Unit Price
The unit price can be calculated by dividing the total price of n items by n:
Elizabeth sold n=12 bows for $12.12, so the unit price is:
$12.12 / 12
=$1.01
The cost of each bow is $1.01
The long division requires us to arrange the number like:
12 | 12.12
The division starts by dividing 12 (of the dividend 12.12) by 12 (the divisor). We get 1. It must be placed atop the dividend::
| 1
12 | 12.12
Now multiply 1x12 and subtract from the dividend:
| 1
12 | 12.12
| -12
|----------
| 0.12
We have found the decimal point. Remove it and add it to the quotient.
| 1.
12 | 12.12
| -12
|----------
| 12
Divide 1 by 12. It's not possible, so we add a 0 to the quotient:
| 1.0
12 | 12.12
| -12
|----------
| 12
Now we divide 12 by 12 again and get 1. This is added to the quotient and subtract 1*12 from the dividend:
| 1.01
12 | 12.12
| -12
|----------
| 12
| -12
| ---------
| 0
The remainder is 0 and the quotient is 1.01
Rena's Rowbot drift 23 feet from Shore followed by 9 more feet the rowboat card current position can be represented by - 23 + - 9 what integer represents the Rowboat current position.
Answer:
The integer that represent the rowboat's current position is;
[tex]-32[/tex]Explanation:
Given in the question;
the rowboat card current position can be represented by;
[tex]-23+-9[/tex]We need to solve to know the rowboat current position;
[tex]\begin{gathered} -23+-9 \\ =-23-9 \\ =-32 \end{gathered}[/tex]The integer that represent the rowboat's current position is;
[tex]-32[/tex]One side of a triangle is 4 more inches than the shortest side. The third side is 3 times the length of the shortest side. If the perimeter of the triangle is 29 inches, write and solve an equation to find the lengths of all 3 side of the triangle.
Answer
The three sides of the triangle have the measures
5 inches
9 inches
15 inches
Explanation
The perimeter of a figure is the sum of the dimensions of its exterior sides.
Let the length of the shortest side of the triangle be x inches
One side of a triangle is 4 more inches than the shortest side, that is, (x + 4) inches.
The third side is 3 times the length of the shortest side. That is, (3x) inches
So, the three sides of the triangle are
x
x + 4
3x
So, the sum of these sides is equal to the perimeter of the triangle, 29 inches.
x + x + 4 + 3x = 29
5x + 4 = 29
5x = 29 - 4
5x = 25
Divide both sides by 5
(5x/5) = (25/5)
x = 5 inches
x + 4 = 5 + 4 = 9 inches
3x = 3 (5) = 15 inches
Hope this Helps!!!
solve for the indicated variable. use / to denote a fraction if needed.
Given the expression:
[tex]-4x+3y=w[/tex]to solve for y, we have to move all the terms and coefficients to the opposite side of the equation. First we move the term 4x to the right side with a positive sign (since it has a negative sign) and the 3 that is multiplying y is going to move to the other side dividing the resulting expression.
We have then:
[tex]\begin{gathered} -4x+3y=w \\ \Rightarrow3y=w+4x \\ \Rightarrow y=\frac{w+4x}{3} \end{gathered}[/tex]therefore, y= (w+4x)/3
7⅕-6⅔=?O A. 1⅕O B. ⅘O C. 13⅗O D. 1 ⅘
We have two mixed fractions
[tex]7\frac{1}{5}-6\frac{2}{5}[/tex]Separate 1 from the seven
[tex]6\frac{6}{5}-6\frac{2}{5}[/tex]Subtract the integers
6 - 6 = 0
Combine the fractions
[tex]\frac{6}{5}-\frac{2}{5}=\frac{4}{5}[/tex]Answer: Option B
Bill can repair a transmission in 8 hours. It takes Henry 10 hours to do the same job. If they begin the job together and then Bill leaves after 3 hours, how long will it take Henry to finish?
Answer: Henry will take 3.25 hours to finish the work alone.
Explanation
Given
• Bill can repair a transmission in 8 hours.
,• It takes Henry 10 hours to do the same job.
,• If they begin the job together and then Bill leaves after 3 hours, how long will it take Henry to finish?
Procedure
Bill does 1/8 of the job per hour, while Henry does 1/10 of the work per hour. They work together 3 hours. If we assume their works are additive (no interference from one another), and considering that:
[tex]rate\times time=\text{work done}[/tex]Then we can build the following relation:
[tex](\frac{1}{8}+\frac{1}{10})\times3=\text{ work done}[/tex]Simplifying:
[tex]\text{ work done}=(\frac{5+4}{40})\times3=(\frac{9}{40})\times3=\frac{27}{40}[/tex]The job at the 3 hours will be 27/40 done. Then, Henry has to finish the rest of the work, which is:
[tex]\frac{40}{40}-\frac{27}{40}=\frac{13}{40}[/tex]Finally, to calculate the time it will take Henry to do the job, we have to do the following:
[tex]\frac{1}{10}\times t=\frac{13}{40}[/tex][tex]t=\frac{\frac{13}{40}}{\frac{1}{10}}=\frac{130}{40}=\frac{13}{4}\approx3.25h[/tex]If c= 13 and angle B = 25degrees, find a.
Given;
[tex]\begin{gathered} \text{hypotenuse side c=13} \\ \text{Angle B= 25}^o \\ \text{adjacent side a=unknown} \\ \cos \theta=\frac{adjacent}{hypotenuse} \\ \cos 25=\frac{a}{13} \\ a=13\cos 25 \\ a=11.8 \end{gathered}[/tex]The length of side a=11.8 to the nearest tenth.
Find the area of the shapes belowMust show all steps including formula and units!
Answer:
[tex]\begin{gathered} a)1.33m^2 \\ b)123m^2 \\ c)62.5ft^2 \end{gathered}[/tex]Explanation:
We were given the following information:
Figure 1:
This is a trapezium
The area is calculated as shown below:
[tex]\begin{gathered} Base_1=2.0m \\ Base_2=1.8m \\ Height=0.7m \\ Area=\frac{Base_1+Base_2}{2}\times Height \\ Area=\frac{2.0+1.8}{2}\times0.7 \\ Area=1.9\times0.7 \\ Area=1.33m^2 \end{gathered}[/tex]Figure 2:
This is a rectangle
The area is calculated as shown below:
[tex]\begin{gathered} Length=15m \\ Width=8.2m \\ Area=Length\times Width \\ Area=15\times8.2 \\ Area=123m^2 \end{gathered}[/tex]Figure 3:
This is a rectangle
The area is calculated as shown below:
[tex]\begin{gathered} Length=12.5ft \\ Width=5ft \\ Area=Length\times Width \\ Area=12.5\times5 \\ Area=62.5ft^2 \end{gathered}[/tex]Does sinx =1/2 have infinite solutions
ANSWER
Yes, it does
EXPLANATION
We want to know if the given function has infinite solutions:
[tex]\sin x=\frac{1}{2}[/tex]The given function is a periodic function. It has a period of 2π radians (360 degrees).
This implies that for every revolution from a solution of the given function, there is another value of x which has the exact same function.
In other words, there are infinite values of x for which its sine is 1/2.
Therefore, it has infinite solutions.
I'll send picture of graph and questions
do you see the answering tab?
the question is find the slope of CE?
what is the calculate slope?
are you there?
12 is the calculate slope?
Verify the slope
we have the points
L(-3,-3) and N(4,1)
m=(1+3)/(4+3)
m=4/7
the slope is 4/7
answer is the third optionPlease, Do you understand all the steps so far?
the function is i
Write all classifications that apply to the real number -5.natural number, terminating decimalrational, integer, natural numberrational, integer, whole number, natural number, terminating decimalrational, integer, terminating decimal
Consider that the given number is '-5'.
In all the mentioned choices, the classifications are given as, natural numbers, terminating decimal, rational, integer, whole number.
Let us discuss -5 for each of these classifications one at a time:
Natural Number:
The integer number equal to 1 or greater than 1, are termed Natural Numbers. Since -5 does not satisfy this condition, that is, -5 is not greater than 1. So it cannot be called a natural number.
Rational Number:
A real number is said to be rational is it can be written in the form p/q such that 'q' must be non-zero. The number -5 can be represented as -5/1, that satisfies the condition. So thcan be considered as rational.
Write the polynomial in standard form. Then classify the polynomial by degree and by number of terms. 4x^4+3x^4-x^4Write the polynomial in standard form. Simplify your answer.
Explanation.
The question gives a polynomial and asks us to classify the polynomial according to
1. In standard form
2. The degree
3. The number of terms
To do so, let us understand what a polynomial means
A polynomial is defined as an expression that is composed of variables, constants, and exponents, that are combined using mathematical operations such as addition, subtraction, multiplication, and division.
Part 1
For the polynomial
[tex]4x^4+3x^4-x^4[/tex]We will first have to write the polynomial in standard form. To do so, we will have to simplify
[tex]\begin{gathered} 4x^4+3x^4-x^4=x^4(4+3-1) \\ =x^4(7-1) \\ =x^4(6) \\ =6x^4 \end{gathered}[/tex]So the standard form of the polynomial is 6x⁴
Part 2
we have the polynomial as
[tex]6x^4[/tex]We can see that the highest power is 4
Classification according to Degree.
so in our case, since we have the highest degree to be 4
Thus, the degree is 4. The name given to a polynomial with degree 4 is called Quartic
Part 3
We are to also classify according to the number of terms
The standard form of the polynomial is
[tex]6x^4[/tex]We can observe that it has just one term
A polynomial with one term is called monomial
A monomial is an algebraic expression with a single term but can have multiple variables and a higher degree too.
Therefore, the answer is Monomial
sales tax in a certain community is 7% if the sales tax on a new car was 1400 what was the selling price of the car
hello
the cost of the sale tax = 1400
the percentage of the tax = 7%
selling price = ?
[tex]\begin{gathered} 7=\frac{1400}{x}\times100 \\ \frac{7}{100}=\frac{1400}{x} \\ \text{cross multiply both sides } \\ 7\times x=100\times1400 \\ 7x=140000 \\ \text{divide both sides by 7} \\ \frac{7x}{7}=\frac{140000}{7} \\ x=20000 \end{gathered}[/tex]from the calculation above, the selling price of the car is 20,000
Chad originally had a rectangle garden with the area of 2X ^2square meters .He decided to make a new garden that was larger than his original garden. The area of the new garden is 2x^2+6x+4 square meters. Which of the following expressions represents the difference between the area of his new garden and the area of the original garden .I just need a brief explanation with the answer
The area of original graden = 2x^2
Area of new garden =
[tex]2x^2+6x+4[/tex]Substract the area =
[tex]2x^2+6x+4-2x^2=6x+4[/tex]Difference between the area of his new garden and the area of the original garden is (6x + 4_
Answer: d) 6x + 4
Find the measure of angle one and angle two if angle 3 =78° and angle 4=102°
Given the diagram
Given that <3 =78 degrees and
<4 = 102 degrees.
To get angle 1 (<1):
< 1 and <4 are corresponding angles
When two lines are crossed by another line (called the Transversal), the angles in matching corners are called Corresponding Angles.
Therefore: <1 = <4 = 102 degrees
[tex]<1=102^0[/tex]To get angle 2 (<2)
<2 and <3 are also corresponding angles
therefore
<2 = <3 =78 degrees
This means that
[tex]<2=78^0[/tex]Determine whether y varies directly with x. if so, find the constant of the variation.y-6x=0
First, we have to isolate the variable y:
y-6x=0
y= 6x
We can see that if x changes its value, it also does the y variable.
So, y varies directly with x.
The constant of variation is:
y =k x
Where k is the constant.
In this case , the constant of variation is 6.
Museum admission cost $9 and tickets to the mammoth exhibit cost $8. The expression 9p + 8p represents the cost in dollars for p people to visit the museum and attend the exhibit. Enter the simplified expression by combining like terms. Step 1 out of 1:Use a bar model to represent the problem. Each square represents p, or 1p.____________9p____________8p____(p) (p) (p) (p) (p) (p) (p) (p) (p) ll (p) (p) (p) (p) (p) (p) (p)Count the number of (p)s to find a simplified expression. A simplified expression for the cost in dollars is __.
Given the expression:
9p + 8p
To simplify the expression by combining the like terms, we have:
9p = (p) (p) (p) (p) (p) (p) (p) (p) (p)
8p = (p) (p) (p) (p) (p) (p) (p) (p)
Now, let's combine both ps:
9p + 8p = (p) (p) (p) (p) (p) (p) (p) (p) (p) + (p) (p) (p) (p) (p) (p) (p) (p) = 17p
After counting the number of p, we have 17p.
Therefore, a simplified expression for the cost in dollars is $17p
ANSWER:
$17p
Thirty 8th graders signed up for running club,however nine dropped out before the first2practice. If 46 2/3% of the club are 8th graders,how many total students are in the runningclub?
