The distance between Reeta and the school when the cyclists arrive the home for this case is found to be 2 km
How to form mathematical expressions from the given description?You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example, if it is asked to increase some items by 4, then you can add 4 in that item to increase it by 4. If something is, for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert descriptions to mathematical expressions.
How to find the speed of an object?
If the object is going linearly, and at a constant speed, then the speed of that object is given by the distance it travelled to the time it took to travel that distance.
If the object travelled D distance in T units of time, then that object's speed is
[tex]Speed = \dfrac{D}{T}[/tex]
Given that:
Distance from school to home = 5 kmWalking speed = 4 km / hoursCycling speed = 5 times walking speed = 20 km / hourThey all go and come together to and from school/home.On Monday: Nikita and Peter are coming by cycle, and Reeta walks.Cycle punctures at four-fifth of the way home = [tex]\dfrac{4}{5}\times 5[/tex] from school (as they're coming towards home, so went from school)After a puncture, cyclists walk to homeTo find the Distance of Reeta from school when the cyclist reaches home.Suppose at time 0 hours, all three people departed from school (on that Monday).
After 't' hours, suppose the cycle gets punctured.
Then, as the cycle was going by 20 km/hour speed, so in 't' hours, it must have covered d kilometres (suppose),
then we get:
[tex]S =\dfrac{D}{T}[/tex]
[tex]20=\dfrac{d}{t}[/tex]
d = 20t
This distance is measured from school. But we know that this distance is 4 km, so we get:
20t = 4
t = 1 / 4
The remaining 1 km (as the home is 5 km away from school and 4 km is already travelled) is walked by Cyclists. And walking speed is 5 km/hour, so let they take T hours to travel that 1 km walking, then we get:
5 = 1 / T
t = 0.2 hours
So, the total time cyclists took to reach home from school is: 0.2+0.2=0.4 hours
Reeta is walking that whole 5 km.
The time the cyclist reached home, Reeta had walked for 0.4 hours as they had started at the same time, and it took cyclists 0.4 hours to reach home.
Thus, we have:
Time is taken 0.4 hours, speed of Reeta = walking speed= 5 km/hour, then we get:
D = S x T
D = 5 x 0.4 = 2 km
So Reeta was 2 km away from school when cyclists reached home on that Monday.
Thus, the distance between Reeta and the school when the cyclists arrive at the home for this case is found to be 2 km
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Please help me find the answer to this problem.
Answer:
numerator - is 2, 15, 18, 6
denominator - is 12, 14, 33, 8, 64
Step-by-step explanation:
2/10, 4/12, 8/14, 9/33, 1/8, 12/64, 15/55, 18/66, 6/32
The first buses to X and Y leave a bus station at 7 am
Buses to X leave every 25 minutes.
Buses to Y leave every 20 minutes.
When will the buses to X and Y next leave at the same time
The time at which the buses will leave at the same time is 8:40 am.
What is a factor?A factor is a number that divides another number, leaving no remainder
Example: 3 x 2 = 6
2 is a factor of 3.
We have,
Buses:
X leaves every 25 minutes.
Y leaves every 20 minutes.
We need to find the least common multiples of 25 and 20.
25 x 4 = 100
20 x 5 = 100
100 is our least common multiple of 25 and 20.
We see that,
4 is a factor of 24 which gives 100.
This means after 4 times, bus X will leave with bus Y at the same time.
5 is a factor of 20 which gives 100.
This means after 5 times, bus Y will leave with bus X at the same time.
The first buses to X and Y leave a bus station at 7 am.
After 100 minutes, buses X and Y will leave at the same time.
= 7am + 100 minutes
= 7 + 60 minutes + 40 minutes
= 7 + 1 hour + 40 minutes
= 8:40 am
Thus,
The time at which the buses will leave at the same time is 8:40 am.
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The measures of the angles of a triangle are shown in the figure below solve for X
Answer:
36
Step-by-step explanation:
We know all angles in a triangle must add up to 180°
The square in the triangle that angle is equal to 90°
We can now solve for x
90 + 54 + x = 180
144 + x = 180
x = 36
That is your answer
- Kan Academy Advance
Which of these tables does NOT represent a function?
Find the magnitude of the sum of the vectors <4,5> and <-2,2>. Round your answer to the nearest 100th.
Answer:
[tex]||v||\approx7.28[/tex]
Step-by-step explanation:
Sum of the vectors
[tex]\langle4,5\rangle+\langle-2,2\rangle=\langle4+(-2),5+2\rangle=\langle2,7\rangle[/tex]
Magnitude of the resultant vector
[tex]||v||=\sqrt{x^2+y^2}=\sqrt{2^2+7^2}=\sqrt{4+49}=\sqrt{53}\approx7.28[/tex]
HELPPPP WITH MATH HOMEWORK PLS
Answer:
The length of the wing is 480 centimeters
Step-by-step explanation:
2 cm on the drawing is 192 cm on the acutal wing
2 = 192
divide both sides by 2
1 = 96
since the drawing has a length of five cm, multiply both sides by 5
5 = 480
therefore, 5 cm on the drawing is equal to 480 cm on the actual wing
What is the sum of the two
expressions?
(4/5x+13) - (5/8x − 6)
Answer: 7/40x + 19
Step-by-step explanation:
---Distribute the negative sign
4/5x + 13 - 5/8x + 6
---Get common denominators on the fractions
32/40x + 13 - 25/40x + 6
---Combine like terms
(32/40x - 25/40x) + (13 + 6)
7/40x + 19
Answer: 7/40x + 19
Hope this helps!
please help i dont get it... (average rate of change)
10.
The graph shows the price, in dollars, of a new digital toy for different levels of supply.
(image provided)
What is the average rate of change?
Answer:
-3
Step-by-step explanation:
Formula for average rate of change :
A(x) = f(a) - f(b) / a - bSolving :
A(x) = 115 - 85 / 5 - 15A(x) = 30/-10A(x) = -3A consumer takes a loan of $150,000 to be repaid in monthly constant installments over 10 years. the nominal interest rate compounded monthly for this loan is 3.6331%.
Answer:
$10.862005 million
Step-by-step explanation:
150,000*1.036331 monthly
12*10=120
$150,000*1.036331 ^120=$10.862005 million
seams very unrealistic lol
Answer:$10.862005 million
Step-by-step explanation:
150,000*1.036331 monthly
12*10=120
$150,000*1.036331 ^120=$10.862005 million
GIVING BRAINLIEST!!!!!
Step-by-step explanation:
144 degree is right answer.
Answer:
144°
Step-by-step explanation:
The central angle is 360°. Since it has 5 divisions, the angle of each division is 72°.
From B to D, it requires 2 rotations.
Rotation angle needed = 72° × 2Rotation angle needed = 144°I need the numbers please con y’all help me
Answer:
y=2/3x+4
Step-by-step explanation:
4 is y-intercept
2/3 is the slope (rise/run)
Answer: y = [tex]\frac{2}{3}[/tex]x + 4
Step-by-step explanation:
This is in slope-intercept form. We are missing the m and the b value. See attached for more information.
[m aka the slope]
Starting from point (-6, 0), counting up 2 units, then right 3 units to point (-3, 2), gives us a slope of [tex]\frac{2}{3}[/tex] via rise-over-run
[b aka the y-intercept]
The line intersects the y-axis at positive 4.
-> This value is "4"
write 8.31752 to correct 3 decimal places
Answer:
8.318
Step-by-step explanation:
writing a number in three decimal places means writing the number in a way that there will be three digits in the number after the decimal point.
to three decimal places= 8.318
50 points Select the correct answer
Which expression is equivalent to the given expression? Assume the denominator does not equal zero.
Answer:The answer is A: b^4/a
Step-by-step explanation:now i dont rly have an explaination but i got this in my test so ik its right!
100% verrified!
Cookie jar contains 6 vanilla cookies, 4 chocolate cookies, and 9 lemon cookies.
one cookie is randomly picked from the jar.
find p (a vanilla cookie) =
p (a chocolate or lemon cookie) =
p (not a lemon cookie) =
p (a vanilla or chocolate or lemon) =
p (a peanut butter cookie) =
p (a vanilla cookie) = 6/19
p (a chocolate or lemon cookie) = 13/19
p (not a lemon cookie) = 10/19
p (a vanilla or chocolate or lemon) = 10/19
p (a peanut butter cookie) = [There's no peanut in the info you gave, sorry]
If you can simplify the fractions, then simplify
An ordinary (fair) die is a cube with the numbers 1 through 6 on the sides (represented by painted spots). Imagine that such a die is rolled twice in succession and that the face values of the two rolls are added together. This sum is recorded as the obtcome of a single trial of a random experiment. Compute the probability of each of the following events. Event A: The sum is greater than 6. Event B: The sum is divisible by 4. Write your answers as fractions.
Answers:
P(A) = 7/12
P(B) = 1/4
====================================================
Explanation:
Instead of having one die, let's say we have two dice. I'll make one red and the other blue.
I'll be using the dice chart shown below. The red and blue values add up to the black numbers inside the table. For instance, we have 1+1 = 2 in the upper left corner. There are 6*6 = 36 sums total.
Using that table, we can see the following:
There are 6 copies of "7"There are 5 copies of "8"There are 4 copies of "9"There are 3 copies of "10"There are 2 copies of "11"There is 1 copy of "12"In total, we have 6+5+4+3+2+1 = 21 instances where the two dice add to something larger than 6.
This is out of 36 ways to roll two dice.
Therefore P(A) = 21/36 = (3*7)/(3*12) = 7/12
-----------------------------------
If a number is divisible by 4, then it is a multiple of 4.
The multiples of 4 found in the table are: 4, 8, 12
We have
3 copies of "4"5 copies of "8"1 copy of "12"This gives 1+5+3 = 9 values that are a multiple of 4
P(B) = 9/36 = (1*9)/(4*9) = 1/4
Find the equation of a line that passes through the point (2,4) and has a gradient of 1/3 . leave your answer in the form y = m x + c
Answer:
y = mx + b
y = 1/3x + b
Use (2,4) to find b
4 = 1/3(2) + b
b = 4 - 2/3
b = 12 - 2
3
b = 10/3
The equation will be:
The equation will be: y = 1/3x + 10/3
solve the inequality 9.5+6x>=42.1
Answer:
x >/= 8.6
Add 9.5 to 42.1 then divide by 6
Step-by-step explanation:
which postulate or theorem proves that these two triangles are congruent?
a. ASA Congruence Postulate
b. SAS Congruence Postulate
c. AAS Congruence Theorem
d. HL Congruence Theorem
On a recent math test, Carlos had to find the volume of the rectangular prism below. He gave the answer of 60 in3, which was marked incorrect. Help Carlos understand how to correctly find the volume of the prism.
A cube that is eight inches in length, ten inches in width, and six inches in height.
Answer:
480 in
Step-by-step explanation:
Rectangular Prism Formula :
V=whl
Which,
W = Width
H = Height
L = Length
Solve:
Given that:
Length = 8 in
Width = 10 in
Height = 6 in
Since the formula is:
V = whl
Then,
V = 8 × 10 × 6
V = 80 × 6
V = 480 in
Kavinsky
In circle H with m/GHJ = 82 and GH = 12 units, find the length of arc GJ.
Round to the nearest hundredth.
H
The length of the arc GJ is 17.17 units if the in circle H with m/GHJ = 82 and GH = 12 units.
What is a circle?It is described as a set of points, where each point is at the same distance from a fixed point (called the centre of a circle)
We have angle GHJ = 82 units
Length of GH = 12 units
We know:
s = 2πr(θ/360)
s = (2π)12(82/360)
s = 17.17 units
Thus, the length of the arc GJ is 17.17 units if the in circle H with m/GHJ = 82 and GH = 12 units.
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Carl used 10 2/9 of an inch of string to tie a parcel and another 5 1/4 of an inch of string to tie a box, how much string is left if he started with 20 inches?
(please put you solution)
Answer:
4 19/36
Step-by-step explanation:
we have to subtract the sum of 10 2/9 and 5 1/4 from 20 to get the answer.
=> 10 2/9 + 5 1/4
As a c/d is a + c/d,
10 2/9 + 5 1/4 can also be written as 10+5+2/9+1/4
now we have to simplify it
=> 10+5 = 15
=> 2/9 = (2*4)/9*4) = 8/36, 1/4 = (1*9)/(4*9) = 9/36
now we have the same denominators
add,
8/36 + 9/36 = (8+9)/36 = 17/36
=> now we know that 10 2/9 + 5 1/4 is 15 17/36 ( which is 15 + 17/36)
=> next step is to convert 15 17/36 into an improper fraction
15 17/36 = [(15*36)+17]/36 = [540+17]/36 = 557/36
=> now we just have to subtract 557/26 from 20
20 - 557/36 = [(20*36)-557]/36 = [720-557]/36 = 163/36
=> we can convert 163/36 into a mixed fraction if we want to
163/36 converted into mixed fraction is 4 19/36
hope this helps :)
Graph on the same axes: y =x^2-4 and y=4-x^2. Write an equation for the part of the graph which is above of the x-axis.
The graph can be seen at the end, and the piecewise function for the part above the x-axis is:
f(x) = x^2 - 4 if x ∈ (-∞, -2] or x ∈ [2, ∞)
f(x) = 4 - x^2 if x ∈ (-2, 2).
How to write the equation?
First, we need to graph both functions, so we can see when each one is positive, the graphs of:
y = x^2 - 4
y = 4 - x^2
Can be seen at the end.
So, the first function is positive in the interval (-∞, -2] and [2, ∞), and the second function is positive in the interval (-2, 2)
So for the part of the function above the x-axis we have a piecewise function:
f(x) = x^2 - 4 if x ∈ (-∞, -2] or x ∈ [2, ∞)
f(x) = 4 - x^2 if x ∈ (-2, 2).
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Answer:
y= |x^2-4|
Step-by-step explanation:
Once you graph y=x^2-4 and y=4-x^2, you will get a graph like the first picture. The equation for the parts above the x-axis would be y=|x^2-4| and would graph like the second picture.
I need some help on this question please
Answer:
D
Step-by-step explanation:
everything that should happen at x+4 happens now at x. that is what that means.
so, the graph shifts 4 units to the left.
What is the simplified value of the exponential expression 16 Superscript one-fourth?
2
4
Answer:
[tex]2[/tex]
Step-by-step explanation:
[tex] {16}^{ \frac{1}{4} } \: is \: the \: same \: as \\ \\ \sqrt[4]{16} = \sqrt[4]{ {4}^{2} } [/tex]
Note we broke down the 16 into 4 squared*. This is because 4 squared is the same as 16. The four and the two would cancel each other leaving:
[tex] \sqrt[2]{4} \;\\ or \\ \: \sqrt [2]{{2}^{2}} [/tex]
Like before the two and the two would cancel each other out leaving:
[tex]2[/tex]
Answer:
C. 2
Step-by-step explanation:
edge
help for 10 points that is all i have
Answer:
22 in. and o.5 ft i think so
Please help
Use the following data set to answer questions 9-16:
11, 18, 8, 15, 24, 14 9.
9. Identify the median. Round to the nearest tenth.
10. Calculate the mean. Round to the nearest tenth.
11. Calculate the mode. Round to the nearest tenth.
12. Predict how the median will change if a 21 is added to the data set. Identify the new median.
13. Predict how the mean will change if an 18 is added to the data set. Calculate the new mean.
Answer:
9. Median: 14
10. Mean: 14.1
11. Mode: No Mode
12. New Median: 14.5
13. New Mean: 14.625
You are in business and have a product that sells for $10 that 1,000 people buy each month You want to make a profit and wonder whether you should raise the price in increments of a dollar For each dollar you raise the price , you lose 100 customersHow many dollars can you increase in price to maximize your profit or should you increase in price at all?
Based on the attached photo and explanation below, the price should not be increased at all.
How to know when profit is maximized?Note: See the attached photo for the calculation of Revenues at Different Number of Customers and Prices.
Every other being equal, profit is maximized when revenue is at the maximum,
From the attached photo, it can be seen that revenue is at the maximum or the highest when the price is $10 and the number of customers is 1,000.
Increasing the price in increments of a dollar results in a fall in revenue progressively until it reaches $0.
Therefore, the price should not be increased at all.
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100 POINTS I WILL MARK BRAINLIST
Solve this equation using the method of completing the square:
3x^2 + 24x - 24 = 0
Potential answers:
x = -2 +/- 4sqrt6
x = 4 +/- 2sqrt6
x = 2 +/- 4sqrt6
x = -4 +/- 2sqrt6
Answer:
[tex]\boxed{\sf x = -4 \pm 2\sqrt{6} }[/tex]
Explanation:
3x² + 24x - 24 = 0
factor the coefficient
3(x² + 8x) -24 = 0
Halve the second term and square it
3(x + 4)² -24 -3(4)² = 0
simplify the answer
3(x + 4)² -72 = 0
add 72 on both sides
3(x + 4)² = 72
divide both sides by 3
(x + 4)² = 24
square root both sides
x + 4 = ±√24
subtract both sides by 4
x = -4 ± 2√6
Answer:
[tex]x=-4\pm2\sqrt{6}[/tex]
Step-by-step explanation:
Completing the square for quadratic in the form [tex]ax^2+bx+c=0[/tex]
Given equation:
[tex]3x^2+24x-24=0[/tex]
Factor out 3:
[tex]\implies 3(x^2+8x-8)=0[/tex]
Divide both sides by 3:
[tex]\implies x^2+8x-8=0[/tex]
Add 8 to both sides:
[tex]\implies x^2+8x=8[/tex]
[tex]\textsf{Add }\: \left(\dfrac{b}{2}\right)^2\: \textsf{ to both sides}:[/tex]
[tex]\implies x^2+8x+\left(\dfrac{8}{2}\right)^2=8+\left(\dfrac{8}{2}\right)^2[/tex]
[tex]\implies x^2+8x+16=8+16[/tex]
[tex]\implies x^2+8x+16=24[/tex]
Factor the left side:
[tex]\implies (x+4)^2=24[/tex]
Square root both sides:
[tex]\implies x+4=\pm2\sqrt{6}[/tex]
Subtract 4 from both sides:
[tex]\implies x=-4\pm2\sqrt{6}[/tex]
please answer question below asap!
Answer:
36 students.
Step-by-step explanation:
5 + 7 = 12.
So the number of students must be a multiple of 12.
So as the number is between 25 and 43 it must be 36.
x: y = 1:5 Which is the correct equation? A y = 5x By= C y=x-4 D y=x+4
I'm leaning towards A but don't want totake the risk with a hour detention on the line if I get it wrong
