The area of a sector of a circle is
18 pie cm². The radius of the circle is
6 cm. The angle in the sector is
Answers
Answer:
The angle in the sector is 180°.
Because the area of circle is 36 pie cm². So the angle is the half of 360°.
[tex]\boxed{\begin{array}{l} \\ \sf\huge{ \quad \underline{Answer} } \\ \\ \underline{ \underline\textsf{ Area of sector is given by : }} \\ \\ \dashrightarrow \sf{ A = \dfrac{ \theta}{360 \degree} \times \pi {r}^{2} } \\ \\ \dashrightarrow\sf{18 \pi = \dfrac{ \theta}{360 \degree} \times \pi {(6)}^{2} } \\ \\ \dashrightarrow \dfrac{ \theta}{360 \degree} = \dfrac{18 \pi}{ \pi(36)} \\ \\ \dashrightarrow \theta = 360 \degree \times \dfrac{1}{2} \\ \\ \dashrightarrow\theta = 180 \degree \\ \\ \end{array} } [/tex]
Related Questions
How do you solve longest side?
Answers
The cosine rule tells us
The third side (or c lets say):
c^2 = a^2 + b^2 - 2ab•cos(A)
The cost to hire a tent consists of two parts. $c + $d per dayThe total cost for 4 days is $27. 10 and for 7 days is $34. 30. Write down two equations in c and d and solve them
Answers
The cost to hire a tent consists of a fixed cost of $17.50 and a variable cost of $2.40 per day.
Let's call the total cost of hiring a tent for 4 days as T4, and the total cost of hiring a tent for 7 days as T7.
The first equation is the cost for 4 days:
T4 = c + 4d
The second equation is the cost for 7 days:
T7 = c + 7d
We know the values of T4 and T7 from the problem statement:
T4 = $27.10 and T7 = $34.30
We can now use these two equations and their corresponding values to solve for c and d:
Substitute the value of T4 into the first equation:
$27.10 = c + 4d
Substitute the value of T7 into the second equation:
$34.30 = c + 7d
Now we have a system of two equations with two variables (c and d).
Subtract 4d from both sides of the first equation:
$27.10 - 4d = c
Subtract c from both sides of the second equation:
$34.30 - c = 7d
Now we can substitute the value from step 4 into step 5:
$34.30 - $27.10 + 4d = 7d
7d = $34.30 - $27.10 + 4d
3d = $7.20
d = $7.20 / 3 = $2.40
Now we have the value of d, we can substitute it back into the first equation to find the value of c:
$27.10 = c + 4d
$27.10 = c + 4($2.40)
$27.10 = c + $9.60
c = $27.10 - $9.60
c = $17.50
Therefore, c= $17.50 and d= $2.40
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Augustus has made a pile of 2,000 candies, and he is giving away 25 candies a day from this pile. When will he have 350 candies left in this pile
Answers
350 = -25x + 2000
-1650 = -25
x = 66 days
What is the paradox in The Importance of Being Earnest?
Answers
The drama "The Importance of Being Earnest" contains many inconsistencies. Algernon's criticism of the lower class for not providing a better moral example for the upper class is paradoxical because the higher class must set the standard because it is the ruling class.
What is a paradox?A remark that logically contradicts itself or runs counter to one's expectations is referred to as a paradox.
It is a claim that, despite appearing to be supported by genuine premises and sound reasoning, leads to a logically untenable or self-contradictory conclusion.
One of the most straightforward yet well-known paradoxes is the liar paradox, sometimes known as the liar's paradox statement.
A paradox exists when someone says, "This statement is a lie" or "This statement is false," because if it were true, the statement would be speaking the truth.
In "The Importance of Being Earnest", the play has multiple contradictions.
Because the upper class is required to lead because it is the governing class, Algernon's dissatisfaction with the lower class for not setting a better moral example for the upper class is paradoxical.
Therefore, the drama "The Importance of Being Earnest" contains many inconsistencies. Algernon's criticism of the lower class for not providing a better moral example for the upper class is paradoxical because the higher class must set the standard because it is the ruling class.
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please help i need it by tomarrow
Answers
Answer:
2-6
3-9
5-15
6-18
2-6
4-12
5-15
8-24
Step-by-step explanation:
Multiply by 3
the product of 12 and the number n
Answers
Answer:
12n is the answer because 12 is and n if we multiply both of them it will be 12n.
Answer & Step-by-step explanation:
1. 3n= 12 divided 3 on both sides
n= 4
2. 6n=12 divide 6 on both sides
n= 2
3. 12n=12 divide 12 on both sides
n= 1
4. 5n = 12 divided 5 on both sides
n = 1.4
5. 8n=12 divide 8 on both sides
n= 1.5
Find the missing term in the arithmetic sequence −14, _, _, 46
Answers
To find the missing terms, we can use the formula for the nth term of an arithmetic sequence: a_n = a_1 + (n - 1)d, where a_n is the nth term, a_1 is the first term, and d is the common difference.
Plugging in the values from the given sequence, we have:
a_2 = -14 + (2 - 1) * 60 = -14 + 60 = 46
a_3 = -14 + (3 - 1) * 60 = -14 + 120 = 106
So, the missing terms are 46 and 106.
The ratio of the four sides of a trapezoid is 2:1:1:1.$ The area of the trapezoid is 27*sqrt3. Find the length of the median of the trapezoid.
Answers
The length of the median = 6[tex]\sqrt{3}[/tex]
If we call the longer base "a" and the shorter base "b", then we know that:
a:b = 2:1
Since the ratio of the four sides is 1:1:1:1, we know that the height, median and the longer base are all equal.
We can use that information to determine the area of the trapezoid. The formula for the area of a trapezoid is:
Area = (a + b) * h / 2
We know that the area is 27[tex]\sqrt{3}[/tex] and the height and median are equal, so we can set up the equation:
(a + b) * h / 2 = 27[tex]\sqrt{3}[/tex]
We also know that a:b = 2:1, so we can substitute that in:
(2b + b) * b / 2 = 27[tex]\sqrt{3}[/tex]
Simplifying, we get:
3b^2 = 54 * [tex]\sqrt{3}[/tex]
So the length of the median (h) is b
= [tex]\sqrt{(54 * \sqrt{3} / 3) }[/tex]
= 6[tex]\sqrt{3}[/tex]
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A person places $51200 in an investment account earning an annual rate of 5. 4%, compounded continuously. Using the formula V = Pe^{rt}V=Pe
rt
, where V is the value of the account in t years, P is the principal initially invested, e is the base of a natural logarithm, and r is the rate of interest, determine the amount of money, to the nearest cent, in the account after 6 years
Answers
The amount of money in the account after 6 years is $68,847.56
To solve this problem, you can use the formula for compound interest,
V = Pe^(rt)where V is the final value of the account, P is the initial principal, r is the annual interest rate (expressed as a decimal), and t is the number of years the money is invested.
The formula for compound interest, V = Pe^(rt) is used to calculate the future value of an investment. It takes into account the effect of compounding, which means that interest is earned not only on the initial investment but also on the accumulated interest over time.
Plugging in the given values, we have
V = 51200e^(0.0546) = 51200e^0.324. e^0.324 is approximately 1.38, so the final value of the account is 512001.38 = $68,847.56
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To get an A in her math class, Jada needs to have at least 90% of the total number of points possible. The table shows Jada’s results before the final test in the class.
1. ) Does Jada have 90% of the total possible points before the final test? Explain how you know.
2. ) Jada thinks that if she gets at least 92 out of 100 on the final test, she will get an A in the class. Do you agree? Explain
Answers
1) Jada does not have 90% of the total possible points before the final test.
2) If Jada gets at least 92 out of 100 on the final test, she will not get an A in the class.
From the following table of Jada’s results before the final test in the class the total number of points possible:
150 + 100 + 100 + 100 = 450
And Jada’s total points before the final test:
141 + 87 + 81 + 91 = 400
To check whether Jada have 90% of the total possible points before the final test, we find the percentgae of Jada’s total points.
(400/450) × 100 = 88.89%
This means, Jada does not have 90% of the total possible points before the final test.
After final test, the total number of points possible: 450 + 100 = 550
And if she gets at least 92 out of 100 on the final test, her total points would be,
400 + 92 = 492
And the percentgae of Jada’s total points would be,
(492/550) × 100 = 89.45%
Given that Jada needs to have at least 90% of the total number of points possible.
so, she will notl get an A in the class.
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Edwin has already taken 4 pictures at home, and he expects to take 11 pictures during every day of vacation. Is the total number of pictures taken proportional to the number of days spent on vacation?
Answers
Yes
Explained:
For every day he spends on holiday there will be 11 photos takes so to the ratio of days on holiday to photos taken it will be 1:11 and each day is 11 photos therefore yes the number of pictures takes in proportional to the number of days spent on vacation
Can you help me with this
Answers
The graph of the given equation y=2x+1 is attached below.
How to find the function which was used to make graph?There are many tools we can use to find the information of the relation which was used to form the graph.
A graph contains data of which input maps to which output.
Analysis of this leads to the relations which were used to make it.
For example, when the graph of a function is rising upwards after a certain value of x, then the function must be having increasingly output for inputs greater than that value of x.
If we know that the function crosses x axis at some point, then for some polynomial functions, we have those as roots of the polynomial.
The equation y=2x+1 gives the following information:
The slope is 2
The line intercepts is 1 on the y axis
First, we would put a point or a dot on (0,1) on the y axis. Then start making 2 points above and below my original point. IT would do this by using the slope 2/1.
By using my slope we know that (1,3) and (-1,-1).
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How do you read XYZ coordinates?
Answers
The XYZ coordinates are read as x-axis, y-axis and z-axis respectively.
Here we know that the x-axis is the horizontal line along which the wall to your left and the floor intersect where as the y-axis is the horizontal line along which the wall to your right and the floor intersect and the z-axis is the vertical line along which the walls intersect.
Here we also know that x-coordinate is measured along the east west axis, the y-coordinate is measured along the north south axis, and the z-coordinate measures height or elevation.
And it is used for a three-dimensional structure where the x-axis and y-axis represent the first two dimensions and the z-axis is the third dimension.
And in a graphic image, the axes x and y denote width and height and the z denotes depth.
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Please help asap people kept giving me wrong answers. Due tonight in a couple hours +25pts
ES = ___ units
Round your answer to the nearest tenth.
Answers
The value of ES will be;
⇒ ES = 10.63 units
What is Line segment?Line segment is a part of the line which have two endpoints and bounded by two distinct end points and contain every point on the line which is between its endpoint.
Given that;
The coordinate of E = (- 3, - 4)
The coordinate of S = (4, 4)
Now,
Since, The coordinate of E = (- 3, - 4)
The coordinate of S = (4, 4)
Hence, The value of ES is find as;
⇒ ES = √ (4 - (-3))² + (4 - (-4))²
= √ 7² + 8²
= √ 49 + 64
= √ 113
= 10.63
Thus, The value of ES = 10.63 units
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BANKING Twin brothers Amare and Jermaine each received $1000 for graduation. Amare invests his money in an account that pays 2.25% compounded daily. Jermain invests his money in an account that pays 2.25% compounded
annually.
Part A
Which brother will have more money at the end of 10 years?
A) Amare
B) Jermaine
C) The accounts will be equal.
Part B
To the nearest cent, how much more money? $
Answers
A) Amaire have more money than Jermaine after 10 years.
B) By [tex]5.387*10^{11}[/tex]% Amaire has more money than Jermaine.
What is compound interest?
The interest charged on a loan or deposit is known as compound interest. It is the idea that we employ the most frequently on a daily basis. Compound interest is calculated for an amount based on both the principal and cumulative interest.
Amare and Jermaine has initial amount = $1000
Amare spend his money that pays 2.25% compounded daily.
where are Jermain invest his money that pays 2.25% compounded annually.
Formula of Compound interest that compounded daily
final amount = [tex]A(1+\frac{r}{365})^{365t}[/tex]
where A is initial amount and t is time in years .
final amount after 10 years
final amount = [tex]1000(1+\frac{2.25}{365})^{365*10}[/tex]
final amount = 1000×[tex]1.00616^{3650}[/tex]
final amount = 1000×5.51×[tex]10^{9}[/tex]
final amount = $5.51 ×[tex]10^{12}[/tex]
Formula of Compound interest that compounded annually
final amount = [tex]A(1+\frac{r}{100})^{t}[/tex]
where A is initial amount and t is time in years .
final amount after 10 years
final amount = [tex]1000(1+\frac{2.25}{1000})^{10}[/tex]
final amount = 1000×[tex]1.00225^{10}[/tex]
final amount = 1000×1.0227
final amount = $1022.7
Part A :
Amare has more money after 10 years.
part B :
percent more money = [($5.51 ×[tex]10^{12}[/tex] - 1022.7)/1022.7]*100=[tex]5.387*10^{11}[/tex]%
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1. Which of these pairs of quantities are proportional to each other? For the quantities that are
proportional, what is the constant of proportionality?
a. Radius and diameter of a circle
b. Radius and circumference of a circle
c. Radius and area of a circle
d. Diameter and circumference of a circle
e. Diameter and area of a circle
Answers
a. Radius and diameter of a circle is proportional
b. Radius and circumference of a circle is proportional
c. Radius and area of a circle is not proportional
d. Diameter and circumference of a circle is proportional
e. Diameter and area of a circle is not proportional
Given that,
We have to find the pair of quantities are proportional to each other.
We know that,
What are ratio and proportion?In its most basic form, a ratio is a comparison between two comparable quantities.
In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.
If one quantity is increased by a constant k, the other will decrease by the same constant k in the case of inverse proportion, and vice versa.
We know
a. Radius and diameter of a circle is proportional because d=2r
b. Radius and circumference of a circle is proportional because C = 2πr
c. Radius and area of a circle is not proportional because A = πr² non linear relationship.
d. Diameter and circumference of a circle is proportional C = πd
e. Diameter and area of a circle is not proportional A = πd²
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Find the length of the third side. If necessary, round to the nearest tenth
Answers
On solving the provided question, we can say that it is right angle triangle provided, so cos 60 = 3/H => 1/2 = 3/H => H = 6
What is triangle?A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.
it is right angle triangle provided,
so
cos 60 = 3/H
1/2 = 3/H
H = 6
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For questions 3 – 4, use the table to answer the questions.
This table shows the high schools in a metro district and whether they offer hockey and golf.
High school Hockey Golf
East Valley ✔
Central
Lincoln ✔ ✔
Davis
West Pine ✔ ✔
Adams ✔
North River ✔ ✔
A high school is chosen at random from this list.
Let event A = The high school has a hockey team.
Let event B = The high school has a golf team.
3. Which high schools offer both hockey and golf?
What is P(A ∩ B)?
4. Which high schools offer hockey or golf or both?
What is P(A ∪ B)?
Answers
We have P(A ∩ B) is 2/5 and P(A ∪ B) is 5/5.
Lincoln and West Pine high schools offer both hockey and golf.
P(A ∩ B) is the probability that a randomly chosen high school has both a hockey team and a golf team. The probability that a school picked at random offers both hockey and golf is 2/5 (Lincoln and West Pine are the only schools that offer both out of 5 total schools.)
East Valley, Lincoln, West Pine, Adams and North River high schools offer hockey or golf or both.
P(A ∪ B) is the probability that a randomly chosen high school has either a hockey team or a golf team or both. The probability that a school picked at random offers either hockey or golf or both is 5/5 (All 5 high schools in the district offer at least one of the sports.)
Therefore, the correct answers of the problem statement are P(A ∩ B) is 2/5 and P(A ∪ B) is 5/5.
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Select the interval where f is negative.
Answers
Answer: A
Step-by-step explanation:
Based on the graph, we know that it is negative if it is under the x-axis. It is also indicated by the negative labels.
A: correct
Looking at choice A, it says the interval is from -4<x<-2. This means we have to find x=-4 and x=-2. On the graph, that interval is below the x-axis, so it is negative.
B: incorrect
Looking at choice B, it says the interval is from -1<x<1. This means we have to find x=-1 and x=1. On the graph, that interval is above the x-axis, so it is positive, not negative.
C: incorrect
Looking at choice C, it says the interval is from 2<x<4. This means we have to find x=2 and x=4. On the graph, that interval is above the x-axis, so it is positive, not negative.
Therefore, A is the correct answer.
Explain why the initial value of any function of the form
f(x)= a(b) is equal to a.
Answers
Hello there!
Initial value is the y-intercept so x = 0. Then b⁰ = 1 because x⁰ = 1 if x ≠ 0. So the value of function is a * 1 which is equal to a.
Step-by-step explanation: The initial value of any function of the form f(x)= a(b) is equal to a because this type of function is a linear equation, which means that the rate of change (slope) is constant. This means that the output is always equal to the input multiplied by a constant, which is the coefficient a. Therefore, when the input (x) is equal to 0, the output (f(x)) is equal to 0 multiplied by a, which is equal to a.
Tori bought one share of Macy's stock on Nov 1, 2016 for $33. 38. Four years later, she sold it and the closing price for that day was $5. 9. A) How much money did she gain/lose with this stock? b) What is her rate of return?
Answers
(a) He made $382.05. This was the amount of money he made from the stock.
(b) The investment yielded a 96.40% return.
How can I find out how much I made and what my investment returned?
The amount of money made is calculated by dividing the price at which the stock was sold by the price at which it was purchased. If this figure is negative, money was lost; if positive, money was made.
Tori lost money when she purchased one share of Macy's stock on November 1, 2016, for $33.38 and then sold it for $5.09 on that same day's closing price.
= $5.09 - $33.38
= -$28.29
Her rate of return will be:
= -28.29/33.38 × 100
= -84.75%
The amount he made with the stock is indicated below taking into account the values of the problem:
778.38 - 396.33 = $382.05.
The return on the investment is given by the amount earned/lost divided by the initial value, and multiplied by 100% to obtain the value as a percentage, hence it is of:
382.05/396.33 x 100% = 96.40%.
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Pls help me with math
Answers
Answer:1
Step-by-step explanation:;
A person loans his friend $500. They agree to an annual interest rate of 5%.
Write an expression for computing the amount owed on the loan, in dollars, after 1 years If no payments are made.
Answers
If no payments are made then the then after 1 year the interest will go by 5% , therefore the amount to be paid will become , P + 25 = 525 $.
Principle + 5% of 500
Therefore, the equation becomes ,
Amount = P + 25
To calculate the interest ,
interest = principal × interest rate × term
= 500 x 5 x 1
= 2500.
A loan is defined as a thing or money which is borrowed, especially a sum of money that is expected to be paid back with an interest rate which is fixed by both the parties.
Loans are typically taken or granted by by corporations, financial institutions, and governments. They allow for growth in the overall money supply in an economy and open up competition by lending to new businesses.
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Chelsea wants to determine the number of people in her school who read news reports on the Internet daily. She asks five people in her language arts class. Which improvements could Chelsea make to her sample to increase the validity of the results
Answers
The three choices are increase the sample size, pick individuals from various grade levels and in all language arts classes, pick the fourth student.
what is sample size?
The number of observations utilized to calculate estimates for a given population is referred to as the sample size. From the population, a sample size was chosen. The term "sample size" describes the number of subjects or observations that make up a study. n is typically used to represent this number.
The three choices are increase the size of the sample, pick individuals from various grade levels and in all language arts classes, pick the fourth student.
It's important to take into account the following data:
The sample size should be raised in order to boost the result validity, The students should be chosen from among the various grade levels and For all language kinds, a student should be chosen every fourth student.
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is -0.0022 is smaller than -0.022
Answers
Answer: No, -0.0022 is not less that -0.022
Step-by-step explanation:
1. We know that the bigger the negative number the lesser it is ( 0.022 is a bigger number than 0.0022) but since it's a negative number it's less in value.
Select all that are equivalent to sin∠GFH
A. Sin∠GEJ
B. Sin∠EGJ
C. Cos∠FGH
D. Cos∠GEJ
E. Cos∠GFH
F. Tan∠GEJ
Answers
All that is the equivalent angle to the given angle sin∠GFH is cos∠GEJ.
Corresponding angles are those angles which are created in the matching corners or corresponding corners with the transversal when two parallel lines are intersected by any other line (i.e. the transversal).
From the image, we get JE and HF are parallel.
So ∠GFH and ∠GEJ are corresponding angles. That means they are equal.
⇒sin(∠GFH) = sin(∠GEJ).
From triangle GFH, ∠GFH + ∠FGH = 90.
⇒sin(∠GFH) = cos(∠FGH).
Again ∠FGH = ∠EGJ.
⇒sin(∠GFH) = cos(∠EGJ)
All that is equivalent to sin∠GFH is cos(∠EGJ).
Thus, the correct answer is D.
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The Garcia family bought 400 yards of fencing to enclose a circular wildflower garden. They will use all of the fencing whats the area
Answers
The area of the windflower garden that is enclosed by a circular fence of 400 yards length is equal to 12732.39 square yards.
What is circumference of a circle?The measurement of the circle's perimeter, also known as its circumference, is called the circle's border. It is the length around the border of the circular object or the circle itself.
What is the formula for calculating the perimeter of a circle?The formula for calculating the perimeter of a circle is ,
Perimeter/ Circumference of a circle = 2 * pi * r, where pi = 3.14 and r is the radius of the circle.
Taking the given information in the question, i.e circumference of the circular fencing wire , i.e C = 400 yards
or , 2 * pi * r = 400
or , r = 400/(2* 3.14)
r = 63.66 yards
Now the area of the circular fence is given by,
Area = pi * r^2
Area = 3.14 * 63.66^2
Area = 12732.39 square yards
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The spinner is spun 75 times. What is the experimental probability of spinning the given result? Round your answer to the nearest hundredth if necessary. Outcome A B C D Frequency 20 11 14 30 B or C
Answers
The experimental probability of spinning of B or C is 1/3.
In the given question, the spinner is spun 75 times.
We have to find the experimental probability of spinning of B or C.
The given data is:
Outcome A B C D
Frequency 20 11 14 30
Total frequency = 20 + 11 + 14 + 30
Total frequency = 75
The probability of spinning B = Frequency of B/Total Frequency
The probability of spinning B = 11/75
The probability of spinning C = Frequency of C/Total Frequency
The probability of spinning C = 14/75
Now the experimental probability of spinning of B or C;
P(B or C) = P(B) + P(C)
P(B or C) = 11/75 + 14/75
P(B or C) = (11 + 14)/75
P(B or C) = 25/75
P(B or C) = 1/3
Hence, the experimental probability of spinning of B or C is 1/3.
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noah ia taking a multiple choice test with a total of 20 points available. Each question is worth exactly 1 point. What would be Noah's test score (out of 20) if he got 3 questions wrong? What would be his score if he got questions wrong?
Answers
Answer:
17
I wish you luck in your assignments.
John has the option to take the bus or a taxi to work each
day.
.
The bus costs $3. 00 per mile.
The taxi has a flat rate of
$4. 00 plus $1. 00 per mile.
Complete the blanks:
At _____miles, both the bus and the taxi will cost _____ dollars.
Answers
At 2 miles, both the bus and the taxi will cost $6.
What is an equation?
A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.
Given that the fare on bus is $3 per mile.
The taxi fare of taxi is $4. 00 plus $1. 00 per mile.
Assume that at x miles both fare will be the same.
The fare for x miles in bus is $3x.
The fare for x miles in taxi is $4 + $x
Equate to the fares:
3x = 4 + x
Subtract x from both sides:
3x - x = 4
2x = 4
Divide both sides by 2:
x = 4/2
x = 2.
The fare for 2 miles in bus is $3×2 = $6.
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