The equation of the line passing through the points (6, 5) and (8, -2) is[tex]y = -\frac{7}{2} x + 26[/tex].
What is the equation of the line?The formula for equation of line is expressed as;
y = mx + b
Where m is slope and b is y-intercept.
Determine the slope of the line.
Given the two points are (-7, -3) and (1, 2)
We can find the slope of the line by using the slope formula:
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values:
m = (-2 - 5) / (8 - 6)
m = -7/2
Using the point-slope form, plug in one of the given points and slope m = -7/2 to find the equation of the line.
Let's use the point (6, 5):
y - y₁ = m(x - x₁)
[tex]y - 5 = -\frac{7}{2}( x - 6 )\\\\y - 5 = -\frac{7}{2} x + 21\\\\y = -\frac{7}{2} x + 21 + 5\\\\y = -\frac{7}{2} x + 26[/tex]
Therefore, the equarion of the line is [tex]y = -\frac{7}{2} x + 26[/tex].
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A circle is centered at (4, −7) and has a radius of 5. Which of the following is the equation of this circle?
Group of answer choices
(x − 4)2 + (x + 7)2 = 5
(x − 4)2 + (x + 7)2 = 25
(x + 4)2 + (x − 7)2 = 5
(x + 4)2 + (x − 7)2 = 25
The equation of circle whose center is at (4,-7) and radius is "5 units", is (b) (x − 4)² + (x + 7)² = 25.
We know that the equation of a circle which have center at the coordinate (h, k) and has a radius as "r" is represented by the formula ⇒ (x - h)² + (y - k)² = r²,
In this case, the center of the circle is situated at the coordinate (4, -7) and the radius is 5.
So, we substitute these values into the "circle-equation" to get;
⇒ (x - 4)² + (y + 7)² = 5²,
⇒ (x - 4)² + (y + 7)² = 25,
Therefore, the correct option is (b): (x − 4)² + (y + 7)² = 25.
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The given question is incomplete, the complete question is
A circle is centered at (4, −7) and has a radius of 5. Which of the following is the equation of this circle?
(a) (x − 4)² + (x + 7)² = 5,
(b) (x − 4)² + (x + 7)² = 25,
(c) (x + 4)² + (x − 7)² = 5,
(d) (x + 4)² + (x − 7)² = 25.
Complete part (a) and part (b) given the following system of equations. x+y=0 -3x+4y=14. Solve this system graphically.
Answer:
Step-by-step explanation:
[tex]\left \{ {{x+y=0} \atop {-3x+4y=14}} \right.[/tex] ⇔ [tex]\left \{ {{y=-x} \atop {y=\frac{3}{4} x+ \frac{7}{2} }} \right.[/tex]
please helppp
here is the picture is about Row Ops
Multiplying row 1 of the matrix by 1 / 4 would give a resultant matrix of [ 1 / 2 0 | 3 / 4 ]
[ - 1 5 | 4 ].
How to multiply the matrix row ?The question wants to multiply the first row of the matrix alone, with the fraction, 1 / 4.
First step is then to multiply the first row by the fraction of 1 / 4 :
( 1 / 4 ) x 2 = 1 / 2
( 1 / 4 ) x 0 = 0
( 1 / 4 ) x 3 = 3 / 4
The results acquired can then be input into the matrix which would then give a resultant matrix of :
[ 1 / 2 0 | 3 / 4 ]
[ - 1 5 | 4 ]
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A farmer separated 7 hens from a group of chickens and placed them in a new coop If these 7 hens represent 20% of the total number of chickens the farmer owns, how many chickens does the farmer own?
The total number of chickens the farmer owns is 35.
What is percentage?A quantity or proportion can be expressed as a percentage of 100 by using the word "percentage." It is represented by the sign %.
For instance, when we state that 50 percent of a group of people are women, we mean that 50 out of every 100 people in the group are women.
We can deduce here the total chickens the farmer owns in % = 100%
Hens placed in a new coop = 20% = 7
Let the total number of chickens = x
Thus,
7 / x = 20 / 100
To solve for x, we can cross-multiply and simplify:
7 × 100 = 20 × x
700 = 20x
x = 35
Thus, the total number of chickens = 35.
