They would meet 30 times after 10 minutes.
Since Nick and Sally run on the 100m straight track, and Nicks's speed is 3m / s, while Sally's speed is 2m / s, if they both start from two sides of the track, running towards each other continuously, to determine how many times they would meet each other after 10 minutes the following calculation should be performed:
30 x 20 + 2 x 20 = 60 + 40 = 100 10 minutes = 600 seconds 600/20 = X 30 = X
Therefore, they would meet 30 times after 10 minutes.
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two mountain bikers leave from the same parking lot and head in opposite directions on two different trails. the first rider goes 8km due east, then rides due south for 15km. The second rider goes 8km due west, then changes directions and rides 20 degrees west of due north for 15km. Both riders have been traveling for 23km, but which one is further from the parking lot?
Applying the required rule or theorem, it can be concluded that the second biker is farther from the parking lot. The distance of the bikers to the parking lot are:
i. First biker = 17.0 km
ii. Second biker = 20.22 km
The path of travel of both bikers would form a triangle. Applying the Pythagoras theorem to the path of the first biker would give his distance from the starting point. While applying the cosine rule to the path of second rider would gives his distance to the starting point.
Thus,
a. To determine the distance of the first biker from the parking lot.
Let the required distance be represented by x. Applying the Pythagoras theorem, we have:
[tex]hyp^{2}[/tex] = [tex]adj 1^{2}[/tex] + [tex]adj 2^{2}[/tex]
[tex]x^{2}[/tex] = [tex]8^{2}[/tex] + [tex]15^{2}[/tex]
= 64 + 225
= 289
x = [tex]\sqrt{289}[/tex]
= 17
x = 17 km
Thus, the first biker is 17.0 km from the starting point.
b. To determine the distance of the second biker from the parking lot.
Let the required distance be represented by x. So that applying the cosine rule, we have:
[tex]c^{2}[/tex] = [tex]a^{2}[/tex] + [tex]b^{2}[/tex] - 2ab Cos θ
[tex]x^{2}[/tex] = [tex]8^{2}[/tex] + [tex]15^{2}[/tex] - 2(15*8) Cos (180 - 20)
= 64 + 225 - 240 Cos 160
= 289 - 240 * -0.5
[tex]x^{2}[/tex] = 289 + 120
= 409
x = [tex]\sqrt{409}[/tex]
= 20.2237
x = 20.22 km
Thus, the second biker is 20.22 km from the starting point.
Therefore, the second biker is farther from the parking lot.
A sketch of the path of travel for the two bikers is attached for more clarifications.
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Solve for x. I need help understanding my math.
Answer:
x = 33
Step-by-step explanation:
11 - 4 = 7
You need to make that fraction equal 11
33/3 = 11
I hope this helps!
List the angles of A KLM with vertices
K(-2,-2), L(2, 6), M(7, -2) in order
from smallest to largest.
The required angles from smallest to largest are m<M < m<L < m<K
Given the coordinate of the triangle KLM given as K(-2,-2), L(2, 6), M(7, -2)
The angle opposite the side KL is m<MThe angle opposite the side KM is m<LThe angle opposite the side LM is m<KGet the measure of KL, KM and LM using the distance formula as shown:
[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y)_1)^2}[/tex]
For the length KL with coordinate points K(-2,-2), L(2, 6)
[tex]KL=\sqrt{(2-(-2))^2+(6-(-2))^2}\\KL=\sqrt{4^2+8^2}\\KL=\sqrt{16+64}\\KL=\sqrt{80}\\KL =4\sqrt{5}[/tex]
For the length KM with coordinate points K(-2,-2), M(7, -2)
[tex]KM=\sqrt{(7-(-2))^2+(-2-(-2))^2}\\KM=\sqrt{9^2+0^2}\\KM=\sqrt{81}\\KM=9[/tex]
The length LM with coordinate points L(2,6), M(7, -2)
[tex]LM=\sqrt{(7--2)^2+(-2-6)^2}\\LM=\sqrt{5^2+(-8)^2}\\LM=\sqrt{25+64}\\LM=\sqrt{89}[/tex]
From the distances, we can see that side LM > KM > KL. Hence the required angles from smallest to largest are m<M < m<L < m<K
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Can someone help help me
Answer:
15π/2 ft
Step-by-step explanation:
Arc length is given by the formula ...
s = rθ . . . . . r = radius; θ = central angle in radians
A 135° arc has a radian measure of (135)(π/180) = 3π/4. The radius of a circle with a 20 ft diameter is (20 ft/2) = 10 ft. So, the arc length is ...
s = (10 ft)(3π/4) = 30π/4 ft = 15π/2 ft
the sum of two numbers x and y is 18 and their difference is 14. how is that written as an equation
Answer:
16 and 2
Step-by-step explanation:
16+2=18
16-2=14
Solve for x in the hanger below
Answer:
x=3
Step-by-step explanation:
How many fish are in the aquarium in the restaurant?
Answer:
Which Restaurant and aquarium
Step-by-step explanation:
If you tell the name I can answer it
Hey y’all please help me ASAP.
Answer:
the top right box
Step-by-step explanation:
Answer:
-g-8≥9
Step-by-step explanation:
Just ask.
Hope this helps. :)
If you want 10 points answer my question
Plz
A car is traveling at 55km/hr and has a mass of 1200 kg. What is the momentum of the car?
Thank you for whoever solves this, I will make sure to add brainliest if possible
Answer:
66,000 kg·km/hr
Step-by-step explanation:
p = mass × velocity
p = (1200 kg) × (55 km/hr) = 66,000 kg·km/hr
_____
Additional comment
Here, we have used the standard metric units for momentum. The units you choose can be any mass·velocity units that meet your needs.
What is the domain and range of this graph??
Answer: D: (-∞, ∞)
R: (-∞, ∞)
Step-by-step explanation:
Since the end points are arrows and have no set stopping point we can assume the answer is all real numbers, also known as infinity
write 2 equivalent expressions for each and find the total price the price of a belt is $30 the belt is makeup 60%
Calculator
What is the value of x
Answer:
71.8
Step-by-step explanation:
There are 100 students in the sixth grade. The ratio of boys to girls is 2:3. How many more girls than boys are in the sixth grade?
Answer: I Think you will make 100 time 2 divide 3
Step-by-step explanation:
i'm not sure, have a nice day
1 point
4.) Tom's goal is to save an average of $55 a week for six weeks. For the
first five weeks he saved 45, 60, 25, 50, 55. What is the smallest amount he
can save in week 6 to meet his goal?
80
55
95
65
Paul has thirteen coins in his piggy bank. Some of the coins are quarters, some are nickels, and he has a total of $3.55. Which system of equations can be used to determine how many quarters, x, and how many nickels, y, he has?
A.
x + y = 13
0.25x + 0.5y = 3.55
B.
x + y = 13
0.25x + 0.05y = 3.55
C.
x + y = 13
25x + 5y = 3.55
D.
x + y = 3.55
0.25x + 0.05y = 13
Answer:
The answer is B
If the Fed's reserve requirement is 5 percent, then what quantity of excess reserves does the Bank of Cheerton now hold?
The quantity of excess reserves that the Bank of Cheerton now hold is $210
From the attached table, the amount generated on the reserve is $4,200
If the Fed's reserve requirement is 5 percent, then the quantity of excess reserves that the Bank hold is given as:
Quantity of excess reserves = 5% of $4,200
Quantity of excess reserves = 0.05 * 4200
Quantity of excess reserves = $210
Hence the quantity of excess reserves that the Bank of Cheerton now holds is $210.
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Suppose you have 5 different colored shirts (grey, white, black, brown, and orange) and 4 kinds of pants (jeans, sweatpants, khakis, and plaid).
What is the probability on Monday you wear a grey shirt with jeans and put it in the laundry, then on Tuesday wear a black shirt with sweatpants?
OA)
OB)
OC)
OD
Done and Review
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INTL 0
Answer:
A
i will go with a. hope to help u
Need help desperately
Answer:
a) 4cd²
b) 3a²b³
Step-by-step explanation:
a) 8c⁴d⁵/2c³d³
1: you would divide the 8 by 2
2: subtract the exponents on c so it would be 4-3 = 1
3: subtract the exponents on d so it would br 5-3 = 2
4: put it all together so it would be 4c¹d² but you dont need the 1 above c
b) 1: divide 9 by 3
2: subtract exponents on a so it would be 3-1 = 2
3: subtract exponents on b so it would be 5-2 = 3
4: put it all together so it would be 3a²b³
hope this helped!! :)
Answer:
a. 4cd² b. 3a²b³
Step-by-step explanation:
[tex]\frac{8c^4d^5}{2c^3d^3}[/tex]
= [tex]\frac{8}{2} ( \frac{c^4}{c^3} )(\frac{d^5}{d^3})[/tex]
= [tex]\frac{4}{1} (\frac{c}{1}) (\frac{d^2}{1} )[/tex] Reduce number. Substract exponent largest power
smallest power
= 4cd²
b. [tex]\frac{9a^3b^5}{3ab^2}[/tex]
[tex]\frac{9}{3} (\frac{a^3}{a} ) (\frac{b^5}{b^2} )[/tex]
[tex]\frac{3}{1} (\frac{a^2}{1}) (\frac{b^3}{1} )[/tex] Reduce number. Substract exponent largest power
smallest power
= 3a²b³
Suppose you want to have $600,000 for retirement in 20 years. Your account earns 9% interest. How much would you need to deposit in the account each month?
I don’t understand this question
Answer:
1/64
Step-by-step explanation:
Answer: that would be 1/64
Step-by-step explanation:
for this type of question you put it 1/ such as:[tex]\frac{1}{8*8}[/tex] i got 8*8 because of The 8^2
and 8*8=64 therefor the answer is 1/64
*you put it over 1 to get rid of the negative exponents*
HELP PLEASE. The product of the roots of the equation ax^2+x-24=0 is equal to -2 2/5. Find the value of a in the equation.
The value of a in the equation is 10
The root of the equation is determined using the equation shown below:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]
Given the quadratic equation ax^2+x-24=0;
a = ab = 1c = -24The product of the quadratic equation is c/a
Product = c/a
- 2 2/5 = -24/a
-12/5 = -24/a
-12a = 5 * -24
-12a = -120
a = 10
Hence the value of a in the equation is 10
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Compare to ax^2+bx+c
b=1c=-24a=aProduct of roots=c/a
ATQ
[tex]\\ \tt\hookrightarrow \dfrac{c}{a}=-2\dfrac{2}{5}[/tex]
[tex]\\ \tt\hookrightarrow \dfrac{-24}{a}=\dfrac{-12}{5}[/tex]
[tex]\\ \tt\hookrightarrow \dfrac{24}{a}=\dfrac{12}{5}[/tex]
[tex]\\ \tt\hookrightarrow 12a=120[/tex]
[tex]\\ \tt\hookrightarrow a=10[/tex]
Solve 7,030 ÷ 3 using the division algorithm ?????????????????
Answer: 2,343.3333 repeating, or just 2,343 1/3
Step-by-step explanation:
If you divide, your answer comes out to be 2,343.3333 repeating or 2,343 1/3.
Over what interval is the graph of
y=-2 + 1x - 2 increasing?
how many would juile see?
Answer:
12Step-by-step explanation:
4*4*__=48
16*__=48
48/16=3
3*4=12
Answer:
12 boxes on the right side
Step-by-step explanation:
4 going across and 3 rows so 12 boxes
48 divided by 3 is 16 but divided by 4 is 12
since there are 16 boxes at the top its a good inference that there's
only 3 flat rows meaning per every flat there would be 4 boxes and 3 rows
there would be 12 boxes on the right side.
HELP please it’s due in a hour
Answer:
5 m, 2 m, 2.5 m, 2 m, 2.5 m, 4 m.
Step-by-step explanation:
First find the length of the 2 missing sides. Remember that the picture is WAY out of proportion, so the sides won't be what they look like.
Since the left side is 4 and the right side is 8 cm, the missing left side is 4 cm.
Since the top side is 5 and the bottom side is 10 cm, the missing top piece is 5 cm.
So the sides starting at the bottom right and going clockwise are 10, 4, 5, 4, 5, 8 cm. Multiply each of these * 0.5 and call them meters.
5 m, 2 m, 2.5 m, 2 m, 2.5 m, 4 m.
Please help me I need help
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Josh went to a restaurant for dinner. The cost of the
meal was $24 with a discount of $2. If the total bill includes
an 8% sales tax and a 14% tip, what is the discount
percent? What was the total bill including the tax and the
tip?
Answer:
17.41 Dollars
Step-by-step explanation:
First, you take the discount, which is 2 dollars, so now the cost without any additional costs is 22 dollars. Next, find 8 percent of 22 by multipling 22*0.08 and then you get 1.76. Subtract that from 22 and 20.24. Then take 14 percent of 20.24 by multiplying it by 0.14, which you get 2.8336. Round that down and you get 2.83. Subtract that from that and you get 17.41.
Use the original price and the markdown to find the retail price.
Original price: $130; Markdown: 28%
Answer:
The retail price would be $93.6
Step-by-step explanation:
This is because you can divide 130 by 100 to find 1% of such, and you'll get 1.3. Then, multiply 1.3 by 72, which makes 72% of the original price, to come find your answer, $93.6. Hope this helps!
At the pool, three out of every seven kids are not wearing goggles. Which of the following is the fraction of kids who are not wearing goggles?
A : 4/7
B : 3/7
C : 3/4
D : 4/3
Answer:
B.3/7
Step-by-step explanation: