3. The mean of 7 test scores is 85. Of the 7 tests scores, 6 are shown: 75, 82, 82, 83, 90, 95. What is the 7th test score?​

Answer:

B

Step-by-step explanation:

first you would need to do the inverse of sine to get the angle since normal sine would give you the length and you need the angle.

An easy way to remeber sine, cosine and tangent is

SOH CAH TOA

sin= opposite/ hypotenuse

cosine= adjacent/ hypotenuse

tangent= opposite/adjacent.

first label your triangle with the sides hypotenuse, adjacent and opposite.

hypotenuse is the longest side that is diagonal in this case like ab

opposite is the side that is opposite the angle you are looking for, so in thsi case line cb

adjacent is the like next to the angle you are trying to find so in thsi case like ac

and since we know sine inverse = opposite/hypotenuse = angle

(we are using sine for this question since that is what the question is asking for)

we simply do

sine inverse= 3/5

so the answer is B

i hope this helps! :)

Answer:B

Step-by-step explanation: im sure because i answer that in school im correct

Answer:

Well,

[tex]0.5(5-7x)=8-(4x+6)\\-3.5x+2.5=-4x+2\\0.5x+2.5=2\\0.5x=-0.5\\x=-1[/tex]

Step-by-step explanation:

Hope this helps!^^

Answer: -1

Step-by-step explanation:

first you want to simplify 0.5 (5-7x) which will get you 2.5 - 3.5x

then you will do the same for the other side move the xs to one side then treat it like any other problem

When driving in normal conditions on a rural roadway, your following distance should be four seconds or more because it gives you more time to respond to any unexpected occurrences that might occur. therefore option d) four seconds or more is correct.

Following distance is the amount of space between a car and the car in front of it when driving on the road. It's essential to keep a safe following distance because it gives you more time to react if the car in front of you makes a sudden stop or starts to slow down. It's critical to keep a safe following distance because it's not always possible to avoid sudden stops or slow-downs.

A rural roadway is a road that runs through the countryside. In comparison to city roads, rural roads are less congested, with less traffic and less likelihood of accidents. As a result, it's essential to maintain a safe following distance when driving on rural roads because they're often long and wide, with higher speed limits and less congestion than city roads.

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To estimate x, we can use the fact that 5% is approximately equal to 1/20. Therefore, if 5% of x is about 10 hours, then we can estimate that 1/20 of x is also about 10 hours.

Multiplying both sides of the equation 1/20 x = 10 by 20, we get x = 200.

To check our answer, we can verify that 5% of 200 hours is indeed about 10 hours.

We used the multiplication property of equality to solve for x, which states that we can multiply both sides of an equation by the same non-zero number without changing the solution. In this case, we multiplied both sides by 20.

Answer: 475 is ur answer

Step-by-step explanation:

Answer:

-9 and -2

Step-by-step explanation:

-9 and -2

two negatives multiply to make a positive (18)

and -9 add -2 is -11

The points A', B', and C' are  (3, 1), (0, 3) and (-2, 4) respectively. The solution has been obtained by using the concept of transformation.

What is transformation?

Transformations allow for the translation, rotation, and reflection of shapes on a coordinate plane. Any line, point, or vector can be rotated, translated, or reflected.

We are given coordinates of triangle ABC as A (1, -3), B (3, 0) and C (4, -2).

Now, we need to rotate the triangle ABC 90 degrees about the origin.

We know that the rotation rule for rotating 90 degrees about the origin is that (x, y) becomes (y, -x).

So, from this we get the coordinates as

A' (3, -1)

B' (0, -3)

C' (-2, -4)

Now, on reflecting it over the x - axis, we get

A' (3, 1)

B' (0, 3)

C' (-2, 4)

Hence, the points A', B', and C' are  (3, 1), (0, 3) and (-2, 4) respectively.

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"type of orange" because it is a bar graph therefore it is supposed to be categories, not numbers :)

The polynomial to represent the volume of the rectangular prism is:

V = (0.5x - 3) × (x - 4) × (x + 5)

Simplifying this expression gives V = 0.5x³ - 6.5x² - 23x + 60

How to calculate the volume (V) of a rectangular prism?
The volume (V) of a rectangular prism can be calculated using the formula V = l × w × h, where l, w, and h are the length, width, and height of the prism respectively.

Here, the length (l) can be represented by (0.5x - 3), the width (w) can be represented by (x - 4), and the height (h) can be represented by (x + 5).

Therefore, the polynomial to represent the volume of the rectangular prism is:

V = (0.5x - 3) × (x - 4) × (x + 5)

Simplifying this expression gives V = 0.5x³ - 6.5x² - 23x + 60

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This problem can be solved by the unitary method. If Lee Ann bought 2 cartons of yoghurt, she would take 16 days to finish two cartoons as there were 8 yoghurt in each cartoon.

The unitary method involves first determining the value of a single unit, followed by the value of the necessary number of units.

Always write the things that need to be calculated on the right side and the things that are known on the left side to simplify things. In the aforementioned issue, the number of apples is known, but it is unclear what they are worth. It should be noted that issues with this method are solved using the concepts of ratio and proportion.

Let's say you go to the store to buy six apples. You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples. Recognizing the units and values is crucial when applying the unitary method to a problem.

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Answethe two digit is a multiple of 5

Step-by-step explanation:

the two-digit number is 65 so, options that must be true are a and b.

Addition is a basic arithmetic operation that combines two or more numbers to produce a sum or total

Let x stand for the tens digit and y for the units digit.

x + y = 11 (the digits of the two-digit number sum to 11)

x - y = 1 (the positive difference of the digits is 1)

Adding these two equations gives:

2x = 12

So x = 6.

Substituting x = 6 into either of the equations gives y = 5.

Therefore, the two-digit number is 65.

Now we can check which of the options is true:

a. The two-digit number has a product of 30 digits.

6 x 5 = 30, so this is true.

b. The number has two digits and is a multiple of 5.65 is a multiple of 5, so this is true.

c. The two-digit number is even.

65 is not even, so this is false.

d. The two-digit number is 83.

The two-digit number is 65, not 83, so this is false.

Therefore, the options that must be true are a and b.

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The 95% confidence interval for the mean mass of the population is 24.57 ± 1.06. The upper limit of the 95% confidence interval is 25.63.

Given the masses, in grams, of ten ball bearings taken at random from a batch are: 25.9, 24.7, 23.4, 24.5, 25.0, 26.9, 26.4, 25.8, 23.2, 21.9

We have to calculate a 95% confidence interval for the mean mass of the population, supposed normal, from which these masses were drawn.The formula for the Confidence Interval is given by,

CI = X bar± tα/2 * (s/√n)

Where,

CI = Confidence Interval

Xbar = Sample mean

tα/2 = α level of significance/2 (α is the level of significance)

s = sample s

tandard deviationn = sample size

tα/2 = t-distribution value for α/2 and (n-1) degrees of freedomtα/2 for α = 0.05 and (n-1) degrees of freedom

tα/2 = 2.262

Hence,CI = X bar ± tα/2 * (s/√n)

CI = 24.94 ± 2.306 * (1.618/√10)

CI = 24.94 ± 1.36

Upper limit of 95% confidence interval

x2 = 24.94 + 1.36= 26.30

Rounded off to two decimal places, x2 is 26.30.

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Where the above mean exist, the values of x and y  are 10.5 and 3.5 respectively.

The total number of people surveyed is 24. So we can write:

Frequency of 0 sisters + Frequency of 1 sister + Frequency of 2 sisters + Frequency of 3 sisters = Total frequency

5 + x + 5 + y = 24

x + y = 14 --- (1)

Also, we know that the mean number of sisters is 1.25. This means that the total number of sisters divided by 24 should be equal to 1.25. So we can write:

0 × 5 + 1 × x + 2 × 5 + 3 × y = 1.25 × 24

x + 3y = 21 --- (2)

Now we have two equations (1) and (2) with two variables (x and y). We can solve for x and y by simultaneous equations.

Multiplying equation (1) by 3, we get:

3x + 3y = 42 --- (3)

Subtracting equation (2) from equation (3), we get:

2x = 21

x = 10.5

Substituting the value of x in equation (1), we get:

10.5 + y = 14

y = 3.5

Therefore, the values of x and y are 10.5 and 3.5 respectively.

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Answer:

24 sin(3x) cos(3x)

Step-by-step explanation:

To find:-

Answer:-

The given function to us is ,

[tex]:\sf\implies y = 4sin^2(3x) \\[/tex]

To find it's derivative we would have to use Chain rule of differentiation , which is ;

[tex]:\sf\implies \pink{ \dfrac{dy}{dx}=\dfrac{dy}{du}\cdot \dfrac{du}{dx}} \\[/tex]

Taking the given function,

[tex]:\sf\implies y = 4sin^2(3x) \\[/tex]

Differentiate both sides with respect to x,

[tex]:\sf\implies \dfrac{dy}{dx}=\dfrac{d}{dx}4sin^2(3x)\\[/tex]

We can take out the constant as ,

[tex]:\sf\implies \dfrac{dy}{dx}= 4 \dfrac{d}{dx}sin^2(3x) \\[/tex]

Multiply and divide by sin(3x) as ,

[tex]:\sf\implies \dfrac{dy}{dx}= 4 \bigg( \dfrac{d(sin^23x)}{d(sin3x)}\times \dfrac{d\ sin3x}{dx}\bigg)\\[/tex]

Differentiation of sin(nx) is n cos(nx) and

[tex]:\sf\implies \pink{ \dfrac{d(x^n)}{dx} = nx^{n-1} }[/tex]

So that ,

[tex]:\sf\implies \dfrac{dy}{dx}= 4 ( 2sin(3x) \cdot 3cos(3x))\\[/tex]

Simplify,

[tex]:\sf\implies\pink{ \dfrac{dy}{dx}= 24\ sin(3x) \ cos (3x)}\\[/tex]

Hence the derivative of the given function is 24 sin(3x) cos(3x) .

[tex]\rule{200}2[/tex]

Related formulae :-

[tex]\boxed{\boxed{\begin{minipage}{5cm}\displaystyle\circ\sf\;\dfrac{d}{dx}(sin\;x)=cosx \\\\ \circ \;\dfrac{d}{dx}(cos\;x) = -sinx \\\\ \circ \; \dfrac{d}{dx}(tan\;x) = sec^{2}x \\\\ \circ\; \dfrac{d}{dx}(cot\;x) = -csc^{2}x \\\\ \circ \; \dfrac{d}{dx}(sec\;x) = secx \cdot tanx \\\\ \circ \; \dfrac{d}{dx}(csc\;x) = -cscx \cdot cotx \\\\ \circ\; \dfrac{d}{dx}(sinh\;x)=coshx \\\\ \circ\; \dfrac{d}{dx}(cosh\;x)= sinhx \\\\ \circ\;\dfrac{d}{dx}(tanh\;x)=sech^{2}h \\\\ \circ\;\dfrac{d}{dx}(coth\;x)=-csch^{2}x \\\\ \circ\;\dfrac{d}{dx}(sech\;x) =-sechx \cdot tanhx \\\\ \circ\;\dfrac{d}{dx}(csch\;x) = -cschx \cdot cothx\end{minipage}}}[/tex]

[tex]\rule{200}2[/tex]

Answer:

[tex]\dfrac{\text{d}y}{\text{d}x}=12 \sin (6x)[/tex]

Step-by-step explanation:

To find the derivative of y = 4sin²(3x), use the chain rule.

[tex]\boxed{\begin{minipage}{5.4 cm}\underline{Chain Rule for Differentiation}\\\\If $y=f(u)$ and $u=g(x)$ then:\\\\$\dfrac{\text{d}y}{\text{d}x}=\dfrac{\text{d}y}{\text{d}u}\times\dfrac{\text{d}u}{\text{d}x}$\\\end{minipage}}[/tex]

The given function can be written as:

[tex]y=4(\sin 3x)^2[/tex]

Let y = 4u², where u = sin(3x).

Differentiate the two parts separately.

[tex]\dfrac{\text{d}y}{\text{d}u}=8u \quad \text{and} \quad \dfrac{\text{d}u}{\text{d}x}=3 \cos (3x)[/tex]

Put everything into the chain rule formula:

[tex]\begin{aligned} \implies \dfrac{\text{d}y}{\text{d}x}& =\dfrac{\text{d}y}{\text{d}u}\times\dfrac{\text{d}u}{\text{d}x}\\\\&=8u \times 3 \cos (3x)\\\\&=24u \cos (3x)\\\\&=24 \sin (3x) \cos (3x) \end{aligned}[/tex]

Simplify using the sine double angle identity:

[tex]\boxed{\sin (2 \theta)= 2 \sin \theta \cos \theta}[/tex]

[tex]\begin{aligned} \implies \dfrac{\text{d}y}{\text{d}x}&=24 \sin (3x) \cos (3x) \\\\&=12(2 \sin (3x) \cos (3x))\\\\&=12 \sin (2 \cdot 3x)\\\\&=12 \sin (6x)\end{aligned}[/tex]

Therefore:

[tex]\dfrac{\text{d}y}{\text{d}x}=12 \sin (6x)[/tex]

[tex]\hrulefill[/tex]

[tex]\boxed{\begin{minipage}{5.8 cm}\underline{Differentiating $ax^n$}\\\\If $y=ax^n$, then $\dfrac{\text{d}y}{\text{d}x}=nax^{n-1}$\\\end{minipage}}[/tex]

[tex]\boxed{\begin{minipage}{5.8 cm}\underline{Differentiating $\sin (ax)$}\\\\If $y=\sin(ax)$, then $\dfrac{\text{d}y}{\text{d}x}=a \cos (ax)$\\\end{minipage}}[/tex]

Answer:

Answer is 28

Step-by-step explanation:

Length = 5

Width = 9

Perimeter = length*2 + width*2

Perimeter = 5*2 + 9*2

Perimeter = 10 + 18 = 28

the area of the porch is 228 square centimeters. To calculate the area of a porch, we need to use the formula for the area of a rectangle, which is:

Area = length x width

In this case, the length of the porch is 19 cm and the width is 12 cm. So, we can plug these values into the formula:

Area = 19 cm x 12 cm

Area = 228 cm^2

Therefore, the area of the porch is 228 square centimeters.

It's important to note that when we use the term "area," we are referring to the amount of space that is enclosed within the boundaries of the porch. In other words, we are calculating the size of the surface area of the porch, which is measured in square units.

Knowing the area of a porch can be useful in a variety of contexts. For example, if you were planning to install new flooring on the porch, you would need to know the area in order to calculate how much material you would need to purchase. Similarly, if you were planning to paint the porch, you would need to know the area in order to estimate how much paint you would need to cover the surface.

In summary, the area of a porch can be calculated by multiplying its length and width, and is measured in square units.

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Assuming the table models a linear equation, we will get the complete table:

minutes: 10         40         89.3        150        360

cost:       200    225.7      268        320        500

Here we can assume that the table models a linear equation of the form:

y = ax+  b

Where a is the rate of change and b is the y-intercept.

If we know two points on the line, let's say:

(x₁, y₁) and (x₂, y₂), then the rate of change is:

a = (y₂ - y₁)/(x₂ - x₁)

In the table we have two pairs:

(10, 200) and (150, 320)

Then the rate is:

a = (320 - 200)/(150 - 10)

a = 12/14 = 6/7

Then we can write:

y = (6/7)*x + b

To find the value of b, we can replace one of the two points there, using (10, 200) we will get:

200 = (6/7)*10 + b

200 = 60/7 + b

200 - 60/7 = b

1400/7 - 60/7 = b

1340/7 = b

Then the line is:

y = (6/7)*x + 1340/7

Now to complete the table, just replace the correspondent values in the equation.

for the first value we have x = 40

y = (6/7)*40 + 1340/7 = 225.7

if x = 360

y = (6/7)*360 + 1340/7 = 500

if y = 268

268 = (6/7)*x + 1340/7

x = (268 - 1340/7)*(7/6)

x = 89.3

Then the complete table is:

minutes: 10         40         89.3        150        360

cost:       200    225.7      268        320        500

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Answer:

Step-by-step explanation:

These steps in the design process are often iterative, meaning that architects may revisit earlier steps as they refine and develop the design. The overall goal of the design process in architecture is to create a functional, safe, and aesthetically pleasing building that meets the needs and goals of the client.

The following are the steps in the design process, organized in architecture:

Programming: In this first step, architects work with their clients to understand the project requirements, goals, and objectives. They may gather information about the site, zoning and building codes, budget, and other constraints.

Schematic Design: In this step, architects use the information from the programming phase to create rough sketches and drawings that show the basic layout and massing of the building. This phase is an opportunity to explore various design options and to get feedback from the client.

Design Development: In this step, the architects refine the design, incorporating structural and mechanical systems, and developing detailed drawings and specifications. This phase also includes working with consultants such as engineers and contractors.

Construction Documents: In this step, the architects prepare the final construction documents, which include detailed drawings and specifications that will be used by contractors to build the project.

Bidding and Negotiation: In this step, the architects help the client solicit bids from contractors and negotiate the terms of the construction contract.

Construction Administration: In this final step, the architects oversee the construction process, ensuring that the project is built according to the design documents and that any changes or issues are addressed.

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The values of the variable x are 7 and -1. Options B and D

Functions are simply defined as those equations, expressions or laws that shows the relationship between two variables.

These variables are;

From the information given, we have that;

f(x) = 16

f(x) =  x² - 6x + 9

Now, equate the two functions, we have;

x² - 6x + 9 = 16

collect the like terms

x² - 6x + 9 - 16 = 0

subtract the values

x² - 6x - 7 = 0

solve the quadratic equation

x² - 7x + x - 7 = 0

x(x - 7) + 1( x - 7)

Then, x = 7 and -1

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it is important to note that the sample size of 1000 subjects is large enough for statistical inference, but the significance level must be taken into account when interpreting the results.

No. Since the tests were performed at the 1% significance level, as many as 10 subjects may have done significantly better than random guessing.

When conducting hypothesis testing, the significance level (in this case, 0.01 or 1%) is the probability of rejecting the null hypothesis when it is actually true. This means that there is a 1% chance of observing a significant result purely by chance, even if the null hypothesis (in this case, that the subjects do not have ESP) is true.

In this scenario, nine subjects performed significantly better than random guessing, which may suggest that they have ESP. However, due to the possibility of observing significant results by chance, it is not proper to conclude that these nine people have ESP. There is still a chance that these results are purely coincidental.

Additionally, it is important to note that the sample size of 1000 subjects is large enough for statistical inference, but the significance level must be taken into account when interpreting the results.

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The answer is D: w = 85-25/ 5. This equation represents the number of weeks it will take Paul to save enough money to buy the skateboard.

Equations are useful for solving problems, finding unknown values, determining rates of change, and understanding relationships between different variables.

The equation can be written as w = (85 - 25)/5, where 85 is the cost of the skateboard, 25 is the amount he has already saved, and 5 is the Subtracting 85-25, the equation is essentially asking how many 5s are in 60.

The answer is 12, which is the number of weeks it will take Paul to save enough money for the skateboard.

This can be verified by multiplying 12 by 5, which equals 60.

Thus, the correct answer is D: w = 85-25/ 5.

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Question :

Paul gets $5 every week for doing his chores. He is saving his money to buy a skateboard that costs $85. He has already saved $25. Which equation describes the number of weeks (w) that it will take Paul to save enough money to buy the skateboard?

A : w = 85 / 5

B : w = 85 - 25

C : w - 85 / 5 - 25

D: w = 85-25/ 5

Among the answer choices, the line that represents a row perpendicular to y = 1 is x = 4.

Coordinate geometry, also known as analytic geometry, is a branch of mathematics that deals with the study of geometric figures using coordinates.

The line y = 1 is a horizontal line that goes through all points on the y-axis with a y-coordinate of 1.

To find a line perpendicular to it, we need to find a line that has a slope that is the negative reciprocal of the slope of y = 1. The slope of y = 1 is 0, so the slope of the perpendicular line is undefined (since any number divided by 0 is undefined).

Therefore, the perpendicular line must be a vertical line, and its equation would be of the form x = c, where c is a constant.

Hence, among the answer choices, the line that represents a row perpendicular to y = 1 is x = 4.

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The area of circle with radius 4 centimetres and the special math constant, pi to be 3. 142 is equals to the 50.3 cm².

Area of a shape is defined as the total spece covered by shape in two-dimensional. In geometry, the area enclosed circle is calculated by π times the square of radius of circle. Formula of Area = π × r², where 'r' is the radius. The units of area are square of units of radius that if radius in feet then unit of area will be square feet. We have a circle with radius say r = 4 cm.

The value of specific math constant, pi ( i.e., π) is equals to be 3.142. We have to determine the area of circle. The area of circle, A = π× 4²

=> A = 16π

=> A = 16× 3.142

=> A = 50.272 ~ 50.3 cm²

Hence, the required area value is 50.3 cm².

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Complete question:

The above figure completes the question.

Work out he area of this circle. Take pi to be 3. 142 and give your answer to 1 decimal place

Answer:

[tex] \sqrt{36 + x {}^{2} } - (2) {}^{2} \\ 6 + x + - 2 \\ 6 - 2 + x \\ 4 + x \\ \: \:answer = 4 + x \\[/tex]

To find the area of the shaded polygon, we had to assume that each dotted line was one unit. In which case, the coordinates are:

Hence, the area of the polygon is A [tex]\approx[/tex] 11.15 units.

To get the area of the polygon, we must determine the length of all it's sides.

a) A-B is given by the distance formula:

distance = √((x2 - x1)² + (y2 - y1)²)

where (x1, y1) and (x2, y2) are the coordinates of the two points.

Using this formula, we can calculate the distance between points A(1,4) and B(5,6) as follows:

distance = √((5 - 1)² + (6 - 4)²)

= √(16 + 4)

= √(20)
A-B = 4.47213595

A-B [tex]\approx[/tex] 4.47

b)
To find B-C we use the same method:
B-C = 3.16 units.

c)
To find C- D we use the same method:
C- D  [tex]\approx[/tex] 3.16 units.

d) to find D-A  we use the employ the same method:
D - A [tex]\approx[/tex] 2.83



Since this is an irregular quadrilateral, we will require the use of the
length of one of it's diagonals which is also computed using the distance formula to get: 4.47 Units.


Calculate the perimeter of ABCD

Perimeter of ABCD = AB + BC + CD + AD

Perimeter of ABCD = 4.4721359549996 + 3.1622776601684 + 3.1622776601684 + 2.8284271247462

Perimeter of ABCD = 13.625118400083


Calculate the semi-perimeter (s) of ABCD

s  =   Perimeter ÷ 2

s  =   13.625118400083 ÷ 2

s = 6.8125592000413


Calculate the Area (A) using Brahmagupta's Formula

A = √[(s - a)(s - b)(s - c)(s - d)]

A = √(6.8125592000413 - 4.4721359549996)(6.8125592000413 - 3.1622776601684)(6.8125592000413 - 3.1622776601684)(6.8125592000413 - 2.8284271247462)

A = √(2.3404232450417)(3.6502815398729)(3.6502815398729)(3.9841320752951)

A = √(124.24555320337)
A = 11.14654893693

A [tex]\approx[/tex] 11.15 units.

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We then substitute -1 for x in the equation x + y = 4 to get -1 + y = 4, which we can then subtract -1 from both sides to get y = 5. The solution is x = -1 and y = 5.

3x + y = 7

-x + y = 1

Add the equations together:

2x + 2y = 8

Divide both sides by 2:

x + y = 4

Subtract the second equation from the first:

-x + y = 1

x - y = -3

Add the equations together:

2x = -2

Divide both sides by 2:

x = -1

Substitute -1 for x in the equation x + y = 4:

-1 + y = 4

Subtract -1 from both sides:

y = 5

The solution is x = -1 and y = 5.

We begin by solving the system of linear equations by elimination. We need to get the variables to one side of the equation and the constants to the other side. We start by adding the two equations together: 3x + y = 7 and -x + y = 1. This gives us 2x + 2y = 8, which we can then divide both sides by 2 to get x + y = 4. We then subtract the second equation from the first to get -x + y = 1 and x - y = -3. We then add these two equations together to get 2x = -2 and divide both sides by 2 to get x = -1. We then substitute -1 for x in the equation x + y = 4 to get -1 + y = 4, which we can then subtract -1 from both sides to get y = 5. The solution is x = -1 and y = 5.

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Just make a flat line for each time the car stops.

Hope this helps.