Abel cycled at an average speed of 10 km/h from his home to the neighbourhood park.
On reaching the park, he cycled back home along the same route at an average speed of
8 Km/h. He took 1 1/5 hours for the whole journey. How long did he take to cycle from the park
to his home?
Answers
Answer:
Time = Distance / Speed
Time is taken from home to park = d / 10
Abel cycled back from the park to his home at an average speed of 8 km/h. The time taken for this part of the journey can be calculated using the same formula:
Time = Distance / Speed
Time is taken from park to home = d / 8
According to the given information, the total time taken for the whole journey is 1 1/5 hours, which is equivalent to 6/5 hours.
Total time is taken = Time from home to park + Time from park to home
6/5 = d/10 + d/8
To simplify the equation, let's find the least common multiple (LCM) of 10 and 8, which is 40:
(6/5) * 40 = (d/10) * 40 + (d/8) * 40
48 = 4d + 5d
48 = 9d
d = 48/9
d = 16/3 km
Now, to find the time taken from the park to Abel's home, we substitute the distance value:
Time from park to home = (16/3) / 8
Time from park to home = (16/3) * (1/8)
Time from park to home = 16/24
Time from park to home = 2/3 hour
Since 2/3 of an hour is equal to 40 minutes, Abel took 40 minutes to cycle from the park to his home.
Therefore, Abel took 40 minutes (or 2/3 of an hour) to cycle from the park to his home.
Related Questions
In 1980 a movie ticket cost $2.50. Now a movie ticket costs about $10.
What is the percent change? Percent increase or decrease?
I
Answers
((10-2.50)/2.50) = 3 * 100 = 300%
There is a 300% increase
explain how the values of a and c in ax^2+bx+c help you determine whether you can use a perfect square trinomial factoring pattern
Answers
Answer:
Step-by-step explanation:
So essentially, it actually doesn't just rely on the a and c values, it also has a little to do with the b value.
If you divide the c term by the a term, and the number is a perfect square, and moreover, if you divide the b term by the a term, then divide it by 2, and then square it, if it equals the c term, then you have a perfect square.
For example, 2x^2 + 12x + 18
if you divide 18/2, you get 9 ( a perfect square)
if you then divide the b term (12) by the a term (2), you get 6, which if you divide by 2, you get 3, and then if you square, you get 9, try this pattern, and if it works, then the expression can be factored using a perfect square trinomial factoring pattern.
The triangles below are congruent and their corresponding parts are marked
Answers
∠A ≅ ∠Z
you can determine this by seeing that both angles have two curved lines, therefor showing they have the same measurement.
∠B ≅ ∠Y
you can also determine this by seeing that they both have one curved line showing that they share the same measurement.
∠C ≅ ∠X
once again, you can determine this by seeing that both angles are marked with three curved lines, meaning they share the same measurements.
line AB ≅ line ZY
just like before, you can determine that they are equivalent to each other by seeing that both lines have three dashes showing that they have the same measurement.
line AC ≅ line ZX
you can determine these lines are equivalent because they both have one dash showing they are the same length as each other.
line BC ≅ line YX
once again, both lines have two dashes, showing that they are equivalent in length.
ΔCAB ≅ XZY
you can determine this by seeing that all three angles and all three sides on both triangles share measurements with the other triangle
At Camille's Hats, 70% of the hats in the store are baseball caps. If there are 28 baseball caps, how many hats are in the store?
Answers
Answer:
40 hats
Step-by-step explanation:
28=70% of what number?
28=0.70·w
divide both sides of the equation by 0.70 to solve for w (whole)
Answer:
40 hats
Step-by-step explanation:
(x + 3)(x + 7) ≡ x2 + ax + 21
Answers
please help me now help me nowww please
Answers
Answer:
A. 1
B. 3
C. 2
D. 5
E. 4
F. 6
Find the length of BE Show exact steps to solve
Answers
Given the line segment BE
As shown:
BC = 3x + 47
CD = y
BD = x + 27
CE = x + 26
DE = 10
To find the length of BE, we will find the values of x and y
So,
\(\begin{gathered} y=BD-BC \\ y=(x+27)-(3x+47) \\ y=-2x-20\rightarrow(1) \\ y=x+26-10 \\ y=x+16\rightarrow(2) \end{gathered}\)Solve the equations (1) and (2) for x
\(\begin{gathered} x+16=-2x-20 \\ x+2x=-20-16 \\ 3x=-36 \\ x=-\frac{36}{3}=-12 \end{gathered}\)Substitute at (2) to find y
\(y=x+16=-12+16=4\)The length of BE = BC + CD + DE
\(BE=(3x+47)+y+10\)Substitute with x and y:
\(\begin{gathered} BE=3\cdot-12+47+4+10 \\ BE=25 \end{gathered}\)So, the answer will be ⇒ BE = 25
David found a vintage watch his father lost 38 years ago. The watch’s date showed that it had worked for over two years after his father lost it. When David found the watch, it was 3 times as old as when his father lost it. How old was the watch when David’s father lost it?
Answers
According to the given information, the watch worked for over two years after his father lost it. So, the total age of the watch becomes "x + 2" years.
When David found the watch, it was 3 times as old as when his father lost it. This means the age of the watch at that time was 3 times "x".
Since the total age of the watch when David found it was the sum of the age when his father lost it and the additional years it worked, we can set up the following equation:
(x + 2) = 3x
Now, let's solve the equation to find the value of "x" (the age of the watch when David's father lost it):
x + 2 = 3x
2 = 3x - x
2 = 2x
x = 1
Therefore, the watch was 1 year old when David's father lost it.
Answer:
Step-by-step explanation:
Hey there,
Here's my reasoning regarding the problem:
Let's assume that the watch at the time it was lost was x years old.
When it was picked it was 3 times as old as it was when it was lost therefore it's currently 3x. The time between when it was lost and when it was found is 38 years. We can break this down into a simple algebraic formula:
3x - x = 38
2x = 38
x = 19
Which statement about the location of √7 on the number line is true?
A= It is located at the number 7 on the number line.
B= It is located at the number 3.5 on the number line.
C= It is located between the numbers 2 and 3 on the number line.
D=It is located between the numbers 4 and 9 on the number line
Answers
Explanation
The square root of a number is “what number times itself”
2 x 2 = 4
3 x 3 = 9
7 is between 4 and 9 so C is the correct answer
Which decimal number is equal to 3/18 ?
A. 0.167
B. 0.16¯
C. 0.16¯¯¯¯
D. 0.167¯¯¯¯¯
Answers
Answer:
Second option
Step-by-step explanation:
In order to find the answer to this question you have to divide the numerator into the denominator remembering that whole numbers have a secret decimal point to the right of itself.
\(\frac{3}{18}\)
\(\frac{3}{18} =3\div18\)
\(3\div18=0.16666666666\)
= 0.16666666666 or 0.16 repeating
Hope this helps.
Simplify the following expression:
√-36+√-100+ 7
O A. 7+ 16i
OB. 7+√136i
O C. 16
C. 16 - 7i
O D. 23 + 0i
Answers
√-36 + √-100 + 7
To simplify this expression, we need to first remove the negative radicals. We can do this by squaring both sides of the equation:
√-36 = -6
√-100 = -10
Substituting these values back into the expression, we get:
-6 + -10 + 7 = -19 + 7 = -12
So, the simplified expression is:
-12
Since the expression is already in its simplified form, there is no need to factor it further.
Sketch a graph of f(x)={- 5 if x < -2 2x-1 if-2 < x≤ 2 0 if x>2. (piecewise)
Answers
A graph of the given piecewise-defined function is shown in the image below.
What is a piecewise-defined function?In Mathematics and Geometry, a piecewise-defined function simply refers to a type of function that is defined by two (2) or more mathematical expressions over a specific domain.
Generally speaking, the domain of any piecewise-defined function simply refers to the union of all of its sub-domains. By critically observing the graph of this piecewise-defined function, we can reasonably infer and logically deduce that it is constant over several intervals or domains such as x > 2 and x < -2.
In conclusion, this piecewise-defined function has a removable discontinuity.
Read more on piecewise function here: brainly.com/question/18670055
#SPJ1
Using the present value approach, solve the following:
Tom has $100 in a bank account that pays a guaranteed 5% interest rate each year. How much would Tom have at the end of Year 3?
Answers
Answer:
Step-by-step explanation:
$100x0.5x1=$5
Eight members of a school marching band are auditioning for 3 drum major
positions. How many ways can students be chosen to be drum major?
*
Answers
Answer:
Step-by-step explanation:
ms. nolan finances a car by making down payment of $6,000. she then makes equal monthly payments to pay off the loan. after the first monthly payment, she has $14,100 left on the loan. after the fourth monthly payment, she has $13,200 left on the loan.
part a what is ms. nolan's monthly payment? enter the answer in the box.
part b how much will ms. nolan have paid the car after she makes all of the payments? enter the answer in the box.
Answers
Part A: $225 is her monthly payment.
Part B: She will have paid $20,325.
Part A Explanation: 14,100 - 13,200 is 900. Then you divide 900 by 4. 4 being the months. When you divide that, You get, 225.
Part B Explanation: You have the $6000 dollar down payment, plus the $14,225 total is payments. It equals 20,325.
Hope this helps!
Answer:$40
Step-by-step explanation:
There are 713 identical plastic chips number one through 713 in a box what is the probability of reaching into the box and randomly drawing the chip number to 564 express your answer as a simplified fraction or decimal rounded to four decimal places
Answers
The probability of randomly drawing the chip number 564 is 1 / 713 or 0.0014
What is the probability?
Probability is used to determine the odds that a random event would happen. The odds that the event would happen is a distribution that lies between 0 and 1.
If it is certain that the event would occur, the probability value would be 1. If it is certain that the event would not occur, the probability value would be 0. If it is equally likely that the event would happen or not happen, the probability value would be 0.5.
The more likely the event is to happen, the closer the probability value would be to 1. The less likely it is for the event not to happen, the closer the probability value would be to zero.
The probability of randomly drawing the chip number 564 = number of chips numbered 564 / total number of chips
1 / 713 = 0.0014
To learn more about probability, please check: https://brainly.com/question/13234031
#SPJ1
D What is the constant rate of change shown in the graph below?
2
3
0.5
1
Answers
Answer: 3
Step-by-step explanation:
Ali, Basti and Cian stand at three points A, B and C respectively. Suppose that the measure of angle ABC is 50 degrees , the measure of angle BAC is 60 degrees and Ali is exactly 150 ft away from Basti. Find the distance between Basti and Cian.
Answers
The distance between Basti and Cian is approximately 138.2 ft. Option D
To find the distance between Basti and Cian, we can use the Law of Sines, which relates the lengths of sides to the sines of their opposite angles in a triangle.
Let's label the points: A, B, and C. Ali is at point A, Basti is at point B, and Cian is at point C.
Given:
Angle ABC = 50 degrees (angle opposite side AC)
Angle BAC = 60 degrees (angle opposite side BC)
Ali is 150 ft away from Basti (side AB)
We want to find the distance between Basti and Cian, which is side BC.
Using the Law of Sines, we have:
BC/sin(50) = AB/sin(60)
Substituting the known values:
BC/sin(50) = 150/sin(60)
To find BC, we can rearrange the equation:
BC = (150/sin(60)) * sin(50)
Using a calculator to evaluate the expression:
BC ≈ 138.2 ft
Option D is correct.
For more such questions on distance visit:
https://brainly.com/question/30395212
#SPJ8
Why is 2 + (−3) equal to −1 HELP
Because it is 3 units to the left of 2 on a horizontal number line
Because it is 3 units to the right of 0 on a horizontal number line
Because it is 3 units to the left of 0 on a horizontal number line
Because it is 3 units to the right of 2 on a horizontal number line
Answers
Answer:
The answer is A
Its A.
Reasoning: Because I Took The Test
Please help !!! Find the measure of the exterior angle, formed by the sculpture and the ground, marked below in red.
Answers
Step-by-step explanation:
the inner and the outer angle at a vertex of a triangle are complementary angles or a linear pair of angles.
that means together they have 180°.
180 = inner + outer = 48 + outer
outer = 132°
the exterior angle is 132°.
i need help and don’t know what to do
Answers
⇒The next three terms of the sequence are 0, 1 and 2.
⇒The graph does not represent a function.
What is sequence?
In mathematics, a sequence is a list of components, usually numbers, where the components' order is important. Here, everything fits into a predetermined pattern. In real life, we encounter sequences frequently. Sequences include things like house numbers in a row, salary increases over time (by a set dollar amount or percentage), book pages, etc.
A list of numbers (or other components) that follow a specific pattern is called a sequence. Olivia, for instance, has been given a job with a starting monthly pay of $1,000 and a $500 annual raise. Are you able to determine her monthly pay for the first three years? $1000, $1500, and $2000 will be the amounts. Observe how Olivia's pay over a number of years forms a sequence because the numbers always increase by $500, following a pattern.
⇒The next three terms of the sequence are 0, 1 and 2.
⇒The graph does not represent a function.
Learn more about sequence link below
https://brainly.com/question/6561461
#SPJ1
What
is an arithmetic sequence with a common difference of −2?
Answers
Answer:
An arithmetic sequence with a common difference of −2 is 20,18,16,14,12..
Step-by-step explanation:
An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is same. Here, the common difference is -2, which means that each term in the sequence is obtained by subtracting 2 from the previous term.
To find the arithmetic sequence with a common difference of -2, you can start with an first term and then subtract 2 successively to find the subsequent terms.
Let the initial term is 20. Subtracting 2 from 20, we get 18. Subtracting 2 from 18, we get 16. Continuing this pattern, we subtract 2 from each subsequent term to generate the sequence. The arithmetic sequence with a common difference of -2 starting from 20 is
20,18,16,14,12
In this sequence, each term is obtained by subtracting 2 from the previous term, resulting in a common difference of -2.
-Is x= 4 a solution of 2(x - 3) + 7 = 23? How do you know?
Answers
Answer:
x = 11
Step-by-step explanation:
Simplify \(2(x-3)+7\)
Apply the distributive property.
\(2x - 6 + 7= 23\)
\(2x+1=23\)
Move all terms not containing x to the right side of the equation.
Subtract 1 from both sides of the equation.
\(2x =23-1\)
\(2x=22\)
Divide each term by 2 and simplify
\(\frac{2x}{2} = \frac{22}{2}\)
Cancel the common factor of 2
\(x = \frac{22}{2}\)
Divide 22 by 2
\(x = 11\)
No 4 is not a solution of the equation becouse it would be an inproper solution
Let’s substitute x = 4 in a given equation
LHS = 2(x-3) + 7
= 2 (4-3) + 7 ( substituting x = 4)
= 2(1) + 7
= 2 + 7
= 9
RHS = 23
Here, as we can see by substituting x = 4, in the given equation, LHS ≠ RHS.
Hence, it’s not a correct solution
HURRY WILL GIVE BRANLIEST!!!!!!!
Answers
Answer:
√17
Step-by-step explanation:
An irrational number is a number that cannot be expressed as a ratio of two integers. Or in other words, an irrational number can't be expressed as a fraction. You really cant divide one integer by another integer to get √17, so that makes it an irrational number.
The Smith family pays a rate of 27 mills in property tax. The assessed value of their home is $98,000. What is their property tax?
Answers
Their property tax would be =$ 26,460
Calculation of property taxA mill is one-thousandth of a dollar, and in property tax terms is equal to $1.00 of tax for each.
Therefore 27 mills = $27 for every $1,000 of assessed value, or 2.7%.
To calculate the property tax would
= 27/100× 98,000
= 2646000/100
=$ 26,460
Therefore, Their property tax would be =$ 26,460
Learn more about percentage here:
https://brainly.com/question/24304697
#SPJ1
please please help me
Answers
Answer:
a) Angle(A+B+C) = 180°
3x - 2° + x - 2° + 2x + 4° = 180°
6x = 180°
x = 30°
<A = 3(30°) - 2° = 88°
<B = 30° - 2° = 28°
<C = 2(30°) + 4° = 64°
b) at point Q
3y + 6y = 180°
y = 20°
<Q = 3(20°) = 60°
<S = 20°
x = 180° - (<S + <Q)
x = 180° - (80°)
x = 100°
<R = 100°
Find the lower quartile for the data. {63, 74, 63, 76. 73, 70, 74, 69, 69, 65, 70, 70, 72, 70, 65}
A. 65
B. 68
C. 66
D. 67
Answers
Answer:
65
Step-by-step explanation:
The lower quartile for the given data is 65. To calculate this, we first need to sort the data in ascending order: {63, 63, 65, 65, 69, 70, 70, 70, 70, 72, 73, 74, 74, 76}. The lower quartile is then calculated as the median of the lower half of the data, which is 65.
Given that ∆MTW ≅ ∆CAD, which angles are corresponding parts of the congruent triangles?
∠W ≅ ∠C
∠W ≅ ∠D
∠W ≅ ∠A
Answers
∠T ≅ ∠A
Step-by-step explanation:
Since, ∆MTW ≅ ∆CAD
Therefore, ∠T ≅ ∠A (cpct)
andrea rents a bike for 8 hours and pays $42 for the rental tomorrow she wants the same bike but only needs it for 6 hours what equation can she use to figure out how much she will need to pay
Answers
Answer:
8x=42 where x is hourly cost
so x = 21/4
6*x = 63/2 $
Step-by-step explanation:
Khalid carried water bottles to the field to share with his team at halftime. The water bottles weighed
a total of 50x2 + 30x + 10 ounces.
Which factorization could represent the number of water bottles and weight of each water bottle?
A 5 (10x2 + 15x + 2)
B 2 (25x²15x + 5)
C (52 + 2) (102 + 5)
D 10 (5.2² + 3x + 1)
Answers
Answer:
Answer: D
\( {50x}^{2} + 30x + 10\)
• first factorise out 10:
\( = 10(5 {x}^{2} + 3x + 1)\)
• then find factors of the quadratic equation in the bracket: