Explanation: For this question we have 4 zeros so x can be as follows
x = -1 or x = -2 or x = -3 or x = -4
We can turn the equalities above into factors as follows
[tex]\begin{gathered} x=-1\rightarrow x+1=0 \\ x=-2\rightarrow x+2=0 \\ x=-3\rightarrow x+3=0 \\ x=-4\rightarrow x+4=0 \end{gathered}[/tex]Step 1: Now that we have the factors we can build a function and simplify it as follows
[tex]\begin{gathered} y=(x+1)(x+2)(x+3)(x+4) \\ y=(x^2+2x+x+2)(x^2+4x+3x+12) \\ y=(x^2+3x+2)(x^2+7x+12) \\ y=x^4+7x^3+12x^2+3x^3+21x^2+36x+2x^2+14x+24 \\ y=x^4+7x^3+3x^3+12x^2+21x^2+2x^2+36x+14x+24 \\ y=x^4+10x^3+35x^2+50x+24 \end{gathered}[/tex]Final answer: So the final answer is
[tex]y=x^4+10x^3+35x^2+50x+24[/tex].
ellusRotate the triangle 270° counterclockwisearound the origin and enter the newcoordinates.Enter thenumber thatbelongs in thegreen boxA (31.0 A(1,-1)B(4,-2)C II )BC.0D 2.-4)
A rotation of 270° counterclockwise is given by the following rule:
[tex](x,y)\rightarrow(y,-x)[/tex]Apply that rule to the coordinates of A, B, and C to find the coordinates of A''', B''', and C'''.
[tex]\begin{gathered} A(1,-1)\rightarrow A^{\prime\prime\prime}(-1,-1) \\ B(4,-2)\rightarrow B^{\prime\prime\prime}(-2,-4) \\ C(2,-4)\rightarrow C^{\prime\prime\prime}(-4,-2) \end{gathered}[/tex]Please just give me the answer straightforward I don’t need an explanation
Explanation
We are given the function
[tex]y=\frac{1}{2}(3)^{-2x}+6[/tex]First, we have to find the y-intercept
The y-intercept is the point where the graph intersects the y-axis. From the graph, the y-intercept is 6.5
To get the horizontal asymptote
We approach a horizontal asymptote by the curve of a function as x goes towards infinity.
From the graph above,
The horizontal asymptote is
[tex]y=6[/tex]For the transformation
Convert: 15 meters=centimeters
EXPLANATION
The relationship between the meters and centimeters is the following:
[tex]1\text{ meter=100 centimeters}[/tex]By applying the unit method, we can get the conversion, as follows:
[tex]Number\text{ of }centimeters=15\text{ meters*}\frac{100\text{ centimeters}}{1\text{ meter}}[/tex]Multiplying terms:
[tex]Number\text{ of centimeters=1500 centimeters}[/tex]The solution is 1500 centimeters.
hey can someone pls help me with this drag and drop assignment? I’ll appreciate it :)
By using formula of area and circumference of circle, the results obtained are
1) Length of fencing used = 62.8 ft
2) Area of hot tube cover = 5024 sq. inch
3) More wall space required = 34.54 sq. inch
4) Diameter of wheel = 37 inch
What is area and circumference of circle?
Area of the circle is the total space taken by the circle.
Circumference of the circle is the length of the boundary of the circle.
Here,
1) Radius = 10ft
Length of fencing used = Circumference of circle = [tex]2\pi r[/tex]
= [tex]2\times 3.14\times 10[/tex]
= 62.8 ft.
