Performance task: A parade route must start And and at the intersections shown on the map. The city requires that the total distance of the route cannot exceed 3 miles. A propos route is shown.
Part A: Why does the proposed route not meet the requirement?
Part B: Assuming that the roads used for the
route are the same and the end point is the same,
at what intersection could the parade start so the
total distance is as close to 3 miles as possible?
Part C: The city wants to station video cameras halfway down each road in the parade. Using your answer to Part B, what are the coordinates of locations for the cameras?
Answers
Answer:
Part A: The proposed route does not meet requirement because it is longer than the maximum required length of 3 miles
Part B: For the total distance is as close to 3 miles as possible, the start point of the parade should be at the point on Broadway with coordinates (9.941, 4.970)
Part C: The coordinates of the cameras stationed half way down each road are;
For central avenue; (4, 2)
For Broadway; (7.97, 2.49)
Step-by-step explanation:
Part A: The length of the given route can be found using the equation for the distance, l, between coordinate points as follows;
[tex]l = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}[/tex]
Where for the Broadway potion of the parade route, we have;
(x₁, y₁) = (12, 3)
(x₂, y₂) = (6, 0)
[tex]l_1 = \sqrt{\left (0 -3\right )^{2}+\left (6-12 \right )^{2}} = 3 \cdot \sqrt{5}[/tex]
For the Central Avenue potion of the parade route, we have;
(x₁, y₁) = (6, 0)
(x₂, y₂) = (2, 4)
[tex]l_2 = \sqrt{\left (4 -0\right )^{2}+\left (2-6 \right )^{2}} = 4 \cdot \sqrt{2}[/tex]
Therefore, the total length of the parade route =-3·√5 + 4·√2 = 12.265 unit
The scale of the drawing is 1 unit = 0.25 miles
Therefore;
The actual length of the initial parade =0.25×12.265 unit = 3.09 miles
The proposed route does not meet requirement because it is longer than the maximum required length of 3 miles
Part B:
For an actual length of 3 miles, the length on the scale drawing should be given as follows;
1 unit = 0.25 miles
0.25 miles = 1 unit
1 mile = 1 unit/(0.25) = 4 units
3 miles = 3 × 4 units = 12 units
With the same end point and route, we have;
[tex]l_1 = \sqrt{\left (0 -y\right )^{2}+\left (6-x \right )^{2}} = 12 - 4 \cdot \sqrt{2}[/tex]
y² + (6 - x)² = 176 - 96·√2
y² = 176 - 96·√2 - (6 - x)²............(1)
Also, the gradient of l₁ = (3 - 0)/(12 - 6) = 1/2
Which gives;
y/x = 1/2
y = x/2 ..............................(2)
Equating equation (1) to (2) gives;
176 - 96·√2 - (6 - x)² = (x/2)²
176 - 96·√2 - (6 - x)² - (x/2)²= 0
176 - 96·√2 - (1.25·x²- 12·x+36) = 0
Solving using a graphing calculator, gives;
(x - 9.941)(x + 0.341) = 0
Therefore;
x ≈ 9.941 or x = -0.341
Since l₁ is required to be 12 - 4·√2, we have and positive, we have;
x ≈ 9.941 and y = x/2 ≈ 9.941/2 = 4.97
Therefore, the start point of the parade should be the point (9.941, 4.970) on Broadway so that the total distance is as close to 3 miles as possible
Part C: The coordinates of the cameras stationed half way down each road are;
For central avenue;
Camera location = ((6 + 2)/2, (4 + 0)/2) = (4, 2)
For Broadway;
Camera location = ((6 + 9.941)/2, (0 + 4.970)/2) = (7.97, 2.49).
This exercise is necessary to use the given map information and then make the distance between points, in this way we find that:
A)The proposed route does not meet requirement because it is longer than the maximum required length of 3 miles.
B) Broadway and Cedar Street
C) [tex]Central \ Avenue(4, 2)Broadway (7.97, 2.49)[/tex]
So from the distance between points and the informed map we have:
A) The equation for the distance, as follows:
[tex]l=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]
Where for the Broadway potion of the parade route, we have:
[tex](x_1,y_1)=(12,3)\\(x_2,y_2)=(6,0)[/tex]
Applying the values in the formula given above, we have:
[tex]l_1=\sqrt{(0-3)^2+(6-12)^2}=3\sqrt{5}[/tex]
For the Central Avenue potion of the parade route, we have:
[tex](x_1, y_1) = (6, 0)(x_2, y_2) = (2, 4)[/tex]
Applying the values in the formula given above, we have:
[tex]l_2=\sqrt{(4-0)^2+(2-6)^2}=4\sqrt{2}[/tex]
Therefore, the total length of the parade route:
[tex]3\sqrt{5} + 4\sqrt{2} = 12.265 \\0.25*12.265 unit = 3.09\ miles[/tex]
B) The two streets that are the same distance apart are the streets: Broadway and Cedar Street.
C) The coordinates of the cameras stationed half way down each road are:
For Central Avenue:
[tex]Camera \ location = ((6 + 2)/2, (4 + 0)/2) = (4, 2)[/tex]
For Broadway:
[tex]Camera\ location = ((6 + 9.941)/2, (0 + 4.970)/2) = (7.97, 2.49)[/tex]
See more about distance at brainly.com/question/989117
Related Questions
Can anyone please do these questions? This is Unit 1 Geometry basics Homework 5 Angle Relationships.
Answers
Answer:
Step-by-step explanation:
11). 6x + 7 = 8x - 17 [Since vertical angles are equal in measure]
8x - 6x = 17 + 7
2x = 24
x = 12
12). (11x - 15) + (5x - 13) = 180°
16x - 28 = 180°
16x = 180 + 28
16x = 208
x = 13
13). Since DB⊥AC,
m∠CBD = 90°
m∠CBE + m∠DBE = 90°
(5x - 42) + (2x - 1) = 90°
7x - 43 = 90
7x = 133
x = 19
14). Since QS bisects angle PQR,
m∠PQS = m∠RQS
10x + 1 = [tex]\frac{82}{2}[/tex]
10x + 1 = 41
10x = 40
x = 4
15). 10x - 61 = 18y + 5 [Vertical angles]
10x - 18y = 61 + 5
10x - 18y = 66
5x - 9y = 33 ------(1)
(18y + 5) + (x + 10) = 180 [linear pair of angles are supplementary]
18y + x + 15 = 180
x + 18y = 165 ------(2)
By adding equation (1)×2 and equation (2)
(10x - 18y) + (x + 18y) = 66 + 165
11x = 231
x = 21
16). (5x - 17) + (3x - 11) = 180 [[linear pair of angles are supplementary]
8x - 28 = 180
8x = 180 + 28
8x = 208
x = 26
(3x - 11)° = 78 - 11
= 67°
67° + 90° + (2y + 5)°= 180° [Sum of angles on a line]
162 + 2y = 180
2y = 180 - 162
2y = 18
y = 9
17). NP bisects ∠MNQ.
Therefore, m∠MNQ = 2(m∠PNQ)
8x + 12 = 2×78
8x + 12 = 156
8x = 156 - 12
8x = 144
x = 18
m∠MNQ = (8x + 12)° = 156°
m∠RNM = m∠ONQ [Vertical angles]
(3y - 9)° = 180° - m∠MNQ
3y - 9 = 180 - 156
3y - 9 = 24
3y = 33
y = 11
Using the knowledge of the angle relationships to create an equation, the value of x and y in the image given are:
11. x = 12
12. x = 13
13. x = 19
14. x = 4
15. x = 21; y = 8
16. x = 26; y = 9
17. x = 18; y = 11
Applying the knowledge of angle relationships, we can solve each given problem by first, creating a an equation from the relationship between angles, then solve for the variables.
11. [tex]6x + 7 $ and $ 8x - 17[/tex] are vertical angles.
Since vertical angles are congruent, therefore:[tex]6x + 7 = 8x - 17[/tex]
Solve for x[tex]6x - 8x = -7 - 17\\\\-2x = -24\\\\x = 12[/tex]
12. [tex]11x - 15 $ and $ 5x - 13[/tex] are linear pair angles.
Since, the sum of linear pair angles equals 180 degrees, therefore:[tex](11x - 15) + (5x - 13) = 180[/tex]
Solve for x[tex]11x - 15 + 5x - 13 = 180\\\\16x - 28 = 180\\\\16x - 28 + 28 = 180 + 28\\\\16x = 208\\\\x = 13[/tex]
13. <DBE and <CBE are complementary angles.
Since the some of complementary angles equals 90 degrees, therefore,[tex]m \angle DBE + m \angle CBE = 90[/tex]
Substitute[tex](2x - 1) + (5x - 42) = 90[/tex]
Solve for x[tex]2x - 1 + 5x - 42 = 90\\\\7x - 43 = 90\\\\7x = 90 + 43\\\\7x = 133\\\\x = 19[/tex]
14. Since QS bisects <PQR, therefore,
m<PQS = 1/2(PQR)
Substitute[tex]10x + 1 = \frac{1}{2} (82)[/tex]
Solve for x[tex]10x + 1 = 41\\\\10x = 41 - 1\\\\10x = 40\\\\x = 4[/tex]
15. [tex](x + 10) $ and $ (10x - 16)[/tex] are linear pair angles.
Since the sum of linear pair angles equals 180 degrees, therefore,[tex](x + 10) + (10x - 16) = 180\\[/tex]
Solve for x[tex]x + 10 + 10x - 61 = 180\\\\11x - 51 = 180\\\\11x = 180 + 51\\\\11x = 231\\\\x = 21[/tex]
Find y:Since [tex](10x - 61) $ and $ (10y + 5)[/tex] are vertical angles, they are congruent. Therefore,
[tex](10x - 61) = (10y + 5)[/tex]
Plug in the value of x and solve for y[tex]10(21) - 61 = 18y + 5\\\\149 = 18y + 5\\\\149 - 5 = 10y\\\\144 = 18y\\\\8 = y\\\\\mathbf{y = 8}[/tex]
16. Since [tex](5x - 17) $ and $ (3x - 11)[/tex] are linear pair, their sum equals 180 degrees. Therefore,
[tex](5x - 17) + (3x - 11) = 180[/tex]
Solve for x[tex]5x - 17 + 3x - 11 = 180\\\\8x - 28 = 180\\\\8x = 180 + 28\\\\8x = 208\\\\x = 26[/tex]
Find y:[tex](2y + 5) + 90 + (3x - 11) = 180[/tex] (angles on a straight line = 180 degrees)
Plug in the value of x and solve for y[tex]2y + 5 + 90 + 3(26) - 11 = 180\\\\2y + 5 + 90 + 78 - 11 = 180\\\\2y + 162 = 180\\\\2y = 180 - 162\\\\2y =18\\\\y = 9[/tex]
17. Since NP bisects <MNQ, therefore,
[tex]m \angle PNQ = \frac{1}{2}(m \angle MNQ)[/tex]
Substitute[tex]78 = \frac{1}{2}(8x + 12)[/tex]
Solve for x[tex]78 \times 2 = 8x + 12\\\\156 = 8x + 12\\\\156 - 12 = 8x \\\\144 = 8x\\\\18 = x\\\\x = 18[/tex]
[tex]m \angle RNM + m \angle MNQ = 180^{\circ}[/tex] (linear pair)
Substitute[tex](3y - 9) + (8x + 12) = 180[/tex]
Plug in the value of x and solve for y[tex]3y - 9 + 8(18) + 12 = 180\\\\3y - 9 + 144 + 12 = 180\\\\3y + 147 = 180\\\\3y = 180 - 147\\\\3y = 33\\\\y = 11[/tex]
Therefore, using the knowledge of the angle relationships to create an equation, the value of x and y in the image given are:
11. x = 12
12. x = 13
13. x = 19
14. x = 4
15. x = 21; y = 8
16. x = 26; y = 9
17. x = 18; y = 11
Learn more here:
https://brainly.com/question/18963166
a patio has an area of 120 square feet. the length of the patio is 12 feet. what is its width
Answers
w = 10 feet
Step-by-step explanation:Area formula
A = l×w
120ft² = 12ft×w
w = 120ft²/12ft
w = 10 feet
Help needed ASAP will give BRAINLIEST
Answers
Answer:
177.2 i think
Step-by-step explanation:
NEED EXPLANATION AND PROCESS!!!
Answers
Answer:
x = 133
y = 43
Step-by-step explanation:
x + 47 = 180
so x is 133
47 + y = 90
so y is 43
PLEASE HELP!!!Choose the name of the angle notated by the arc(SHOW WORK) A.MPO B.NPO C.LPM D.PLO
Answers
B. NPO
Explanation:Because P is the middle letter in the arc.
Answer: B. NPO
Step-by-step explanation: the angle has to be in middle
Evaluate the expression for d = 43.4.
Write your answer as a decimal or whole number.
4.4(d − 35) =
Answers
Answer:
36.96
Step-by-step explanation:
given
d = 43.4
equation
4.4(d - 35) =
plug d in
4.4(43.4 - 35) =
solve within parentheses
4.4(8.4) =
multiply
36.96
Evaluate the expression when a=3.
a^2+12
Answers
[tex]3^{2} + 12 = 9 + 12 = 21[/tex]
The answer is 21.
Answer:
The correct answer is 21.
Step-by-step explanation:
To solve this problem, we simply substitute 3 for a in the expression.
Given the expression,
a^2 + 12
we should replace "a" with 3, as denoted by the problem, giving us:
(3)^2 + 12
Now, we simplify using the order of operations. PEMDAS tells us that we should simplify what is in the parentheses first because it has an exponent.
9 + 12
Now, we can just add the two remaining terms together, giving us:
21
Therefore, the answer is 21.
Hope this helps!
What is the same value as the expression 7/5+2 1/4+1.6
Answers
Felipe earns $9 per hour for helping his grandmother with her yard work. Write and solve a multiplication equation to find how many hours he must help his grandmother I’m order to earn $54
Answers
Answer:
Felipe work for 6 hours to earn $54
Step-by-step explanation:
I guess I was help full for u
plz follow me for more updates
What property is (6+2)+4=4+(6+2)
Answers
Answer: commutative property of addition
Step-by-step explanation:
(a+b)+c=a+(b+c) -- Commutative property of addition
Commutative property of addition is when the numbers are added, the sum are the same, regardless of the order of numbers.
Thus, (6+2)+4=4+(6+2) is commutative property of addition.Hope this helps!! :)
Please let me know if you need further explanation with properties of addition.
Is the equation x9 – 5x3 + 6 = 0 quadratic in form? Explain why or why not.
Answers
Answer:
NOO
Step-by-step explanation:
In order for an equation to be quadratic, the highest degree that is needed is two. The highest exponent provided is 3 therefore no it is not a quadratic function
A. Without computing each sum, find which is greater, O or E, AND by how much.
O = 1 + 3 + 5 + 7 + ... + 101
E = 2 + 4 + 6 + 8 + ... + 102
and need to explain it
Answers
Answer:
Www
Step-by-step explanation:
What value of x is in the solution set of 2(3x - 1) = 4x - 6?
EO
-10
Answers
Answer:
D) -1
Step-by-step explanation:
6x-2≥4x-6
6x-4x≥-6+2
2x≥-4
x≥-4÷2
x≥-2
Only -1 is greater than -2 in the list.
Answer:
x = - 1
Step-by-step explanation:
Given
2(3x - 1) ≥ 4x - 6 ← distribute parenthesis on left side
6x - 2 ≥ 4x - 6 ( subtract 4x from both sides )
2x - 2 ≥ - 6 ( add 2 to both sides )
2x ≥ - 4 ( divide both sides by 2 )
x ≥ - 2
The only value in the list greater than - 2 is - 1
x = - 1 is in the solution set
Find the value of the remaining variable in the formula. Use 3.14 as an approximation for a (pi).
P=2L+2W (perimeter of a rectangle); L = 4, W= 2
P =
Enter your answer in the answer box.
Answers
Answer:
P = 12
Step-by-step explanation:
Given formula for the perimeter 'P' of a rectangle is,
P = 2L + 2W
If the values of L and W are,
L = 4 and W = 2
Perimeter of the rectangle = 2(L + W)
= 2(4 + 2)
= 2 × 6
= 12 units
Therefore, value of remaining variable 'Perimeter' = 12 units
(There is no use of 'pi' in calculating the perimeter of a rectangle).
11. Your class is taking a trip to a museum that is 190 miles away. The bus can travel at 55
miles per hour. At least how many hours should your class plan for the trip to the museum?
Answers
When ax3 +x2 -2x +b is divided by x+1, the remainder is 10. When it is divided by x-3, the remainder is -46. What is the value of a and b?
Answers
Step-by-step explanation:
Given
X+ 2 = 0
X = -2
on putting in polynomial
-8a +2b= 0
- 8a = 2b
b = -4a
Now
when divided by x - 1 give remainder -15
so
x - 1 = -15
x = -14
on putting in polynomial
-2744a + 198 + 14b - 4 = -14
-2744a + 56a = - 208
-2688a = -208
a = 168/13
Now
b = 672/13
The next two numbers in the series 1 , 4 , 9 , 16 , 25 ,....................are
Answers
Answer:
36, 49
explanation:
The pattern in this series is going by perfect squares:
(1)² = 1(2)²= 4(3)² = 9(4)² =16(5)² = 25From this, we can tell the next 2 numbers in the series will be:
(6)²=36(7)²=49If g(x-1) = (2-g(x))/8 and g(1) = 3, find the value of g(2).
Answers
Answer:
-22
Step-by-step explanation:
g(2-1)=g(1)=(2-g(2))/8=3
2-g(2)=24
-g(2)=22
g(2)=-22
Point D best represents which of the following numbers?
tot
14
14.5
15
15.5
16
Answers
Answer:
yea your correct and 16.5
Step-by-step explanation:
Answer:
???
Step-by-step explanation:
???
What is the common multiplier in the proportion? 6 over 8 = 9 over 12
Answers
Answer:
The common multiplier is 24
Step-by-step explanation:
6/8 9/12
8,16,24
12,24
6/8 × 3/3= 18/24
9/12× 2/2= 18/24
-
=\80
2.4
()
14 15
0
L: 2
4
А) . 1
( - ) 90
| —
Answers
Answer:
....
Step-by-step explanation:
what is 1 1/3 divided by 3/5
Answers
rounded answer: 2.23
Answer:
6.11
Step-by-step explanation:
First divide 11by 3 and 3by 5.And divide the answer of 11by 3 by 3by5
Question 14(Multiple Choice Worth 4 points)
(01.04 LC)
Solve the inequality 4x - 6 > 6x - 20.
x> 7
x<7
x<2
x>2
Answers
Step-by-step explanation:
4(7)-6,6(7)-20
28-6,42-20
22,22
22/22
=1
4(2)-6,6(2)-20
8-6,12-20
2,-8
-8/2
=-4
Answer:
Its B
Step-by-step explanation:
Really need help with #20! I'll give brainliest!
Answers
Answer: 1 year (year 15)
Step-by-step explanation:
109.5-86.0=23.5
128.4-109.5=18.90
140.8-128.4=12.4
158.7-140.8=17.9
182.1-158.7=23.4
23.5+18.9+12.4+17.9+23.4=96.10
96.10÷5=19.22
200-182.1=17.9
182.1+19.22=201.32 subs
What kind of transformation is illustrated in this figure?
O translation
.
O reflection
dilation
Orotation
Answers
Answer:
translation
Step-by-step explanation:
shape, size, measurement all stayed the same. they just moved locations :)
6+(-3)=
answer question plz
Answers
Answer:
-3
Step-by-step explanation: Because it is just like saying 6-3
Answer:
3
Step-by-step explanation:
6+(-3)
A addition symbol and subtraction symbol both make a negative symbol.
6-3
6-3= 3
Hope this helps!
Please help lol
Answer options:
A. (2.5,4)
B. (2,3)
C. (1.5,3)
D. (2,3.5)
Answers
What is the base of the triangle? A=36mm(2) H= 6mm B=?
Answers
Answer:
Area formula=b*h÷2
b=a÷h*2
b=12
Step-by-step explanation:
So if you multiply the base and height to find a triangle, you'd get the area of a rectangle instead so if you divide by 2, you'd get the area of a triangle
To find the base, you'd reverse the process. You'd divide the area by the height and multiply by 2.
36÷6=6
6*2=12
Hope that helps!
1.5x + 12 = 0.5(5x - 8) a. 1 b. 2 c. 16 d. 20
Answers
Answer:
Isolate the variable by dividing each side by factors that don't contain the variable.
x=16
Step-by-step explanation:
its C
Answer:
x=16
Step-by-step explanation:
First of all we want to distribute 0.5 on 5x and -8
so we are going to divide by 2
1.5x + 12 = 2.5x -4
now we want to put the variables on one side and the numbers on the other side of the equal sign
and to
1.5x +12 = 2.5x -4
-12 -12
1.5x = 2.5x - 16
now we want to move the variable that is on the right to the left side
1.5x = 2.5x - 16
-2.5x -2.5x
-x = -16
change the signs and the answer is
x=16
EXTRA STEP
you have to make sure that your answer is correct so just plug in x and the answers on both sides of the equation must be equal
What is the 50th term of Arithmetic sequence 9,2,-5
Answers
Answer:
- 334
Step-by-step explanation:
There is a common difference between consecutive terms in the given sequence, that is
d = 2 - 9 = - 5 - 2 = - 7
This indicates the sequence is arithmetic with n th term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = 9 and d = - 7 , thus
[tex]a_{50}[/tex] = 9 + (49 × - 7) = 9 - 343 = - 334