Answer:
A
Step-by-step explanation:
The x-value for a function cannot be repeated, i.e. each x-value (domain) must correspond to only one y-value (range).
Unfortunately, the road from Fordyce and Sheridan is closed due to dangerous road conditions caused by the recent bad weather. Find the shortest route between each pair of towns
Answer:
a) Malvern - Sheridan - Pine Bluff
b) Camden - Fordyce - Pine Bluff
c) Benton - Malvern - Sharidan - Arkadepia
d) Benton - Malvern - Sharidan - Arkadepia - Gurden - Camden - Fordyce
e) Benton - Malvern - Sharidan - Arkadepia - Gurden - Camden
Step-by-step explanation:
P.S - The exact question is -
Given - According to a map of Arkansas, a number of good roads connect
some of the towns south of Little Rock. The road between
Malvern and Benton is 23 miles long, and between Benton and Pine
Bluff is 62 miles long. The road between Malvern and Sheridan is
28 miles long, and then from Sheridan to Pine Bluff is 22 miles
long. Arkadelphia is connected to two towns: it is 12 miles from
Gurden and 21 miles from Sheridan. Fordyce has three roads to
these towns: 45 miles to Pine Bluff, 39 miles to Sheridan, and 27
miles to Camden. The road from Gurden to Camden is 38 miles.
To find - Unfortunately, the road from Fordyce to Sheridan is closed due to
dangerous road conditions caused by the recent bad weather. Find
the shortest route between each pair of towns:
a) Malvern and Pine Bluff
b) Camden and Pine Bluff
c) Benton and Arkadelphia
d) Fordyce and Malvern
e) Benton and Camden
Proof -
The figure is as follows :
a)
Shortest route between Malvern and Pine Bluff :
Firstly, put all the vertices to ∞
Start from Malvern ,
Check the shortest distance from the corresponding vertices of Malvern.
Shortest Distance = min { Malvern - Benton, Malvern -Sheridan }
= min { 23, 28 } = 23
⇒Shortest distance is 23 ( Malvern -Benton )
Now,
Check shortest distance from Benton and Malvern
Shortest Distance = min { Benton - Pine Bluff, Malvern -Sheridan }
= min { 62, 28 } = 28
⇒Shortest distance is 28 ( Malvern -Sheridan )
Now,
Check shortest distance from Benton and Sheridan
Shortest Distance = min { Benton - Pine Bluff, Sheridan - Pine-Bluff}
= min { 85, 50 } = 50
⇒Shortest distance is 50 ( Sheridan - Pine-Bluff )
So,
By back tracking , we get
Shortest Route be -
Malvern - Sheridan - Pine Bluff
And the Shortest distance be = 50 miles
b)
Shortest Route between Camden and Pine Bluff
From Camden -
Shortest Distance = min {Camden-Fordyce, Camden-Gurden }
= min { 27, 38 } = 27
⇒Shortest Distance = 27 (Camden-Fordyce )
Now,
Check Shortest distance from Camden and Fordyce
Shortest Distance = min { Camden-Gurden, Fordyce-Pine Bluff }
= min { 38, 72 } = 38
⇒Shortest Distance = 38 ( Camden-Gurden )
Now,
Check Shortest Distance from Gurden and Fordyce
Shortest Distance = min { Gurden-Arkadepia, Fordyce-Pine Bluff }
= min { 50, 72 } = 50
⇒Shortest Distance = 50 ( Gurden-Arkadepia )
Now,
Check Shortest Distance from Arkadepia and Fordyce
Shortest Distance = min { Arkadepia - Sharidan, Fordyce-Pine Bluff }
= min { 71, 72 } = 71
⇒Shortest Distance = 71 ( Arkadepia - Sharidan )
Now,
Check Shortest Distance from Sharidan and Fordyce
Shortest Distance = min { Sharidan - Pine Bluff , Fordyce-Pine Bluff }
= min { 93, 72 } = 72
⇒Shortest Distance = 72 ( Fordyce-Pine Bluff )
So, By Back tracking , we get
Shortest route be
Camden - Fordyce - Pine Bluff
Shortest Distance be 72 miles
c)
Shortest route between Benton and Arkadelphia
By applying the same method ,
If we start from Benton and by using Pine bluff lane, distance be 62 + 45 + 27 + 38 + 12 = 184 miles
And
If we start from Benton and by using Malvern lane, distance be 23 + 28 + 21 = 72 miles
So,
Shortest Route be -
Benton - Malvern - Sharidan - Arkadepia
Shortest distance be 72 miles
d)
Shortest route between Fordyce and Malvern
By applying the same method ,
If we start from Malvern and by using Benton lane, distance be 23 + 62 + 45 = 130 miles
And
If we start from Malvern and by using Sharidan lane, distance be 28 + 21 + 12 + 38 + 27 = 126 miles
So,
Shortest Route be -
Benton - Malvern - Sharidan - Arkadepia - Gurden - Camden - Fordyce
Shortest distance be 126 miles
e)
Shortest route between Benton and Camden
By applying the same method ,
If we start from Benton and by using Pine Bluff lane, distance be 62 + 45 + 27 = 134 miles
And
If we start from Benton and by using Malvern lane, distance be 23 + 28 + 21 + 12 + 38 = 122 miles
So,
Shortest Route be -
Benton - Malvern - Sharidan - Arkadepia - Gurden - Camden
Shortest distance be 122 miles
please help on both!! will give brainliest.
Answer:
6) a) y = −7/2 x , b) y = −1/2 x , c) y = −5/4 x , d) y = −17/10 x
Step-by-step explanation:
For question 5 it needs to have the input and output values or having a domain and range value. So it can't be solved.
(there's an error in this question)
As for question 6,
a) with coordinate (x,y) = (-2,7)
1. To find the equation of a line or gradient,
first find the slope via the formula: -> m = (y2-y1/x2-x1)
If we let (0,0) ➡️ (x1,y1) and
(-2,7) ➡️ (x2,y2) then,
m = (7-0/-2-0) = -7/2 ⬅️ This is the slope of the line/gradient
Now that we have found the slope we can find the equation via the point-slope formula:
(y−y1) = m(x−x1) ;
2. Substituting the slope = -7/2 for
m and any of the two coordinates given. I will use (0,0) be make things easier. We let (0,0) → (x1,y1)
Thus,
y−0 = −7/2 (x-0)
If we simplify this, we simply get
y = −7/2 x ← This is our equation for coordinate (-2,7)
b) with coordinate (x,y) = (2,-1)
1. To find the equation of a line or gradient,
first find the slope via the formula: -> m = (y2-y1/x2-x1)
If we let (0,0) ➡️ (x1,y1) and
(2,-1) ➡️ (x2,y2) then,
m = (-1-0/2-0) = -1/2 ⬅️ This is the slope of the line/gradient
Now that we have found the slope we can find the equation via the point-slope formula:
(y−y1) = m(x−x1) ;
2. Substituting the slope = -1/2 for
m and any of the two coordinates given. I will use (0,0) be make things easier. We let (0,0) → (x1,y1)
Thus,
y−0 = −1/2 (x-0)
If we simplify this, we simply get
y = −1/2 x ← This is our equation for coordinate (2,-1)
c) with coordinate (x,y) = (4,-5)
1. To find the equation of a line or gradient,
first find the slope via the formula: -> m = (y2-y1/x2-x1)
If we let (0,0) ➡️ (x1,y1) and
(2,-1) ➡️ (x2,y2) then,
m = (-5-0/4-0) = -5/4 ⬅️ This is the slope of the line/gradient
Now that we have found the slope we can find the equation via the point-slope formula:
(y−y1) = m(x−x1) ;
2. Substituting the slope = -5/4 for
m and any of the two coordinates given. I will use (0,0) be make things easier. We let (0,0) → (x1,y1)
Thus,
y−0 = −5/4 (x-0)
If we simplify this, we simply get
y = −5/4 x ← This is our equation for coordinate (4,-5)
d) with coordinate (x,y) = (10,-17)
1. To find the equation of a line or gradient,
first find the slope via the formula: -> m = (y2-y1/x2-x1)
If we let (0,0) ➡️ (x1,y1) and
(2,-1) ➡️ (x2,y2) then,
m = (-17-0/10-0) = -17/10 ⬅️ This is the slope of the line/gradient
Now that we have found the slope we can find the equation via the point-slope formula:
(y−y1) = m(x−x1) ;
2. Substituting the slope = -17/10 for
m and any of the two coordinates given. I will use (0,0) be make things easier. We let (0,0) → (x1,y1)
Thus,
y−0 = −17/10 (x-0)
If we simplify this, we simply get
y = −17/10 x ← This is our equation for coordinate (10,-17)
Can someone help?
Solve the following equation for all values of x. Be sure to check for extraneous roots.
Answer:
[tex]x=2[/tex]
Step-by-step explanation:
First, let's multiply both sides by [tex]\sqrt{x+11}[/tex]. If we do this, we would have:
[tex]x-1=\frac{1}{\sqrt{x+11}}\cdot\sqrt{x+11}[/tex]
The [tex]\sqrt{x+11}[/tex] would cancel out and we would be left with:
[tex]x-1=1[/tex]
If we add 1 on both sides, we would get:
[tex]x=2[/tex]
Hope this helps!!!
13 POINTS FOR THIS PLEASE
Answer: Independnt Variable: direct light
Dependnt variable: the plant growth
Step-by-step explanation:
The plant growth depends on the light
Which is the same function as -5x -4=y?
1.f(x)=-5-4
2.f(-4)=-5x
3.f(-5x)=-4
4.f(x)=-5x-4
Write an equation to show how many times greater the value of a 5 in the tens place is than a 5 in the tenths place
find the value of given expression
[tex] \sqrt{4900} [/tex]
Answer:
70 Ans ...........
Step-by-step explanation:
=√4900
= 70
Answer:
√4900=√{70}²=70 is your answer
If ΔABC ≅ ΔDEF, find the measure of ∠B.
Answer:
I believe it is 67 degrees
Step-by-step explanation:
Since all the angles in a triangle add up to 180 degrees, you can subtract 78 and 35 from 180 to get 67.
true or false every trapezoid is a quadrilateral
Answer:
True
Step-by-step explanation:
It has four sides, quadrilaterals are four sided
Answer:
its ture bc it is trapezoid is a quadrilaterals
Given two strings, each extending from a different focus to a common point on an ellipse, what is the relationship
between the two points?
A. They are collinear.
B. They have the same slope.
C. The sum of their lengths is equal to the length of the major axis.
D. The difference of their lengths is equal to the length of the minor axis.
Answer:
It's C
Step-by-step explanation:
Got it correct on Edge
the figure repersents a water trough in the shape of a rectangular prism. the dimenions of a water trough are givin in feet.
Answer:
What do you need, volume?
Step-by-step explanation:
(2.5)×(4)×(7)=V
Talia has a square bedroom. Her family is moving and her bedroom in her new apartment will be 3 feet shorter in one direction and 5 feet longer in the other direction. Write an expression that represents the two binomials you would multiply together to find the area of Talia's new bedroom.
2nd Part
If Talia's old bedroom measured 10 feet by 10 feet, how much larger or smaller will her new bedroom be?
Answer (x represents the first direction and the y represents the second direction):
(x - 3) × (y + 5)New bedroom: 7 ft × 15 ft. Her new bedroom is 5 sq. ft larger than her old bedroomI hope this helps!
Darrens garden is 4 4/6 feet long. Zanique’s garden is 2 1/3 shorter. Find the length of Zanique’s garden.
4 - 2 = 2
If you take 3 and add 3, you get 6, and if you take 1 and add 1 you get 2, so 2/6.
4/6 - 2/6 = 0.33333333333
So I'd say about 2.3333333333 is the length of Zanique's garden, in a fraction... um... 233333333333/10000000000
That's all I could come up with. Don't judge me
Sarah hiked a path that took her from 34 feet below sea level to 52 feet above sea level. What was the change in her elevation?
Answer:
18 feet
Step-by-step explanation:
52 - 34 = 18
Answer:
18
Step-by-step explanation:
52 - 34 = 18 because she went 34 down so that will be a -34 and then she went 52 up and 52 is a positive number so it really is negative -34 + 52 = 18
Please hurry! This is due soon.
Hi!
We can see here that this is a composition question.
And since the composition of g of f of x is x, we can conclude that g(x) is the inverse of f(x) (if you're confused, search up the definition of an inverse function).
To find an inverse function, we can take the f(x) function and change the positions of the x and y variables.
[tex]f(x)=\frac{e^7^x+\sqrt{3}}{2}[/tex]
[tex]y=\frac{e^7^x+\sqrt{3}}{2}[/tex]
[tex]x=\frac{e^7^y+\sqrt{3}}{2}[/tex]
[tex]2x=e^7^y+\sqrt{3}[/tex]
[tex]e^7^y=2x-\sqrt{3}[/tex]
[tex]7y=ln(2x-\sqrt{3})[/tex]
[tex]y=\frac{ln(2x-\sqrt{3})}{7}[/tex]
Which is answer choice A, to check your work, you can solve the composition of g(f(x)), which will get you x.
[tex]g(f(x))[/tex]
[tex]g(\frac{e^7^x+\sqrt{3}}{2})[/tex]
[tex]\frac{ln(2(\frac{e^7^x+\sqrt{3}}{2})-\sqrt{3}}{7}[/tex]
2s cancel.
[tex]\frac{ln(e^7^x+\sqrt{3})-\sqrt{3}}{7}[/tex]
The natural log and e cancel.
[tex]\frac{7x+\sqrt{3}-\sqrt{3}}{7}[/tex]
[tex]\sqrt{3}[/tex]s cancel.
[tex]\frac{7x}{7}[/tex]
7s cancel.
[tex]x[/tex]
Hope this helps!
Solve x2 – 18 = 3x by using the Quadratic Formula.
Answer:
(x+3)(x-6)
Step-by-step explanation:
use photomath
What is the distance between points (5,2) and (1,-3) on the coordinate plane?
Answer:
6.403124
Step-by-step explanation:
The blinker on Brendan's Bugatti blinks 12 times every 48 seconds. How many times will the blinker blink in 24 seconds? answer ASAP thanks you.
Answer:
6
Step-by-step explanation:
Please help I’m struggling
Please please help help please please help me please ASAP and no link thank you
Answer:
(-3,-4) is the coordinate for the yellow circle
Answer:
(-3,-4)
Step-by-step explanation:
You always put the x coordinate (-3) first and then the y coordinate (-4) and use parentheses
Can someone pls help me
Answer:34 1/2 cubes can fit
Step-by-step explanation: multiply all of them by 2
Find the Volume (nearest integer):*
Answer:
the correct answer is 4) 1692
Which expression is equivalent to 8x-12y+32?
Answer:
i had the same question, it's "C"
Step-by-step explanation:
Answer:16(0.5x-0.75y+2)
Step-by-step explanation:
The number of 5p, 10p, and
20p coins in a jar are in the
ratio 7:4:3. If there are
5p coins are worth 70p
calculate the total value of
the money in the jar.
Answer:
Step-by-step explanation:
70p/5=14
14*4=56*10=560p
14*3=42*20=840p
840+560+70=1470
=1470p or (£14.70)
The total value of money in the jar is 270p.
What is addition?Combining objects and counting them as one big group is done through addition. In arithmetic, addition is the process of adding two or more integers together. Addends are the numbers that are added, and the sum refers to the outcome of the operation.
Given:
The number of 5p, 10p, and 20p coins in a jar are in the ratio 7:4:3.
That means,
Number of 5p coins are 5x, 10p coins are 4x and 20p coins are 3x.
And 5p coins are worth 70p.
That means, x = 70p/5p
x = 14
So,
The total worth of coins are,
= 70p + 80p + 120p
= 270p
Therefore, the worth of the coins are 270p.
To learn more about the addition;
brainly.com/question/29464370
#SPJ2
PLEADE HELP QUICK WILL MARK BRAINLIEST!!! ITS SIMPLFT IF UR GOOD AT THAT PLESEE HELP
Answer:
1) a8
2) 6^5
3) 7^2 b^8
4) 30k^6 h^8
5) y^9/3x^2
125 is what percent of 200?
write as an equation pls
Answer:
160%Step-by-step explanation:
Let the missing percentage be x%
We can also write that as x/100
According to the question,
[tex]125 \times \frac{x}{100} = 200 \\ 125x = 200 \times 100 \\ 125x = 20000 \\ x = \frac{20000}{125} \\ x = 160[/tex]
aaa please help - What score do you have to get on a 40 point test to receive a 90% ?
Answer: 36
Step-by-step explanation:
To find out the score, you would divide the total number of points (40) by 100 and then times it by the percentage you want (90).
Hope this helps :)
i need help ASAP please
Answer:
(-3,2)
Step-by-step explanation:
the x component should be less than or equal to 3.
the y component is greater than -2.
Go through each option and you'll see that the only option that satisfies both conditions is 3.
ANSWER FOR BRAINLEST (BEST TO EXPLAIN WILL GET IT)
Answer:
-7g+13
Step-by-step explanation:
b) because combining like terms results in:
g-8g=7g
and
15-2= 13
heeeeeeeellllpppp wiilll ggiivvee bbrraaiinnlliieesstt
Answer:
c
Step-by-step explanation: