Answer:
(3ab^3+2c^6)(9a^2b^6-6ab^3c^6+4c^12)
Step-by-step explanation:
Given:
Polynomial 27a^3 b^9+8c^18
Factoring the given polynomial
27a^3b^9 can be written as
=3^3.a^3.b^3^3
=(3ab^3)^3
Also 8c^18 can be written as
=2^3.c^6^3
=(2c^6)^3
Hence Polynomial 27a^3 b^9+8c^18 can be written as
=(3ab^3)^3+(2c^6)^3
Applying sum of cubes formula i.e. a^3 + b^3=(a+b)(a^2 – ab + b^2)
=(3ab^3+2c^6)(9a^2b^6-6ab^3c^6+4c^12) !
10.5, 14, 17.5, 21, 24.5, ...
What is an explicit rule for this sequence in simplified form?
The explicit rule for the given sequence is to add 3.5 to each previous term.
Explanation:The given sequence is:
10.5, 14, 17.5, 21, 24.5, ...
The explicit rule for this sequence is that each term is obtained by adding 3.5 to the previous term. So, the nth term of the sequence can be represented by the formula:
Tn = Tn-1 + 3.5
where Tn is the nth term of the sequence and Tn-1 is the previous term.
Final answer:
The explicit rule for the sequence 10.5, 14, 17.5, 21, 24.5, ... is a_n = 7 + 3.5n.
Explanation:
The sequence given is 10.5, 14, 17.5, 21, 24.5, ... and we need to find an explicit rule for this sequence in simplified form. Observing the sequence, we see that each term is increasing by 3.5. Therefore, the common difference in this arithmetic sequence is 3.5. We can express the nth term of the sequence using the formula:
an = a1 + (n - 1)d, where a1 is the first term and d is the common difference.
Since the first term a1 is 10.5 and d is 3.5, the rule for the nth term is:
an = 10.5 + (n - 1)(3.5)which simplifies to an = 7 + 3.5n.
Which equation can be used to solve for b?
Using the law of tangents:
Tan(angle) = Opposite leg / Adjacent leg
Tan(30) = b / 8
Rewrite to solve for b:
b = 8 * tan(30)
The first answer is correct.
Answer:
b = 8 * Tan 30
Step-by-step explanation:
Points to remember
Trigonometric ratio
Tan θ = Opposite side/Adjacent side
From the figure we can see that a right angled triangle ABC
Bc = 8ft, <C = 90° and <B = 30°
To find the equation of finding the b
We have,
Tan θ = Opposite side/Adjacent side
Tan 30 = AC/BC = b/8
b = 8 * Tan 30
Rose bought three feet of ribbon how many inches of ribbon did Rose buy
Answer:
36 I used a calculator
Step-by-step explanation:
Please give me brainliest you get point by answering questions and then once you answer 1 you can give me brainliest by clicking the crown
Answer:
36 inches of ribbon
Step-by-step explanation:
There are 12 inches in each foot of ribbon, 12 times 3 is 36. She bought 36 inches of ribbon.
5.4%
0.052%
105%
5.2%
[tex]\bf r=\sqrt{\cfrac{A}{P}}-1~~ \begin{cases} P=425\\ A=470 \end{cases}\implies r=\sqrt{\cfrac{470}{425}}-1\implies r=\sqrt{\cfrac{94}{85}}-1 \\\\\\ r\approx 0.051609\implies \stackrel{\textit{converting it to percentage}}{r\approx 0.051609\cdot 100}\implies r\approx 5.1609\implies \stackrel{\textit{rounded up}}{r=5.2}[/tex]
what is the GCF of 6 and 15
Answer:
3
Step-by-step explanation:
obtain the GCF by listing factors of both numbers
factors of 6 are : 1, 2, 3, 6
factors of 15 are : 1, 3, 5, 15
The common factors are : 1, 3
the GCF is 3
A survey was conducted at a local elementary school. Students were asked to identify their favorite color. The percentages of students who chose each color are shown.
Please fill out:
It is/is not likely that you will choose a person whose favorite color is red.
It is most likely that you will choose a person whose favorite color is _____.
The probability that you choose a student who picked red as his or her favorite color is ___%, but the probability that you chose a person who picked another color is ___%.
Answer:
It is not likely that you will choose a person whose favorite color is red.
It is most likely that you will choose a person whose favorite color is something other than red.
Step-by-step explanation:
The probability that you choose a student who picked red as his or her favorite color is 45%, but the probability that you choose a person who picked another color is 55%.
It is not likely that you will choose a person whose favorite color is red. It is most likely that you will choose a person whose favorite color is blue. The probability that you choose a student who picked red as his or her favorite color is 10%, but the probability that you chose a person who picked another color is 90%.
To solve this problem, we need to analyze the given percentages of students who chose each color as their favorite. The percentages provided are as follows:
- Red: 10%
- Blue: 40%
- Green: 20%
- Yellow: 15%
- Purple: 10%
- Orange: 5%
The total probability of all possible outcomes must equal 100%. In this case, the sum of the percentages of all colors equals 100%, confirming that the probabilities are correctly distributed among the color choices.
Now, let's address the first part of the question: It is/is not likely that you will choose a person whose favorite color is red. Since red has the lowest percentage (10%), it is the least likely choice among all the colors. Therefore, it is not likely that you will choose a person whose favorite color is red.
Next, we determine which color is most likely to be chosen. Since blue has the highest percentage (40%), it is the most likely choice. Thus, it is most likely that you will choose a person whose favorite color is blue.
To calculate the probability of choosing a student who picked red as their favorite color, we use the given percentage for red, which is 10%. This is the probability of randomly selecting a student who prefers red.
Finally, to find the probability of choosing a person who picked any color other than red, we subtract the probability of choosing red from the total probability (100%). This gives us 100% - 10% = 90%. Therefore, the probability that you chose a person who picked another color is 90%.
In conclusion, the probability of choosing a student who likes red is 10%, and the probability of choosing a student who likes any other color is 90%. The most likely color to be chosen is blue.
Identify all the sets to which the number belongs choose from rational number whole number or integer 1.256 I think irrational correct me if I’m wrong♀️
Answer:
Rational
Step-by-step explanation:
1.256 is not a whole #, and it's also not an integer. An integer is basically whole #s and their opposites. The # is not irrational. 1.256 is a terminating decimal, and can be turned into a fraction. 1.256 = 1 32/125.
The number 1.256 is a rational number because it can be expressed as a ratio of two integers (1256/1000). It is not a whole number or an integer due to its decimal component.
The question is whether the number 1.256 belongs to the sets of rational numbers, whole numbers, or integers. Contrary to the student's initial thought, 1.256 is not an irrational number. Instead, it is a rational number because it can be expressed as a ratio of two integers.
Specifically, 1.256 can be written as 1256/1000, where both the numerator and denominator are integers. Therefore, this number belongs to the set of rational numbers. It is not a whole number or an integer, as both of these sets require numbers without fractional or decimal components.
alvin's age is two time elga's age. the sum of their age is 54. what is elga's age
27 is the best answer I can think of cause 54/2 =27 which is Elgas age
which of the following graphs represents a function that has a positive leading coefficient
Answer:
Options B, C, and D.
Step-by-step explanation:
The first graph is a parabola. Since it opens downwards, it means the leading coefficient is negative.
The third graph is also a parabola. Since it opens upwards, it means it has a positive leading coefficient.
The second and fourth graphs represents a polynomial with an odd degree. Since both polynomial goes rises on the left and keeps rising on the right, their leading coefficients are positive.
The correct options are:
B, C , and D
Answer: graph b and graph c and graph D
Step-by-step explanation: Just took the quiz
Please help with these 2 questions! Thank you
Answer:
15. h⁻¹ (x) = 5x-6/2
16. (g.f)x = 4x^2 -2x -1
Step-by-step explanation:
15. Find Inverse of h(x) = 2x+6 /5
Let y = 2x+6/5 we need to find value of x
Multiplying both sides with 5
5y = 2x+6
Adding -6 on both sides
5y -6 = 2x
Dividing both sides by 2
5y-6/2 = x
Now replace y with x our answer will be:
h⁻¹ (x) = 5x-6/2
16. f(x) =2x-1 and g(x) = x^2 -2 find (g.f)x
(g.f)x can be written as: g(f(x))
We know f(x) = 2x-1 so, put value of f(x) into x of g(x).
Putting values we get:
(g.f)x = g(f(x))= (2x-1)^2 -2
= 4x^2 -2x +1 -2
= 4x^2 -2x -1
so, (g.f)x = 4x^2 -2x -1
What’s the answer for this problem
A. 11
B. 5
C. -5
your answer would be B. 5
Answer:
5
Step-by-step explanation:
Given a matrix [tex]\left[\begin{array}{ccc}a&b&\\c&d&\\\end{array}\right][/tex]
Then the determinant = ad - bc
For the matrix [tex]\left[\begin{array}{ccc}2&3&\\1&4&\\\end{array}\right][/tex]
determinant = (2 × 4) - (3 × 1) = 8 - 3 = 5
Part 6
want to line the front of the school with cylinder shaped beams filled with moon sand. Each beam is 37 feet tall with a diameter of 8 feet.
What is the total volume of each beam?
You are given a container with a 50,000 sq ft of sand for your beams.
1. How many beams can you fill with this sand?
2. Will you have any sand left over? If so how much?
What did you do to get your answers to question 1 and 2? Describe your work in detail.
Answer:
Part 1) The volume of each beam is [tex]1,858.88\ ft^{3}[/tex]
Part 2) You can fill [tex]26\ beams[/tex]
Part 3) Yes, the amount of sand left over is [tex]1,669.12\ ft^{3}[/tex]
Step-by-step explanation:
Part 1) What is the total volume of each beam?
The volume of a cylinder is equal to
[tex]V=\pi r^{2} h[/tex]
we have
[tex]h=37\ ft[/tex]
[tex]r=8/2=4\ ft[/tex] ----> the radius is half the diameter
assume
[tex]\pi=3.14[/tex]
substitute the values
[tex]V=(3.14)(4)^{2} (37)[/tex]
[tex]V=1,858.88\ ft^{3}[/tex]
Part 2) How many beams can you fill with this sand?
we know that
You are given a container with a 50,000 sq ft of sand for your beams
Note Is a 50,000 cubic foot of sand instead of 50,000 sq ft of sand
Divide the total volume of sand by the volume of each beam to obtain the number of beams
[tex]50,000/1,858.88=26.9\ beams[/tex]
Round down
[tex]26.9=26\ beams[/tex]
Part 3) Will you have any sand left over? If so how much?
yes
[tex]50,000-26(1,858.88)=1,669.12\ ft^{3}[/tex]
(HELP ASAP PLEASE!!)
When Ella does 13 push-ups and 7 sit-ups, it takes a total of 60 seconds. In comparison, she needs 96 seconds to do 13 push-ups and 19 sit-ups. How long does it take Ella to do each kind of exercise?
It takes Ella ___ seconds to do a push-up and ___ seconds to do a sit-up.
The answer is:
It takes Ella 3 seconds to do a push-up and 3 seconds to do a sit up.
Why?To find how many seconds Ella took to do a push-up and a sit-up we must write two equations using the given information.
Let be "x" the time needed to push-ups and "y" be the time needed to do sit-ups.
So, writing the equations we have:
First equation,
If she can do 13 push-ups and 7 sit-ups in 60 seconds, we have:
[tex]13x+7y=60[/tex]
Second equation,
If she can do 13 push-ups and 19 sit-ups in 96 seconds, we have:
[tex]13x+19y=96[/tex]
Now, creating a system of equations, and using the reduction method to solve it, we have:
[tex]\left \{ {{13x+7y=60} \atop {13x+19y=96}} \right.[/tex]
Multiplying the first equation by -1, we have:
[tex]\left \{ {{-13x-7y=-60} \atop {13x+19y=96}} \right.[/tex]
[tex]\left \{ {{-13x-7y=-60} \atop {13x+19y=96}} \right\\\\12y=36\\\\y=\frac{36}{12}=3[/tex]
Then, substituting "y" into the first equation, we have:
[tex]13x+7y=60[/tex]
[tex]13x+7(3)=60[/tex]
[tex]13x+21=60[/tex]
[tex]13x=60-21=39[/tex]
[tex]x=\frac{39}{13}=3[/tex]
Hence, we have that It takes Ella 3 seconds to do a push-up and 3 seconds to do a sit up.
Have a nice day!
* George scored on average of 80% of three tests.
What scored must he get on the burth tests to
bring his average to 85%
Answer: 100%
Step-by-step explanation:
100 + 80 + 80+ 80 = 340 (total scores of 4 tests)
340 divided by the number of tests 4 = 85
George would need to score 100% on his next test to bring his test average from 80 to 85.
Solve the equation below for x.
| 2(x+5)= 3(x-4)
Answer:
x=22
Step-by-step explanation:
2(x+5)=3(x-4)
2x+10=3x-12
-x=-22
x=22
Step 1: Distribute the numbers outside the parentheses to each number inside the parentheses
(2 * x) + (2 * 5) = (3 * x) + (-4 * 3)
2x + 10 = 3x - 12
Step 2: Combine like terms
2x goes with 3x. To do this subtract 2x to both sides (subtraction is the opposite of addition)
(2x - 2x) + 10 = (3x - 2x) - 12
0 + 10 = x - 12
10 = x - 12
10 goes with -12. To do this add 12 to both sides (addition is the opposite of subtraction)
10 + 12 = x + (-12 + 12)
22 = x + 0
22 = x
Check:
2(22 + 5) = 3(22 - 4)
2(27) = 3(18)
54 = 54
Hope this helped!
~Just a girl in love with Shawn Mendes
The pentagon shown could be reflected over which line to be carried onto itself?
Answer:
paraell
Step-by-step explanation:
Mr. Granville needs some plywood that is about three over four-inch thick. Which plywood is closest to three over four-inch thick?
A
Image of plywood A D X . . . that is . . . begin fraction . . . thirteen over sixteen . . . end fraction . . . inches thick
B
Image of plywood C D X . . . that is . . . begin fraction . . . eleven over thirty two . . . end fraction . . . inches thick
C
Image of plywood A B X . . . that is . . . begin fraction . . . one over two . . . end fraction . . . inches thick
D
Image of plywood C R X . . . that is . . . begin fraction . . . three over eight . . . end fraction . . . inches thick
Answer:
The plywood that is closest to three over four-inch thick is thirteen over sixteen inches thick
Step-by-step explanation:
we have
3/4 in
Verify each value
case A) 13/16 in
we know that
3/4 in=12/16 in ----> multiply by (4/4)
Find the difference
13/16-12/16=1/16 in
case B) 11/32 in
we know that
3/4 in=24/32 in ----> multiply by (8/8)
Find the difference
24/32-11/32==13/32 in
case C) 1/2 in
we know that
1/2 in=2/4 in ----> multiply by (2/2)
Find the difference
3/4-2/4=1/4 in
case D) 3/8 in
we know that
3/4 in=6/8 in ----> multiply by (2/2)
Find the difference
6/8-3/8=3/8 in
Compare the values of the difference and find the less value
we have
case A) 1/16=2/32 in
case B) 13/32 in
case C) 1/4=8/32 in
case D) 3/8=12/32 in
The less value is case A) 2/32 in
therefore
The plywood that is closest to three over four-inch thick is thirteen over sixteen inches thick
A class had 11 boys and 9 girls in it. What percent of the class are boys?
A. 11%
B. 45%
C. 55%
D. 82%
Hello There, the answer is C. 55%!
To solve, get the total (11 boys + 9 girls = 20 total students). Put the number of boys over the total, representing it as a fraction, 11/20. Now convert this t a precent by dividing 11 by 20 and multiplying the result by 100.
11 divided by 20 = 0.55
0.55 times 100 = 55%
So, 55% is your final answer. I hope this helps and have a great day!
The percent of the class that are boys is Option(C) 55% .
What percent of class are boys ?It is given that a class had 11 boys and 9 girls in it.
Thus the total number of students in the class is = (11 + 9) = 20
The percent of boys is given by -
(Number of boys / Total number of students) * 100 %
⇒ Percent of boys = 11/20 * 100 %
∴ Percent of boys = 55%
Therefore, the percent of the class that are boys is Option(C) 55% .
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At most, Sybil types 56 words per minute.
Which inequality represents this situation?
A.
w 56
B.
w 56
C.
w 56
D.
w 56
they are all the same???
Answer:
a
Step-by-step explanation:
What allergens do the graham crackers contain
Answer:
Eggs and Nuts
Step-by-step explanation:
Some graham crackers contain eggs and nuts
maria rented a minivan for $54 per day for 8 days and drove 1452 miles .She was allowed 150 free miles ,and was charged 25 cents for each additional miles . what was the total rental cost
Answer:
54×8=432 1452-150=1302×.25=325.50+432.00=757.50
Step-by-step explanation:
Identify this conic section. x 2 + y 2 = 25 line circle ellipse parabola hyperbola
Answer:
circle
Step-by-step explanation:
The equation
x² + y² = r²
Represents a circle centred at the origin with radius r
x² + y² = 25 ← is in this form and
is a circle centre (0, 0) with r = 5
ANSWER
circle
EXPLANATION
The given equation is
[tex] {x}^{2} + {y}^{2} = 25[/tex]
To determine the type of conic, we analyze the coefficient and sign of the quadratic terms.
If the coefficient of the quadratic terms are equal and have the same sign,then the conic is a circle.
If the coefficient of the quadratic terms are equal and have opposite signs,then the conic is a hyperbola.
If the coefficient of the quadratic terms are not equal and have the same sign,then the conic is an ellipse.
Since the coefficients are all 1 and the signs are positive, the given conic is a circle.
Can you guys please help me with this question I’m having a hard time with this lesson please help! The question s in the picture thank you god bless you!
Answer:
5 rolls
Step-by-step explanation:
If the perimeter around the square footage of the ceiling is equal to 12 + 12 + 12 + 12 = 48, even though the number is 48, in order to have all of the footage covered, Katie would need to buy (at least) 5 rolls.
Hope I helped and please give me brainliest!
Find the value of x if y =1/4x and 5x-8y=33
Answer:
x=11
Step-by-step explanation:
y= 1/4x
5x-8y=33
5x-8(1/4x)=33
x=11
Answer:
11
Step-by-step explanation:
Given that ,
⇒ y = 1/4x and
⇒ 5x - 8y = 33
We can write 1st equation as ,
⇒ 4y = x
Put x = 4y in 2nd Equation ,
⇒ 5*4y - 8y = 33
⇒ 20y - 8y = 33
⇒ 12y = 33
⇒ y = 33/12
Put this in 1st ,
⇒ 33/12 = 1/4 x
⇒ x = 33/12 × 4
⇒ x = 33/3
⇒ x = 11 .
Suki has 54 rock songs, 92 dance songs and 12 classical songs on her playlist. If Suki’s music player randomly selects a song from the playlist, what is the probability that the song will not be a classical song?
Answer:
92.4% or 73/79
Step-by-step explanation:
You have to add up all the individual songs, which is 158. Then add up the number of songs that aren't classical, which is 146. Then divide 146 by 158 which gives you your answer.
To find the probability that a randomly selected song from Suki's playlist is not a classical song, follow these steps:
1. **Find the total number of songs**: Add up the number of rock songs, dance songs, and classical songs to get the total number of songs in Suki's playlist.
Total number of songs = Number of rock songs + Number of dance songs + Number of classical songs
Total number of songs = 54 rock songs + 92 dance songs + 12 classical songs
Total number of songs = 158 songs
2. **Calculate the probability of selecting a classical song**: To calculate the probability of selecting a classical song, divide the number of classical songs by the total number of songs.
Probability of selecting a classical song = Number of classical songs / Total number of songs
Probability of selecting a classical song = 12 / 158
3. **Calculate the probability of not selecting a classical song**: The probability of not selecting a classical song is the complement of the probability of selecting a classical song. To get this probability, subtract the probability of selecting a classical song from 1.
Probability of not selecting a classical song = 1 - Probability of selecting a classical song
Probability of not selecting a classical song = 1 - (12 / 158)
4. **Compute the final probability**: Perform the subtraction from step 3 to get the final probability.
Probability of not selecting a classical song = 1 - (12 / 158)
Probability of not selecting a classical song ≈ 0.92405 (rounded to five decimal places)
Therefore, when Suki's music player randomly selects a song, the probability that the song will not be a classical song is approximately 0.92405, or 92.405%.
one side of a regular hexagon is x+2 its perimeter is?
Answer:
6 x + 12
Step-by-step explanation:
Hexagon = 6 sides
1 side = x + 2
( Multiply by 6 to get 6 sides )
6 sides = 6 x + 12
The perimeter of a regular hexagon with a side length of x + 2 would be 6x + 12. This is achieved by multiplying the length of one side (x + 2) by 6 (total sides in a hexagon).
Explanation:The perimeter of any regular shape is given by the sum of its sides. In a regular hexagon, all sides are equal. Therefore, if one side is x + 2, then the perimeter would be six times that side length. This is because a hexagon has six sides. So, if we multiply the length of one side (x + 2) by 6 the result will be the total perimeter. Hence, the perimeter of the regular hexagon would be 6(x + 2), which simplifies to 6x + 12.
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At a breakfast buffet, 54% of people choose coffee for their beverage while 16% choose juice. Also, 12% choose both coffee and juice. What percentage of people chose coffee only?
Answer:
The answer is 42%.
Step-by-step explanation:
If we make a Venn diagram, we get 12% in the middle, meaning that 12% of people chose both coffee and juice.
54% is the total amount of people who chose coffee, including the % of people who chose coffee as well as juice.
So, we need to subtract 12% from 54%, therefore giving us 42%.
The percentage of people choose coffee only is 42%.
We have given that,
At a breakfast buffet, 54% of people choose coffee for their beverage while 16% choose juice. Also, 12% choose both coffee and juice.
If we make a Venn diagram, we get 12% in the middle, meaning that 12% of people chose both coffee and juice.
What is the percentage?This free percentage calculator computes a number of values involving percentages, including the percentage difference between two given values.
54% is the total amount of people who chose coffee, including the % of people who chose coffee as well as juice.
So, we need to subtract 12% from 54%, therefore giving us 42%.
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A fireplace contains 72 bricks along its bottom row. If each row above decreases by 6 bricks, what is the function that shows the bricks on the 14th row?
Answer:
[tex]a_n=78-6n[/tex]
[tex]a_{14}=78-6(14)[/tex]
Step-by-step explanation:
To solve this, we are using the formula for the nth term of an arithmetic progression:
[tex]a_n=a_1+(n-1)d[/tex]
where
[tex]a_1[/tex] is the first term of the progression
[tex]d[/tex] is the difference
[tex]n[/tex] is position of the term in the progression
We know for our problem that the bottom row contains 72 bricks, so [tex]a_1=72[/tex]. We also know that each row above decreases by 6 bricks, so the difference is -6 ([tex]d=-6[/tex]).
Replacing the values:
[tex]a_n=72+(n-1)(-6)[/tex]
[tex]a_n=72-6n+6[/tex]
[tex]a_n=72-6n+6[/tex]
[tex]a_n=78-6n[/tex]
Where [tex]n[/tex] is the row
Since we want to now the number of bricks in the 14th row, [tex]n=14[/tex]:
[tex]a_{14}=78-6(14)[/tex]
[tex]a_{14}=78-84[/tex]
[tex]a_{14}=-6[/tex]
Since bricks can't be negative, we can conclude that this is an impossible real-life situation.
A theater company advertises prices of $13 for adult tickets and $9 for student tickets. On a given day, there were 210 tickets sold, earning a total of $2130.
Which system of equations correctly represents this situation where a represents the number of adult tickets sold and s represents the number of student tickets sold?
{13a+9s=210a+s=2130
{a+s=2109a+13s=2130
{9a+13s=210a+s=2130
{a+s=21013a+9s=2130
Let A = adult and s = student.
Multiply the cost of an adult ticket by number of adults: 13a.
Do the same for students: 9s
Add those together to get total money made:
13a + 9s = $2130
Then add the number of each tickets sold to get total sold:
a +s = 210 tickets.
13a + 9s = $2130, a +s = 210
The last answer is correct.
a car and a lorry started travelling at the same time from town r to town s. When the car arrived in town s, Th lorry had only travelled 0.6 of the journey. the lorry needed 45 min more to complete the journey. the lorry travelled a constant speed of 60 km/h. find the distance between the two towns.
Answer:
112.5 km
Step-by-step explanation:
The lorry needed 45 minutes to travel the remaining 0.4 of the journey and was traveling at 60 km/hr.
First, convert minutes to hours:
45 min × (1 hr / 60 min) = 0.75 hr
Now use distance equation:
distance = rate × time
0.4d = 60 × 0.75
d = 112.5
The distance between the towns is 112.5 km.