an extraneous solution. There are two solutions: x=2 and x=3. There is only one solution: x=3. The solution x=2 is an extraneous solution. There is only one solution: x=3. The solution x=1 is an extraneous solution.
Answers
The best reflects solution of the equation is, There is only one solution: x = 3. The solution x = 2 is an extraneous solution.
What is extraneous solution?
An extraneous solution is a root of a converted equation that is not a root of the original equation because it was left out of the original equation's domain is referred to as a superfluous solution.
We are given the following equation,
(x / x - 1) - (1 / x - 2) = (2x - 5)/(x^2 - 3x + 2)
Solving the given equation we have,
(x^2 - 3x + 1) / (x^2 - 3x + 2) = (2x - 5) / (x^2 - 3x + 2)
x^2 - 3x + 1 = 2x - 5
x^2 - 5x + 6 = 0
x^2 - 3x - 2x + 6 = 0
x(x - 3) - 2(x - 3) = 0
(x - 3)(x - 2) = 0
(x - 3) = 0, (x - 2) = 0
x = 3, x = 2
At x = 2 the denominator of the equation will be 0. So solution of the equation is not valid at x = 2.
Therefore, x = 3 is the only one solution. The solution x = 2 is an extraneous solution.
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Ryan's car used 9 gallons to travel 396 miles. How many miles can the car go on one gallon of gas?On the double number line below, fill in the given values, then use multiplication or division to find the missing value.
Answers
Given:
At 9 gallons, it can travel 396 miles.
Find: At one gallon, it can travel ___ miles.
Solution:
First, let's fill in the number line with the information we have.
Then, to find the missing value ?, let's do cross multiplication.
[tex]\begin{gathered} ?\times9=1\times396 \\ ?\times9=396 \end{gathered}[/tex]Then, divide both sides of the equation by 9.
[tex]\begin{gathered} \frac{?\times9}{9}=\frac{396}{9} \\ ?=44 \end{gathered}[/tex]Therefore, on 1 gallon of gas, the car can travel 44 miles.
Translate this phrase into an algebraic expression.Six less than the product of 13 and Mai's heightUse the variable m to represent Mai's height.
Answers
If m is the Mai's height you can write for the given description:
13m - 6
The previous expression means six less than the product of 13 and Mai's height.
i need help in this please
Answers
The isosceles right is given in the diagram below
We are to rotate clockwise about point B as the origin
Rotating ABC 180° Clockwisely, we have
Rotating ABC 270° clockwise about B, we have
We now combine the four triangles together in the diagram below
Explain why m<1>m<3.which statement below can be made, according to the corollary to the Triangle Exterior Angle Theorem?
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In the given image you have that m∠1 is lower than angle m∠3 becasue it is clear that angle ∠1 is an angle greater than 90° and angle ∠3 is lower than 90°. Then m∠1 > m∠3.
Now, in order to determine which of the given statements is true for the given figure, you take into account that the exterioir angle theorem stablishes that the measure of an exterior angle of the triangle is greater that any of the measure of the remote interioir angles of the triangle.
Thus, you can notice that the measure of the external angle ∠1 is greater than the measure either angle ∠4 or angle ∠2.
Hence, following statement is true:
m∠1 > m∠4 and m∠1 > m∠2
You choose a marble from the bag. What is the probability you will NOT choose blue?1/25/72/72
Answers
Given a sample and required to get the probability of a particular outcome, we make a couple of considerations including:
- Sample Space: The universal set
- Required Outcome
We can identify these variables as:
Sample space: total number of marbles = 7
Required outcome: Not blue = 7 - 2 = 5
Probability is given as:
[tex]\begin{gathered} P=\text{ }\frac{\text{number of required outcome}}{Sample\text{ space}}=\frac{5}{7} \\ P=\frac{5}{7} \end{gathered}[/tex]Let f(x) = 2x² + 14x – 16 and g(x) = x+8. Perform the function operation and then find the domain of the result.(x) = (simplify your answer.)
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We need to find the following division of the functions f(x) and g(x):
[tex]\frac{f}{g}(x)=\frac{f(x)}{g(x)}=\frac{2x^2+14x-16}{x+8}[/tex]We can note that the numerator can be rewritten as
[tex]2x^2+14x-16=2(x^2+7x-8)=2(x+8)(x-1)[/tex]Then the division can be written as:
[tex]\frac{f}{g}(x)=\frac{f(x)}{g(x)}=\frac{2(x+8)(x-1)}{x+8}[/tex]From this result, we can cancel out the term (x+8) from both sides and get,
[tex]\frac{f}{g}(x)=\frac{f(x)}{g(x)}=2(x-1)[/tex]Therefore, the result of the division is:
[tex]\frac{f}{g}(x)=2(x-1)[/tex]which domain is all real numbers:
[tex]x\in(-\infty,\infty)[/tex]