5
If 12 cans of food can feed 8 dogs for one week,
how many cans of food would be needed to feed
6 dogs for two weeks?
possible answers
9
12
16
18
Answers
If 12 cans of food can feed 8 dogs for one week, 1.5 cans of food can feed 1 dog for one week.
Now, there are 6 dogs in need of food for 2 weeks. 6 times 1.5 = 9. 9 times 2 (weeks) is 18. Therefore, 18 cans of food would be needed to feed 6 dogs for 2 weeks
Related Questions
If QS = 7, what is TU?
Answers
\(TU = 2QS = 2(7)\)
\(\implies \bf TU = 14\)
This is 9th-grade math
Answers
An inequality for the graph above is y ≤ -3x + 6.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.First of all, we would determine the slope of this line;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (-3 - 6)/(3 - 0)
Slope (m) = -9/3
Slope (m) = -3
At data point (0, 6) and a slope of -3, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 6 = -3(x - 0)
y = -3x + 6
y ≤ -3x + 6 (since the solid line is shaded below).
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A taxi company charges $3 per ride plus $1.50 for each mile traveled. Andrea wants to spend no more than $24 on a taxi ride. How many miles can Andrea travel? Select all that apply. PLEASE HELP!!
A. 18
B. 16
C. 14
D. 12
E. 10
Answers
Answer:
losien yo hablo español espero que alguien mas te ayude
Answer:
Your answer would be C , D, E
Step-by-step explanation
Have a Great day!
A country's population in 1990 was 154 million.
In 2001 it was 159 million. Estimate
the population in 2005 using the exponential
growth formula. Round your answer to the
nearest million.
P= Aekt
Answers
Using the exponential growth formula, the population in 2005 was 161 million.
The equation f(x) = a(1 + r)^x can also be used to compute exponential growth, where: The function is represented by the word f(x). The initial value of your data is represented by the a variable. The growth rate is represented by the r variable. To calculate growth rates, divide the difference between the starting and ending values for the period under study by the starting value.
Growth factor = (159/154) for the eleven-year period between 1990 and 2001.
The population growth might thus be described by the exponential equation
p(t) = 154(159/154)^(t/11), where t is the number of years since 1990.
The model forecasts a population of... p(15) = 154(159/154)^(15/11)
= 160.86 = 161 million
In 2005, there were about 161 million people living there.
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Correct Question:
A country's population in 1990 was 154 million. In 2001 it was 159 million. Estimate the population in 2005 using the exponential growth formula. Round your answer to the nearest million.
Asap helppppp fast :)))
Answers
Answer:
There is 2145.52 cubic inches of air in the ball
Step-by-step explanation:
A round ball is an example is hollow sphere. In order to find how much air the ball holds, the volume of the sphere needs to be found.
Given
Radius = r = 8 in
The volume of sphere is given by:
\(V = \frac{4}{3} \pi r^3\)
Putting the values we get
\(V = \frac{4}{3} * \frac{22}{7} * (8)^3\\V = \frac{4}{3} * \frac{22}{7} * 512\\V = \frac{45056}{21}\\V = 2145.52\ in^3\)
Hence,
There is 2145.52 cubic inches of air in the ball
If a cheetah runs for 4 seconds and runs 120 meters, how many seconds does it take a cheetah to run 270 meters? Explanation Please
Answers
Answer:
The cheetah needs 9 seconds to run 270 meters
Step-by-step explanation:
Proportions
Given the rate of change of the distance traveled by a cheetah is constant, we can predict the time taken to travel any distance.
The cheetah runs 120 for 4 seconds. The rate of change is:
\(\frac{120\ m}{4\ s}=30\ m/s\)
This is the cheetah's speed.
To run 270 meters, we divide the distance by the speed to find the time:
\(t=\frac{270}{30}=9\)
The cheetah needs 9 seconds to run 270 meters
An online fax company, EFaxlt.com, has a customer plan where a subscriber pays a monthly subscription fee of $12.75 dollars and can send/receive 40 fax pages at no additional cost. For each page sent or received past the 40 page limit, the customer must pay an overage fee of $0.06 per page. The following expression gives the total cost, in dollars, to send p pages beyond the plan's monthly limit. C = 0.06p + 12.75
If the monthly bill under this plan comes out to be $16.47, what was the total number of pages that were sent or received?
Answers
The number of pages that were sent or received beyond the 40 page limit under the plan was 70 pages.
Given that an online fax company, EFaxlt.com, has a customer plan where a subscriber pays a monthly subscription fee of $12.75 dollars and can send/receive 40 fax pages at no additional cost. For each page sent or received past the 40 page limit, the customer must pay an overage fee of $0.06 per page.
Let p be the number of pages that were sent or received beyond the 40 page limit under the plan. Thus, the total number of pages sent or received within the plan is (40 + p).Since the monthly bill under this plan comes out to be $16.47, the total cost, in dollars, to send p pages beyond the plan's monthly limit is given byC = 0.06p + 12.75= $16.47Therefore,0.06p + 12.75 = 16.47Solve for p,0.06p = 16.47 - 12.750.06p = 3.72p = 3.72/0.06p = 62
Therefore, the number of pages that were sent or received beyond the 40 page limit under the plan was 70 pages (p + 40)
The total number of pages that were sent or received beyond the plan's monthly limit was 70 pages.
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if a short-day (long-night) plant flowers, you know that it received if a short-day (long-night) plant flowers, you know that it received more consecutive hours of darkness than its critical period. fewer consecutive hours of darkness than its critical period. fewer consecutive hours of light than its critical period. more consecutive hours of light than its critical period.
Answers
If a short-day (long-night) plant flowers, you know that it received more consecutive hours of darkness than its critical period.
This is because short-day plants (also known as long-night plants) require a certain period of uninterrupted darkness (usually around 12-16 hours) to trigger flowering. If the plant receives more hours of darkness than its critical period, it will flower.
If it receives fewer hours of darkness than its critical period, it will not flower. Similarly, long-day (short-night) plants require a certain period of uninterrupted light to trigger flowering. If they receive more hours of light than their critical period, they will flower, but if they receive fewer hours of light than their critical period, they will not flower.
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In the function f(x) = 36x² / 15x - 6, how would you get 36x²?
Answers
The value of the term 36x² will be equal to f(x). (15x - 6 ).
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given function is f(x) = (36x²) / ( 15x - 6 ). The value of the term will be calculated as,
f(x) = 36x² / 15x - 6
36x² = f(x).(15x - 6)
Therefore, the value of the term 36x² will be equal to f(x). (15x - 6 ).
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How many yards are equal to 144 inches? (15 points)
Select one:
a. 4 yards
b. 12 yards
c. 36 yards
d. 5,184 yards
Answers
Answer:
A- 4 yards
Step-by-step explanation:
Hope this helps!
Have a nice day <3
After changing the unit of 144 inches into yards the number equivalent to 144 inches is 4 yards. Hence option (a) is true.
Given that,
Change the number 144 inches into yards.
Used the concept of measurement unit which stated that,
A measurement unit is a standard quality used to express a physical quantity. Also, it refers to the comparison between the unknown quantity with the known quantity.
Since we know that,
1 yards = 36 inches
1 inch = 1/36 yards
So, we can change the number 144 inches into yards,
1 inch = 1/36 yards
144 inches = 144/36 yards
= 4 yards
Therefore, 144 inches is equivalent to 4 inches.
Option (a) is true.
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Solve for x:
(5x + 12) = 18
Answers
Answer:
x=6/5
Step-by-step explanation:
5x+12=18→ 5x=18-12
5x=6 divide
x=6/5
Answer:
x=6/5
Step-by-step explanation:
(5x+12)=18
5x+12=18
5x=18-12
5x=6
x=6/5
A - 57 7/9
B- 11 2/3
C- 48 2/9
D-28 2/3
Answers
Answer:
i would say B is the answer
Step-by-step explanation:
Answer:
A is the correct answer.
Step-by-step explanation:
V=l*b*h
=4 1/3 * 3 1/3 * 4 ft^3
=13/3 * 10/3 * 4 ft^3
=520/9
= 57 7/9
If 10400 dollars is invested at an interest rate of 8 percent per year, find the value of the investment at the
end of 5 years for the following compounding methods, to the nearest cent.
(a) Annual: $
(b) Semiannual: $
(c) Monthly: $
(d) Daily: $
Answers
The interest estimated by compounding methods are-
(a) Annual: n = 1; CI = $860
(b) Semiannual: n = 2; CI = $862.
(c) Monthly: n = 12; CI = $865
(d) Daily: n = 365; CI = $855
Explain the term compound interest?When you add the interest you have already earned back into the principal balance, you are earning compound interest, which increases your profits.The formula for computing the compound interest is -
CI = A - P
A = P(1 + r/100nt)∧rt
In which,
CI = compound interestP = principal ($10,400)n = number of times compoundedr = rate of interest (8%)t = time (5 year)(a) Annual: n = 1
A = 10,400(1 + 8/500)∧5
A = 10,400 x 1.08
A = 11,260
CI = 11,260 - 10,400
CI = $860
(b) Semiannual: n = 2
A = 10,400(1 + 8/1000)∧10
A = 10,400 x 1.089
A = 11,262
CI = $862.
