A girl delivering newspapers travels 2 blocks west, 5 blocks north, and then 6 blocks east.
What is her resultant displacement?
___blocks at
____ ° counterclockwise from east.
Answers
Define the displacement in the east as positive and displacement north as positive in y.
1st travel = (-2, 0) 2 blocks west
2nd travel = (0, 5) 5 blocks north
3rd travel = (6, 0) 6 blocks east
Add x and y components for total displacement
Total x-displacement = -2 + 0 + 6 = 4
Total y-displacement = 0 + 5 + 0 = 5
The resultant displacement (from the Pythagorean theorem) is
d = √(4² + 5²) = 6.403 blocks
The angle that the resultant makes with the x-axis is
tan θ = 5/4 = 1.25
θ = tan⁻¹ 1.25 = 51.3°
Answer:
6.4 blocks
51.3° counterclockwise from east
Related Questions
3x+1<2x-3 what is x
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3x less 2x-4
x less -4
how to determine if a number is prime or composite
Answers
Answer:
Look at how many factors it has.
If it has 2, it's prime.
If it has 3 or more, it's composite.
Step-by-step explanation:
I hope it helps!
Which of the following expressions is equal to 5 - 2m?
7 - 2(m + 1)
7 - (2m - 5)
7 - 2(m - 2)
Answers
△RST is mapped to △R′S′T′ using the rule (x, y)→(x, −y) followed by (x, y)→(3x, 3y) .
Which statement correctly describes the relationship between △RST and △R′S′T′ ?
△RST is not congruent to △R′S′T′ because the rules do not represent a sequence of rigid motions.
△RST is congruent to △R′S′T′ because the rules represent a reflection followed by a rotation, which is a sequence of rigid motions.
△RST is congruent to △R′S′T′ because the rules represent a reflection followed by a translation, which is a sequence of rigid motions.
△RST is congruent to △R′S′T′ because the rules represent a rotation followed by a translation, which is a sequence of rigid motions.
Answers
(y->-y) followed by a dilation (x->3x, y->3y). Reflections and rotations ARE congruent because rigid motions, but dilations/contractions change size, are NOT rigid, and therefore NOT congruent.
Question 2 says: With out multiplying, determine the sign of the product
(19)(-2)(37)(-0.8)(122)
A.Positive
B.Negative
C.The product is zero
Answers
in this case, there are two negatives, the the product is a positive number
Write y-6x-9=0 in function notation
Answers
y - 6x - 9 = 0
y = 6x + 9
now, to put it in function notation, sub in f(x) for y
f(x) = 6x + 9 <== function notation
hope this helps:D
plz give brainiest
Find the domain and range of the following function ƒ(x) = 3|x + 7| - 2?
A.Domain: [-2,∞) Range: (-∞,∞)
B.Domain: (-2,∞) Range: (-8∞,∞)
C.Domain: (-∞,∞) Range: [-2,∞)
D.Domain: (-∞,∞) Range: (-2,∞)
Answers
Answer:
D.Domain: (-∞,∞) Range: (-2,∞)
is the right answer.
Step-by-step explanation:
Given is a function as
[tex]f(x) = 3|x+7|-2[/tex]
This is an absolute value function hence the minimum value of
|x+2|=0
Hence the range cannot be below -2
For maximum no limit
[tex]Range = [-2,\infty)[/tex]
Domain can be any real value
Hence option d is correct answer.
Answer:
A) domain: (-∞, ∞) range: (-∞, ∞)
Step-by-step explanation:
How many feet does it take to go from 0 to 60?
Answers
A sample of water is heated from 10.0 (degrees Celsius) to 15.0 (degrees Celsius) by the addition of 125 J of heat. What is the mass of the water?
(I understand what the question is asking me and I know that I have to use the formula q=m•c•DT but I don’t understand how to plug in a specific heat capacity if they don’t give it to me. Please help!!)
Answers
what is 10 times as much as 1.0
Answers
Hope this helps!!
Find the distance between the given points . find the midpoint of the segment with the given endpoints. round to the nearest tenth, if necessary
Answers
Find area of a rectangle
Answers
Area = l*w = 72
L = 72/w
Perimeter = 2l+ 2w
44 = 2(72/w) +2w
22 = 72/w +w
W^2-22w +72 =0
(w-18) (w-4) = 0
W = 18
L = 4
Which of the following terms are like 3x^2y? Select all that apply.
3xy
3x^2y^2
-10x^2y
12xy^2
12x^2y
Answers
-10x^2y
12xy^2
12x^2y
all have Roots of x=0 and y=0
for a school field trip, there must be 1 adult to accompany 12 students, 3 adults to accompany 36 students, and 5 adults to accompany 60 students. Show that the relationship between the number of adults and the number of students is a proportional relationship. then write an equation for the relationship?
Answers
x is amount of adult
y is the student
-i hope this helps and have a wonderful day!!
PLEASE HELP ME ANSWER THIS
Answers
Answer:
25
Step-by-step explanation:
It is the product of the 3rd row of the first matrix with the second column of the second matrix:
(5)(8) +(-2)(6) +(1)(-3) = 40 -12 -3 = 25
Is the mass of one pound of lead greater than less than or equal to one pound of feathers?
Answers
The correlation coefficient (r) between the number of miles driven x and the number of gallons of gasoline used y is 0.925
What percent of the variation in the number of gallons of gasoline can be explained by differences in the number of miles driven?
7.5%
14.4%
85.6%
92.5%
Answers
Answer:
OptionC
Step-by-step explanation:
Given that the correlation coefficient (r) between the number of miles driven x and the number of gallons of gasoline used y is 0.925
Coefficient of determination = square of r
= 0.8556
=85.6%
Hence the percent of the variation in the number of gallons of gasoline can be explained by differences in the number of miles driven is 85.6%
Option C
A rectangle with an area of 120 in 2 has a length 8 inches longer than two times its width. What is the width of the rectangle?
Answers
width = x
length = 2x+8
area = l x w
x(2x+8)=120
2x^2+8x−120=0
x^2+4−60=0
(x+10)(x−6)=0
x=−10 and x=6
width has to be a positive number
Width = 6
inches.
Suppose a college student pays $500 for tuition fees. However, she also has to pay $350 for her textbooks (ouch!). What percent of her total education costs does she pay for her books?
Answer: Her books represent
percent (as a decimal) of her total costs.
Write your answer to the nearest tenth of a percent, but in decimal form. For example, if you saved 34.67%, you would round to 34.7% and enter .347 as your answer.
Answers
Textbook costs = $350
Total cost = 500 + 350 = $850
Percent of costs due to textbooks = 100*(350/850) = 41.1765%
Her books represent 41.2% of her total costs.
Answer: 0.412
The line graphed by the original function f(x)=13x+1 is translated to g(x)=13x−17 using the mapping statement f(x)↦f(x)+k. What is the value of k?
Answers
k = g(x) - f(x)
k = 13x - 17 -(13x +1)
k = 13x -17 - 13x -1
k = -18
Complete the pattern 5, 10, 30, 60, 180
Answers
5*2=10
10*3=30
30*2=60
60*3=180
180*2=360
360*3=1,080
Deangelo has $7 worth of dimes and quarters in a jar. He has 7 more quarters than dimes. How many of each coin does he have? Enter your answers in the boxes. _dimes and _ quarters
Answers
q = d + 7
0.10d + 0.25(d + 7) = 7
0.10d + 0.25d + 1.75 = 7
0.35d = 7 - 1.75
0.35d = 5.25
d = 5.25 / 0.35
d = 15 <=== there are 15 dimes
q = d + 7
q = 15 + 7
q = 22 <== there are 22 quarters
Answer:
There are 15 dimes and 22 quarters in the jar.
Step-by-step explanation:
Deangelo has $7 worth of dimes and quarters in a jar.
Let he has d number of dimes and q number of quarters in a jar.
0.10d + 0.25q = 7 -------(1)
He has 7 more quarters than dimes.
q = d + 7 -------(2)
We replace the value of y from equation 2 in the equation 1
0.10d + 0.25(d + 7) = 7
0.10d + 0.25d + 1.75 = 7
0.35d = 7 - 1.75
0.35d = 5.25
d = [tex]\frac{5.25}{0.35}=15[/tex] dimes
Now we put this value in the equation number 2
q = 15 + 7 = 22
Therefore, number of dimes and quarters are 15 and 22 respectively.
Urgent PLEASE!!!!!!!!!!!!!!!!!!
A bicycle manufacturing company makes a particular type of bike. Each child bike requires 4 hours to build and 4 hours to test. Each adult bike requires 6 hours to build and 4 hours to test. With the number of workers, the company is able to have up to 120 hours of building time and 100 hours of testing time for a week. If c represents child bikes and a represents adult bikes, determine which system of inequality best explains whether the company can build 20 child bikes and 6 adult bikes in the week.
No, because the bike order does not meet the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100
No, because the bike order does not meet the restrictions of 4c + 4a ≤ 120 and 6c + 4a ≤ 100
Yes, because the bike order meets the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100
Yes, because the bike order meets the restrictions of 4c + 4a ≤ 120 and 6c + 4a ≤ 100
Answers
20(4) +6(6) = 80 +36 = 116 total building time
20(4) +6(4) = 80 +24 = 104 total testing time ( this is greater than the allowed 100 hours)
Answer is: No, because the bike order does not meet the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100
Answer:
?
Step-by-step explanation: got 2 ur my streaks back up my n1g but i agree with the other person feel me.
If a barber is capable of cutting the hair of 35 people per day and he works 7 days per week, how many haircuts could he give during the months of april, may, and june?
Answers
April=1,225
May=1,225
All June April and May is 3,675 haircuts
BD =4x + 5 and BF =9x
How to slove this problem
Answers
The centroid theorem, the value of x is: 2.5.
According to the centroid theorem, the centroid of a triangle is two-thirds of the distance from each midpoint to each vertex.
