The radius of the circle is r=10 in.
The circumference of the circle is,
[tex]\begin{gathered} C=2\pi r \\ =2\pi\times10 \\ =20\pi \\ =62.83in \end{gathered}[/tex]Thus, the exact value of circumference is 20pi inches and the approximate value is 62.83 in.
Solve the problem. Students in a math class took a final exam. They took equivalent forms of the exam in monthly intervals thereafter. The average score S(t), in percent, after t months was found to be given by 6) - 70-20In (t.1). *20. Find Slu). 20 OSTU - 70 STO OSD- t + 1 20 0 st) SO) = -20 In
Find the derivative of S(t)=70-20ln(t+1)
[tex]\begin{gathered} \frac{dS(t)}{dt}=0-20\cdot\frac{1}{t+1}\cdot1 \\ \frac{dS(t)}{dt}=\frac{-20}{t+1} \\ \end{gathered}[/tex]The derivative is -20/t+1
Compare the Mixed Numbers. Convert the imroner fraction to mixed nu
1) Comparing those Mixed numbers we can stat which is greater, lesser than, or equal by dividing the numerator by the denominator and adding to the whole number:
[tex]\begin{gathered} 2\frac{5}{8}=\frac{8\cdot2+5}{8}=\frac{21}{8}=2.625 \\ 2\frac{1}{2}=\frac{2\cdot2+1}{2}=\frac{5}{2}=2.5 \\ 2\frac{5}{8}>\text{ 2}\frac{1}{2} \\ 2\frac{2}{8}=2\frac{1}{4}\text{ } \\ 1\frac{3}{8}<2\frac{3}{8} \\ 1\frac{5}{8}=\frac{8\cdot1+5}{8}=\frac{13}{8}=1.625 \\ 2\frac{3}{4}=2.75 \\ 1\frac{5}{8}<2\frac{3}{8} \\ \\ 1\frac{2}{4}=1\frac{1}{2}=1+0.5=1.5 \\ 1\frac{2}{8}=1\frac{1}{4}=1.25 \\ 1\frac{2}{4}>1\frac{2}{8} \\ \\ 2\frac{7}{8}>1\frac{7}{8} \end{gathered}[/tex]So there are cases when the fraction is the same we just need to compare the whole number.
But in most cases, dividing the numerator by the denominator and writing it as a decimal number is really helpful
3) So the answers are:
[tex]1\frac{3}{8}<2\frac{3}{8},2\frac{2}{8}=2\frac{1}{4},\text{ }2\frac{5}{8}>\text{ 2}\frac{1}{2},\text{ }1\frac{5}{8}<2\frac{3}{8},\text{ }1\frac{2}{4}>1\frac{2}{8},\text{ }2\frac{7}{8}>1\frac{7}{8}[/tex]Which of the following equations could represent a town with an initial population of 875 people and an annual growth rate of approximately 2%?y=875 - 1.02V=875 -1.02%y = 875(2)Dy=875 (1.02)
Answer:
D. y=875(1.02)^x
Explanation:
Initial population = 875 people
Growth rate = 2%
The population after x years can be modeled below:
[tex]\begin{gathered} y=875(1+2\%)^x \\ =875(1+\frac{2}{100})^x \\ =875(1+0.02)^x \\ y=875(1.02)^x \end{gathered}[/tex]The correct choice is D.
The linear functions f(x) and g(x) are represented on the graph, where g(x) is a transformation of f(x):A graph with two linear functions; f of x passes through 0, negative 1 and 5, 14, and g of x passes through negative 6, negative 1 and negative 1, 14.Part A: Describe two types of transformations that can be used to transform f(x) to g(x). Part B: Solve for k in each type of transformation. Part C: Write an equation for each type of transformation that can be used to transform f(x) to g(x).
Let's write the equation for every function:
Since f(x) passes through (0,-1) and (5,14), the equation will be given by:
[tex]\begin{gathered} (x1,y1)=(0,-1) \\ (x2,y2)=(5,14) \\ m=\frac{14-(-1)}{5-0}=\frac{15}{5} \\ m=3 \end{gathered}[/tex]Using the point-slope equation:
[tex]\begin{gathered} y-y1=m(x-x1) \\ y-(-1)=3(x-0) \\ y+1=3x \\ y=3x-1 \\ f(x)=3x-1 \end{gathered}[/tex]Using the same procedure for g(x):
[tex]\begin{gathered} (x1,y1)=(-6,-1) \\ (x2,y2)=(-1,14) \\ m=\frac{14-(-1)}{-1-(-6)}=\frac{15}{5}^{} \\ m=3 \\ \end{gathered}[/tex][tex]\begin{gathered} y-y1=m(x-x1) \\ y-(-1)=3(x-(-6)) \\ y+1=3x+18 \\ y=3x+17 \\ g(x)=3x+17 \end{gathered}[/tex]Now we have our functions:
[tex]\begin{gathered} f(x)=3x-1 \\ g(x)=3x+17 \end{gathered}[/tex]Part A:
We can translated f(x) k units up in order to get g(x) ( A vertical translation)
[tex]f(x)=3x-1+k[/tex]Or, we can translated f(x) k units to the left in order to get g(x) ( A horizontal translation)
[tex]f(x)=3(x+k)-1[/tex]We can see a graph of the functions:
Where the red function is f(x) and the blue function is g(x).
Part B:
Since both functions must be equal:
[tex]\begin{gathered} f(x)=g(x) \\ so\colon \\ 3x-1+k=3x+17 \end{gathered}[/tex]Solve for k:
[tex]\begin{gathered} k=3x+17-3x+1 \\ k=18 \end{gathered}[/tex]-----------------------
For the other case, let's use the same procedure:
[tex]\begin{gathered} 3(x+k)-1=3x+17 \\ 3x+3k-1=3x+17 \\ 3k=3x+17-3x+1 \\ k=\frac{18}{3} \\ k=6 \end{gathered}[/tex]Part C:
For the vertical translation:
[tex]3x-1+18[/tex]For the horizontal translation:
[tex]3(x+6)-1[/tex]If four friends collected 9 1/3 bags of treats and shared them among themselves equally,how many bags of treats did each person get?
It is given that four friends collected 9 1/3 bags of treats.
[tex]9\frac{1}{3}=\frac{28}{3}\text{ bags}[/tex]Now 28/3 bags divided equally among 4 friends will be:
[tex]\frac{\frac{28}{3}}{4}=\frac{28}{12}=\frac{7}{3}=2\frac{1}{3}\text{ bags}[/tex]Hence the total number of bags that each person will receive is 7/3 bags or 2 1/3 bags.
Write an equation for the quadratic that passes through: (0,9),(−6,9), (−5,4)
The general form of a quadratic is:
[tex]y=ax^2+bx+c[/tex]We need to plug in the 3 pair of points into "x" and "y" and simultaneously solve the 3 equations for a, b, and c.
Putting (0,9):
[tex]\begin{gathered} 9=a(0)^2+b(0)+c \\ c=9 \end{gathered}[/tex]Putting (-6,9):
[tex]\begin{gathered} 9=a(-6)^2+b(-6)+c \\ 9=36a-6b+9 \\ 36a=6b \\ a=\frac{6b}{36} \\ a=\frac{b}{6} \end{gathered}[/tex]Putting (-5,4):
[tex]\begin{gathered} 4=a(-5)^2+b(-5)+9 \\ 4=25a-5b+9 \\ 25a-5b=-5 \end{gathered}[/tex]We substitute a=b/6 into this equation and solve for b:
[tex]\begin{gathered} 25(\frac{b}{6})-5b=-5 \\ \frac{25b}{6}-5b=-5 \\ \frac{25b-30b}{6}=-5 \\ -5b=-30 \\ b=6 \end{gathered}[/tex]Thus, "a" will be:
[tex]\begin{gathered} a=\frac{b}{6} \\ a=\frac{6}{6} \\ a=1 \end{gathered}[/tex]Thus, we have a = 1, b = 6, c = 9
The equation is:
[tex]\begin{gathered} y=1x^2+6x+9 \\ y=x^2+6x+9 \end{gathered}[/tex]On a unit circle, 0 = 30°. Identify the terminal point and tan e.
A unit circle is a circle with a radius of 1 unit.
The angle θ = 30⁰'
The terminal points are:
[tex]undefined[/tex]A triangle has a 30 degree angle and two sides that are each 6em in length. Select ALL the statements below that are TRUE1. The triangle might be an equilateral triangle (having all the same sides and angles) 2. One of the angles in triangle must be 120 3. The length of the third side must be 11cm or smaller4. One of the angles in the triangle might be 50
The value of x can be determined as,
[tex]\begin{gathered} x+30+30=180 \\ x=120 \end{gathered}[/tex]In triangle ABC,
[tex]\begin{gathered} BCThus, option (2) is the correct solution.1. 12,5); x+y=72x-3y = 1 What are the steps
As the given lines are:
[tex]\begin{gathered} x+y=7\ldots\ldots\ldots\ldots(1) \\ 2x-3y=-11\ldots\ldots\ldots.(2) \end{gathered}[/tex]To find the system of linear equation:
multiply equation (1)by 3 and then add in equation 2:
[tex]\begin{gathered} 3(x+y)+2x-3y=3(7)-11 \\ 3x+3y+2x-3y=21-11 \\ 5x=10 \\ x=2 \end{gathered}[/tex]Now put the value of x in equation 1:
[tex]\begin{gathered} 2+y=7 \\ y=5 \end{gathered}[/tex]Given: a = 7 and b = 2 Then the m∠A=_?_ . ROund to the nearest degree. Enter a number answer only.
m∠A of the given rectangular triangle is 74.05°.
Why is Pythagoras useful?In two dimensions, the Pythagorean Theorem is helpful for navigation. You may calculate the shortest distance using it and two lengths. … The two legs of the triangle will be north and west, and the diagonal will be the shortest line separating them. Air navigation can be based on the same ideas.Three positive numbers a, b, and c make up a Pythagorean triple if their sum, a2 + b2, equals their sum, c2. A typical way to write such a triple is (a, b, c), and a well-known example is (3, 4, 5). For any positive integer k, (ka, kb, kc) is a Pythagorean triple if (a, b, c) is one as well.Given :
a = 7
b = 2
∠c =90°
according to Pythagoras theorem
c =[tex]\sqrt[n]{a^2 + b^2}[/tex]
c = [tex]\sqrt{7^2 + 2^2}[/tex]
c≈7.28011.
to find m∠A
Sin A = [tex]\frac{opp. side}{Hypotenuse}[/tex] = 7/7.28011 = 0.9615
∠A = sin⁻¹ 0.9615
m∠A = 74.05°.
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You have 3 black cups, 10 Green cups, 9 purple cups, and 19 gray cups. what is the ratio between purple and green cups?
We chave 9 purple cups and 10 green cups, so we can write the ratio between purple and green cups as 9:10 or "9 to 10".
Answer: 9:10
If there are three black, four white, two blue, and four gray socks in a drawer, what would be the probability of picking a black sock as a fraction in simplest form?1/103/91/33/13
The probability of getting a black sock out of the drawer is given by the ratio between the amount of black socks in the drawer by the total amount of socks in the drawer.
We know that we have 3 black socks, now we just need to calculate the total amount of socks. We have three black, four white, two blue, and four gray socks in a drawer, then, the total is given by
[tex]3+4+2+4=13[/tex]We have a total of 13 socks in the drawer, therefore, the probability of getting a black sock out of the drawer is given by
[tex]\frac{3}{13}[/tex]And this is the fraction in the most simplified version.
A football team is losing by 14 points near the end of a game. The team scores two touchdowns (worth 6 points each) before the end of the game. After each touchdown, the coach must decide whether to go for 1 point with a kick (which is successful 99% of the time) or 2 points with a run or pass (which is successful 45% of the time). If the team goes for 1 point after each touchdown, what is the probability that the coach’s team wins? loses? ties? If the team goes for 2 points after each touchdown, what is the probability that the coach’s team wins? loses? ties?
From the question, there are some scenarios we need to cater for:
- The team is down 14 points.
- It is a given that the team scores 2 touchdowns whatever the case. This means the team has 12 points in the bag.
- That leaves 2 points to overturn the loss, or draw or lose
If the team wins:
The team can only win if they score their 2 points runs twice. i.e. An increase in 4 points from the two plays would overturn the score and the team would lead the game by 2 points.
The question asks us to find the probability of the team winning if the team goes for 2 points after each 6-point touchdown.
We can solve this as:
[tex]\begin{gathered} \text{Probability of scoring 2 =} \\ P(2)=45\text{ \%=0.45} \\ \\ \therefore\text{Probability of scoring 2 the first time AND Probability of scoring 2 the second time=} \\ P(2)\times P(2)=0.45\times0.45=0.2025 \\ \\ \therefore\text{probability of the team winning by going for 2 points twice=} \\ 0.2025\times100\text{ \%} \\ =20.25\text{ \%} \end{gathered}[/tex]If the team loses:
If the team loses, there are some scenarios to take into consideration:
1. If the team tries 1 point plays and succeeds one time and failing the other time
2. If the team tries 1 point plays and fails twice.
3. If the team tries 2 point plays and they fail twice. (i.e. if they succeed even once, they can draw the match
Solve the system of equations: 2x + 3y = 8 and 3x - 3y = 12.
1) In this problem, let's solve this given system of equations by the method of Elimination.
We can start by adding both equations simultaneously:
[tex]\begin{gathered} 2x+3y=8 \\ 3x-3y=12 \\ --------- \\ 5x=20 \\ \\ \frac{5x}{5}=\frac{20}{5} \\ \\ x=4 \end{gathered}[/tex]Now, that we know the quantity of x, let's plug it into any of those equations. Most of the time, we opt to plug it into the simpler equation.
[tex]\begin{gathered} 2x+3y=8 \\ 2(4)+3y=8 \\ 8+3y=8 \\ -8+8+3y=8-8 \\ 3y=0 \\ \frac{3y}{3}=\frac{0}{3} \\ \\ y=0 \end{gathered}[/tex]2) Thus, the answer is (4,0)
Find the slope intercept equation of the line that has the given characteristics. Slope 1.3 and y intercept (0,-6)
We want to find the equation of the line in slope intercept form with the following values.
Slope = 1.3 and y-intercept ( 0, -6)
The equation of a line with slope m and y intercept (0,c) is;
[tex]y=mx+c[/tex]Thus, the equation of the line is;
[tex]y=1.3x-6[/tex]6-4x=6x-8x-8. what does x =
Start by balancing it out.
First +4x to both sides:
6=6x-4x-8
Then +8 to both sides:
14=6x-4x
As 6x-4x=2x
14=2x
Finally, divide both sides by 2:
7=x
So, the answer is x = 7
Write in form y=mx+b-3y = -6x - 24
Let's solve the equation for y:
[tex]\begin{gathered} -3y=-6x-24 \\ y=\frac{-6x-24}{-3} \\ y=\frac{-6x}{-3}-\frac{24}{-3} \\ y=2x+8 \end{gathered}[/tex]Therefore we have:
[tex]y=2x+8[/tex]For this equation we have that the slope is 2 and the y-intercept is 8.
Solve using substitution x=-9-4x+4y=20
The solution of the simultaneous equation using substitution is
(x ,y) = (-9,-4) .
The given system of equation are:
x=-9............................................1
-4x+4y=20 ...............................2
Now we will simplify the equation 2
or, -x + y = 5
now we will substitute the value of x in the equation 2
or, -(-9) + y = 5
or, 9+ y= 5
or, y = -4
Two or more algebra equations that share variables, such as x and y, are said to be simultaneous equations. Since the equations are resolved simultaneously, they are known as simultaneous equations. Each equation represents a straight line.
These equations alone could have an endless number of solutions. There are several ways to solve the simultaneous linear equations.
The simultaneous equations can be solved using one of four methods:
substitutioneliminationaugmented matrix method.Graphical methodHence the values of x and y are -9 and -4 respectively.
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could you please help
From the trapezoid,
x + ( 31 + 38 ) + y = 180 ------------ equ 1
x + y + 69 = 180
x + y = 180 - 69
x + y = 111 .................... equ 2
Also, x + 31 + 90 = 180
x + 121 = 180
x = 180 -121
x = 59.....................equ 3
put x = 59 in equ 2 ,
59 + y = 11
y = 111 - 59
y = 52 ------------------equ 4
Find the range of allowable values based on the given information. round to the nearest tenth. 50; can vary by 30%
The allowable values are;
[tex]35\text{ to 65}[/tex]Here, we want to get the allowable values for the given information
To do this, we need to find the percentage value
That would be;
[tex]\frac{30}{100}\times50\text{ = 15}[/tex]Now, the allowable values can be in both direction
Greater than 50 or less than 50
When greater, we add; when lesser, we subtract
Thus, we have it as;
[tex]\begin{gathered} 50-15\text{ to 50+15} \\ 35\text{ to 65} \end{gathered}[/tex]I need help can u help me?
Mark has ten pens.
Kate has 5 times as many pens as mark has
Number of pen kate has = 5 (number of pens of Mark)
y is the number of Kates pen
y = 5( Number of pens of Mark)
y=5(10)
y= 5 x 10
Answer : C) y = 5 x 10
Answer:
Where is the math question?
Diagram of the adjacent picture frame has outer dimensions = 24 cm x 28 cm and inner dimensions 16 cm x 20 cm. Find the area of each section of the frame, if the width of each section is same.
The area of the inner section is 320 cm^2
The area of the bigger section is 96 cm^2 (bigger trapezoid)
The area of the smaller trapezoid is 80 cm^2
Here, we want to calculate the area of each section of the frame
As we can see, there are 5 sections of the frame
The inner section represented by a rectangle and 4 adjoining shapes looking like a trapezoid
The inner part of the frame is a rectangle that measures 16 cm by 20 cm
Now, for the trapezoid part, we have 2 different sets
The first two set, has a longer length 28 cm, and shorter length of 20 cm
The second set has a longer length of 24 cm and a shorter length of 16 cm
Now, to get the area of the trapezoid, we need the height of the trapezoid which is called the width in this case. This measure corresponds to a measure of 4 cm on the two sets
Mathematically, the area of a trapezoid is;
[tex]A\text{ = }\frac{1}{2}(a\text{ + b)h}[/tex]Where a is the longer length and b is the shorter length with h representing the width of 4 cm
For the bigger trapezoid, we have;
[tex]\frac{1}{2}(28+20)4=96cm^2[/tex]For the smaller trapezoid, we have;
[tex]\frac{1}{2}\times(24_{}+16)\text{ 4 = }80cm^2[/tex]Then, we have the inner section as;
[tex]\begin{gathered} \text{Area = length }\times\text{ width} \\ =\text{ 16 cm }\times20cm=320cm^2 \end{gathered}[/tex]Multiply Polynomials. Find the product and write answers in standard form
Step 1
Given;
[tex]5m^3(n^6)(6n^5)[/tex]Required; To multiply the polynomials
Step 2
Write the answers in standard form.
Rearrange the question and write like terms close to each other
[tex]5\times6\times n^6\times n^5\times m^3[/tex]Simplify using the following law of indices
[tex]a^b\times a^n=a^{b+n}[/tex][tex]\begin{gathered} 5\times6=30 \\ n^6\times n^5=n^{6+5}=n^{11} \\ m^3=m^3 \end{gathered}[/tex]Hence the combined answer will be;
[tex]30m^3n^{11}[/tex][tex]5m^3(n^6)(6n^5)=30m^3n^{11}[/tex]Answer;
[tex]30m^3n^{11}[/tex]A grain bin is in the combined shape of a right cylinder and right cone, both of which have diameters of 10 feet.(a) Find the volume of the cylindrical portion of the bin to the nearest cubic foot.(b) Find the volume of the conical portion of the bin to the nearest cubic foot.(c) The bin is to be filled completely with dry corn that weighs 45 lbs per cubic foot. Of there are 2,000 pounds per ton, how many total tons of corn can be placed in the bin?
ANSWER :
a. 628 cubic foot
b. 52 cubic foot
c. 1.17 ton
EXPLANATION :
The volume formula of a cylinder is :
[tex]V=\pi r^2h[/tex]The volume formula of a cone is :
[tex]V=\frac{1}{3}\pi r^2h[/tex]From the problem, we have a diameter of 10 ft, so the radius is r = 5 ft
Cylinder's height is 8 ft and cone's height is 2 ft
a. volume of cylinder part :
[tex]\begin{gathered} V=\pi(5)^2(8) \\ V=628ft^3 \end{gathered}[/tex]b. volume of cone part :
[tex]\begin{gathered} V=\frac{1}{3}\pi(5)^2(2) \\ V=52ft^3 \end{gathered}[/tex]c. The combine volume is 628 + 52 = 680 cubic foot
A dry corn weighs 45 lbs per cubic foot.
That will be :
[tex]52ft^3\times\frac{45lbs}{ft^3}=2340lbs[/tex]There are 2000 pounds per ton, so that will be :
[tex]2340lbs\times\frac{1ton}{2000lbs}=1.17ton[/tex]heyy could you help me out I have been stuck in this problem for a long time I sent a pic of the problem by the way
Given two triangles ABC and DEF
They have the following:
1. AC = DF
2. 3. AB = DE
4.
so, if we take 1, 2 and 3
the triangles are congruent using SAS
And if we take 1 , 2 and 4
the triangle are congruent using ASA
So, the answer is the options: D and E
Which of the following is not a true postulate.Through any three noncollinear points there is exactly one planeThrough any two points there is exactly one plane.If two distinct lines intersect, then they intersect in exactly one point.If two distinct planes intersect, they intersect in exactly one line.
Answer:
Through any two points there is exactly one plane.
Step-by-Step explanation:
Postulate: Statement that is believed to be true, just without proof.
The first one is correct, that is, it is a true postulate.
The third statement is correct.
The fourth statement is also correct.
The answer is the second postulate.
It is stated that:
Through any two points there is exactly one plane.
But the correct postulate is:
Through any two points there is exactly one line.
So the answer is:
Through any two points there is exactly one plane.
Algebraic fractions are fractions that contain variables, exponents, and operations with polynomials.O TrueO False
Solution
An algebraic fraction is a fraction whose numerator and denominator are algebraic expressions.
Algebraic fractions are fractions that contain variables, exponents, and operations with polynomials.
O True Answer
O False
Rita is a software saleswoman. Let y represent her total pay (in dollars). Let x represent the number of copies of English is Fun she sells. Suppose that x and y are related by the equation 1900+110x=Y.
, if she does not sell any of English,x = The number of copies of English is Fun she sells
y = Total pay
[tex]y=1900+110x[/tex]Therefore,
a.
Her change in total pay for each copy of English is fun can be computed below.
(0, 1900) (1, 2010)
[tex]m=\frac{2010-1900}{1-0}=110[/tex]Her change in total pay for each copy of English is fun she sells = $110
b.
Her total pay if she does not sell any of English is fun is the y-intercept. Therefore,
[tex]\begin{gathered} y=1900+110x \\ y=1900+110(0) \\ y=\text{ \$1900} \end{gathered}[/tex]Her total pay if she does not sell any of English is fun = $1900
Note you can model it to the slope-intercept equation.
[tex]\begin{gathered} y=mx+b \\ \text{where} \\ m=\text{change in total pay for each copy of English is fun she sells } \\ b=\text{Her total pay if she does not sell any of English is fun} \end{gathered}[/tex]
what is the lcm of 6 and 8
to determine the lcm of 6 and 8, express these numbers as the product of prime numbers:
6 = 2x3
8 = 2x2x2
the same factors determine the lcm. In this case, the factors
Write the equation of a perpendicular and parallel line to the following: (in picture)
anIf we have an equation of the form
[tex]y=mx+b[/tex]then the equation of the perpendicular will be
[tex]y=-\frac{1}{m}x+c[/tex]where c is any arbitrary constant determined by the point the line must pass through,
Now in our case, we have
[tex]y=-10x+20[/tex]Therefore, the equation of the perpendicular line will be
[tex]y=\frac{1}{10}x+c[/tex]We must choose c such that the above line passes through (-2,2).
Putting in y = 2 and x = 2 from (-2, 2) gives
[tex]2=\frac{1}{10}(-2)+c[/tex][tex]2=-\frac{1}{5}+c[/tex][tex]\therefore c=\frac{11}{5}.[/tex]Hence, the equation of a line perpendicular y = -10x + 20 and passing through (-2, 2) is
[tex]y=\frac{1}{10}+\frac{11}{5}[/tex]Now we find the equation of a line parallel to y = -10x+20 and passing through (-2,2).
Now, the slope of the parallel line is the same as that of the original equation; therefore the equation for the parallel line we have is
[tex]y=-10x+k[/tex]We find k by using the point (-2,2) and substituting x = -2 and y = 2 into the above equation to get
[tex]2=-10(-2)+k[/tex][tex]2=20+k[/tex][tex]\therefore k=-18.[/tex]Hence, the equation of the parallel line is
[tex]y=-10x-18[/tex]