Let x be number or ounces of a 5% alcohol solution, then:
[tex]x(0.05)+17(0.10)=(x+17)(0.06)[/tex]Solving the above equation for x, we get:
[tex]\begin{gathered} 0.05x+1.7=0.06x+1.02 \\ 0.01x=1.7-1.02 \\ 0.01x=0.68 \\ x=68 \end{gathered}[/tex]Therefore, you must add 68 ounces of the 5% alcohol solution.
The point S is plotted on the coordinate grid below. Plot the point S', the reflection
of S over the x-axis.
Click on the graph to plot a point. Click a point to delete it.
Answer:
(1, -2)
Step-by-step explanation:
Reflecting a point over the x-axis means [tex](x,y) \longrightarrow (x, -y)[/tex].
Find the coordinates of the circumcenter of triangle PQR with vertices P(-2,5) Q(4,1) and R(-2,-3)
The given triangle has vertices at:
[tex]\begin{gathered} P(-2,5) \\ Q(4,1) \\ R(-2,-3) \end{gathered}[/tex]In the coordinate plane, the triangle looks like this:
There are different forms to find the circumcenter, we are going to use the midpoint formula:
[tex]M(x,y)=(\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]Apply this formula for each vertice and find the midpoint:
[tex]M_{P,Q}=(\frac{-2+4}{2},\frac{5+1}{2})=(1,3)[/tex]For QR:
[tex]M_{Q,R}=(\frac{4+(-2)}{2},\frac{1+(-3)}{2})=(1,-1)[/tex]For PR:
[tex]M_{P,R}=(\frac{-2+(-2)}{2},\frac{5+(-3)}{2})=(-2,1)[/tex]Now, we need to find the slope for any of the line segments, for example, PQ:
We can apply the slope formula:
[tex]m=\frac{y2-y1}{x2-x1}=\frac{1-5}{4-(-2)}=\frac{-4}{6}=-\frac{2}{3}[/tex]By using the midpoint and the slope of the perpendicular line, find out the equation of the perpendicular bisector line, The slope of the perpendicular line is given by the formula:
[tex]\begin{gathered} m1\cdot m2=-1 \\ m2=-\frac{1}{m1} \\ m2=-\frac{1}{-\frac{2}{3}}=\frac{3}{2}_{} \end{gathered}[/tex]The slope-intercept form of the equation is y=mx+b. Replace the slope of the perpendicular bisector and the coordinates of the midpoint to find b:
[tex]\begin{gathered} 3=\frac{3}{2}\cdot1+b \\ 3-\frac{3}{2}=b \\ b=\frac{3\cdot2-1\cdot3}{2}=\frac{6-3}{2} \\ b=\frac{3}{2} \end{gathered}[/tex]Thus, the equation of the perpendicular bisector of PQ is:
[tex]y=\frac{3}{2}x+\frac{3}{2}[/tex]If we graph this bisector over the triangle we obtain:
Now, let's find the slope of the line segment QR:
[tex]m=\frac{-3-1}{-2-4}=\frac{-4}{-6}=\frac{2}{3}[/tex]The slope of the perpendicular bisector is:
[tex]m2=-\frac{1}{m1}=-\frac{1}{\frac{2}{3}}=-\frac{3}{2}[/tex]Let's find the slope-intercept equation of this bisector:
[tex]\begin{gathered} -1=-\frac{3}{2}\cdot1+b \\ -1+\frac{3}{2}=b \\ b=\frac{-1\cdot2+1\cdot3}{2}=\frac{-2+3}{2} \\ b=\frac{1}{2} \end{gathered}[/tex]Thus, the equation is:
[tex]y=-\frac{3}{2}x+\frac{1}{2}[/tex]This bisector in the graph looks like this:
Now, to find the circumcenter we have to equal both equations, and solve for x:
[tex]\begin{gathered} \frac{3}{2}x+\frac{3}{2}=-\frac{3}{2}x+\frac{1}{2} \\ \text{Add 3/2x to both sides} \\ \frac{3}{2}x+\frac{3}{2}+\frac{3}{2}x=-\frac{3}{2}x+\frac{1}{2}+\frac{3}{2}x \\ \frac{6}{2}x+\frac{3}{2}=\frac{1}{2} \\ \text{Subtract 3/2 from both sides} \\ \frac{6}{2}x+\frac{3}{2}-\frac{3}{2}=\frac{1}{2}-\frac{3}{2} \\ \frac{6}{2}x=-\frac{2}{2} \\ 3x=-1 \\ x=-\frac{1}{3} \end{gathered}[/tex]Now replace x in one of the equations and solve for y:
[tex]\begin{gathered} y=-\frac{3}{2}\cdot(-\frac{1}{3})+\frac{1}{2} \\ y=\frac{1}{2}+\frac{1}{2} \\ y=1 \end{gathered}[/tex]The coordinates of the circumcenter are: (-1/3,1).
In the graph it is:
A circle and two distinct lines are drawn on a sheet of paper what is the largest possible number of points of intersection of these figures (it is Q29)
Answer:
C 5
Step-by-step explanation:
The two lines can both intersect the circle twice, and can intersect each other once, so 2 + 2 + 1 = 5
Reece increases the amount of money he pays into his savings account by 4% each year. This year, he paid £3000 into his account. To the nearest penny, how much did Reece pay into his account a) 1 year ago? b) 10 years ago?
The money deposited 1 year ago is $2884.61 and the money deposited 10 years ago is $2142.85.
Given that, Reece increases the amount of money he pays into his savings account by 4% each year.
What is savings account?A savings account is a bank account at a retail bank. Common features include a limited number of withdrawals, a lack of cheque and linked debit card facilities, limited transfer options and the inability to be overdrawn.
We know that, simple interest = (P×R×T)/100
a) P=$x, R=4% and T=1 year
SI=3000-x
⇒ 3000-x = (x×4×1)/100
⇒ 3000-x=0.04x
⇒ 1.04x=3000
⇒ x=3000/1.04
⇒ x=$2884.61
Money deposited 1 year ago is $2884.61.
b) P=$y, R=4% and T=10 year
SI=3000-y
⇒ 3000-y = (y×4×10)/100
⇒ 3000-y = 0.4y
⇒ 1.4y = 3000
⇒ y=3000/1.4
⇒ y=$2142.85
Therefore, the money deposited 1 year ago is $2884.61 and the money deposited 10 years ago is $2142.85.
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A sample has a sample proportion of 0.3. Which sample size will produce the widest 95% confidence interval when estimating the population parameter?A. 36B. 56C. 68D. 46
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
sample proportion = 0.3
widest 95% confidence interval
sample = ?
Step 02:
p = 0.3
1 - α = 0.95 =>> z α/2 = 1.96
We must check each value to find the solution.
A. sample = 36
[tex]\begin{gathered} 0.3-1.96\cdot\sqrt[]{\frac{0.3\cdot0.7}{36}}=0.3-0.1499 \\ 0.3+1.96\cdot\sqrt[]{\frac{0.3\cdot0.7}{36}}=0.3+0.1499 \end{gathered}[/tex]confidence interval (0.1501 , 0.4499)
difference = 0.2998
B. sample = 56
[tex]\begin{gathered} 0.3-1.96\cdot\sqrt[]{\frac{0.3\cdot0.7}{56}}=0.3\text{ - }0.120 \\ 0.3+1.96\cdot\sqrt[]{\frac{0.3\cdot0.7}{56}}=\text{ 0.3 + }0.120 \end{gathered}[/tex]confidence interval (0.18 , 0.42)
difference = 0.24
Analyzing these two values, we can conclude that the widest confidence interval will be for the smallest sample.
The answer is:
Sample = 36
Floyd is an aspiring music artist. He has arecord contract that pays him a base rate of$200 a month and an additional $12 for eachalbum that he sells. Last month he earned atotal of $644.Write an equation to determine the numberof albums (a) Floyd sold last month.Find the number of albums Floyd sold lastmonth.albums
Explanation:
Equate the given data to solve for x.
$200 + $12x = $644.
To determine the number of albums sold, Let x be the number of album sold by Floyd last month.
200 + 12x = 644
12x =644-200
12x = 444
x = 444/12
x= 37.
Floyd has sold 37 albums last month.
Answer:
The equation to determine the number of albums Floyd sold last month is 200+12x = 644.
and the number of album Floyd sold last month is 37.
Identify the range of the function shown in the graph. 10 8 4 -10-8-4-2 8 10 O A. -2< y < 2 O B. {-2, 2) O C. y is all real numbers OD. Y > 0
Answer
Option B is correct.
Range: y is all real numbers.
Explanation
The range of a function refers to the region of values where the function can exist. It refers to the values that the dependent variable [y or f(x)] can take on. It is the region around the y-axis that the graph of the function spans.
For this question, we can see that the graph spans over the entire y-axis.
Hence, the range of this function shown in the graph is all real number.
Hope this Helps!!!
Find the slope of the two points: (-3,-2) & (5, -8)
ter Numerical value ONLY. NO Decimals
*
[tex](\stackrel{x_1}{-3}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{-8}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-8}-\stackrel{y1}{(-2)}}}{\underset{run} {\underset{x_2}{5}-\underset{x_1}{(-3)}}} \implies \cfrac{-8 +2}{5 +3} \implies \cfrac{ -6 }{ 8 } \implies - \cfrac{ 3 }{ 4 }[/tex]
Aldo gets paid biweekly. His gross pay for each pay period is $850.He has 16% withheld for taxes and 7% withheld for personal deductionsWhat is the amount of his annual net pay?a. $8,160b. $17,340c. $17,017d. $17,680
First, we compute the 16% of $850 and the 7% of $850:
[tex]\begin{gathered} 850(0.16)=136 \\ 850(0.07)=59.5 \end{gathered}[/tex]Then, after deductions, Aldo gets paid $850-$136-$59.5=$654.5 biweekly. Therefore, since he gets paid biweekly we multiply $654.5 per 26 and get that Aldo earns $17017 per year.
Answer: Option C.
hardest question on brainly stumbles college students!
Applying the vertical angles theorem and other properties, the value of x is 20. The reason for each statement has been explained below.
What are Vertical Angles?A pair of vertical angles are formed when two straight lines intersect each other at a common point. The angles that face each other directly are vertical angles and they are congruent or equal to each other.
Given the diagram below, to find the value of x, the following are the each reason that justifies each of the statements in each step:
Statement Reasons
1. m∠DOB = m∠DOE + m∠BOE 1. Angle Addition Postulate
2. m∠DOB = 90 + x 2. Substitution
3. m∠AOC = m∠DOB 3. Vertical Angels Theorem
4. 110 = 90 + x 4. Substitution
5. x = 20 5. Algebra
To solve using algebra, step 4 is solved as explained below:
110 - 90 = 90 + x - 90
20 = x
x = 20.
Therefore, applying the above steps and reasons that includes the use of vertical angles theorem, the value of x is determined to be: x = 20.
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5 In nahiangle Bcm. Ireos B = / 13 which function also cauals
Given data:
The given measurement of angle C is 90 degrees.
The given value of cos(B) =5/13.
The sum of all angles of triangle is,
[tex]\begin{gathered} \angle A+\angle B+\angle C=180^{\circ} \\ \angle A+\angle B+90^{\circ}=180^{\circ} \\ \angle A+\angle B=90^{\circ} \\ \angle B=90^{\circ}-\angle A \end{gathered}[/tex]Substitute the above value in the given expression.
[tex]\begin{gathered} \cos (90^{\circ}-A)=\frac{5}{13} \\ \sin A=\frac{5}{13} \end{gathered}[/tex]Thus, the correct answer is sin(A), so the third option is correct.
3. The sum of two consecutive odd integersis 168. What are the integers?
Integers are numbers such as
[tex]N=\text{ }.\ldots\text{-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9}\ldots.[/tex]And odd numbers are
[tex]1\text{ 3 5 7 9 11 13 }\ldots[/tex]HELP PLEASEEEEE!!!!!!
The one rational number between -0.45 and -0.46 is -0.455.
What is defined as the term rational number?Rational are numbers which can be specified in the form p/q, in which p and q are integers and q≠. The distinction among rational numbers as well as fractions is that fractions cannot include a negative denominator or numerator. As a result, the denominator and numerator of such a fraction have been whole numbers (denominator 0), whereas the numerator and the denominator of rational numbers are integers.For the given question.
The two rational number are given as;
-0.45 and -0.46.
To find the on rational number lying between the two given rational number is to take the average of both numbers.
= (-0.45 + (-0.46))/2
= -0.91/2
= -0.455
Thus, the one rational number between -0.45 and -0.46 is -0.455.
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A sprinkler rotates back and forth from point A to point B. The water reaches 8 meters from the base of the sprinkler.What is the length of the arc AB, rounded to the nearest tenth of a meter? Use 3.14 for [tex]\pi[/tex]
20.9m
1) Since we want to know the length of that arc, and the angle is written in degrees, let's use a formula to find this out:
[tex]\begin{gathered} l=\frac{\alpha}{360}\cdot2\pi R \\ l=\frac{150}{360}\cdot2(3.14)\cdot8 \\ l=20.93\approx20.9m \end{gathered}[/tex]2) Rounding off to the nearest tenth we have the length of this arc is 20.9, m
Sonia opened a savings account and then added the same amount to the savings account every week. After 5 weeks, her savings account had a total of $45. After 10 weeks, her savings account had a total of $70. Which equation represents the amount of money (y), in dollars, in Sonia's savings account after x weeks?
First let's find the amount Sonia puts in her account each week.
To do so, let's find the amount increased between weeks 5 and 10:
[tex]70-45=25[/tex]The account increased $25 in 5 weeks, so for each week, we have:
[tex]\frac{25}{5}=5[/tex]So Sonia puts $5 in her account each week. Now, we need to find the initial value in the account. If after 5 weeks the account has $45, we can subtract $45 by 5 times the amount per week:
[tex]45-5\cdot5=45-25=20[/tex]So the initial amount is $20.
Now that we have the initial amount and the amount she puts per week, we have the following equation for the amount of money y after x weeks:
[tex]y=5x+20_{}[/tex]So the correct option is the third one.
find the value of x for which r parallels s. then find the measures of angles 1 and 2 measure angle 1= 80-2xmeasure angle 2= 93-3xthe value of x for which r parallels s is....measure of angle 1 is.....°measure of angle 2 is.....°
Since the lines r and s are parallel the angles 1 and 2 must be equal
write an equation
[tex]80-2x=93-3x[/tex]solve the equation for x
[tex]\begin{gathered} 80-2x=93-3x \\ -2x+3x=93-80 \\ x=13 \end{gathered}[/tex]the value for x in which r and s are parallel must be 14
measure of angle 1 and 2 must be 54°
The table shows the earnings and the number of hours worked for five employees. complete the table by finding the missing values.
The first employee
[tex]\begin{gathered} He\text{ earns a total of \$12.75} \\ \text{His working rate is \$}8.50\text{ per hour} \\ \text{Hours he workd can be calculated below} \\ \text{ \$8.50 = 1 hour} \\ \text{ \$12.75 =?} \\ \text{ number of hours=}\frac{12.75}{8.50} \\ \text{ number of hours = 1.5 hours} \end{gathered}[/tex]The second employee
[tex]\text{ earning per hour = }\frac{19.09}{2.3}=\text{ \$8.3 per hour}[/tex]The third employee
[tex]\begin{gathered} \text{ \$7.75=1 hour} \\ \text{ \$26.}35=\text{?} \\ \text{ number of hours=}\frac{26.35}{7.75}=3.4\text{ hours} \end{gathered}[/tex]The fourth employee
[tex]\text{earning per hour = }\frac{49.50}{4.5}=\text{ \$}11\text{ per hour}[/tex]The fifth employee
[tex]\text{earning per hour=}\frac{31.50}{1.5}=\text{ \$21 per hour}[/tex]I need help on doing this finding the slope of a line
Given:
[tex](x_1,y_1)=(1,6)and(x_2,y_2)=(6,1)[/tex][tex]\text{Slope(m)=}\frac{y_2-y_1}{x_2-x_1}[/tex][tex]\text{Slope(m)=}\frac{1-6}{6-1}[/tex][tex]\text{Slope(m)}=-\frac{5}{5}[/tex][tex]\text{Slope (m)=-1}[/tex]True or False? When the first coordinate is positive, that point is located to theright of the x-axis.TrueFalse
True
Explanations:Note that when you have the position of a point as (x, y), the first coordinate is the x - axis while the second is the y - axis.
Also note that, to the right of the x axis, you have positive numbers while you have negative numbers to the left.
We can then conclude that When the first coordinate is positive, that point is located to the right of the x-axis
Please help with this problem my son is having problems showing his work an understanding how. Solve x2 – 6x = 16 using the quadratic formula method. Show your work. Then describe the solution.
Solution
We are given the quadratic equation
[tex]x^2-6x=16[/tex]We want to solve by using the quadratic formula method
Note: Given a quadratic equation
[tex]ax^2+bx+c=0[/tex]The formula method is given
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]From
[tex]\begin{gathered} x^2-6x=16 \\ x^2-6x-16=0 \\ \text{Comparing with the general form of a quadratic equation} \\ a=1 \\ b=-6 \\ c=-16 \end{gathered}[/tex]Substituting the parameters intot the quadratic formula
and
Therefore,
[tex]x=8,-2[/tex]Please answer part a and b questions are in the picture
Part A
we have that
A(4) ----> looking at the graph
A(4) means----> population in the year 1994
so
A(4)----> less than 2 million
and
B(4) -----> greater than 2 million
therefore
the answer Part a is option B
Part B
there is only one value of t where A(t)=B(t)
the value of t is 6 (the year 1996)
a number, twice that number, and one-third of that number added. the result is 20. what is the number?
Answer:
6
Step-by-step explanation:
Let x = the number
2x = twice the number
1/3 x = one-third of the number
x + 2x + 1/3 x = 20
Combine like terms.
3 1/3 x = 20
Change 3 1/3 to an improper number.
10/3 x = 20
Times by 3/10 on both sides.
3/10 • 10/3 x = 20•3/10
x = 60/10
x = 6
Check:
6 + 2(6) + 1/3(6)
= 6 + 12 + 2
= 20 check!
6. Find the domain and range of V(x) in this context.7. Think of V(x) as a general function without the constraint of modeling the volume of a box. What would be the domain and range of V(x)?8. Use correct notation to describe the end behavior of V(x) as a function without context.
We have , that measure of the side of the square is x
Therefore
l=26-2x
w=20-2x
h=x
Therefore the Volume function is
[tex]V=(26-2x)(20-2x)x[/tex]Then we simplify
[tex]V(x)=4x^3-92x^2+520x[/tex]6.In the context of obtaining a Volume we can't have negative numbers for x and for the function by observing the graph
Domain
[tex]0\le x\le10[/tex]Therefore for the range
[tex]0\: 7.Because we have a polynomial
the domain without the constrain
[tex]-\infty\: the range without the constrain[tex]-\infty\: 8.Since the leading term of the polynomial is 4 x^{3}, the degree is 3, i.e. odd, and the leading coefficient is 4, i.e. positive. This means
[tex]\begin{gathered} x\to-\infty,\text{ }f(x)\to-\infty \\ x\to\infty,f(x)\to\infty \end{gathered}[/tex]Help I need a example for graphing two variable inequalities
Solution:
To graph, a linear inequality in two variables (say, x and y ), first get y alone on one side. Then consider the related equation obtained by changing the inequality sign to an equals sign. The graph of this equation is a line.
If the inequality is strict ( < or > ), graph a dashed line. If the inequality is not strict ( ≤ and ≥ ), graph a solid line.
For example,
Consider the linear inequality in two variables below
[tex]y\leq4x-8[/tex]Step 1:
Put x=0 and find y
[tex]\begin{gathered} y=4x-8 \\ y=4(0)-8 \\ y=0-8 \\ y=-8 \\ (0,-8) \end{gathered}[/tex]Step 2:
Put y=0 and find x
[tex]\begin{gathered} y=4x-8 \\ 0=4x-8 \\ 4x=8 \\ \frac{4x}{4}=\frac{8}{4} \\ x=2 \\ (2,0) \end{gathered}[/tex]Hence,
We are going to use the coordinates below to graph the inequality using a solid line because
The inequality sign used is greater than or equal to
[tex](0,-8),(2,0)[/tex]Hence,
The graph of the inequality will be
Need help Instructions: Find the measure of each angle Calculate the length of each side Round to the nearest tenth
Given,
The length of the perpendicular is 4.
The measure of the hypotenuse is 14.
Required:
The measure of each angle of the triangle.
As it is a right angle triangle,
The measure of angle C is 90 degree.
By using the trigonometric ratios,
[tex]\begin{gathered} cosA=\frac{AC}{AB} \\ cosA=\frac{4}{14} \\ A=cos^{-1}(\frac{4}{14}) \\ A=73.4^{\circ} \end{gathered}[/tex]By using the trigonometric ratios,
[tex]\begin{gathered} sinB=\frac{AC}{AB} \\ sinB=\frac{4}{14} \\ B=sin^{-1}(\frac{4}{14}) \\ B=16.6^{\circ} \end{gathered}[/tex]Hence, the measure of angle A is 73.4 degree, angle B is 16.6 degree and angle C is 90 degree.
Solve this inequality X-1 less than or equal to 9
Solution of an inequality
We can express the solution (s) of inequalities in several forms.
Here we will use two of them: The set-builder notation and the interval notation.
Let's solve the inequality
x - 1 ≤ 9
Adding 1 to both sides of the inequality:
x ≤ 10
The solution in words is "all the real numbers less than or equal to 10"
In set-builder notation:
{x | x <= 10}
In interval notation: (-inf, 10]
Show exact steps to solve and show the image!Don't mind the pink writing
1)To construct the line parallel to given line passing through given point, first take a point on the line.
2)Here in the problem that point is Q.
3)Join PQ.
4)After joining PQ, copy the angle made by PQ by constructing the arc MN with steel point of compass on Q. Keep same disttance and get arc M'N' by keeping steel point on P. Then measure length MN on the angle PQR and cut arc by placing steel point on M' and cutting the arc to get point N'.
5) Join PN' and extend till point S.
6) PS is parallel to QR.
The local humane society is restocking on cat food to prepare for kitten season. Very young kittens need kitten formula which costs $4.00 per bottle. Older kittens need wet cat food which costs $1.50 per can. Answer numbers 5 and 6. 15) Write an algebraic expression to describe how much the humane society will spend on kitten supplies based on the number of bottles and the number of cans they buy. 16) How much money (before tax) will the humane society spend if they buy 5 bottles of kitten formula and 12 cans of wet cat food? Show your work.
Lets call B the nuber of bottles they will buy and C the number of cans.
Then, if each bottle cost $4, the cost of all the bottles will be 4B.
If each can cost $1.50, then, the total cost of the cans is 1.5C.
If we add this two costs, we have the expression we need:
[tex]\text{Cost}=4B+1.5C[/tex]If they buy 5 bottles of kitten formula and 12 cans of wet cat food, we have B=5 and C=12, and the cost is:
[tex]\text{Cost}=4B+1.5C=4\cdot5+1.5\cdot12=20+18=38[/tex]They will spend $38.
A = P + PRT/100Make P the subject from the formula.
ANSWER
[tex]P=\frac{100A}{100+RT}[/tex]EXPLANATION
We want to make the subject of the formula in the given equation:
[tex]A=P+\frac{PRT}{100}[/tex]First, factorize the right-hand side of the equation:
[tex]A=P(1+\frac{RT}{100})[/tex]Simplify the bracket:
[tex]A=P(\frac{100+RT}{100})[/tex]Now, divide both sides by the term in the bracket:
[tex]\begin{gathered} \Rightarrow P=A\cdot\frac{100}{100+RT} \\ \Rightarrow P=\frac{100A}{100+RT} \end{gathered}[/tex]That is the answer.
what's the leading term and constant of -.5x^5+1.5
We have the following polynomial:
[tex]-0.5x^5+1.5[/tex]And we have to determine which is the leading term, and the constant term of that polynomial.
1. To determine that we know that the leading term is that term in the polynomial that contains the highest power of the variable. In this case, the variable is x, and the term with the highest variable is:
[tex]-0.5x^5\rightarrow\text{ This is the leading term}[/tex]2. To determine the constant term, we have to remember that this term is not associated with the variable, that is, is not a coefficient of the variable. Therefore, the constant term is 1.5.
Hence, in summary, we have that:
[tex]\text{ Leading term: }-0.5x^5[/tex]And
[tex]\text{ Constant term: }1.5[/tex]