Given:
BD = 4x + 5
BF = 9x
Thus:
BD = 2/3(BF)
Replace 4x + 5 = 2/3(9x) with
4x + 5 = 6x
4x - 6x = -5
-2x = -5
x = 5/2
x = 2.5
As a result of the centroid theorem, the value of x is: 2.5.
Complete question:
Point D is the centroid of △ABC. Use the given information to find the value of x.
BD=4x+5 and BF=9x
x=
how to solve log base 5 of x + log base 5 of (4x-1)
Answers
As the bases are the same the number doesn't matter
Log (a) + log(b) =log (ab)
Log(4x^2-x)
(x )(4x-1)
x=0.25 or x=0
Log(4×0.25^2-0.25) = log(0) = Infinity
Same with 0. So no answer
To solve for log base 5 of x + log base 5 of (4x-1), combine the two logarithms using the property that the sum of logarithms is equal to the logarithm of the product: log base 5 of x + log base 5 of (4x-1) = log base 5 of (x(4x-1)).
To solve the logarithmic expression log5(x) + log5(4x-1), we can combine the two logarithms using the property that the sum of logarithms is equal to the logarithm of the product. This gives us:
log5(x) + log5(4x-1) = log5(x(4x-1))
So the solution to the expression is log5(x(4x-1)).
Which of the following sets is a function?
{(0, 1), (-2, 8), (5, 19), (2, 8)}
{(1, 0), (11, 0), (-5, 7), (1, 9)}
{(17, -8), (1, 16), (53, 9), (1, 23)}
Answers
{(0,1), (-2,8), (5,19), (2,8)}....this has no repeating x values and is therefore, a function
A collection of dimes and nickels is worth $5.60. The ratio of dimes to nickels is 3:2. How many dimes and how many nickels are there?
Answers
$5.60 is just 560 pennies
3 dimes is just 30 pennies
2 nickels is just 10 pennies
so, the ratio from dimes to nickels is a ratio of 30:10 pennies, or 3:1 then, for a total amount of 560 pennies.
[tex]\bf \cfrac{dimes}{nickels}\qquad 3:2\qquad\cfrac{\stackrel{pennies}{30}}{\stackrel{pennies}{10}}\implies \cfrac{30}{10}\implies \cfrac{3}{1}\implies 3:1~ratio \\\\\\ \cfrac{\stackrel{dimes}{pennies}}{\stackrel{nickels}{pennies}}\qquad 3:1\qquad \cfrac{3}{1}\implies \cfrac{3\cdot \frac{560}{3+1}}{1\cdot \frac{560}{3+1}}\implies \cfrac{3\cdot 140}{1\cdot 140}\implies \cfrac{420}{140}\\\\ -------------------------------[/tex]
[tex]\bf \textit{now, how many dimes in 420 pennies?}\quad \cfrac{420}{10}\implies 42~dimes \\\\\\ \textit{and how many nickels in 140 pennies?}\quad \cfrac{140}{5}\implies 28~nickels\\\\ -------------------------------\\\\ 42~dimes + 28~nickels\implies \$5.60[/tex]
There are 42 dimes and 14 nickels there if the collection of dimes and nickels is worth $5.60
First, we need to convert dimes and nickel to pennies to have:
1 dime = 10 pennies
1 nickel = 5 pennies
Since the ratio of dimes to nickels is 3:2, this shows that we have 30 dimes and 10 pennies
Total pennies = 30 + 10 = 40 pennies
Since the total collection of dimes and nickels is worth $5.60, this means that the total collections in pennies are 560 pennies ($1 is 100 pennies)
Number of pennies for the ratio of 30 = 30/40 * 560
Number of pennies for the ratio of 30 = 420
Number of dimes = 420/10 = 42 dimes
Number of pennies for the ratio of 10 = 10/40 * 560
Number of pennies for the ratio of 10 = 140
Number of nickel = 140/10 = 14 nickels
Hence there are 42 dimes and 14 nickels there if the collection of dimes and nickels is worth $5.60
Learn more here: https://brainly.com/question/25090040
One inlet pipe can fill an empty pool in 4 hours, and a drain can empty the pool in 8 hours. how long will it take the pipe to fill the pool if the drain is left open?
Answers
Given that one inlet pipe can fill an empty pool in 4 hours. The outlet pipe can empty the pool in 8 hours. We know that rate x time = work done.
Rate = work done / time
Rate of inlet pipe = ¼ hours.
Rate of outlet pipe = 1/8 hours
Here 1 represent the work completed.
Let x be the time taken to fill the pool by the inlet pipe if the drain is left.
Work done by inlet pipe – work done by outlet pipe = 1 work completed.
x/4 – x/8 = 1.
To solve the rational equation, first we clear the fractions by multiplying it with LCD (4,8)=8 to each item.
8(x/4) – 8(x/8) = 8(1)
2x – x = 8
X = 8
Time taken for the pipe to fill the pool if the drain is left open = 8 hours
What is the value of x? x+13=9
Enter your answer in the box in simplest form.
x =
Answers
x=6
that answer is 6