Given:
First term 9
Common difference -2
Required:
Find a formula for the nth term of the arithmetic sequence.
Explanation:
The general formula for the nth term of the an arithmetic sequence is given by the formula:
[tex]a_n=a+(n-1)d[/tex]Where a = first term
d = common difference
Put a = 9 and d = -2 in the formula.
[tex]\begin{gathered} a_n=9+(n-1)(-2) \\ a_n=9-2(n-1) \\ a_n=9-2n+2 \\ a_n=-2n+11 \end{gathered}[/tex]Final Answer:
The nth term of the arithmetic sequence is
[tex]a_n=-2n+11[/tex]Tonya leaves home on her motorcycle and travels 12 miles east and 7 miles north. How far in Tonya from her original starting point?
The distance is 13.892 miles.
Given:
Distance travelled in east is 12 miles.
Distance travelled in north is 7 miles.
The objective is to find how far is tonya from the starting point.
The distance between starting point and ending point can be calculated using Pythagorean theorem.
Consider the given figure as,
By applying Pythagorean theorem,
[tex]AC^2=AB^2+BC^2[/tex]Now, substitute the given values in the above formula.
[tex]\begin{gathered} x^2=12^2+7^2 \\ x^2=144+49 \\ x^2=193 \\ x=\sqrt[]{193} \\ x=13.892 \end{gathered}[/tex]Find the restricted values of x for the following rational expression. If there are no restricted values of x,indicate "No Restrictions".x² +8x² - x - 12AnswerHow to enter your answer (opens in new window)Separate multiple answers with commas.KeypadKeyboard ShortcutsSelecting a radio button will replace the entered answer value(s) with the radio button value. If the radiobutton is not selected, the entered answer is used.
Answer:
To find the restricted values of x for the given rational expression,
[tex]\frac{x^2+8}{x^2-x-12}[/tex]The above expression is defined only when x^2-x-12 not equal to 0.
x values are restricted for the solution of x^2-x-12=0
To find the values of x when x^2-x-12=0.
Consider, x^2-x-12=0
we get,
[tex]x^2-x-12=0[/tex][tex]x^2-4x+3x-12=0[/tex][tex]x\left(x-4\right)+3\left(x-4\right)=0[/tex]Taking x-4 as common we get,
[tex]\left(x-4\right)\left(x+3\right)=0[/tex]we get, x=4,x=-3
The restricted values of x are 4,-3.
we get,
[tex]x\ne4,-3[/tex]Answer is:
[tex]x\ne4,-3[/tex]What is the y intercept of this table?Х 0,3,6. y 5,11,17
We are given a table of x-values and their corresponding y values for a function. We are asked to express the y-intercept.
Since the table reads that for x= 0 the associated value id y = 5, then right from that info we can say that the function intercepts the y axis at the point y=5.
In coordinate pair point it reads like: (0, 5)
Recall that the y-intercept is the point at which the function crosses the y-axis, and that happens when x = 0.
I’m stuck on how to verify number 7 and how to find the possible value for sin theta
Given:
There are given the trigonometric function:
[tex]sec^2\theta cos2\theta=1-tan^2\theta[/tex]Explanation:
To verify the above trigonometric function, we need to solve the left side of the equation.
So,
From the left side of the given equation:
[tex]sec^2\theta cos2\theta[/tex]Now,
From the formula of cos function:
[tex]cos2\theta=cos^2\theta-sin^2\theta[/tex]Then,
Use the above formula on the above-left side of the equation:
[tex]sec^2\theta cos2\theta=sec^2\theta(cos^2\theta-sin^2\theta)[/tex]Now,
From the formula of sec function:
[tex]sec^2\theta=\frac{1}{cos^2\theta}[/tex]Then,
Apply the above sec function into the above equation:
[tex]\begin{gathered} sec^2\theta cos2\theta=sec^2\theta(cos^2\theta-s\imaginaryI n^2\theta) \\ =\frac{1}{cos^2\theta}(cos^2\theta-s\mathrm{i}n^2\theta) \\ =\frac{(cos^2\theta-s\mathrm{i}n^2\theta)}{cos^2\theta} \end{gathered}[/tex]Then,
[tex]\frac{(cos^{2}\theta- s\mathrm{\imaginaryI}n^{2}\theta)}{cos^{2}\theta}=\frac{cos^2\theta}{cos^2\theta}-\frac{sin^2\theta}{cos^2\theta}[/tex]Then,
From the formula for tan function:
[tex]\frac{sin^2\theta}{cos^2\theta}=tan^2\theta[/tex]Then,
Apply the above formula into the given result:
So,
[tex]\begin{gathered} \frac{(cos^{2}\theta- s\mathrm{\imaginaryI}n^{2}\theta)}{cos^{2}\theta}=\frac{cos^{2}\theta}{cos^{2}\theta}-\frac{s\imaginaryI n^{2}\theta}{cos^{2}\theta} \\ =1-\frac{s\mathrm{i}n^2\theta}{cos^2\theta} \\ =1-tan^2\theta \end{gathered}[/tex]Final answer:
Hence, the above trigonometric function has been proved.
[tex]sec^2\theta cos2\theta=1-tan^2\theta[/tex]Ed earns a $100 commission on each computer he sells plus a base salary of $50,000 . His total income last year was 75,000 . Which equation can be used to find how many computers Ed sold last year ? A. 50,000 + 100x = 75,000 B. 50,000 - 100 x = 75,000 C. 75,000 + 100x = 50,000
ANSWER
50,000 + 100x = 75,000
STEP-BY-STEP EXPLANATION:
Given parameters
• Ed base salary = $50, 000
,• Commission on each computer sells = $100
,• Total income = $75,000
Let x be the number of computers sold
Total income = base salary + commission * number of cars sold
75000 = 50000 + 100* x
50,000 + 100x = 75, 000
Hence, the equation that can be used to find the number of cars sold is
50,000 + 100x = 75,000
2(3x + 8) = 6x + 16How many solutions does this equation have
Answer:
The equation has infinite number of solutions
Explanation:
Given the equation:
2(3x + 8) = 6x + 16
To know how many solutions this equation has, we need to solve it and see.
Remove the brackets on the left-hand side
6x + 16 = 6x + 16
The expression on the left-hand side is exactly the same as the one on the right-hand side, this reason, there is infinite number of solutions that would satisfy this.
Mr. Eric’s business class has 91 students, classified by academic year and gender, As illustrated in the following table. Mr. Eric randomly chooses one student to collect yesterday’s work. What is the probability that he selects a female, given that he chooses randomly from only the juniors? Express your answer as a fraction.
Given:
Eric’s business class has 91 students
Mr. Eric randomly chooses one student to collect yesterday’s work
We will find the probability that he selects a female, given that he chooses randomly from only the juniors
As shown from the table:
The number of females from the juniors = 6
The number of juniors = 6 +13 = 19
So, the probability will be =
[tex]\frac{6}{19}[/tex]What is 44.445 to the nearest hundredth
Answer:
44.45
Explanation:
Given 44.445
We are to convert to the nearest hundredth
Since the last value at the back is greater than 4, we will add 1 to the preceding value behind it to make it 5 as shown
44.445 = 44.4(4+1) [1 is added to the second value from the back
44.445 = 44.45
Hence the value to nearest hundredth is 44.45
Find the distance between (-4, 2) and (10, 2) c. -14d. 14
The distance between two points (a, b) and (c, d) is given by:
[tex]\sqrt[]{(c-a)^2+(d-b)^2}[/tex]For points (-4, 2) and (10, 2), we have:
a = -4
b = 2
c = 10
d = 2
Thus, the distance between those points is
[tex]\sqrt[]{\lbrack10-(-4)\rbrack^2+(2-2)^2}=\sqrt[]{(10+4)^2+0}=\sqrt[]{14^2}=14[/tex]Therefore, the answer is 14.
Which products are greater than 2 5/6?A.1/8 × 2 5/6B.2 5/6 × 2 5/6C.2 5/6 × 1 5/8D.5/6 × 2 5/6E.6/5 × 2 5/6
First, we need to change the mixed number to an improper fraction:
[tex]2\frac{5}{6}=\frac{(6\cdot2)+5}{6}=\frac{17}{6}\approx2.83[/tex]Now let's evaluate each of the options:
A.
[tex]\frac{1}{8}\times2\frac{5}{6}=\frac{1}{8}\times\frac{17}{6}=\frac{1\cdot17}{8\cdot6}=\frac{17}{48}\approx0.354[/tex]B.
[tex]2\frac{5}{6}\times2\frac{5}{6}=\frac{17}{6}\times\frac{17}{6}=\frac{17\cdot17}{6\cdot6}=\frac{289}{36}\approx8.02[/tex]C.
[tex]2\frac{5}{6}\times1\frac{5}{8}=\frac{17}{6}\times\frac{13}{8}=\frac{17\cdot13}{6\cdot8}=\frac{221}{48}\approx4.60[/tex]D.
[tex]\frac{5}{6}\times2\frac{5}{6}=\frac{5}{6}\times\frac{17}{6}=\frac{5\cdot17}{6\cdot6}=\frac{85}{36}\approx2.36[/tex]E.
[tex]\frac{6}{5}\times2\frac{5}{6}=\frac{6}{5}\times\frac{17}{6}=\frac{6\cdot17}{5\cdot6}=\frac{17}{5}\approx3.4[/tex]Now, we can conclude that options B, C, and E are greater than 2 5/6.
15. A beekeeper estimates that his bee population will triple each year.
Answer:
[tex]P\mleft(x\mright)=150(3^x)[/tex]Explanation:
The initial number of bees = 150
[tex]P(0)=150[/tex]The beekeeper estimates that his bee population will triple each year. Thus, after 1 and 2 years:
[tex]\begin{gathered} P(1)=150\times3 \\ P(2)=150\times3\times3=150\times3^2 \end{gathered}[/tex]Continuing in like manner, after x years:
[tex]P(x)=150(3^x)[/tex]P(x) is the required function.
Suppose that the manufacturer of a gas clothes dryer has found that, when the unit price is p dollars, the revenue R (in dollars) is R(P) = -9p2 + 18,000p. What unitprice should be established for the dryer to maximize revenue? What is the maximum revenue?
Suppose that the manufacturer of a gas clothes dryer has found that, when the unit price is p dollars, the revenue R (in dollars) is R(P) = -9p2 + 18,000p. What unit
price should be established for the dryer to maximize revenue? What is the maximum revenue?
we have the quadratic equation
[tex]R(p)=-9p^2+18,000p[/tex]this is a vertical parabola, open downward
the vertex represents a maximum
Convert to factored form
Complete the square
factor -9
[tex]R(p)=-9(p^2-2,000p)[/tex][tex]R(p)=-9(p^2-2,000p+1,000^2-1,000^2^{})[/tex][tex]\begin{gathered} R(p)=-9(p^2-2,000p+1,000^2)+9,000,000 \\ R(p)=-9(p^{}-1,000)^2+9,000,000 \end{gathered}[/tex]the vertex is the point (1,000, 9,000,000)
therefore
the price is $1,000 and the maximum revenue is $9,000,000Problem N 2
we have the equation
[tex]C(x)=0.7x^2+26x-292+\frac{2800}{x}[/tex]using a graphing tool
the minimum is the point (8.58,308.95)
therefore
Part a
the average cost is minimized when approximately 9 lawnmowers ........
Part b
the minimum average cost is approximately $309 per mower
which of the following gives the line of symmetry
To be able to reflect the trapezoid to itself, the reflection must be at the point where the figure will be divided symmetrically.
For a trapezoid, it must be reflected at the center of its base.
In the given figure, the center of the base of the trapezoid falls at x = 4.
Thus, to reflect it by itself, it must be reflected at x = 4.
The answer is letter B.
how do I know what exponent and base I use when I simplify an exponent, for example, 16^1/4 become (2^4)^1/4 which becomes 2. How do I know I have to use 2^4 instead of another number like 4^2 that is still equal to 16. Why can't I use a different number that is equal to the same thing?
Answer:
Reason:
16^1/4=(2^4)^1/4
Explanation:
You can use either 4^2 or 2^4 both gives the same answer.
In order to simplify the steps we use 2^4.
we get,
[tex]16^{\frac{1}{4}^{}^{}}=(2^4)^{\frac{1}{4}}[/tex][tex]=2^{4\times\frac{1}{4}}[/tex]4 in the power got cancelled and we get,
[tex]=2[/tex]Alternate method:
If we use 4^2 we get,
[tex]16^{\frac{1}{4}}=(4^2)^{\frac{1}{4}}[/tex][tex]=4^{2\times\frac{1}{4}}[/tex][tex]=4^{\frac{1}{2}}[/tex]we use 4=2^2,
[tex]=(2^2)^{\frac{1}{2}}=2[/tex]In order to get answer quicker we appropiately use 2^4=16 here.
Rules in exponent:
[tex]a^n\times a^m=a^{n+m}[/tex][tex]\frac{a^n}{a^m}=a^{n-m}[/tex][tex]\frac{1}{a^m}=a^{-m}[/tex][tex](a^n)^m=a^{n\times m}[/tex][tex]4^{3\times\frac{1}{2}}=4^{\frac{3}{2}}[/tex]use 4=2^2, we get
[tex]=2^{2\times\frac{3}{2}}[/tex]2 got cancelled in the power, we get
[tex]=2^3[/tex][tex]=8[/tex]we get,
[tex]4^{3\times\frac{1}{2}}=8[/tex]what are the consecutive perfect cubes which added to obtain a sum of 100?441?
Answer:add 341 more cubes and that shall be your answer
1,2, 3 and 4 are the consecutive perfect cubes which added to obtain a sum of 100.
What is Number system?A number system is defined as a system of writing to express numbers.
Consecutive perfect cubes which added to obtain a sum of 100
Perfect cubes are the numbers that are the triple product of the same number.
1³+2³+3³+4³
One cube plus two ube plus three cube plus four cube
1+8+27+64
One plus eight plus twenty seven plus sixty four.
100
1,2, 3 and 4 are the consecutive perfect cubes which added to obtain a sum of 100.
Hence, 1,2, 3 and 4 are the consecutive perfect cubes which added to obtain a sum of 100.
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what is the fill in for the diagram drop downs drop down 1: is it a reflexive property, equivalent equation or transitive property of equality.drop down 2: does it have subtraction property of equality, divison of equality or reflexive property and lastly drop down 3: is it a substitution, equivalent equation or subtraction property of equality
Remember the following properties of real numbers:
Reflexive property:
This property states that a number is always equal to itself.
This property is different from the equivalent equations property. In fact, two equations that have the same solution are called equivalent equations,
Division property of equality:
This property states that when we divide both sides of an equation by the same non-zero number, the two sides remain equal.
Substitution property of equality:
This property states that if x = y, then x can be substituted in for y in any equation.
We can conclude that the correct answer is:
Answer:Drop Down 1: reflexive property
Drop Down 2: division property of equality.
Drop Down 3: substitution
How do I find the restrictions on x if there are any? [tex] \frac{1}{x - 1} = \frac{5}{x - 10} [/tex]
We have the expression:
[tex]\frac{1}{x - 1}=\frac{5}{x - 10}[/tex]When we have rational functions, where the denominator is a function of x, we have a restriction for the domain for any value of x that makes the denominator equal to 0.
That is because if the denominator is 0, then we have a function f(x) that is a division by zero and is undefined.
If we have a value that makes f(x) to be undefined, then this value of x does not belong to the domain of f(x).
Expression:
[tex]\begin{gathered} \frac{1}{x-1}=\frac{5}{x-10} \\ \frac{x-1}{1}=\frac{x-10}{5} \\ x-1=\frac{x}{5}-\frac{10}{5} \\ x-1=\frac{1}{5}x-2 \\ x-\frac{1}{5}x=-2+1 \\ \frac{4}{5}x=-1 \\ x=-1\cdot\frac{5}{4} \\ x=-\frac{5}{4} \end{gathered}[/tex]Answer: There is no restriction for x in the expression.
Consider the line y=7x-7Find the equation of the line that is perpendicular to this line and passes through the point (-8,5) Find the equation of the line that is parallel to this line and passes through the point (-8,5)
Given:
The equation of a straight line is,
[tex]y=7x-7[/tex]The objective is to find,
a) The equation of perpendicular line passes throught the point (-8,5).
b) The equation of parallel line passes throught the point (-8,5).
Explanation:
The general equation of straight line is,
[tex]y=mx+c[/tex]Here, m represents the slope of the straight line and c represents the y intercept.
a)
For perpendicular lines, the prouct of slope of two lines will be (-1).
By comparing the general equation and the given equation the slope value will be,
[tex]m_1=7[/tex]Now, the slope value of perpendicular line can be calculated as,
[tex]\begin{gathered} m_1\times m_2=-1 \\ 7\times m_2=-1 \\ m_2=-\frac{1}{7} \end{gathered}[/tex]Since, the perpendicular line passes through the point (-8,5), the equation of line can be calculated using point slope formula.
[tex]\begin{gathered} y-y_1=m_2(x-x_1)_{} \\ y-5=-\frac{1}{7}(x-(-8)) \\ y-5=-\frac{1}{7}(x+8) \\ y-5=-\frac{x}{7}-\frac{8}{7} \\ y=-\frac{x}{7}-\frac{8}{7}+5 \\ y=-\frac{x}{7}-\frac{8}{7}+\frac{35}{7} \\ y=-\frac{x}{7}+\frac{27}{7} \end{gathered}[/tex]Hence, the equation of perpendicular line is obtained.
b)
For paralle lines the slope value will be equal for both lines.
[tex]m_1=m_3=7[/tex]Since, the parallal line passes through the point (-8,5), the equation of line can be calculated using point slope formula.
[tex]\begin{gathered} y-y_1=m_3(x-x_1) \\ y-5=7(x-(-8)) \\ y-5=7(x+8) \\ y-5=7x+56 \\ y=7x+56+5 \\ y=7x+61 \end{gathered}[/tex]Hence, the equation of parallel line is obtained.
Write the percent as decimal 49%
Solution;
Given: The given number in percentage is 49 %
Required: Decimal value of given percentage.
Explanation:
Convert percentage into decimal as follows:
[tex]49\text{ \%=}\frac{49}{100}[/tex][tex]49\text{ \%=0.49}[/tex]Therefore, the required answer is 0.49
Final answer: The de
PDonald has xxx twenty-dollar bills and 111 ten-dollar bill
the equation for this problem is
20x +10
where x is the number of bills with 20-dollars
Find the indicated values for the function f(x)= Answer all that is shown
For this problem, we are given a certain function and we need to evaluate it in various points.
The function is given below:
[tex]f(x)=\sqrt{5x-15}[/tex]The first value we need to calculate is f(4), we need to replace x with 4 and evaluate the expression.
[tex]f(4)=\sqrt{5\cdot4-15}=\sqrt{20-15}=\sqrt{5}=2.24[/tex]The second value we need to calculate is f(3), we need to replace x with 3 and evaluate the expression.
[tex]f(3)=\sqrt{5\cdot3-15}=\sqrt{15-15}=0[/tex]The third value we need to calculate is f(2), we need to replace x with 2 and evaluate the expression.
[tex]f(2)=\sqrt{5\cdot2-15}=\sqrt{10-15}=\sqrt{-5}[/tex]The value for this is not real.
Given that line AB is tangent to the circle, find m
Solution:
Given the figure below:
To solve for m∠CAB, we use the chord-tangent theorem which states that when a chord and a tangent intersect at a point, it makes angles that are half the intercepted arc.
Thus,
[tex]m\angle CAB=\frac{1}{2}\times arc\text{ CDB}[/tex]where
[tex]\begin{gathered} m\angle CAB=(4x+37)\degree \\ arc\text{ CDB=\lparen9x+53\rparen}\degree \end{gathered}[/tex]By substituting these values into the above equation, we have
[tex]4x+37=\frac{1}{2}(9x+53)[/tex]Multiplying through by 2, we have
[tex]\begin{gathered} 2(4x+37)=(9x+53) \\ open\text{ parentheses,} \\ 8x+74=9x+53 \end{gathered}[/tex]Collect like terms,
[tex]\begin{gathered} 8x-9x=53-74 \\ \Rightarrow-x=-21 \\ divide\text{ both sides by -1} \\ -\frac{x}{-1}=-\frac{21}{-1} \\ \Rightarrow x=21 \end{gathered}[/tex]Recall that
[tex]\begin{gathered} m\operatorname{\angle}CAB=(4x+37)\operatorname{\degree} \\ where \\ x=21 \\ thus, \\ m\operatorname{\angle}CAB=4(21)+37 \\ =84+37 \\ \Rightarrow m\operatorname{\angle}CAB=121\degree \end{gathered}[/tex]Hence, the measure of the angle CAB is
[tex]121\degree[/tex]which of the following is an even fonction?
g(x)=(x-1)² +1
9(x) = 2x² +1
9(x) = 4x+2
g(x) = 2x
Answer:
g(x)=2x^2 +1 would be the even function
Step-by-step explanation:
To find if a function is even, you substitute -x for every x in the function. If the function stays the exact same, the function is even. For the first one, (x-1)^2 +1, If -x is substituted, we get (-x-1)^2 +1, which is not the same as the original function.
2x^2 +1 = 2(-x)^2 +1 =2x^2 +1 This function is even
(a negative squared will be positive)
4x+2 = 4(-x)+2 =-4x +2 This function is not even
2x = 2(-x) = -2x This function is not even
How does the value of 1 in Maisha’s time compare with the value of 1 in Patti’s time?
You are choosing 4 of your 7 trophies and arranging them in a row on a shelfIn how many different ways can you choose and arrange the trophies?A. 840B. 28C. 24D. 5040
The formula to find how many different ways are there to choose a subgroup of r things from a group of n things is
[tex]\frac{n!}{(n-r)!}[/tex]Here, you have 7 trophies and you want to choose 4 of them, so you have
[tex]\frac{7!}{(7-4)!}\text{ = }\frac{5040}{6}=840[/tex]So there are 840 ways to choose your 4 trophies out of the 7 you have.
Write 3.6x10^-4 in standard form
In order to write the given number in standard form, you take into account that the factor 10^(-4) can be written as follow:
[tex]10^{-4}=\frac{1}{10^4}[/tex]Next, you consider that the number of the exponent in a 10 factor means the number of zeros right side number 1:
[tex]\frac{1}{10^4}=\frac{1}{10000}[/tex]that is, there are four zeros right side of number 1.
Finally, you write the complete number:
[tex]3.6\times10^{-4}=\frac{3.6}{10^4}=\frac{3.6}{10000}[/tex]Tickets to a play cost $10 at the door and $8 in advance.
The theatre club wants to raise at least $800 from the sale of the tickets from the play. Write and
graph an inequality for the number of tickets the theatre club needs to sell. If
the club sells 40 tickets in advance, how many does it need to sell at the door to
reach its goal? Use x to represent the number of tickets sold at the door. Use y
to represent the number of tickets sold in advance.
The system of linear inequality is solved to determine that they need to sell at least 48 door ticket. The graph of the problem is attached below
System of Linear InequalityA system of linear inequalities in two variables consists of at least two linear inequalities in the same variables. The solution of a linear inequality is the ordered pair that is a solution to all inequalities in the system and the graph of the linear inequality is the graph of all solutions of the system.
To solve this problem, we have to write out a system of linear inequality and solve.
x = number of tickets sold at doory = number of tickets sold in advance10x + 8y ≥ 800 ...eq(i)
y = 40 ...eq(ii)
put y = 40 in eq(i)
10x + 8(40) ≥ 800
10x + 320 ≥ 800
10x ≥ 800 - 320
10x ≥480
x ≥ 48
They need to sell at least 48 door tickets to meet the target.
The graph of the inequality is attached below
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=O REAL NUMBERSDistributive property: Integer coefficientsUse the distributive property to remove the parentheses.+(-5u-+*+4)INOPX 5 ?
The given expression is:
[tex]-(-5u-x+4)[/tex]Using the distributive property of multiplication over addition, we have
[tex]\begin{gathered} -(-5u-x+4)=-(-5u)-(-x)-(+4) \\ =+5u+x-4=5u+x-4 \end{gathered}[/tex]Therefore, removing the paranthesis gives:
5u + x - 4
.
⦁ It takes the earth 24 h to complete a full rotation. It takes Mercury approximately 58 days, 15 h, and 30 min to complete a full rotation. How many hours does it take Mercury to complete a full rotation? Show your work using the correct conversion factors.
Answer:
Answer:
58 days, 15 h, and 30 min
Step-by-step explanation:
THE GRAPH OF THIS SYSTEM OF LINEAR INEQUALITIES IS X-2Y< OR EQUAL 6 X> OR EQUAL TO 0 Y< OR EQUAL TO 2GRAPH
The graph of the system of linear inequalities x - 2y ≤ 6 , x ≥ 0 and y ≤ 2 is attached below.
The system of linear inequalities is x - 2y ≤ 6 , x ≥ 0 and y ≤ 2
The solution set of x ≥ 0 includes {x ∈ R , x ≥ 0 }
The solution set of y ≤ 2 includes {y ∈ R , y ≤ 2 }
The solution set of x - 2y ≤ 6 , shows the region of the graph that is below the straight line x - 2y = 6 .
Let us now plot the graph of the straight line x - 2y = 6 with the slope of -1/2 .
At x = 0 , y = - 3
At x = 2 , y = - 2
At x = -4 , y = - 5
hence the graph will pass through the points (0,-3) , (2,-2) and (-4,-5)
The line x = 0 indicates the x-axis and the line y=2 indicates the straight line parallel to x axis passing through (0,2) .
The shaded region of the graph indicates the solution set of the system of inequalities.
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