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Javier and Naida are discussing the elevation of Lima, Peru.
200
150 Lima
100
50+
0+Sea level
-50-
-100+
-150
-200
The elevation of Lima, Peru is 154 meters.
Javier: Lima is 154] meters from sea level.
Naida: Lima is 154 meters above sea level.
Whose statement is true?
Choose 1 answer:
Answer:
Naida's statement is true
Step-by-step explanation:
Since the elevation of Lima, Peru is a positive number, you can automatically tell that it is above sea level since sea level is zero
WILL GIVE BRAINLIEST IF CORRECT
Will report is answer is a guess. Include reasoning behind answer
The image of point R by rotation is equal to R'(x, y) = (- 4, 7).
How to find the image of a point by rotation
The statement of the problem asks us to find the image of point by a kind of rigid transformation known as rotation, whose formula is:
(x, y) → (x · cos θ - y · sin θ, x · sin θ + y · cos θ)
Where:
x, y - Coordinates of the original point.θ - Angle of rotation, in degrees.If we know that x = 4, y = 7 and θ = - 180°, then the coordinates of the image of point R are:
R'(x, y) = (4 · cos 180° - 7 · sin 180°, 4 · sin 180° + 7 · cos 180°)
R'(x, y) = (- 4, 7)
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Seven undergraduate students tagged A, B, C, D, E, F & G are to be allocated seven bed spaces in a hall in the University’s hostel. Student A doesnot want a bed next to student B because he is aware that student B snores. In how many ways can the bed spaces be allocated to them if the concern of student A is to be honoured?
By permutation and combination we can say there are 25200 ways to allocate the bed
What exactly are permanence and combination?Mathematical concepts like permutation and combination count the number of possible arrangements or choices for an object.
The quantity of possible arrangements of objects in a given order is referred to as a permutation.
Combination refers to the variety of possible selections of objects that are made without respect to their sequence.
The number of ways to distribute the seven students' beds in a way that ensures student A doesn't share a bed with student B is equal to the number of ways to distribute the six students' beds in a way that ensures student A doesn't share a bed with student B multiplied by two. (since there are two possible positions for student B).
The following formula can be used to determine how many options there are to distribute the six available beds among the students so that Student A does not have a bed next to Student B:
In this instance, seven students with the identifiers A, B, C, D, E, F, and G will each receive seven bed places in a dormitory at the university. Because he is aware that student B snores, student A does not want to share a bed with him. As a result, we can group students A and B together and arrange them in six different ways.
Then we can arrange the remaining students C, D, E, F and G in 5! ways. Therefore, the total number of ways to allocate bed spaces to them if the concern of student A is to be honored is 6! * 5! = 17,280 .
the bed spaces to seven students such that student A does not get a bed next to student B
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This is for precalc can someone help please
Y= 1/2x+5
X _ Y
-4. ?
-2. ?
0. ?
2. ?
Answer: 0.
Step-by-step explanation:
y-(1/2*x+5)=0 STEP 1:
simplify 1/2
Equation at the end of step 1: 1
y - ((— • x) + 5) = 0
Solve for k and graph the solution. 0≥ k+14 3 > – 2
The graph of the solution set for the inequality -14 ≥ k > -20 is on the image at the end.
How to solve the inequality for k?To do this we just need to isolate the variable k in the middle.
We start with:
0 ≥ (k+14)/3 > – 2
We can multiply both sides by 3:
3*0 ≥ (k+14) > – 2*3
0 ≥ (k+14) > - 6
Now subtract 14 in both sides:
-14 ≥ k > -6 - 14
-14 ≥ k > -20
Then we need to draw an open circle at k = -20 and a closed circle at k = -14, and connect them with a line, like in the image below.
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DISCUSSION QUESTIONS 1. Ongoing efforts have been undertaken in Malaysia to improve the financial reporting and accountability in government agencies. Discuss the efforts. 2. Discuss the extent of application for the key accounting concepts in the public sector. 3. Clearly describe the regulatory framework and procedures for financial reporting in the public sector.
Answer:
1.Ongoing efforts have been undertaken in Malaysia to improve the financial reporting and accountability in government agencies. Discuss the efforts.
Malaysia has been making efforts to improve financial reporting and accountability in government agencies for several years. In 2015, the Malaysian government introduced a new financial reporting framework for government agencies called the Malaysian Public Sector Accounting Standards (MPSAS). This framework is designed to improve financial reporting and ensure that government agencies are held accountable for their financial performance.
The MPSAS framework is based on international accounting standards and is meant to increase transparency and consistency in financial reporting. It includes guidelines for budgeting, financial management, and reporting of financial performance. Additionally, the Malaysian government has established the Accountant General's Department, which is responsible for overseeing financial reporting in government agencies.
Other initiatives aimed at improving financial reporting and accountability in Malaysia include the implementation of electronic financial management systems, the introduction of new financial management guidelines, and the establishment of a Financial Management Committee to oversee financial management across all government agencies.
2.Discuss the extent of application for the key accounting concepts in the public sector.
The key accounting concepts that are applicable to the public sector are similar to those used in the private sector, with some important differences. One of the key differences is that in the public sector, accounting practices are focused on ensuring accountability to the public and ensuring that public funds are used responsibly.
Some of the key accounting concepts that are applicable in the public sector include accrual accounting, budgeting, and financial reporting. Accrual accounting is used to record financial transactions as they occur, regardless of when payment is made or received. This helps to ensure that all financial transactions are recorded accurately and transparently.
Budgeting is also an important accounting concept in the public sector. Governments typically create budgets to allocate funds to various programs and projects. These budgets are then used to monitor financial performance and ensure that resources are used efficiently.
Financial reporting is another key accounting concept in the public sector. Governments are required to report on their financial performance to ensure transparency and accountability. This includes reporting on revenue and expenses, assets and liabilities, and cash flow.
3.Clearly describe the regulatory framework and procedures for financial reporting in the public sector.
The regulatory framework for financial reporting in the public sector typically involves a combination of national and international accounting standards. In Malaysia, the regulatory framework is based on the Malaysian Public Sector Accounting Standards (MPSAS), which are based on international accounting standards.
Under this framework, government agencies are required to prepare financial statements in accordance with MPSAS. These statements include the statement of financial position, statement of financial performance, statement of changes in equity, and statement of cash flows.
Additionally, the Accountant General's Department is responsible for overseeing financial reporting in government agencies. They are responsible for ensuring compliance with MPSAS and for providing guidance on financial reporting issues.
Government agencies in Malaysia are required to submit their financial statements to the Accountant General's Department for review and approval. Once approved, these statements are published and made available to the public.
Overall, the regulatory framework and procedures for financial reporting in the public sector are designed to ensure transparency and accountability in the use of public funds.
What is 6+4 3/4+(-2.5)= explain your answer
The value of 6+4 3/4 +(-2.5) is 3 3/10
What is PEDMAS?PEDMAS is an acronym that shows the correct order of operations in mathematical problems. The full meaning of PEDMAS is ;
Parentheses
Exponents
Division
Multiplication
Addition
Subtraction
This order is followed when solving mathematical problems.
Solving 6+4 3/4 +(-2.5)
= 6+ 19/4 - 5/2
= ( 24+19-10)/4
= 33/10
= 3 3/10
Therefore the value of 6+4 3/4 +(-2.5) is 3 3/10
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10. The time it takes to drain a swimming pool varies inversely with the amount of water being
pumped per hour. If a large pool takes 12 hours to empty at 400 gallons an hour, how many
hours faster can the pool be drained if the pumping rate is increased to 500 gallons per hour?
(teal)
To solve this problem, we can use the formula for inverse variation, which is:
time = k/ rate
where k is a constant of proportionality.
We can start by finding the value of k using the given information. We know that when the pumping rate is 400 gallons per hour, it takes 12 hours to drain the pool. Therefore:
12 = k/400
Multiplying both sides by 400 gives us:
k = 4800
Now we can use this value of k to answer the second part of the question. We want to know how many hours faster the pool can be drained if the pumping rate is increased to 500 gallons per hour. Let's call this new time t:
t = 4800/500
t = 9.6 hours
So the pool can be drained 12 - 9.6 = 2.4 hours faster if the pumping rate is increased to 500 gallons per hour.
HELP ME PLEASE :DDDDDDDD
The expression to find the angle BGC is 11x + 34.
The equation that would help us find the angles of AGB and BGC is 90 = 11x + 46.
The correct equation that would help us find the angles of ABG, AGF, and AGE is 15x + 120 = 180.
What is a complementary angle?In Mathematics and Geometry, a complementary angle refers to two (2) angles or arc whose sum is equal to 90 degrees (90°).
By substituting the given parameters into the complementary angle formula, the sum of the angles is given by;
∠AGB + ∠BGC = 90.
12 + 11x + 34 = 90
11x + 46 = 90
90 = 11x + 46.
Additionally, the sum of all of the angles on a straight line is always equal to 180 degrees. In this scenario, we can reasonably infer and logically deduce that the sum of angles ABG, AGF, and AGE are supplementary angles:
12 + 90 + 15x + 18 = 180°
120 + 15x = 180°
15x + 120 = 180
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The graph of an equation is sketched in the figure.
Describe five ordered-pair solutions of this equation by
using a table.
X
-6
-3
0
3
6
y
☐
I
8-
10-88427
6
40
10
The value of five ordered-pair solutions of this equation by using a table are,
x y
- 6 - 1
- 3 - 2
0 3
3 - 4
6 - 5
We have to given that;
The graph of an equation is sketched in the figure.
Hence, From graph we get;
The value of five ordered-pair solutions of this equation by using a table are,
x y
- 6 - 1
- 3 - 2
0 3
3 - 4
6 - 5
Thus, The value of five ordered-pair solutions of this equation by using a table are,
x y
- 6 - 1
- 3 - 2
0 3
3 - 4
6 - 5
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Navid earns a basic wage of $10.25 an hour. He works for 40 hours a week. He earns 20% more than his basic wage when he works overtime. Navid wants to earn at least $500 this week. Calculate the total number of hours he needs to work. Give your answer to the nearest hour.
A child at a day care can choose one type of writing tool and one type of paper for an art project. The chart shows
the types of writing tools and paper that are available.
Art Project
Type of Writing Tool Type of Paper
Crayon
Marker
Pencil
Construction
Newsprint
Which list shows all the combinations of one type of writing tool and one type of paper that can be used for the art
project?
The list that shows all the combinations is given as follows:
{Crayon, Construction}, {Marker, Construction}, {Pencil, Construction}, {Crayon, Newsprint}, {Marker, Newsprint}, {Pencil, Newsprint}.
What is the Fundamental Counting Theorem?The Fundamental Counting Theorem states that if there are m ways for one trial and n ways for another trial, then there are m x n ways in which the two trials can happen simultaneously.
This can be extended to more than two trials, where the number of ways in which all the trials can happen simultaneously is the product of the number of outcomes of each individual trial, according to the equation presented as follows:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
The options are given as follows:
Writing Tool: Crayon, Marker and Pencil. -> 3 options.Type of Paper: Construction and Newsprint -> 2 options.The total number of options is given as follows:
3 x 2 = 6.
Hence the list is:
{Crayon, Construction}, {Marker, Construction}, {Pencil, Construction}, {Crayon, Newsprint}, {Marker, Newsprint}, {Pencil, Newsprint}.
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Solve the equation without using a calculator
[tex](x^2-9x-1)^{10}+99x^{10}=10x^9(x^2-1)[/tex]
Answer:
x = 5 ± √26-------------------------
Convert the given equation as below:
[tex](x^2-9x-1)^{10}+99x^{10}=10x^9(x^2-1)[/tex][tex](x^2-9x-1)^{10}+99x^{10}=10x^9(x^2-9x-1)+10x^9(9x)[/tex][tex](x^2-9x-1)^{10}+99x^{10}=10x^9(x^2-9x-1)+90x^{10}[/tex][tex](x^2-9x-1)^{10}+9x^{10}=10x^9(x^2-9x-1)[/tex][tex](x^2-9x-1)^{10}-9x^9(x^2-9x-1)=x^9(x^2-9x-1)-9x^9x[/tex]Let's substitute x² - 9x - 1 = t, then the equation is:
[tex]t^9t-9x^9t=x^9t-9x^9x[/tex]Comparing both sides, we see that x = t, so:
x² - 9x - 1 = xx² - 10x - 1 = 0Solving this quadratic equation we get:
x = 5 ± √26Determine whether y=9(-5)^x represents an exponential function
Answer: Yes, y = 9(-5)^x represents an exponential function.
An exponential function is a function in the form y = ab^x, where a and b are constants and b is a positive real number not equal to 1. The base, b, is raised to the power of x, and the resulting value is multiplied by the constant a.
In the given function, we have a = 9 and b = -5. Although b is negative, it is still a real number not equal to 1, so the function is still considered exponential. Furthermore, the exponent x is a variable, which is raised to a constant base -5, meeting the definition of an exponential function.
Therefore, y = 9(-5)^x is an exponential function.
Step-by-step explanation:
Mr Tan calculated the average amount of money collected by all the students in his class during a fund-raising event. If three of his students each collected $32 less, the average amount of money collected would be $146. If eight of his students each collected $18 more, the average amount of money collected would be $156. How many students were there in Mr Tan's class?
There were 56 students in Mr Tan's class.
To solve this problem, we can use the formula for average: average = (sum of all values) / (number of values). Let's assume that there were initially n students in Mr Tan's class, and the average amount collected was x. Then, we can write:
nx = sum of all amounts collected
Now, if three students each collected $32 less, the new sum of amounts collected would be:
(nx - 3*32) = (n-3)(x-32)
And the new average would be:
(n-3)(x-32) / n = 146
Similarly, if eight students each collected $18 more, the new sum of amounts collected would be:
(nx + 8*18) = (n+8)(x+18)
And the new average would be:
(n+8)(x+18) / n = 156
Now we have two equations with two unknowns (n and x). We can solve them using algebraic manipulation. After some simplification, we get:
n = 56 and x = 104
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Question 7 of 10
Using the graphing function on your calculator, find the solution to the system
of equations shown below.
A. x = 5, y = -2
B. More than 1 solution
O C. No solution
OD. x= -2, y = 5
y+ x = 3
y-2x = -12
The solution to the system of equations shown above include the following: A. x = 5, y = -2
How to graphically solve this system of equations?In order to graphically determine the solution for this system of linear equations on a coordinate plane, we would make use of an online graphing calculator to plot the given system of linear equations while taking note of the point of intersection;
y + x = 3 ......equation 1.
y - 2x = -12 ......equation 2.
Based on the graph shown (see attachment), we can logically deduce that the solution for this system of linear equations is the point of intersection of each lines on the graph that represents them, which is represented by this ordered pair [5, -2].
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Rebecca used 4.25pt of milk in her baking recipe. How many cups of milk did she use?
Answer: 8.25
Step-by-step explanation:
It’s similar figure with proportions
Answer:
x = 72 cm
Step-by-step explanation:
Because the two figures are similar, we can create a proportion between one set of similar sides (i.e., the side measuring 48 cm and the side measuring 6 cm) and another set (the side measuring x cm and the side measuring 9 cm. This, will allow us to solve for x:
[tex]\frac{6}{48}=\frac{9}{x}\\ 432=6x\\ 72=x[/tex]
Another way to solve would have been to notice that the scale factor used to create the bigger puzzle piece is 8 since 6 * 48. In order for the smaller figure to be considered similar to the larger, every side had to be multiplied by the same scale factor. Since the scale factor is 6, x must be 72 cm as 9 * 8 = 72
I may be able to figure out part (b) of this one, but I do need help with parts (a) and (c). Any help would be greatly appreciated.
(a) The shape of sampling distribution is not too close to 0 or 1 (b) The mean of standard deviation = 0.033
(c) [tex]P(Z > (P-P + 0.03) / 0.033) = P(Z > 0.91)[/tex]
According to given information:(a) The sampling distribution of p-p is approximately normal by the Central Limit Theorem because both sample sizes are large enough (n₁ = n₂ = 240) and the sample proportions of orange candies are not too close to 0 or 1.
(b) The mean of the sampling distribution of p-p is equal to the difference between the population proportions, which is 0.20 - 0.23 = -0.03. The standard deviation of the sampling distribution of p-p is given by:
sqrt[(p₁q₁/n₁) + (p₂q₂/n₂)]
= sqrt[(0.200.80/240) + (0.230.77/240)]
= 0.033
The standard deviation represents the amount of variation we expect to see in the differences between sample proportions of orange candies from multiple random samples of the same size.
(c) To find P(P-P>0), we need to standardize the difference between the sample proportions and the population difference and then find the probability that the standardized difference is greater than 0. That is:
(P-P - (p₁ - p₂)) / sqrt[(p₁q₁/n₁) + (p₂q₂/n₂)]
= (P-P - (-0.03)) / 0.033
= (P-P + 0.03) / 0.033
Using a standard normal distribution table or calculator, we can find the probability that a standard normal variable is greater than this value. For example, if we use a calculator, we get:
P(Z > (P-P + 0.03) / 0.033) = P(Z > 0.91)
where Z is a standard normal variable. The probability is approximately 0.18. This means that if we take many random samples of 240 M&M's milk chocolate candies and 240 peanut M&M's and calculate the difference between the sample proportions of orange candies, about 18% of the time we would expect to see a difference of 0.03 or greater (favoring M&M's milk chocolate candies).
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An angle measures 158.2° less than the measure of its supplementary angle. What is the measure of each angle?
Answer:
the 2 angles are 169.1° and 10.9°
Step-by-step explanation:
Supplementary angles add to 180
x = first angle
y = second angle = x - 158.2
x + y = 180
x + (x - 158.2) = 180
2x = 180 + 158.2
2x = 338.2
x = 338.2/2 = 169.1
y = 169.1 - 158.2 = 10.9
x + y = 169.1 + 10.9 = 180
PLEASE SOLVE THIS QUICKLY!!!!!
The ratio of the two arc lengths is equal to a / b. (Correct choice: B)
How to find the ratio of two arc lengths
In this problem we must determine the ratio of two arc lengths, that is, the ratio between two circular arcs. The length of a circular arc is described by the following expression:
s = θ · r
Where:
s - Arc length
θ - Angle, in radians.
r - Radius
And the ratio of the length JK to the length MN is:
JK / MN = (θ · a) / (θ · b)
JK / MN = a / b
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what is y= -2/9x +2 in standard form?
Answer:
2x+9y=18
Step-by-step explanation:
Consider the letters in the word SAMPLE. In how many ways can you arrange 5 of the letters?
Answer: 720
Step-by-step explanation: There are 6 choices for the first letter, 5 for the second, 4 for the third and so on. 6*5*4*3*2=720
Step-by-step explanation:
according to the law of combination
⁵C6 note 6 is a base numberCombining formula: 6!/(6-1)! 6!solving 6!/5! 6! :120waysIf your starting salary is $50,000 and you receive a 4% increase at the end of
every year, what is the total amount, in dollars, you will earn over the first 16
years that you work?
Round your answer to the nearest whole dollar, and express your answer
without using commas.
Answer here
SUBMIT
Answer:
Total amount of becomes after 16 year is $93649 .
Which equation has the variable, or missing number, in the correct place to match the given situation? The Mansour family drove a total of 687 miles, starting on Friday and ending on Sunday. They drove 313 miles on Friday and 164 miles on Saturday. How many miles did they drive on Sunday?
part a.
The equation that has the variable in the correct place to match the given situation is: Sunday's mile
part b
the Mansour family drove 210 miles on Sunday.
What is an equation?An equation is described as a formula that expresses the equality of two expressions, by connecting them with the equals sign =..
We have that the equation that has the variable in the correct place to match the given situation is: Sunday's mile
Sunday's miles = Total miles - Friday's miles - Saturday's miles
Sunday's miles = 687 - 313 - 164
Sunday's miles = 210
In conclusion, the Mansour family drove 210 miles on Sunday.
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