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?
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
Is 4.5 natural number?
Answer:
No
Step-by-step explanation:
4.5 IS NOT A WHOLE NUMBER!
Answer:
YES 4.5 IS NATURAL NUMBER
Step-by-step explanation:
How much interest is earned on $470 at
4% for seven years?
are these called interior angles ?
Answer:
yes they are
Step-by-step explanation:
1)n/5=-10 How do we answer this question
Answer: Your answer will be [tex]\frac{-50}{5} =-10[/tex]
Step-by-step explanation: You will have
[tex](5)\frac{n}{5} =-10(5)[/tex] you will have to multiply 5 on both sides. So you will then simplify 5 and 5 to be left with n and multiply -10(5)=-50
So you get [tex]n=-50[/tex]
To rent a certain meeting room, a college charges a reservation fee of $39 and an additional fee of $5.80 per hour. The film club wants to spend at most $73.80 on renting the meeting room.
What are the possible amounts of time for which they could rent the meeting room?
Use t for the number of hours the meeting room is rented, and solve your inequality for t.
Answer:
The inequality is x less than or equal to 6. So the amount of hours they can rent it is 6 hours or less.
Step-by-step explanation:
5.80x + 39 <_ 73.80 ----> subtract 39 on both side to get ---> 5.80x <_ 73.80 -----> then divide by 5.80 on both sides to get ---> x <_ 6.
Hope this helped!
How does the outlier affect the standard deviation in the following set of data?
9 9 10 10 12 15 16 16 17 17 17 20 23 28
5.32
Removing the outlier lowers the standard deviation by 1.09
No outlier
4.23
Answer:
Removing the outlier lowers the standard deviation by 1.09
Step-by-step explanation:
Find the standard deviation of the data WITHOUT the outlier first.
If you don't know how to do standard deviation, here are the steps:
1. Find the mean
2. Subtract the mean by the data set values
3. Square the differences
4. Add the squared numbers together and divide by the number of data set values
5. What you have now is the variance, and all you have to do now is square the variance and you have the standard deviation
Repeat this, but WITH the outlier this time.
Final step, just subtract the smaller number (answer you got from the data with the outlier) by the greater number (answer you got from the data without the outlier) and you have your answer: 1.09!
Without using a calculator, choose the statement that best describes the value of {86}
Answer: my guess is 9
Answer:
there would be the 8 in the tens place and the 6 in the ones place
Step-by-step explanation:
you can see this in a place value chart
Find the mode:
4,5, 4, 3, 5, 1, 6
Answer:
4 and 5Step-by-step explanation:
The mode in a given set of data is the number that appears the most.
4 appears twice
5 appears twice
3 appears once
1 appears once
6 appears once
Explain how to simplify the expression -98 - 31? Using the additive inverse.
Given:
The expression is -98 - 31.
To find:
The value of the given expression using the additive inverse.
Solution:
According to the additive inverse, for any number a,
[tex]a+(-a)=0[/tex]
Using additive inverse, we have
[tex]98+(-98)=0[/tex] ...(i)
[tex]31+(-31)=0[/tex] ...(ii)
Now, using (i) and (ii), we get
[tex]98+(-98)+31+(-31)=0[/tex]
[tex](98+31)+(-98-31)=0[/tex]
[tex]129+(-98-31)=0[/tex]
Subtracting 129 from both sides, we get
[tex]-98-31=-129[/tex]
Therefore, the value of given expression is -129.
I need help I turn this in in less than 20 min
Select all statements
A. Two squares with the same lengths are always congruent
B. Two rectangles with the same side lengths are always congruent
C. two rhombuses with the same side lengths are always congruent
D. two parallelograms with the same side lengths are always congruent
E. two quadrilaterals with the same side lengths are always congruent
Step-by-step explanation:
(A) squares are congruant .
(B) rectangle having equal length of same side is congruent.
(C)it is true because it have same side length are equal.
(D)it is true because same same side length are equal.
(E) it is truebecause same side length are equal.
The statements that are correct in the given question are: options A, B and C.
Quadrilaterals are figures or shape bounded by four straight sides. Thus each quadrilateral has its sum of interior angles to be [tex]360^{o}[/tex]. Examples include; rectangle, square, trapezium, rhombus, kite, parallelogram.
Considering the properties of each quadrilateral given in the question, it can be inferred that;
squares of equal length of sides are congruent. rectangles of equal length of sides are congruent. rhombuses with equal side lengths are congruent. parallelogram with the same side lengths may not be congruent. This is because the angles of the slanting sides may not be the same. quadrilaterals with the same side length may not congruent. Example: rectangle and parallelogram of the same side length are not congruent.Therefore, the appropriate statements that are correct are: options A, B and C.
Visit: https://brainly.com/question/21935574
WHAT IS |3x + 2| > 9
Answer:
Answer will be the 7/3<x>7/3
There is an attachment at the bottom help me please.
Answer:
Fourth option
Step-by-step explanation:
We know that A and B are rational numbers because they can be written as the quotient of two integers. Therefore, that eliminates the first and third options because they state that (at least) one of the numbers is irrational but we know that both are rational, hence, they are incorrect. The second option is incorrect because A · B = [tex]\frac{mn}{pq}[/tex], not [tex]\frac{mp + nq}{pq}[/tex], therefore, the correct answer is the fourth option.
Evaluate the expression for c = –0.3.
Write your answer as a decimal or whole number.
24c^2 =
Answer:
2.16
Step-by-step explanation:
c = -0.3
24c² =
plug in c
24(-0.3)²
solve for the exponent
24(0.09)
multiply
2.16
Combine like terms fir the following expression: -3x+14-11+11x
Answer:
8x + 3
Step-by-step explanation:
In the expression -3x + 14 - 11 + 11x, we have two pairs of like terms that can be combined together:
-3x, 11x
14, -11
If we rewrite this expression with the like terms together, it would look like this:
-3x+11x + 14-11
To make the addition of -3x and 11x easier, we could switch their places in the expression to make it look like this:
11x-3x + 14-11
(Note: Even though we are switching the terms' places, the -3x still keeps its negative sign when you move it around.
11x-3x is 8x and 14-11 is 3.
Therefore, the expression -3x + 14 - 11 + 11x can be simplified by combining like terms into 8x + 3.
please help!
4^x*5^y=20, 4^y*5^x=20^2, x+y=?
Answer:
x + y are either 2 or 4
Step-by-step explanation:
conclusion x + y = 2 OR 4
greastest common factor of 24 and 18
Answer: 6
Step-by-step explanation:
the biggest number that can go into both 24 and 18 evenly is 6. 24/6 is four, and 18/6 is three
Back Next
✓ Check
Question 1
Caroline said the absolute value of -25 is 25. Is she correct? Explain.
Answer:
lolllll
Step-by-step explanation:
For which equations are in the solution for x the same number? 15 – х = -3
3
Answer:
Step-by-step explanation:
First equation:
15 - x = - 3
-x = - 3 - 15
-x = -18 (now negative signs on b.s cut eachother)
[x = 18]
Second equation :
15 - x = 3
-x = 3 - 15
- x = -12 ( now negative sign on b.s cut eachother)
[x = 12]
so x = 18 and x = 12 are not same
HELP ME PLEASE ECPLAIN WHY
Answer:
A≈110.11
using formula 1/4[tex]\sqrt5(5+2\sqrt5)a2[/tex]
Step-by-step explanation:
Mai wants to make a scale drawing of her kitchen. her kitchen is a rectangle with length 6m and width 2m. She decides on a scale of 1 to 40. Mal's Kitchen door is 1.2 m wide. How wide should the door be on the scale drawing?
How wide should the door be on the scale drawing?
cm
Explain how you know
Type your response in the box below.
c. Mai's kitchen table measures 4 cm by 2.5 cm on the scale drawing.
What are the actual measurements of her kitchen table?
Type your answers in the boxes below.
Answer:
Her door should be 3cm on scale
The actual dimension of the kitchen table is
[tex]Length = 1.6m[/tex]
[tex]Width = 1m[/tex]
Step-by-step explanation:
Given
[tex]Scale= 1 : 40[/tex]
[tex]Kitchen\ Dimension= 6m\ by\ 2m[/tex]
[tex]Door\ Width = 1.2m[/tex]
Solving (a): The width of the door on the scale
Represent the scale width with x
So, we have:
[tex]1 : 40[/tex]
and
[tex]x : 1.2[/tex]
Equate both ratios
[tex]1 : 40 = x : 1.2[/tex]
Represent as fraction
[tex]\frac{1}{40} = \frac{x}{1.2}[/tex]
Solve for x
[tex]x = \frac{1.2}{40}[/tex]
[tex]x = 0.03m[/tex]
[tex]x = 3cm[/tex]
Hence, her door should be 3cm on scale
Solving (b): Actual Dimension of the kitchen table
To solve this, we simply multiply the scale dimensions by 40
[tex]Length = 4cm * 40[/tex]
[tex]Length = 160cm[/tex]
[tex]Length = 1.6m[/tex]
[tex]Width = 2.5cm * 40[/tex]
[tex]Width = 100cm[/tex]
[tex]Width = 1m[/tex]
Hence:
The actual dimension is
[tex]Length = 1.6m[/tex]
[tex]Width = 1m[/tex]
Which statement about rational numbers is true?
All rational numbers are fractions.
Rational numbers never have repeating decimals.
Some integers are not rational numbers.
All fractions containing integers are rational numbers.
Answer:
the true one is all fractions containing integers are rational numbers is true
Step-by-step explanation:
i think
Answer:
All fractions containing integers are rational numbers.
Step-by-step explanation:
Geography textbook has a width of 9 inches and a diagonal of 15 inches. What is the length of the
textbook?
Answer:
12 inches
Step-by-step explanation:
The Pythagorean's theorem states that a triangle's hypotenuse's length is equal to a^2+b^2=c^2.
9 is a, b is the length, and c is the 15.
9^2+b^2=225
225-81=144
The square root of 144 is 12, therefore 12 inches is the length.
HELP PLEASEEEE A dressmaker needs to cut 4-inch pieces of ribbon from rolls of ribbon that are 9 feet in length. How many 4-inch pieces can the dressmaker cut from 15 of these rolls of ribbon? How many inches of ribbon does the dressmaker have, in total?
Answer:
1620 peices
Step-by-step explanation:
9 ft = 9 x 12 (12 inches make 1 ft) = 108 x 15 rolls = 1620 inches
1620 inches divided by 4 inches = 405 peices
:)
Which of the following is a solution of x2 + 4x = -8?
O x = -2 - 21
O x = 2 + 21
O x = -4 + 41
O x = 4 - 41
Answer:
[tex]x=2i-2,\:x=-2i-2[/tex]
Step-by-step explanation:
[tex]x^2 + 4x = -8\\\\\mathrm{Solve\:by\:completing\:the\:square}\\\\\mathrm{Write\:equation\:in\:the\:form:\:\:}x^2+2ax+a^2=\left(x+a\right)^2\\\\\mathrm{Solve\:for\:}a,\:2ax=4x:\quad a=2\\\\\mathrm{Add\:}a^2=2^2\mathrm{\:to\:both\:sides}\\\\x^2+4x+2^2=-8+2^2\\\\\mathrm{Simplify\:}-8+2^2:\quad -4\\x^2+4x+2^2=-4\\\\\mathrm{Complete\:the\:square}\\\left(x+2\right)^2=-4\\\\\mathrm{For\:}f^2\left(x\right)=a\mathrm{\:the\:solutions\:are\:}f\left(x\right)=\sqrt{a},\:-\sqrt{a}\\[/tex]
[tex]\mathrm{Solve\:}\:x+2=\sqrt{-4}:\quad x=2i-2\\\\\mathrm{Solve\:}\:x+2=-\sqrt{-4}:\quad x=-2i-2\\\\x=2i-2,\:x=-2i-2\\[/tex]
ockdown Learning Week 2 Higher
A and B are two cities.
b)
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Submit Answer
a) Measure the bearing of B from A.
AX
b) Measure the bearing of A from B.
Answer:
A) measure the bearing of A from B
Josh wrote a whole number using the digits 8,4,7,2,9 and 0. Josh's number has a seven in the thousands and a 2 in the tens place. Josh's number is less then 500,000. Is Josh's number greater than 480,000?
Answer:
4 out of the 6 possible numbers Josh wrote were greater than 480,000, while 2 out of the 6 possible numbers are less than 480,000
Step-by-step explanation:
The given parameters are;
The number with which Josh wrote the whole number = 8, 4, 7, 2, 9, and 0
The number in the thousands of the whole number that Josh wrote = 7
The number in the tens of the whole number that Josh wrote = 2
The value of the whole number that Josh wrote < 500,000
Therefore, we have;
The possible numbers in the hundreds of thousands place = 4, and 2
Which gives the following possible combinations;
The number of ways of selecting the first number = 1 way, the number is 4 to make the value less than 500,000
The number of ways of selecting the second number = 3 ways
The number of ways of selecting the third number = 1 way, the number is 7
The number of ways of selecting the fourth number = 2 ways as there are only two numbers left after filling the second place digit
The number of ways of selecting the fifth number = 1 way, the number is 2
The number of ways of selecting the sixth number = 1 ways
The total number of possible number combinations = 3×2×1 = 6 possible numbers, which are;
487920 or 497820 or 407829 or 407928 or 487029 or 497028
Therefore, 2 out of the numbers are less than 480,000, the remaining 4 possible numbers are larger than 480,000.
What is the value of x?
5 + 2/3x = -x + 20
Please explain:
The value of X is 9.
Solve for x by simplifying both sides of the equation, then isolating the variable.
An airplane flew across the Pacific Ocean. The table
shows the amount of
time and the distance traveled when the airplane was traveling at a
constant speed. Complete the table with the missing values.
time (hours) distance traveled (miles)
row 12
row 23
1,650
row 36
Answer:
1hr= 550 miles