2) Diameter of hot tub cover = 80 inches
Radius of hot tub cover = [tex]\frac{80}{2}[/tex] = 40 inches
Area of hot tub cover = [tex]\pi r^2[/tex]
= [tex]3.14 \times 40 \times 40\\[/tex]
= 5024 sq. inch
3) Radius of one wall clock = 5 inches
Area of one wall clock = [tex]3.14 \times 5 \times 5\\[/tex]
= 78.5 sq. inch
Radius of other wall clock = 6 inches'
Area of other wall clock = [tex]3.14 \times 6 \times 6[/tex]
= 113.04 sq. inch
More wall space required = [tex]113.04 - 78.5[/tex]
= 34.54 sq. inch
4) Distance travelled in one rotation = circumference of circle = 116.18 inches
Let the radius of the tire be r inch
Circumference of tire = [tex]2 \times 3.14 \times r[/tex]
By the problem,
[tex]2 \times 3.14 \times r = 116.18[/tex]
[tex]6.28 r = 116.18\\r = \frac{116.18}{6.28}\\[/tex]
r = 18.5 inch
Diameter of the wheel = [tex]18.5 \times 2\\[/tex]
= 37 inch
To learn more about area and circumference of circle, refer to the link-
https://brainly.com/question/402655
#SPJ1
I'm having trouble with this problem "Solve the equation -8 + 6m = 1/2 (-4m +16) for m"
Let's begin by listing out the given information:
[tex]\begin{gathered} -8+6m=\frac{1}{2}(-4m+16) \\ \end{gathered}[/tex]Let's proceed to expand the bracket. We have:
[tex]\begin{gathered} -8+6m=\frac{1}{2}(-4m+16) \\ -8+6m=-2m+8 \\ \end{gathered}[/tex]We will put like terms together, we have:
[tex]\begin{gathered} 6m+2m=8+8 \\ 8m=16 \\ \text{Divide both sides by ''8'', we have:} \\ m=\frac{16}{8}=2 \\ m=2 \end{gathered}[/tex]+0.049 where t is in hours after 6:00 AM last Sunday12The temperature in Middletown Park at 6:00 AM last Sunday was 434 degrees Fahrenheit. The temperature was changing at a rate given by r(t) = 3.27 cosROUND ALL ANSWERS TO 2 DECIMAL PLACESAt 10 00 AM last Sunday, the temperature in the park was increasing at a rate ofabout 1.68 degrees per hourFrom 6:00 AM to 1:00 PM last Sunday, the temperature in the park increasedby _degreesWhat was the temperature in the park at 1:00 PM last Sunday? _degreesWhat was the temperature in the park at 4:00 PM Last Friday (5 days later)? _degrees
1 ) According to the question, the temperature has been changing according to this function:
[tex]r(t)\text{ =}3.27\text{ }\cos (\frac{\pi t}{12})+0.049[/tex]Where t is the number of hours after 6:00 am last Sunday
b) From 6 am to 1 pm last Sunday, the temperature in the park increased by
6 am to 1 pm = 7 hours, let's plug into that:
[tex]\begin{gathered} r(t)\text{ =}3.27\text{ }\cos (\frac{\pi t}{12})+0.049 \\ r(7)\text{ =}3.27\text{ }\cos (\frac{7\pi}{12})+0.049 \\ r(7)=3.31732 \\ r(7)\approx3.32 \end{gathered}[/tex]The rate of change in 7 hours was approximately 3.32 degrees per hour
c)
The temperature in the park at 6 am was 43.4 ºF. To find the temperature we must find the value for y, 1 pm Last Sunday. Let's plug the value already found: 1.68 for r.
Considering that according to question a, the temperature increased by 1.68º per hour. 6 am to 10 pm: 4 hours
c)
Since the question wants the temperature from 6 am to 1 pm, and it has been increasing by 3.32 degrees per hour, in 7 hours
7 x 3.32 =23.24º
43.4º+23.24=110.04ºF
d) On Friday, 5 days later there was
5 x 24 at 6am + 10 hours =120+10=130 hours
[tex]\begin{gathered} r(130)\text{=}3.27\text{ }\cos (\frac{130\pi}{12})+0.049 \\ r(130)\text{ =2.7}6 \end{gathered}[/tex]Starting from 43.4º F +2.76 =46.16ºF
2v – 5V = -24muti step equation
2v - 5v = -24
2v - 5v = -3v, then
-3v = -24
-3 is multiplying on the left, then it will divide on the right
v = -24/(-3)
v = 8
suppose you have 5 apples and you subtract 2 of them, how many apples are left?
You are doing the next computation: 5 apples - 2 apples = 3 apples
What is the result of 2 apples - 5 apples?
Find the inclination, Ø, of the line with given slope [tex]m = \frac{ - 21}{5} [/tex]
we know that
the slope is equal to the the tangent of the angle
so
m=-21/5
tan(∅)=-21/5
using a calculator
∅=-76.6 degrees
but the angle lies on the second quadrant
so
∅=180-76.6
∅=103 4 degrees
the answer is the option Dbecause the angle lies in the second QuadranttNelson Collins decided to retire to Canada in 10 years. What amount should he deposit so that he will be able to withdraw $80,000 at the end of each year for 25 years after he retires. Assume he can invest 7% interest compounded annually.
Answer
$1,016,699
Explanation
The amount, A that an invested sum of P, becomes over time t, at a rate of r% is given as
A = P (1 + r)ᵗ
For this question,
A = Total amount that the amount invested becomes = $80,000 × 25 = $2,000,000
P = Amount invested at the start of the 10 years before retirement = ?
r = 7% = 0.07
t = 10 years
A = P (1 + r)ᵗ
2,000,000 = P (1 + 0.07)¹⁰
2,000,000 = P (1.07)¹⁰
Note that 1.07¹⁰ = 1.967
2,000,000 = 1.967P
We can rewrite this as
1.967P = 2,000,000
Divide both sides by 1.967
(1.967P/1.967) = (2,000,000/1.967)
P = $1,016,699
Hope this Helps!!!
D. The number of people in the United States with mobile cellular phones was about 142
million in 2002 and about 255 million in 2007. If the growth in mobile cellular phones
was linear, what was the approximate rate of growth per year from 2002 to 2007?
What would the expected number of people to have phones in 2010? 2015? 2020?
Show this information on a graph (years versus the number of users).
Since it is linear, we can assume a function of the form:
[tex]y(x)=mx+b[/tex]Where:
m = Slope = rate of growth
b = y-intercept
So:
[tex]\begin{gathered} x=2002,y=142 \\ 142=2002m+b_{\text{ }}(1) \\ ----------- \\ x=2007,y=255 \\ 255=2007m+b_{\text{ }}(2) \end{gathered}[/tex]Using elimination method:
[tex]\begin{gathered} (2)-(1) \\ 255-142=2007m-2002m+b-b \\ 113=5m \\ m=\frac{113}{5}=22.6 \end{gathered}[/tex]So:
Replace m into (1):
[tex]\begin{gathered} 142=2002(22.6)+b \\ b=-45103.2 \end{gathered}[/tex]The linear equation which represents this model is:
[tex]y=22.6x-45103.2[/tex]The approximate rate of growth per year from 2002 to 2007 is 22.6 million
the expected number of people to have phones in:
[tex]\begin{gathered} x=2010 \\ y=22.6(2010)-45103.2 \\ y\approx323 \end{gathered}[/tex][tex]\begin{gathered} x=2015 \\ y=22.6(2015)-45103.2 \\ y\approx436 \end{gathered}[/tex][tex]\begin{gathered} x=2020 \\ y=22.6(2010)-45103.2 \\ y\approx549 \end{gathered}[/tex]323 million of people will have phones in 2010
436 million of people will have phones in 2015
549 million of people will have phones in 2020
are 4xy^3 and -5x^3 like terms
if sin = -3/5 and cos >0 what is exact value of cot?5/3-4/33/4-4/5
Explanation
Given the following information:
[tex]\begin{gathered} Sin=\frac{-3}{5} \\ Cos>0 \end{gathered}[/tex]This implies that the value of sin is negative while that of cos is positive.
This occurs in the fourth quadrant. This also means that the value of tan is negative.
We know that sin uses the value of the opposite and the hypotenuse.
We need to determine the value of the adjacent.
[tex]\begin{gathered} Adjacent=\sqrt{Hyp^2-Opp^2} \\ where \\ Hyp=5 \\ Opp=3 \end{gathered}[/tex][tex]\begin{gathered} Adjacent=\sqrt{5^2-3^2}=\sqrt{25-9}=\sqrt{16} \\ Adj=4 \end{gathered}[/tex]We know that cot is the reciprocal of tan. The value of tan is given as:
[tex]\begin{gathered} Tan=\frac{Opp}{Adj}=\frac{3}{4} \\ But\text{ tan is negative in the fourth quadrant. } \\ \therefore Tan=\frac{-3}{4} \end{gathered}[/tex]We can now determine the value of cot to be:
[tex]Cot=\frac{-4}{3}(reciprocal\text{ of tan\rparen}[/tex]Hence, the answer is the second option i.e. -4/3.
expand the given number to decimal for by expanding in powers and by using the calculator short cut. 82104nine in powers, write the calculator shortcut extension for 82104nine, convert 82104nine to decimal form.
We have a number expressed in a base of 9, instead of the most common decimal base.
Then, is we have the number 82104 in 9-base, it means that we can expand it as:
[tex]82104_{\text{nine}}=8\cdot9^4+2\cdot9^3+1\cdot9^2+0\cdot9^1+4\cdot9^0[/tex]We then can expand this as:
[tex]82104_{\text{nine}}=8\cdot6561+2\cdot729+1\cdot81+0\cdot9^{}+4\cdot1[/tex]We can finally calculate what this number is in decimal form by finishing simplyfing the expression above:
[tex]\begin{gathered} 82104_{\text{nine}}=8\cdot6561+2\cdot729+1\cdot81+0\cdot9^{}+4\cdot1 \\ 82104_{\text{nine}}=52488+1458+81+4 \\ 82104_{\text{nine}}=54031 \end{gathered}[/tex]Answer:
If we decompose this number given the base 9, we get the following terms:
[tex]82104_{\text{nine}}=8\cdot9^4+2\cdot9^3+1\cdot9^2+0\cdot9^1+4\cdot9^0[/tex]The decimal form of 82104(nine) is 54031.
Solve the following system of equations by finding when they are equal to each othery = -6x + 7 y= 13 - 8x The equations are equal to each other when x = and y=
ANSWER
x = 3, y = -11
EXPLANATION
We want to find the solution to the system of equations by finding when they are equal to one another.
The equations are:
y = -6x + 7
y = 13 - 8x
Now, we equate both of them:
-6x + 7 = 13 - 8x
Collect like terms:
-6x + 8x = 13 - 7
2x = 6
Divide through by 2:
x = 6 / 2
x = 3
From the first equation:
y = -6x + 7
Put the known value of x into the equation:
y = -6(3) + 7
y = -18 + 7
y = -11
Therefore, the equations are equal to each other when x = 3 and y = -11.
Among all of the pairs of numbers whose difference is 12, the smallest product is
We have two numbers x and y such that their difference is 12:
[tex]\begin{gathered} x-y=12 \\ \Rightarrow x=12+y \end{gathered}[/tex]Now, we take the product of them:
[tex]x\cdot y=(12+y)\cdot y=y^2+12y[/tex]The smallest result we can get is 0 (ignoring the negative numbers, because the meaning of "small" implies an absolute value). Looking at the expression above, it is 0 for y = 0. If y = 0 then x = 12, and the difference is:
[tex]x-y=12-0=12[/tex]And their product is:
[tex]x\cdot y=12\cdot0=0[/tex]Identify the like terms. 4y, (–7x), 9y, 13
Like terms are terms that have the same variables of similar exponents.
The given terms are:
4y, (–7x), 9y, 13
You have a $1,475 annual budget for spending onsocial media. The budget increases by 20% forDecember. What is your budget for the month ofDecember?
We have an original annual original budget of $1475. For each month of the year, we have then:
[tex]m=\frac{1475}{12}\approx122.92[/tex]Thus, we have for each month, a monthly budget of $122.92 for spending on social media.
However, in December this budget was increased by 20%, then:
[tex]122.92\cdot\frac{20}{100}=24.58[/tex]Then the budget for the month of December is:
[tex]BD=122.92+24.58\Rightarrow BD=147.5[/tex]James makes wreaths for a living. He can make 6 wreaths in 450 minutes. How many minutes does it take him to make 2wreaths?
150 minutes to make 2 wreaths
1) Gathering the data, and setting a proportion.
Then let's cross multiply.
There is a direct proportionality, between the number
6 wreaths 450 mins
2 x
6x = 900 Dividing by 6
x=150 minutes
Kita Ramin obtained a $3,000 loan to pay for a used car. She agreed to make 12 monthly payments of $266.22. What is the APR?
Answer:
APR = 6.5%
Explanation:
If Kita makes 12 payments of $266.22, the maturity value of the loan will be equal to:
V = 12 x $266.22 = $3194.64
On the other hand, the maturity value is equal to:
[tex]V=P(1+r\cdot t)[/tex]Where P is the initial amount, r is the Annual Percentage Rate APR and t is the time in years. So, replacing V by $3194.64, P by $3000, and t by 1 year (12 months), we get:
[tex]\begin{gathered} 3194.64=3000(1+r\cdot1) \\ 3194.64=3000(1+r) \end{gathered}[/tex]Now, we can solve for r as:
[tex]\begin{gathered} \frac{3194.64}{3000}=\frac{3000(1+r)}{3000} \\ 1.065=1+r \\ 1.065-1=1+r-1 \\ 0.065=r \end{gathered}[/tex]So, the annual percentage rate is 0.065 or 6.5%
Find the quotient for 2,268 and 3
Given a fraction below
[tex]\begin{gathered} \frac{a}{b}=c \\ a=\text{dividend} \\ b=\text{divisor} \\ c=\text{quotient} \end{gathered}[/tex]In other to find the quotient for 2,268 and 3, we would use long division as shown below:
[tex]\frac{2268}{3}[/tex]The quotient of the division is the answer to the long division
Hence, the quotient is 756
Given that Ris between Q and T. I QR= 10 RT= 4 Find QT=
If R is between Q and T, we can conclude:
QR + RT = QT
Where:
QR = 10
RT = 4
therefore:
10 + 4 = QT
QT = 14
Identify the measure of each exterior angle of a regular dodecagon
Solution:
Given:
A dodecagon is a 12-sided polygon.
A regular dodecagon is a figure with sides of the same length and internal angles of the same size.
The sum of exterior angles of a polygon is 360°.
The formula for calculating the size of each exterior angle is;
[tex]\begin{gathered} \text{Each exterior angle = }\frac{360}{n} \\ \text{where n is the number of sides of the polygon} \end{gathered}[/tex]For a dodecagon, n = 12
Hence,
[tex]\begin{gathered} \text{Each exterior angle = }\frac{360}{12} \\ \text{Each exterior angle = }30^0 \end{gathered}[/tex]Therefore, each exterior angle of a regular dodecagon is 30 degrees.
The following equation is a conic section written in polar coordinates.=51 + 5sin(0)Step 2 of 2: Find the equation for the directrix of the conic section.
For a conic with a focus at the origin, if the directrix is
[tex]y=\pm p[/tex]where p is a positive real number, and the eccentricity is a positive real number e, the conic has a polar equation
[tex]r=\frac{ep}{1\pm e\sin\theta}[/tex]if 0 ≤ e < 1 , the conic is an ellipse.
if e = 1 , the conic is a parabola.
if e > 1 , the conic is an hyperbola.
In our problem, our equation is
[tex]r=\frac{5}{1+5\sin\theta}[/tex]If we compare our equation with the form presented, we have
[tex]\begin{cases}e={5} \\ p={1}\end{cases}[/tex]Therefore, the directrix is
[tex]y=1[/tex]In a sequence of numbers, a4= 98, a5= 99.2, a6= 100.4, a7= 101.6, and a8= 102.8. Based on this information,which equation can be used to find an, the nth term in the sequence?
Given:
a4 = 98
a5 = 99.2
a6 = 100.4
a7 = 101.6
a8 = 102.8
Use the arithmetic sequence formula below:
[tex]a_n=a_1+(n-1)d[/tex]Where,
an = nth term
a1 = first term
n = number of terms
d = common differnce
Let's solve for the common differnce.
d = a5 - a4 = 99.2 - 98 = 1.2
Use the 8th term a8, to find the first term:
[tex]\begin{gathered} 102.8=a_1+(8-1)1.2_{} \\ \\ 102.8=a_1+(7)1.2 \\ \\ 102.8=a_1+8.4 \\ \\ a_1=102.8-8.4\text{ = 94.4} \end{gathered}[/tex]Therefore, the first term a1 = 94.4
Thus, the equation for the nth term will be:
Input 94.4 for a1, 1.2 for d in the arithmetic formula above
[tex]\begin{gathered} a_n=94.4+(n-1)1.2 \\ \\ a_n=94.4+1.2n-1.2 \\ \\ \text{combine like terms:} \\ a_n=1.2n+94.4-1.2 \\ \\ a_n=1.2n+93.2 \end{gathered}[/tex]ANSWER:
[tex]a_n=1.2n+93.2[/tex]A radio transmission tower is 579 feet tall. A guy wire is to be attached 6 feet from the top and is to make an angle of 23° with the ground? How many feet long shouldthe guy wire be? Round your answer to the nearest foot and do not write the units.
The Solution:
Representing the problem in a diagram, we have
We are required to find the value of x in the diagram above.
By Trigonometrical Ratio, we have
[tex]\sin 23^o=\frac{573}{x}[/tex]Cross multiplying, we get
[tex]x\sin 23=573[/tex]Dividing both sides by sin 23, we get
[tex]x=\frac{573}{\sin23}=1466.48\approx1466\text{ }[/tex]Therefore, the correct answer is 1466.
The dot plot shows the number of wins for 16 baseball teams. Which statement about thedata is true?.Baseball Team Wins•0123 4 5 6 7 8Number of WinsThere is a data point at 8, so most teams won 8 games.The data are clustered around 2, so most teams won exactly 2games.The data are clustered from 4 to 7, so most toams lost 4 to 7gamos.The data are clustered from 1 to 3, so most teams won 1 to 3games.
We can see on the graph that the dots represent a team, and on the x-axis is the number of wins. Looking at the graph we can see that a lot of teams won around 1-3 and just one team won 8 times, therefore, the correct answer is: The data are clustered from 1 to 3, so most teams won 1 to 3 games
A local health clinic surveys its patients about their waterdrinking habits. It found the data is normally distributed,the mean amount of water consumed daily is 62 ounces, andthe standard deviation is 5.2. How much water, in ounces,do approximately 95% of the patients drink each day?A: 56.8 to 67.2B: 54.2 to 69.8C: 51.6 to 72.4D: 41.2 to 62.0
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
water drinking habits:
mean = 62 ounces
standard deviation = 5.2 ounces
Step 02:
normally distribution:
95% ===> 2 SD
(62 + 5.2 + 5.2) ounces = 72.4 ounces ==> + 2 SD
(62 - 5.2 - 5.2) ounces = 51.6 ounces ==> - 2 SD
The answer is:
51.6 ounces - 72.4 ounces
Find the equation of the linear function represented by the table below in slope-intercept form.Answer: ?(Important: Please check the attached photo before answering the question)
The Slope-Intercept form of the equation of the line is:
[tex]y=mx+b[/tex]Where "m" is the slope of the line and "b" is the y-intercept.
The slope can be found with:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Choose two points from the table. These could be the points (1,-4) and (4,-19). You can set up that:
[tex]\begin{gathered} y_2=-19 \\ y_1=-4 \\ x_2=4 \\ x_1=1 \end{gathered}[/tex]Substituting values, you get that the slope of this line is:
[tex]m=\frac{-19-(-4)}{4-1}=-5[/tex]You can substitute the slope and the first point into the equation in Slope-Intercept form:
[tex]-4=1(-5)+b[/tex]Solve for "b":
[tex]\begin{gathered} -4+5=b \\ b=1 \end{gathered}[/tex]Therefore, the Equation of this line in Slope-Intercept form is:
[tex]y=-5x+1[/tex]Use the formula P = 2l + 2w to find the length l of a rectangular lot if the width w is 55 feet and the perimeter P is 260 feet.l = ? feet
In order to determine the length of the given rectangle, Solve the equation for the perimeter of the rectangle for l and replace w=55ft and P=260ft, and simplify:
[tex]\begin{gathered} P=2l+2w \\ 2l=P-2w \\ l=\frac{P-2w}{2} \\ l=\frac{260ft-2(55ft)}{2} \\ l=\frac{260ft-110ft}{2} \\ l=\frac{150ft}{2}=75ft \end{gathered}[/tex]Hence, the length of the rectangle is 75ft
Dilate the following points by each scale factor (k) provided.P(3, 4) by k=1/2 AndN(4, 15) by k=2
We are asked to dilate the given two points.
P(3, 4) by a scale factor of k = 1/2
Multiply the x and y coordinates by the scale factor.
[tex]P(3,4)\rightarrow P^{\prime}(\frac{1}{2}\cdot3,4\cdot\frac{1}{2})=P^{\prime}(1.5,2)[/tex]Therefore, the dilated point is P'(1.5, 2)
This is an example of reduction.
Similarly,
N(4, 15) by a scale factor of k = 2
Multiply the x and y coordinates by the scale factor.
[tex]N(4,15)\rightarrow N^{\prime}(2\cdot4,2\cdot15)=N^{\prime}(8,30)[/tex]Therefore, the dilated point is N'(8, 30)
This is an example of enlargement.