(c) Monthly: n = 12
A = 10,400(1 + 8/6000)∧60
A = 10,400 x 1.083
A = 11,265
CI = $865
(d) Daily: n = 365
A = 10,400(1 + 8/182500)∧1825
A = 10,400 x 1.0832
A = 11,255
CI = $855
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Name of indian nation flower ?
Answers
Answer:
Arre tum idhar sab India ke baare mai kyu puch rahe the ?¿
Step-by-step explanation:
Comment here
(a) It takes 40 pounds of seed to completely plant a 6-acre field. How many pounds of seed are needed per acre? poundsperacre
Answers
Answer: 6 2/3 or 6.67 pounds per acre (depending on how you write it)
Step-by-step explanation:
40 pounds/ 6 acres
= 6 2/3 or 6.67 pounds per acre
On April 26th, Laura decided to buy her brother a computer for his birthday on May 25th. The computer costs $986, but during a store's pre-memorial day sale the price drops $14 each day. Laura has $427. She earns $42 babysitting each week and was paid on April 25th. Will Laura have enough money to buy the computer before her brother's birthday. Explain your answer
Answers
Yes, Laura will have enough money to buy the computer before her brother's birthday.
What is cost?Cost is the total amount of money, time, and resources required to produce or acquire a product, service, or outcome. It involves the initial outlay of money, time, and resources necessary to produce or acquire something. In addition, it involves any ongoing expenses required to maintain or improve that something. Cost can be a one-time purchase, a long-term investment, or a recurring expense.
At the time of her purchase, Laura had $427 which is $59 short of the $486 computer. She earns $42 each week from babysitting, so if she saves every penny she earns for the next 7 weeks she will have enough money to buy the computer. She will have $294 after the first week of saving, $336 after the second week, $378 after the third week, $420 after the fourth week, $462 after the fifth week, $504 after the sixth week, and $546 after the seventh week. The $546 is more than enough money to purchase the computer before her brother's birthday.
Additionally, the computer's price drops $14 each day, so if Laura waits an extra week to purchase the computer, it will cost her even less. She will have $588 after the eighth week and would only need to spend $400 to purchase the computer.
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Let f(x) = x ^ 3 and g(x) = 3x + 2 Find solutions of the equation f(x) = g(x) by creating a table of integer values of x for - z <= x <= 3 and finding the corresponding values of f and g. Be sure to clearly indicate all values from the table that are solutions of f(x) = g(x)
Answers
The solutions to the equation f(x) = g(x) are x = -1 and x = 2.
To find solutions of the equation f(x) = g(x), we create a table of integer values of x for\(-z < = x < = 3\)and find the corresponding values of f and g:
x = -z ,-2, -1 , 0, 1, 2, 3.
f(x) =\(x^3\) =\(-z^3\), -8, -1, 0, 1, 8 , 2, 7.
g(x) = \(3x + 2\)= -3z+2, -4, -1 , 2, 5, 8, 11.
From the table, we can see that there are two solutions to the equation f(x) = g(x): x = -1 and x = 2. At these values of x, f(x) and g(x) are equal to each other, i.e., f(-1) = g(-1) = -1 and f(2) = g(2) = 8. Therefore, the solutions to the equation f(x) = g(x) are x = -1 and x = 2.
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find the value of x please
Answers
Answer:
A. 40°Step-by-step explanation:
AO = CO = radius
AO = CO ⇒ AB = BC and m∠AOB = m∠BOC = ¹/₂m∠AOC
From BDOE:
m∠EOB + m∠OBC + m∠CDE + m∠DEO = 360°
(65° + 75°) + 90° + x + 90° = 360°
140° + 180° + x = 360°
x = 40°
Determine whether or not the equation below is balanced. If it isn’t balanced, write the balanced form. Also, identify the reactant(s) and product(s) in this equation. Finally, label this as one of the five types of reactions: combination, decomposition, substitution, double replacement, or reversible.
Zn+ HCl → ZnCl2 + H2
Answers
Answer:
1. The equation isn't balanced because there aren't equal numbers of hydrogen or chlorine atoms on both sides of the equation. To correct this, a coefficient of 2 must be placed in front of HCl on the left-hand side of the equation.
Zn+2HCl→ZnCl2+H2
Zn and 2HCl are the reactants; ZnCl2 and H2 are the products. This is a substitution reaction because a free element (Zn) replaces another element (H) in a compound.
2. This is a balanced equation because the same types of atoms and the same numbers of each atom are present on both sides of the equation. 8 S atoms are found on both sides of the equation, and 48 F atoms are found on both sides of the equation. S8 and 24F2 are the reactants; 8SF6 is the product. This is a combination reaction because two substances (S8 and 24F2) undergo a chemical union to form a more complex substance (8SF6).
S8+24F2→8SF6
3. In ferric oxide (Fe3O4), there are 3 atoms of iron (Fe) and 4 atoms of oxygen (O). From the Periodic Table of Elements, we know that the atomic mass of iron is 55.8457 and the atomic mass of oxygen is 15.9994.
Fe3 = 55.8457 × 3 = 167.5371
O4 = 15.9994 × 4 = 63.9976
167.5371 + 63.9976 = 231.5347 (231.535 rounded)
Therefore, the molecular mass of ferric oxide is 231.535.
4. The percentage composition of chlorine in CaCl2 is derived as follows:
The molecular mass of the entire compound is:
Ca = 40.078 × 1 = 40.078
Cl2 = 35.4527 × 2 = 70.9054
40.078 + 70.9054 = 110.9834 (110.983 rounded)
The atomic mass of each element (or its multiple) is divided by the molecular mass of the compound:
Ca = 40.078 ÷ 110.983 = 0.361
Cl2 = 70.9054 ÷ 110.983 = 0.639
Multiplying each by 100 will turn these into percents. Therefore, the percentage composition of chlorine is 63.9%.
5. i. a, c, f, h
ii. e
iii. b, d, g, i
iv. i
Step-by-step explanation:
PENN FOSTER
The given chemical equation represents a type of reaction known as a single replacement (or displacement) reaction. In this reaction, zinc (Zn) displaces hydrogen (H) from hydrochloric acid (HCl) to form zinc chloride (\(ZnCl_2\)) and hydrogen gas (\(H_2\)).
The given chemical equation is:
\(Zn + HCl \rightarrow ZnCl_2 + H_2\)
To determine if the equation is balanced, we need to check if the number of atoms of each element is the same on both sides of the equation.
On the left side (reactant side):
Zinc (Zn) atoms: 1
Hydrogen (H) atoms: 1
Chlorine (Cl) atoms: 1
On the right side (product side):
Zinc (Zn) atoms: 1
Hydrogen (H) atoms: 2 (from\(ZnCl_2 + H_2\))
Chlorine (Cl) atoms: 2 (from \(ZnCl_2\))
The number of hydrogen (H) and chlorine (Cl) atoms is not balanced between the reactants and products. To balance the equation, we need to have the same number of atoms on both sides.
Balanced equation:
\(Zn + 2HCl → ZnCl_2 + H_2\)
Now, the equation is balanced with the following number of atoms on both sides:
On the left side (reactant side):
Zinc (Zn) atoms: 1
Hydrogen (H) atoms: 2
Chlorine (Cl) atoms: 2 (2 from HCl)
On the right side (product side):
Zinc (Zn) atoms: 1
Hydrogen (H) atoms: 2 (from H2)
Chlorine (Cl) atoms: 2 (from ZnCl2)
Identification of reactants and products:
Reactants: Zn (zinc) and HCl (hydrochloric acid)
Products: \(ZnCl_2\) (zinc chloride) and \(H_2\) (hydrogen gas)
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mrs torres is mailing a package that weighs 6.25 pounds. the post office charges by the ounce to mail a package. how much does the package weigh in ounces?
1. 187 ounces
2. 192.2 ounces
3. 100 ounces
4. 200 ounces
PLEASE ANSWER QUICK!!! ( ONLY REPLY IF YOU KNOW THE ANSWER )
Answers
PLEASE HELP ME ILL LOVE YOU FOREVER
Answers
Answer:
x=21
Step-by-step explanation:
61+34 = 95
360( a circle) - 95 = 265
265 +7 +22 = 294
9x+5x=14x
294=14x (divide both by 14 to get x)
X=21
Answer:
x = 21
Step-by-step explanation:
A circle makes a 360 degree turn
So the measure of the arcs should add up to equal 360
That being said we create an equation to solve for x
360 = 61 + 5x - 7 + 34 + 9x - 22
Now we solve for x using basic algebra
Step 1 combine like terms
61 - 7 + 34 - 22 = 66
5x + 9x = 14x
now we have 360 = 14x + 66
step 2 subtract 66 from each side
66 - 66 cancels out
360 - 66 = 294
now we have 294 = 14x
step 3 divide each side by 14
294/14=21
14x/14=x
we're left with x = 21
what central idea about mathematical instruction does the author express in passage 1?
Answers
An all-night study session can help you catch up on school assignments. The only way to become a straight-A student is efficient study habits.
Most students pseudo-work and end up wasting valuable time.
The correct option is (C)
This is based on an article about pseudo-working which is something that students do where they read for long hours and appear very serious in reading when in fact they do not focus on the reading and therefore end up not grasping much.
The author was trying to express that most students do this and that it is simply a waste of time which could have been spent actually studying.
The correct option is (C).
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The given question is incomplete, complete question is:
What central idea about studying does the author express in Passage 1?
A Straight-A students know how to work harder than other students.
B The only way to become a straight-A student is efficient study habits.
C Most students pseudo-work and end up wasting valuable time.
D An all-night study session can help you catch up on school assignments.
Graph the function f(v)= -4v^3 - 28.38v^2 + 195.1488v - 7.16 on your graphing calculator on the interval [-15,15].
Use your calculator's zero, maximum, and minimum features to answer the following questions:
Round all answers to 3 decimal places.:
Answers
The zeros of the function f(v) ≈ -4v³ - 28.38v² + 195.1488v - 7.16 are approximately v ≈ -3.647, v ≈ 2.536, and v ≈ 4.164.
The maximum point is approximately (v, f(v)) ≈ (-7.385, maximum value).
The minimum point is approximately (v, f(v)) ≈ (4.059, minimum value).
To find the zeros of the function, we need to find the values of v where f(v) equals zero. We can do this by solving the equation -4v³ - 28.38v² + 195.1488v - 7.16 = 0.
To find the maximum and minimum points, we can find the derivative of the function f(v) and set it equal to zero to find the critical points.
Then, we can analyze the second derivative to determine whether each critical point corresponds to a maximum or a minimum.
Let's start by finding the zeros of the function:
-4v³ - 28.38v² + 195.1488v - 7.16 = 0
To solve this equation, you can use numerical methods such as Newton's method or a graphing calculator. Here are the rounded solutions to three decimal places:
v ≈ -3.647
v ≈ 2.536
v ≈ 4.164
Next, let's find the critical points by finding the derivative of the function:
f'(v) = -12v² - 56.76v + 195.1488
Setting the derivative equal to zero and solving for v:
-12v² - 56.76v + 195.1488 = 0
Again, you can use numerical methods or a graphing calculator to find the solutions:
v ≈ -7.385
v ≈ 4.059
To determine the nature of each critical point, we need to analyze the second derivative:
f''(v) = -24v - 56.76
Evaluating the second derivative at each critical point:
f''(-7.385) ≈ -126.36
f''(4.059) ≈ 66.48
Since f''(-7.385) is negative, the critical point v ≈ -7.385 corresponds to a maximum.
Since f''(4.059) is positive, the critical point v ≈ 4.059 corresponds to a minimum.
In summary:
The zeros of the function f(v) ≈ -4v³ - 28.38v² + 195.1488v - 7.16 are approximately v ≈ -3.647, v ≈ 2.536, and v ≈ 4.164.
The maximum point is approximately (v, f(v)) ≈ (-7.385, maximum value).
The minimum point is approximately (v, f(v)) ≈ (4.059, minimum value).
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Using the net below, find the surface area of the triangular prism 5 cm 5 cm 4 cm 4 cm 3 cm 3 cm 3 cm 5 cm
Answers
Answer:
54000
Step-by-step explanation:
use multiplication
do ur own work if you want to see if I'm wrong
Ted borrowed $5,600 from his bank for 4 months with interest at 9%. ted paid the note in full on its due date. how much was the check he gave to the bank for payment?
Answers
Ten gave the check of $5768 to the bank for payment.
What is simple interest?Simple interest is calculated based on a loan's principal or the initial deposit into a savings account. Simple interest doesn't compound, so a borrower will never have to pay interest on the interest already accumulated because a creditor will only pay interest on the principal amount.
Formula for simple interest is;-
Simple interest = (principal amount×rate of interest×time duration in years)/100
S.I = (P×R×T)/100
Calculation of the total amount paid by Ted to the bank-
The principal amount is $5,600.
The rate of interest is 9%.
Time duration is 4 months equals 4/12 = 1/3 years.
S.I = (5,600×9×1)/(3×100)
S.I = 168
The simple interest on amount is $168.
Thus, the total amount is S.I + principal amount
Total amount = 168 + 5600
= 5768
Therefore, the total amount paid by the Ted to the bank is $5768.
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PLEASE HELP NO LINKS!! The temperature change in a chemistry experiment was –2C every 30 min.
The initial temperature was 6 C. What was the temperature after 4 h?
Answers
Answer:
what do you mean
Step-by-step explanation:
?
Answer:
The temperature change in a chemistry experiment was -2C every 30 min. The initial temperature was +6C. What was the temperature after 4 h
4 hours = 8 half hours
0, 1, 2, 3, 4, 5, 6, 7, 8 half hours
6, 4, 2, 0, -2, -4, -6, -8, -10
-10 degrees C
Simplify the expression.
74÷(32)
A. −218
B. 218
C. 76
D. −76
Answers
Answer:
Simplify the expression.
Exact Form:
37
16
Decimal Form:
2.3125
Mixed Number Form:
2
5
16
A residual is the difference between _______.
Answers
A residual is the difference between "the measured and predicted values of the quantity of interest".
What is residuals?In regression analysis, a residual would be the difference between an observable and anticipated value.
The formula is;
Residual = Observed value – Predicted value
Some key features regarding the residuals are-
The purpose of linear regression would be to quantify the relationship among one or so more predictor variables one and or more response variables. Linear regression selects the line that best "fits" the data, defined as least squares regression line, to do this. This line generates a prediction for every observation in the dataset, however it is improbable that the regression line's prediction would perfectly match its observed value.The residual is the discrepancy between the predicted and the observed value. The residuals for every observation would represent the vertical distance between both the observation as well as the regression line if we plotted the observed values then overlaid the fitted regression line.To know more about the residual, here
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A man covers 1/3rd of his journey at 15 km/hr & the
remaining at 20 km/hr. If he takes 10 hrs to complete his Journey find the length of his journey
Answers
Answer:
1/3 of his journey=15km/hr &
the remaining at 20 km/hr
20/15/5 =
20/5 =4
15/5= 3 =4*3=
12+10= 22
Answer:
180 km
Step-by-step explanation:
To find the length of the journey, use the time-distance-speed formula.
Let the length of the journey = x km
We know that,
\(\boxed{\bf Time = \dfrac{Distance }{Speed}}\)
Case 1:
\(\sf \dfrac{1}{3}^{rd} \ \text{of the journey} = \dfrac{1}{3}x\)
Speed = 15 Km/hr
\(\sf \text{Time taken to cover one-third of the journey}=\dfrac{1}{3}x \div 15\)
\(\sf = \dfrac{1}{3}x*\dfrac{1}{15}\\\\=\dfrac{1}{45}x\)
Case 2:
\(\sf Remaining \ distance = \dfrac{2}{3}x\)
\(Speed = 20 \ km /hr\)
\(\sf \text{Time take to cover two-third of the distance = }\dfrac{2}{3}x \div 20\)
\(\sf = \dfrac{2}{3}x*\dfrac{1}{20}\\\\\\=\dfrac{1}{3}x*\dfrac{1}{10}\\\\=\dfrac{1}{30}x\)
Total time taken to complete the journey = 10 hrs
\(\sf~~~~~~~ \dfrac{1}{45}x+\dfrac{1}{30}x= 10\\\\\\LCM \ of \ 45 \ \& \ 30 = 90\\\\\dfrac{1*2}{45*2} x+\dfrac{1*3}{30*3}x=10\\\\\\~~~~~~~~~~\dfrac{2}{90}x+\dfrac{3}{90}x=10\\\\\\~~~~~~~~~~~~~~~~~~~ \dfrac{5}{90}x=10\\\\\\\)
\(\sf x = 10*\dfrac{90}{5}\\\\x = 180 \ km\)
Length of the journey = 180 km
The value of y varies directly with x. If x = 15, then y = 12. What is the value of y, when x = 21?
Answers
Answer:
y = 16.8
Step-by-step explanation:
Given that y varies directly with x then the equation relating them is
y = kx ← k is the constant of variation
To find k use the condition x = 15 when y = 12, that is
12 = 15k ( divide both sides by 15 )
\(\frac{12}{15}\) = k, so
k = 0.8 y = 0.8x ← equation of variation
When x = 21, then
y = 0.8 × 21 = 16.8