Given
30 8th graders
9 dropped out before the first practice
Total = 30 - 9 = 21 8th graders
Procedure
46% of the club are 8th graders
T: Total of studetns
[tex]\begin{gathered} 21=T\cdot46\text{ 2/3 \%} \\ T=\frac{21}{0.46666} \\ T=45 \end{gathered}[/tex]The total students in the running club would be 45 students and 21 from 8th graders
Which inequality is represented in the number line below?-5-4-3-2-1 0 1 2 3 4 5OA.-7+2<22+3<4+2OB.-9≤-3x-6≤6OC.-6 ≤ x + 2 ≤ 1OD. 6-3x ≤-9
The Solution:
The correct answer is [option B]
Given:
Required:
To determine the inequality represented by the given number line.
[tex][/tex]The Marching Band is traveling from Minnesota to Florida to perform in a national competition. A train ticket from Minnesota to Florida costs $150 and takes 15 hours of travel time per student. To rent a bus to make the trip, it costs $120 per student and takes 20 hours of travel time per student. The band has $4,800 to spend on the trip and can only spend 720 hours of total travel time. Use the information below.Let x = Students traveling by trainLet y = Students traveling by busTherefore,$150x + $120y < $4,800 and15x + 20y < 720.The graph of these functions is to the right.It is impossible for a negative number of students to go on the trip, so x and y both have to be greater than zero. Therefore, the functions are confined to the first quadrant.Number of students function:N = x + yWhat is the maximum number of students who can attend the trip? A. A maximum of 36 students can attend the trip. B. A maximum of 32 students can attend the trip. C. A maximum of 38 students can attend the trip. D. A maximum of 40 students can attend the trip.
ANSWER
A maximum of 38 students can attend the trip. (Option C).
EXPLANATION
Given:
Number of students function: N = x + y
$150x + $120y < $4,800 ................equ 1
15x + 20y < 720.................................equ 2
where
x = Students traveling by train
y = Students traveling by bus
Multiply equation 2 by -10
[tex]equ\text{ 2 }\times-10\Rightarrow-150x\text{ - 200y < -7200..........................equ 3}[/tex]Add equation 1 and 3
150x + 120y < 4,800
-150x - 200y <-7200
-----------------------------
0x - 80y < -2400
y > 2400/80
y > 30
Substitute the value of y into equation 1 to solve for x
150x + 120y < 4,800
150x + 120(30) < 4800
150x < 4800 - 3600
x < 1200/150
x < 8
Number
Find the equation of the hyperbola that has its foci at (0,-4) ans (10,-4) and whose conjugate axis is 6 units long
We are given the following information
Foci at (0, -4) and (10, -4)
The conjugate axis is 6 units
Recall that the standard form of the equation of hyperbola centered at (h, k) is given by
[tex]\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1[/tex]Where the center is (h, k)
The center (h, k) is the midpoint of the transverse axis given by
[tex]\begin{gathered} (h,k)=(\frac{0+10}{2},\frac{-4+(-4)}{2}) \\ (h,k)=(\frac{0+10}{2},\frac{-4-4}{2}) \\ (h,k)=(\frac{10}{2},\frac{-8}{2}) \\ (h,k)=(5,-4) \end{gathered}[/tex]Let us find the values of a and b
The semi transverse axis (a) is given by
[tex]a=\frac{10-0}{2}=\frac{10}{2}=5[/tex]The semi conjugate axis (b) is given by
[tex]b=\frac{6}{2}=3[/tex]So, the equation of the hyperbola is
[tex]\begin{gathered} \frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1 \\ \frac{(x-5)^2}{5^2}-\frac{(y-(-4))^2}{3^2}=1 \\ \frac{(x-5)^2}{25^{}}-\frac{(y+4)^2}{9^{}}=1 \end{gathered}[/tex]Therefore, the equation of the hyperbola is
[tex]\frac{(x-5)^2}{25^{}}-\frac{(y+4)^2}{9^{}}=1[/tex]Find the sum. Write your answer in scientific notation.(9.7×10^6) + (6.7×10^5)
Explanation
We asked to simplify the question, giving our answer in scientific notation
To add, we will write the given question in the same terms:
[tex](9.7\times10^6)+(^6.7\times10^5)=(97\times10^5)+(6.7\times10^5)[/tex]Hence
[tex]\begin{gathered} we\text{ will have } \\ 103.7\times10^5 \end{gathered}[/tex]The final step will be to express the answer above in the standard scientific notation, we will have:
[tex]1.037\times10^7[/tex]a kite in the shape of a rhombus has diagonals that are 25 in long and 15 in Long what is the area of the kite
The area of a rhombus is given by:
[tex]A=\frac{d_1d_2}{2}[/tex]where d1 and d2 are the diagonals. Then in this case we have:
[tex]A=\frac{25\cdot15}{2}=187.5[/tex]Therefore the area is 187.5 squared inches.
2) Direction: In the diagram below, justify each step of the equation. Statement Reason 3n - 5 = -8(6+5n) A) 3n-5=-48-40n B) 3n-43= -40n C) -43=-43n D) N=1
First:
Statement: 3n - 5 = -8(6 + 5n)
Reason: Given
Second:
Statement: 3n - 5 = -48 - 40n
Reason: Distributive property
Third:
Statement: 3n - 5 - 3n = -48 - 40n - 3n
Reason: Subtraction property of equality
Fourth:
Statement: 0 - 5 = -48 - 43n
Reason: Additive inverse property(left) and combine like terms(right)
Fifth:
Statement: -5 = -48 - 43n
Reason: Additive Identity property
Sixth:
Statement: - 5 + 48 = -43n - 48 + 48
Reason: Addition property of equality
Seventh:
Statement: 43 = -43n
Reason: Addition
Eight:
Statement: n = -1
Reason: Division
-4x < -50 which situation could the inequality represent A divers from sea floor at 4 feet per minute and is now less than 50 feet from the surface. for how many minutes could he have been rising?Helen has been watching a movie for 50 minutes and 4 minutes are left. if she arrived at the movie late how many minutes could the movie be?it is 4 degrees in buffalo and it is 50 degrees below zero in alaska. how many times colder is it in Alaska?imran has been borrowing $4 each week and as a result he is now more than $50 in dept.for how many weeks could he have been borrowing?
If Imran borrows $4 per week, then after x weeks he will borrow 4x dollars
Imran has a debt greater than $50, then:
4x > 50
Dividing by -1 at both sides (note that the sign changes):
-4x < -50
Therefore, the correct choice is D.
To find for how many weeks he could have been borrowing, we need to solve the inequality for x.
4x > 50
x > 50/4
x > 12.5
He could have been borrowing for more than 12 and a half weeks
Graph each equation using x- and y- intercept -5x+y=-10 Other equation-3x-6y=12
10) We have to calculate the x and y intercepts for the line and graph the line:
[tex]-5x+y=-10[/tex]The x-intercept corresponds to the point where y = 0, so we can calculate it as:
[tex]\begin{gathered} -5x+0=-10 \\ -5x=-10 \\ x=\frac{-10}{-5} \\ x=2 \end{gathered}[/tex]The y-intercept corresponds to the point where x = 0, so we can calculate it as:
[tex]\begin{gathered} -5(0)+y=-10 \\ y=-10 \end{gathered}[/tex]With the intercepts, we have two points: (2,0) and (0,-10) and we can use them to graph as:
11) We have to calculate the x and y intercepts for the line and graph the line:
[tex]-3x-6y=12[/tex]The x-intercept is:
[tex]\begin{gathered} -3x-6(0)=12 \\ -3x=12 \\ x=\frac{12}{-3} \\ x=-4 \end{gathered}[/tex]The y-intercept is:
[tex]\begin{gathered} -3(0)-6y=12 \\ -6y=12 \\ y=\frac{12}{-6} \\ y=-2 \end{gathered}[/tex]Then, knowing the intercepts, we know the points (-4,0) and (0,-2) and we can graph the line as:
Graph the image of the figure on the right under the given translation.T(5,3) (x,y)
Notice that the translation transforms the coordinates (x,y) to (x+5,y+3). Then, if the vertex of the original triangle are ( -3,5), (-5,-2), and (-9,4) then the vertex of the transformed triangle are (2,8), (0,1), and (-4,7).
The graph of the new triangle is:
Answer: First image of the options in the question tab.
in the figure below, quadrilateral RATS is a rhombus with diagonals SA and TR interesting at E.
We need to find the length of the sides SR, RT, and the angle m∠TAS.
Finding the length of SR:
We consider that, in a rhombus, all of the sides are equal. So the sides ST and SR have to be equal:
[tex]ST=SR[/tex]Substituting the values of these sides:
[tex]3x+30=8x-5[/tex]We need to solve this equation for x.
Subtract 3x to both sides:
[tex]\begin{gathered} 30=8x-3x-5 \\ 30=5x-5 \end{gathered}[/tex]Add 5 to both sides:
[tex]\begin{gathered} 30+5=5x \\ 35=5x \end{gathered}[/tex]Divide both sides by 5:
[tex]\begin{gathered} \frac{35}{5}=x \\ 7=x \end{gathered}[/tex]Now that we have the value of x, we can find the value of SR:
[tex]\begin{gathered} SR=8x-5 \\ \text{substituting x=7} \\ SR=8(7)-5 \\ \text{Solving the operations:} \\ SR=56-5 \\ SR=51 \end{gathered}[/tex]SR=51
Finding the length of RT:
To find this length we need the value of z. And we can find the value of z considering that the diagonals bisect each other, so each side of a diagonal is equal to the other side of the diagonal. In this case, the blue and the red line in the image are equal:
We have that:
[tex]SE=AE[/tex]Substituting the values of SE and AE:
[tex]3z=4z-8[/tex]And now we solve for z by subtracting 3z to both sides:
[tex]\begin{gathered} 0=4x-3z-8 \\ 0=z-8 \\ \text{Add 8 to both sides:} \\ 8=z \end{gathered}[/tex]With this value of z, we can find the length RT.
RT is the yellow line in the image:
Again we consider that the two sides of the diagonal are equal. Thus, RT is equal to:
[tex]\begin{gathered} RT=5z+5+5z+5 \\ \text{Combining like terms:} \\ RT=10z+10 \\ \text{substituting z=8} \\ RT=10(8)+10 \\ RT=80+10 \\ RT=90 \end{gathered}[/tex]RT=90
Finally, we need to find the angle m∠TAS shown in blue in the image:
Since it is a rhombus, all of the angles in point E are equal to 90°:
So, considering only the triangle inside the rhombus marked in blue
We apply the property of triangles that tells us:
The sum of the internal angles of a triangle is equal to 180°.
So adding all of the blue angles we should get 180:
[tex]90+9y+8+5y-2=180[/tex]And now we solve for y, first, combine like terms:
[tex]96+14y=180[/tex]Subtract 96 to both sides:
[tex]\begin{gathered} 14y=180-96 \\ 14y=84 \end{gathered}[/tex]Divide both sides by 14:
[tex]\begin{gathered} y=\frac{84}{14} \\ y=6 \end{gathered}[/tex]And now that we have the value of y, we can find the value of m∠TAS:
[tex]\begin{gathered} m\angle TAS=9y+8 \\ \text{Substituting y=6} \\ m\angle\text{TAS}=9(6)+8 \\ m\angle TAS=54+8 \\ m\angle TAS=62 \end{gathered}[/tex]m∠TAS=62°
Answer:
SR=51
RT=90
m∠TAS=62°
How much of the circle is shaded? Write your answer as a fraction in simplest form. 1/4 2/5
all added parts must equal 1, therefore:
1/4 + 2/5 + x = 1
Where:
x = shaded part
Let's solve for x:
1/4 + 2/5 + x = 1
13/20 + x = 1
Subtract 13/20 from both sides:
13/20 + x - 13/20 = 1 - 13/20
x = 7/20
Can I get help solving this in 1 minute tops
The slope of a line can be in two forms generally.
It can either be rising or falling
When it rises, the slope comes from the left hand side of the graph and moves upwards. The sign of the slope here is positive and this represents an increasing function. What this means is that as the x-value increase, the y-value increases.
In the second case, we can have a falling line. It comes from the left hand side of the grpah and falls towards the positive x-axis. The slope in this case has a negative value and it is a decreasing function. It represents a decreasing relationship between the x and the y values.
Let us have a pictorial representation of both;
Looking at the pictorial representation, we can see that the given graph looks exactly like the shape on the left
This means that the slope is negative and it represents a decreasing function. So our correct answer ticks in this case are negative slope and decreasing function
Meanwhile, for a constant slope, the value of the function is the same regardless of the x-value. It can be shown as follows;
Plot the points with polar coordinates (-3, -2pi) and (2, pi/4) using the pencil.
P1 = (-3, -2π)
P2 = (2, π/4)
The first number is the length of the line joining the origin and the point, and the second number is the angle between the line and the horizontal axis. For the first point, we see that the angle is -2π. Since this is a circle, for an angle of -2π we finish at the same point. The length is 3 but points to the left side of the origin because the coordinate is -3.
For the second point, we have a line of length 2, and the angle is π/4. Graphically, this is: