Answers
You have the following system of equations:
x + 3y = 1
y = 2x + 5
in order to solve the previous system, replace the expression y = 2x + 5, into the first equation and solve for x, as follow:
x + 3y = 1
x + 3(2x + 5) = 1 apply distribution property
x + 6x + 15 = 1 simplify lef side
7x + 15 = 1 subtrac 15 both sides
7x = 1 - 15
7x = -14 divide by 2 both sides
x = -14/2
x = -7
replace the previous value of x into the second equation to get y:
y = 2x + 5
y = 2(-7) + 5
y = -14 + 5
y = -9
Hence, the solution to the given system of equations is:
x = -7
y = -9
(-7 , -9)
Related Questions
Nate and his family plan to take a 2,438 mile cross-country trip this summer.if they drive 85 miles each day ,how many days will they be driving? explain your answer
Answers
28.68235294117647 days (29 days ) will be taken by nate and his family to take a cross country trip of 2438 miles .
What is division ?Divide is the polar opposite of multiply. You get four in each group when you divide twelve into three equal groups then multiply three groups of four to create twelve. Determining how many equal groups are formed or how many individuals are in each group following a fair distribution is the fundamental goal of splitting.
Calculationspeed = 85miles / day
distance = 2438
time = 2438 / 85 = 28.68235294117647 days
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how many pieces are there in 215 dozen elementary school
Answers
Answer:2580
Step-by-step explanation:215*12=2580
what is the slope of the line
I really want to go to bed I've been staying up all night pls help
Answers
Answer:
The slope is -2
Step-by-step explanation:
Use the rise÷run formula to find the slope of any linear equation
In this case, -2÷1 = -2
Therefore, the slope is -2
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An apartment building is planning on replacing refrigerators in 42 of its units. If the refrigerators cost $501 each, estimate the total cost by rounding both numbers to the nearest 10
Answers
Total Cost = No of Units x Unit cost of refrigerators
Total Cost = 42 x $ 501 = $ 21, 042
Rounding off to the nearest tens,
We have to round down 42 (in $ 21, 042) to 40
Therefore, the total cost will be $ 21, 040
Answer: $21,040
determine the length of . question 15 options: a) 9.17 units b) 6.32 units c) 3.74 units d) 10.77 units
Answers
The length of CD is 6.32 units.
From the question, we have
CB / AB = DB / CB
CB / 14 = 10 / CB
CB² = 14 × 10
CB = √140
using the Pythagorean theorem,
AB² = CB² + AC²
14² = (√140)² + AC²
196 - 140 = AC²
AC = √56
Using the ratio of the similar triangle,
CD / AC = DB / CB
CD / √56 = 10 / √140
CD = (√56 × 10)/√140
CD = 6.32 units
the length of CD is 6.32 units.
Divide:
Repetitive subtraction is the process of division. It is the multiplication operation's opposite. It is described as the process of creating equitable groups. When dividing numbers, we divide a larger number down into smaller ones such that the larger number obtained will be equal to the multiplication of the smaller numbers. One of the four fundamental mathematical operations, along with addition, subtraction, and multiplication, is division. Division is the process of dividing a larger group into smaller groups so that each group contains an equal number of things. It is a mathematical operation used for equal distribution and equal grouping.
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Could you please check my answer? Use the equations to solve the system of equations:Y=0X=7My answer: (7,0)
Answers
ANSWER:
[tex](7,0)[/tex]STEP-BY-STEP EXPLANATION:
We have the following system of equations
[tex]\begin{gathered} x=7 \\ y=0 \end{gathered}[/tex]In the case x = 7, it is parallel to the y axis, through the point 7 in x, and in the case y = 0, it is the same x axis, therefore the intercept is the point (7 , 0)
The solution is:
[tex](7,0)[/tex]What is the solution to the following system of equations? (1
point)
4x + 2y = 12
x - y = 3
(3,0)
(0, 3)
(0, -3)
(2,3)
Answers
x - y = 3
x = y + 3
Using substitution to figure out both x and y
4(y+3) + 2y = 12
4y + 12 + 2y = 12
6y = 0
y = 0
x - 0 = 3
x = 3
(x, y)
(3, 0)
Use trigonometric identities, algebraic methods, and inverse trigonometric functions, as necessary, to solve the following trigonometric equation on the interval [0, 28t).Round your answer to four decimal places, if necessary. If there is no solution, indicate "No Solution."- 15csc?(x) - 1 = -32cot(x)yea
Answers
To solve the equation:
[tex]-15\csc ^2x-1=-32\cot x[/tex]We meed to remember the identity:
[tex]\csc ^2x=\cot ^2x+1[/tex]Plugging this identity in the equation we have:
[tex]\begin{gathered} -15(\cot ^2x+1)-1=-32\cot x \\ -15\cot ^2x-15-1=-32\cot x \\ 15\cot ^2x-32\cot x+16=0 \end{gathered}[/tex]Hence we have the quadratic equation in the cotangent:
[tex]15\cot ^2x-32\cot x+16=0[/tex]To solve it let:
[tex]w=\cot x[/tex]Then we have the quadratic equation:
[tex]15w^2-32w+16=0[/tex]let's use the general formula to solve it:
[tex]\begin{gathered} w=\frac{-(-32)\pm\sqrt[]{(-32)^2-4(15)(16)}}{2(15)} \\ =\frac{32\pm\sqrt[]{1024-960}}{30} \\ =\frac{32\pm\sqrt[]{64}}{30} \\ =\frac{32\pm8}{30} \\ \text{then} \\ w=\frac{32+8}{30}=\frac{40}{30}=\frac{4}{3} \\ \text{ or } \\ w=\frac{32-8}{30}=\frac{24}{30}=\frac{4}{5} \end{gathered}[/tex]Once we know the value of w we can find the value of x, remember the definition of w, then we have:
[tex]\begin{gathered} \cot x=\frac{4}{3} \\ \text{ and} \\ \cot x=\frac{4}{5} \end{gathered}[/tex]Since it is easier to work with the tangent function we will use the fact that:
[tex]\tan x=\frac{1}{\cot x}[/tex]Hence our equations take the form:
[tex]\begin{gathered} \tan x=\frac{3}{4} \\ \text{and} \\ \tan x=\frac{5}{4} \end{gathered}[/tex]Finally to solve the equations we need to remember that the tangent function has a period of pi, therefore we have that:
[tex]\begin{gathered} x=\tan ^{-1}(\frac{3}{4})+\pi n \\ \text{and} \\ x=\tan ^{-1}(\frac{5}{4})+\pi n \end{gathered}[/tex]where n is any integer number. To find the solutions in the interval given we plug n=0 and n=1 in each expression for x; therefore, the solutions in the interval are:
[tex]\begin{gathered} x=0.6435 \\ x=0.8961 \\ x=3.7851 \\ x=4.0376 \end{gathered}[/tex]Find the highest common factor (HCF) of 32, 48 and 72
Answers
Factors of 32= 1, 2, 4, 8, 16, 32
Factors of 48= 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Factors of 72= 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
Describe how to transform the graph of g(x) - Inx into the graph of f(x)- In(x-4)+3
Answers
To transform the graph of g(x) = lnx into the graph of of f(x) = ln(x-4) + 3 we have to translate 4 units to the right and 3 units up.
What is graph transformation?
The technique of altering an existing graph or graphed equation to create a different version of the following graph is known as graph transformation.
As given in the question,
Parent function g(x)=ln x
resultant function f(x)=ln(x-4)+3
By the translation rules :
If f(x) needs to be translated in f(x-h), it mean function shifted right by h unit
and if f(x) needs to be translated in f(x)+k it mean function shifted up by k unit.
As per these rules, graph of g(x) = lnx function shifted right by 4 unit and function shifted up by 3 unit.
Therefore, Translate 4 units to the right and 3 units up.
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Franco is evenly dividing 3 and 1/3 pounds of flour into five containers and would like to know how many pounds of flour will be in each container. Franco sets up the following division problem to find his answer 3 and 1/3 divided by 5Convert Franco’s division problem into a product involving two fractions and find out how many pounds of flour each container will hold
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
3 and 1/3 pounds = flour
5 = containers
Step 02:
We must apply the algebraic rules to find the solution.
[tex]\begin{gathered} \text{flour:} \\ 3\text{ + }\frac{1}{3}\text{ = }\frac{9\text{ + 1}}{3}\text{ = }\frac{10}{3} \\ \end{gathered}[/tex][tex]\begin{gathered} \frac{10}{3}\cdot\text{ }\frac{1}{5}\text{ = }\frac{10}{15}\text{ = }\frac{2}{3\text{ }}\text{ (division =}==>\text{ product)} \\ \\ \end{gathered}[/tex]The answer is:
2/3 pounds of flour
The flu virus
is 8.0 x 10-6
cm in diameter. The
diameter of the plush
version is 1,250,000
times larger than the
microbe. What's the
diameter of the plush flu virus?
Answers
Diameter of the plush flu virus = 10 cm.
What is multiplication?Multiplication is the repeated addition of a number up to given number of times.
Given,
Diameter of the flu virus = 8.0 x [tex]10^{-6}[/tex]
Diameter of the plush flu virus = 1,250,000 × (Diameter of the flu virus)
Diameter of the plush flu virus = 1,250,000 × (8.0 x [tex]10^{-6}[/tex])
= 10 cm
Hence, Diameter of the plush flu virus = 10 cm.
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Directions: Simplify by combining like terms in each of the following expressions.
1. 10s2 + 10s2 - 13st =
2. 13st + - 2st - t2 =
3. x2+ x2 + x3 =
4. 6 x - 6 x + 2 =
5. 24x - 3s - 4t =
6. 86 + 86x - 1 =
7. 4x + 3x - 2 =
8. 7s - 4s + 3s =
9. 12 +11x - 10 x =
10. 12x + 24 x - 3 x - 4 =
11. 16t + 8t - 12t =
12. 17g + 19g - 2g +g =
13. 16 + 16 -16 + 16x =
14. 4s - 3s + 3s =
15. 12t - 11t + t =
(math is my weakest subject pls help 22 points)
Answers
A method that is frequently used to make algebraic expressions simpler.
How to simplify expressions?A method that is frequently used to make algebraic expressions simpler.
1. 10s2 + 10s2 - 13st =s*(20s-13t)
2. 13st + - 2st - t2 = 11st-t2
3. x2+ x2 + x3 = 2x2+x3
4. 6 x - 6 x + 2 =2
5. 24x - 3s - 4t =24x - 3s - 4t
6. 86 + 86x - 1 =86x+85
7. 4x + 3x - 2 = 7x-2
8. 7s - 4s + 3s = 6s
9. 12 +11x - 10 x =x+12
10. 12x + 24 x - 3 x - 4 =33x-4
11. 16t + 8t - 12t =12t
12. 17g + 19g - 2g +g =35g
13. 16 + 16 -16 + 16x = 16+16x
14. 4s - 3s + 3s =4s
15. 12t - 11t + t =2t.
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4. A rectangular garage has a volume of 480 m, a length of 12 m and a width of 8 m. What isthe height of the garage?
Answers
Answer:
5 m
Explanation:
The volume of the rectangular garage can be calculated as:
[tex]\text{Volume }=\text{Length }\times\text{ Width }\times\text{ Height}[/tex]If we replace Volume by 480, Lenght by 12, and Width by 8, we get:
[tex]480=12\times8\times\text{ Height}[/tex]Now, we can solve the equation for the Height as:
[tex]\begin{gathered} 480=96\times\text{ Height } \\ \frac{480}{96}=\frac{96\text{ }\times Height}{96} \\ 5=\text{Height} \end{gathered}[/tex]Therefore, the height of the garage is 5 m
1. MOVIES By the end of its first week, a
movie had grossed $2.3 million. By the
end of its sixth week, it had grossed
$6.8 million. Graph the data with the
week on the horizontal axis and the
revenue on the vertical axis, and draw a
line through the points. Then find and
interpret the slope of the line.
10
Revenue (millions of dollars)
OU
0 2 4 6 8 10
Week
Answers
The first step is to label the points being (1,2.3),(6,6.8) in which the first ordered pairs is the number of weeks, and the second one is the dollars in millions.
Hence, the slope is: m=(6.8-2.3)/(6-1) = 4.5/5 = 9/10 = 0.9
The slope represents the dollar rate in the millions per week. In this case, the movie grossed $0.9 million per week from week one to the sixth week.
d) The diagonal of a rectangular garden measures 11½ m while its width measures 7m. Express the perimeter of the garden as a percentage of its area (3marks).
Answers
We need to know about area and perimeter of a rectangle to solve the problem. The perimeter of the garden as a percentage of its area is 50.5%
The perimeter of a rectangle is the total of all it's sides. The perimeter can be calculated by adding up the sides of the rectangle. The area of a rectangle can be calculated by multiplying the length with the breadth of the rectangle. The diagonal and width of a rectangle are given, we need to find the length using Pythagoras' theorem.
diagonal =11.5m
width=7 m
length=[tex]\sqrt{11.5^{2} -7^{2} }[/tex]=[tex]\sqrt{132.25-49} =\sqrt{83.25}[/tex]=9.12 m
perimeter=2x(l+b)=32.24 m
area= lxb= 9.12x7=63.84 [tex]m^{2}[/tex]
perimeter as percentage of area=32.24/63.84 x100=50.5%
Therefore the perimeter of the rectangle as a percentage of area is 50.5%.
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Find the length of the segment JK in the parallelogram below.
Answers
Answer:
58
Step-by-step explanation:
3x-14=58
+14 +14
3x=72
x=24
solved that now we'll input the factor
3(24)-14
72-14
"58" is your answer
I actually have the answer it just says it’s wrong when I try to submit it. It says that I need to enter the correct number and units. Can anyone help with this?
Answers
Input
[tex]36.2\text{ yards}[/tex]Not
[tex]b=36.2[/tex]What are the rational numbers between 2 & 3
Answers
Answer:
The rational numbers between 2 & 3 include:
1. 4120
2. 4220
3. 4320
4. 4420
5. 4520
6. 4620
7. 4720
8. 4820
9. 4920
10. 5020
Step-by-step explanation:
May I have Brainliest please? I am so close to getting my next ranking! I just need 1 more to become an ACE!! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
is something is greater than 6 , do i include 6
Answers
No, 6 will not be included
Explanation:Let the number greater than 6 be represented by x
The statement "x greater than 6" can be written as:
x > 6
Therefore, 6 will not be included in the list
help meeeeeeeeeeeeee pleaseeeeeeeeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeeeee pleaseeeeeeeeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeeeee pleaseeeeeeeeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
The point of maxima and minima of any function can be known by equating its derivative to zero. The rocket will take 1.5 sec to reach the maximum height and the maximum height is 27 feet.
What is differentiation?The differentiation of a function is defined as the rate change of its value at around a point. It can be written in mathematical form as g'(x) = (g(x + h) - g(x)) /(x + h - x).
Its geometric meaning is that it is the slope of the function at a given point.
Given that,
Initial height of the launching pad is 4 feet,
Initial velocity of rocket is 48 feet/sec,
Height of the rocket as a function of time, h(t) = -16t² + 48t + 3
In order to find the time for maximum height equate h'(t) = 0 as follows,
-32t + 48 = 0
⇒ t = 48 / 32
⇒ t = 3 / 2
⇒ t = 1.5
To find the maximum height find h(t) for t = 1.5 as follows,
h(1.5) = -16 × 1.5² + 48 × 1.5 + 3
= -36 + 60 + 3
= -36 + 63
= 27
Hence, the time taken by the rocket to reach the maximum height is 1.5 sec and the maximum height reached is 27 feet.
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1.2 where was the Declaration of Independence signed
Answers
August 2, 1776, in the Pennsylvania State House.
Step-by-step explanation:After much debate, the Second Continental Congress ultimately agreed to the Declaration of Independence, and then signed it
PLS HELP ASAP(100 POINTS)
A linear function is shown on the graph.
A linear function beginning with open circle at negative 3 comma negative 5 and ending with an open circle at 3 comma 7.
What is the domain of the function?
{y | −5 ≤ y ≤ 7}
{y | −5 < y < 7}
{x | −3 ≤ x ≤ 3}
{x | −3 < x < 3}
Answers
Answer:
{x | −3 ≤ x ≤ 3
Answer:
{x | −3 ≤ x ≤ 3}
Step-by-step explanation:
pretty sure its right
A rectangle with dimensions of 4 units by 5 units is enlarged by a scale factor of 1.2. By what percent does its area increase?
Answers
The area of any shape after dilation is equal to the area of the original shape multiplied by the square of the scale factor:
[tex]A_{\text{new}}=k^2\cdot A_{\text{original}}[/tex]Where
A_new indicates the area of the shape after the dilation
A_original is the area of the original shape
k is the scale factor
The first step is to determine the area of the original shape and the new shape, using the formula:
[tex]A=w\cdot l[/tex]The original shape has dimensions 4 and 5, so its area is:
[tex]\begin{gathered} A_{\text{original}}=4\cdot5 \\ A_{\text{original}}=20 \end{gathered}[/tex]Next is to determine the area of the shape after the dilation (A_new)
The scale factor is k=1.2
[tex]\begin{gathered} A_{\text{new}}=k^2\cdot A_{\text{original}} \\ A_{\text{new}}=(1.2)^2\cdot20 \\ A_{\text{new}}=1.44\cdot20 \\ A_{\text{new}}=28.8 \end{gathered}[/tex]Now that we calculated both areas, we can determine the increase percentage.
- First, calculate the increase (I), which is the difference between the area of the new shape and the area of the original shape:
[tex]\begin{gathered} I=A_{\text{new}}-A_{\text{original}} \\ I=28.8-20 \\ I=8.8 \end{gathered}[/tex]-Second, divide the increase by the original area and multiply the result by 100
[tex]\begin{gathered} \frac{I}{A_{\text{original}}}\cdot100 \\ \frac{8.8}{20}\cdot100 \\ 0.44\cdot100=44 \end{gathered}[/tex]This means that the area increased 44% after the dilation
Given m(x): { (9 0), (8, -8), (-4, 8), (0, -4) , (-8, 3) }. Find m(-8)
8
0
4
3
Answers
Answer:
B.C.
Step-by-step explanation:
on/8cc2ae7c-5cc0-4693-ab64-cce744de5774/b9c41130-96e8-4a04-a4cc-dbc9dab72adfNorfleet CasenReview -BookmarkThe art club has a goal to raise at least $500 by selling paintings to the student body for $15 each. They have already spent $70 buyingpaint. Which inequality could be used to find the number of paintings the art club needs to sell to reach their goal?
Answers
The art club has a goal to raise at least $500 by selling paintings to the student body for $15 each. They have already spent $70 buying
paint. Which inequality could be used to find the number of paintings the art club needs to sell to reach their goal?
we have that
Let
x -----> the number of paintings
so
the inequality that represent this situation is given by
[tex]15x-70\ge500[/tex]solve for x
[tex]undefined[/tex]What is the equation of the line below
Answers
The given graph is of the equation y = x - 2
How to represent an equation in a graph?Select x-values and enter them into the equation to graph a function. You will obtain a y-value once those values have been entered into the equation. The coordinates of a single point are made up of the x and y values.
Step 1 is to determine the variables.
Step 2: Establish the range of the variable
Determine the graph's scale in step three.
Step 4 is to give each axis a number, a label, and a title.
5. Select the data points and plot them on the graph.
6. Create the graph.
After understanding the "how" of drawing a graph you will surely understand how to decide which equation's graph it is.
The given graph is of the equation
y = x - 2
because as in the graph
the slope cuts the points x = 4 and y = 2
and when we substitute this value in the above mentioned equation we get
2 = 4 - 2
which satisfies the condition .
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F(x)=2x and g(x)= sqrt(x+1)Find (fg)(x)
Answers
First, let us define what (fg)(x) is:
[tex](fg)(x)=f(x)\times g(x)[/tex]Given:
[tex]f(x)=2x[/tex][tex]g(x)=\sqrt[]{x+1}[/tex]So the solution to (fg)(x) will be:
[tex]\begin{gathered} =2x\times\sqrt[]{x+1} \\ =2x\text{ }\sqrt[]{x+1} \end{gathered}[/tex]In a high school, 20% of the students own a supercharged Greased Lightning 409 car while the other 80% own a feeble Milquetoast car. Last year the students owning a 409 received 60 speeding tickets while the students owning a Milquetoast received 10 speeding tickets. That means that a student owning a 409 was k times more likely to receive a ticket than a student owning a Milquetoast. What is the value of k?
Answers
The value of k is 6
In this question, we have been given In a high school, 20% of the students own a supercharged Greased Lightning 409 car while the other 80% own a feeble Milquetoast car. Last year the students owning a 409 received 60 speeding tickets while the students owning a Milquetoast received 10 speeding tickets.
A student owning a 409 was k times more likely to receive a ticket than a student owning a Milquetoast.
We write this statement in mathematical expression form as,
60 = 10 * k
We need to find the value of k
Consider above equation,
60 = 10 * k
k = 60/10
k = 6
Therefore, the value of k is 6
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Using the paths shown, how long is the shortest route from Hampton to Lexington?
Answers
In this case, we have to add mixed numbers to find the shortest path from the shown alternatives. We need to work with mixed numbers, fractions, and even decimals.
To answer this question, we know that:
1. The path from Hampton to Middletown is 8 + 1/4 mi.
2. Now, we have two alternatives to go from Middletown to Campbell:
First, we have a path that is equivalent to 6 + 1/8 mi (direct). On the other path, we need to go from Middletown to Danville, and then to Campbell. The measure of the latter path is then:
[tex]3\frac{3}{8}+3\frac{3}{8}=(3+\frac{3}{8})+(3+\frac{3}{8})=(\frac{8\cdot3+3\cdot1}{8})+(\frac{8\cdot3+3\cdot1}{8})[/tex]Thus, we have:
[tex]\frac{(24+3)}{8}+\frac{(24+3)}{8}=\frac{27+27}{8}=\frac{2\cdot(27)}{8}=\frac{2}{8}\cdot27=\frac{1}{4}\cdot27=\frac{27}{4}[/tex]Which is equivalent to:
[tex]\frac{27}{4}=\frac{24}{4}+\frac{3}{4}=6+\frac{3}{4}=6\frac{3}{4}=6.75mi[/tex]If we compare the measures of the two paths, we have that:
a. The path from Middletown to Campbell (directly) is equal to:
[tex]6\frac{1}{8}=6+\frac{1}{8}=6.125mi[/tex]b. The path from Middletown to Danville, and then from Danville to Campbell is equal to 6.75 miles (it is longer).
Therefore, the shortest path, in this part of the "journey", is equal to 6.125 miles or 6 + 1/8 miles.
Now, the complete measure of the path from Hamptom to Lexington is the sum of:
1. The measure of the path from Hamptom to Middletown (8 + 1/4 miles) plus
2. The measure of the path from Middletown to Campbell (6 + 1/8 miles) (directly) plus
3. The measure of the path from Campbell to Lexington (5 + 3/4 miles).
And this is, numerically, as follows:
[tex](8+\frac{1}{4})+(6+\frac{1}{8})+(5+\frac{3}{4})=8+6+5+\frac{1}{4}+\frac{3}{4}+\frac{1}{8}[/tex][tex]19+\frac{4}{4}+\frac{1}{8}=19+1+\frac{1}{8}=20+\frac{1}{8}=20\frac{1}{8}mi[/tex]We can express the latter result as a fraction as follows:
[tex]20+\frac{1}{8}=\frac{20\cdot8+1\cdot1}{8}=\frac{160+1}{8}=\frac{161}{8}mi[/tex]Therefore, the shortest route from Hamptom to Lexington is:
1. As a fraction:
[tex]\frac{161}{8}mi[/tex]2. Or as a mixed number:
[tex]20\frac{1}{8}mi[/tex][Notice that we sum two fractions with the same denominator above:
[tex]\frac{1}{4}+\frac{3}{4}=\frac{3+1}{4}=\frac{4}{4}=1[/tex].]