Write the equation of the line in fully simplified slope-intercept form.​

The distance covered by a car in one hour is 36.15 miles, and the distance covered by a car using 1 gallon of fuel is 12.05 miles.

A thing that moves quickly and with high speed, covering a lot of ground in a short time. On the other hand, a slow-moving object traveling at a low speed covers a comparatively small distance in the same amount of time. An object with zero speed does not move at all.

Given:

A car traveled at a constant speed for 4 hours and covered 144.6 miles,

The fuel used = 12 gallons,

Calculate the distance covered in 1 hour as shown below,

The distance covered in 1 hour = 144.6 / 4

The distance covered in 1 hour = 36.15 miles

Calculate the distance traveled using 1 gallon of fuel,

The distance traveled using 1 gallon of fuel = 144.6 / 12

The distance traveled using 1 gallon of fuel = 12.05 miles.

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The graph in this problem shows a proportional relationship, because the line passes through the origin, and the rate of change is of 40.

A proportional relationship is a special case of a linear function, with an intercept of zero.

The slope is the constant of proportionality, hence the proportional relationship has the equation defined as follows:

y = kx.

Hence the constant is given as follows:

k = y/x.

Two points from the graph are given as follows:

(1,40) and (2,80).

The constants for each point are given as follows:

The constants are the same for each point, hence the graph represents a proportional relationship.

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the actual area of the bedroom is 324 square feet

What is square?

Having four equal sides, a square is a quadrilateral. There are numerous square-shaped objects in our immediate environment. Each square form may be recognised by its equal sides and 90° inner angles. A square is a closed form with four equal sides and interior angles that are both 90 degrees. Numerous different qualities can be found in a square.

Given the square bedroom have 3 feet side

The area of the bedroom is = 3² = 9 sq inch

1/2 inch = 3 feet

1 inch = 6 feet

1 square inch = 36 square feet

9 square inch = 36*9 = 324square feet

Hence the actual area of the bedroom is 324 square feet

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Based on the margin of error, an estimate of the total number of feral cat complaints for planet Purple is A. Between 1018.5 and 1361.5 complaints.

The margin of error shows the statistical difference between the actual and projected or estimated results.

The margin of error gives the difference between the upper limit and the lower limit of the sample estimate.

With the margin of error, one establishes a level of confidence or the confidence interval in the sample results.

The total number of cities on planet Purple = 4,500

Random sample size = 350 cities

Average complaints = 3.4

Margin or error = ± 0.49

Upper limit = 1,361.5 [350 x (3.4 + 0.49)]

Lower limit = 1,081.5 [350 x (3.4 - 0.49)]

Thus, using the margin of error, an estimate of feral cat complaints hovers over Option A.

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get trolled

Step-by-step explanation:

troll people make them get trolled

Answer:

Step-by-step explanation:

to round a decimal, well it depends if it asks you to round to tenths, thousandths or hundredths sometimes even cents..

If you were to be given 5.5567 and it says to round to the hundredth place then you would look at the two points so 5. 55 and then look at the number beside it which is 6 and because 6 is bigger it would round up so you'd get 5.56 hopefully you understood that even if it's just a little..

Answer: f(5)=9.5

Step-by-step explanation:

If the graph displays f(x)=(-1/2)x+12, then the answer for f(5) would be 9.5.

However, if the graph/line varies from this, (and is not just a straight line or y=mx+b,) the answer will be different as well.

Given the information you gave me though, this is the best I can do. Please check the given graph/equation before inputting the above answer.

Step-by-step explanation:

If the iPod has many thousands of songs, it's safe to assume that the number of 80s songs, songs picked by one of the kids, and songs that you like are all significant. Therefore, the probabilities that the first song will be an 80s song, a song picked by one of the kids, or not one of your songs are roughly equal to the percentage of each type of song on the iPod.

For example, the probability that the first song will be an 80s song is roughly 15%, since only 15% of the songs on the iPod are 80s songs (80s songs make up 100% - 60% - 25% = 15% of the iPod's music). Similarly, the probability that the first song will be a song picked by one of the kids is roughly 25%, and the probability that the first song will not be one of your songs is roughly 40% (100% - 60% = 40%).

Note that these probabilities are only approximate, since the songs on the iPod are chosen randomly and the actual probabilities may vary slightly.

Answer:(1x2)+(4divided by 2)

Step-by-step explanation:

The equation of the line is y - 1 = -1/4( x + 5/4).

Here we have to find the equation of the line.

Data given:

Point on the line= (-5/4, 1)

slope(m) = -1/4

The formula of the equation of the line:

y - y1 = m(x - x1)

where m = slope of the line

(x1, y1) = point on the line

Now putting the values in the equation we have:

y - 1 = -1/4( x- (-5/4))

y - 1 = -1/4( x + 5/4)

Therefore the equation of the line is y-1 = -1/4( x + 5/4).

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The maximum volume of the box in terms of A will be √3A/4 -3√3/4 cu cm.

It is given that the box has an open top and a square base.

This implies length = breadth.

Let them be x cm

Now, the area of the box is A sq cm

This means

lb + 2bh + 2lh = A

or, x² + 2xh + 2xh = A

or, 4xh + x² = A

or, h = A/4x - x/4

Now volume (V) = lbh

= x²(A/4x - x/4)

= Ax/4 - x³/4

Now to maximize volume we will first differentiate with respect to x and equate it to zero. Hence we get

V' =0

or, A/4 - 3x²/4 = 0

or 3x²/4 = A/4

or, x² = 3

or, x = √3

Now t check whether this gives us the maximum volume we will calculate V"(√3)

V" = -3x/2

V"(√3) = -3√3/2

Since V"(√3) is negative we will get maximum value for x = √3

Now the volume is

A√3/4 - (√3)³/4

= √3A/4 -3√3/4 cu cm

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The element b₂₄ is the number in the second row and fourth column of the matrix, and we can see that it is equal to 10.

For a matrix M, the element Mₐₙ is the element in the a-th row and in the n-th column.

In this case we want to find b₂₄, so you need to look at the element that is in the second row (counting from the top) and in the fourth column (counting from the right) that element is a 10, then we can conclude:

b₂₄ = 10

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Answer:

The most appropriate method for solving the first system of equations would be elimination. This can be done by adding the two equations together, which will eliminate one of the variables and leave us with an equation in terms of the remaining variable. We can then solve for the value of this variable and substitute it back into one of the original equations to find the value of the other variable.

For the second system of equations, substitution would be the most appropriate method. This is because one of the equations can be rearranged to solve for the value of one of the variables, which can then be substituted into the other equation. This will eliminate one of the variables and allow us to solve for the value of the remaining variable.

For the third system of equations, graphing would be the most appropriate method. This is because both equations are in the form "y = mx + b," which is the standard form of a linear equation. We can graph both equations on the same coordinate plane and find the point of intersection, which will give us the values of both variables.

The value of x is 10°.

What is triangle?

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.

Given:

In ΔRST, m ∠R = (5x+15), m ∠S = (6x+8), m ∠T = (4x+7)

Since the addition of three angles of triangle is 180 degrees.

So,

          m ∠R + m ∠S + m ∠T = 180°

(5x + 15) + (6x + 8) + (4x + 7) = 180°

                               15x + 30 = 180°

                                       15x = 180° - 30°

                                       15x = 150°

                                           x = 10°

Hence, the value of x is 10°.

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Answer:

Splitting is where numbers in an equation are broken apart to make it easier to calculate.

Step-by-step explanation:

Splitting is where numbers in an equation are broken apart to make it easier to calculate. Ex:

21 * 7

20 * 7 + 1 * 7 =

140 + 7

147

The system of equations - 2x + 5y = - 2 and 4x - 10y = 4 has infinitely many solutions.

Graphical solutions of a system of equations are way of finding the intersection points of all the equations given.

A system with two or more than two equations has a solution only when they have a common intersection point.

Given, A system of equations - 2x + 5y = - 2...(i) and 4x - 10y = 4...(ii).

Now, multiplying eqn(i) by 2 it becomes - 4x + 10y = - 4...(iii).

Now, by Adding (ii) and (iii) we get,

0x + 0y = 0.

So, 0 = 0, and hence these are coinciding lines with infinitely many solutions.

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The correct statements regarding the confidence intervals is given as follows:

The 90% confidence interval for juniors is (.549, .744), and the 90% confidence interval for seniors is (.545, .762). Since the intervals overlap, there is not enough evidence to say there is a difference between regular exercise rates among juniors and seniors.

A confidence interval of proportions has the bounds given by the rule presented as follows:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which the variables used to calculated these bounds are listed as follows:

The confidence level is of 90%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.9}{2} = 0.95[/tex], so the critical value is z = 1.645.

For juniors, the parameters are given as follows:

[tex]n = 65, \pi = \frac{42}{65} = 0.646[/tex]

Then the lower bound of the interval is of:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.646 - 1.645\sqrt{\frac{0.646(0.354)}{65}} = 0.549[/tex]

The upper bound of the interval is of:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.646 + 1.645\sqrt{\frac{0.646(0.354)}{65}} = 0.744[/tex]

For seniors, the parameters are given as follows:

[tex]n = 52, \pi = \frac{34}{52} = 0.654[/tex]

Then the lower bound of the interval is of:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.654 - 1.645\sqrt{\frac{0.654(0.346)}{52}} = 0.545[/tex]

The upper bound of the interval is of:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.654 + 1.645\sqrt{\frac{0.654(0.346)}{52}} = 0.762[/tex]

The intervals overlap, hence there is not enough evidence to conclude that there is a difference.

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For the function k(x) = 80, must have an x- value of 5 < x ≤ 6 in the given graph.

The greatest integer function takes the greatest integer that is less than or equal to a specified value.

Mathematically, the greatest integer function ⌊x⌋ can be defined as follows:

⌊x⌋ = n, where n ≤ x < n + 1 and 'n' is an integer.

According to the given question,

The function is below as

⇒ k (x)

We have to determine the value of k (x) = 80

As per the given graph, the required solution would be as: [x] + 5

Here ⌊x⌋ = 5, where 5 < x ≤ 5 + 1 and '5' is an integer.

5 < x ≤ 6

Thus, the required value of x would be 5 < x ≤ 6 for the given function k(x) = 80.

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No, the slopes are not perpendicular. The slope of 3 is three times larger than the slope of 1/-3, so the two slopes form an angle that is less than 90 degrees.

1. The slope of a line is the ratio of the vertical change to the horizontal change in the line, this is also known as the rise over run.

2. The slope of the first line is 1/-3 and the slope of the second line is 3.

3. To determine if the two slopes are perpendicular, we need to calculate the angle between them.

4. The angle between two slopes is equal to the arctan(slope1/slope2).

5. Using the formula, we can calculate the angle between the two slopes to be 63.43 degrees.

6. Since this angle is less than 90 degrees, the two slopes are not perpendicular.

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From the information given, Ashley's age is 27

how to calculate the value:

Let the four siblings' ages be;

Ashley's age is x, x + 1, x + 2, x + 3.

If their combined ages equal 100

We possess

x + x + 1 + x + 2 + x + 3 = 100

assemble similar terms

4x + 6 = 100

4x = 100 - 6

4x = 96

Set the topic to "x"

x = 96/ 4

x = 24

But Ashely is x + 3 = 24 + 3 = 27 years old.

Thus, Ashley's age is 27

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The missing angles in the triangle is as follows:

A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees.

∠3 = 55 degrees (vertically opposite angles)

Vertically opposite angles are congruent to each other.

The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two remote interior angles of the triangle.

Using exterior angle theorem ,

105 = ∠5 + 55

∠5 = 105 - 55

∠5 = 50 degrees

∠4 = 180 - 50 - 55

∠4 = 75 degrees

Therefore, the other triangle is an isosceles triangle. This means the base angles are equal.

Hence,

∠1  = ∠2 = x

2x + 55 = 180

2x = 180 - 55

2x = 125

x = 125 / 2

x = 62.5 degrees.

Hence,

∠1  = ∠2 = 62.5 degrees.

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Therefore, the length of the c from the given figure comes out to be c= 10.63cm.

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

Here,

The hypotenuse, or longest side in a right triangle, is side c, which is our unknown. With the use of Pythagorean's Theorem, we have

[tex]7^{2} +8^{2} =c^{2}[/tex]

which simplifies to

[tex]7^{2} +8^{2} =c^{2}[/tex]

and

49 + 64 = [tex]c^{2}[/tex]

and

  [tex]c^{2}[/tex] = 113

c = 10.63 cm

Therefore, the length of the c from the given figure comes out to be c= 10.63cm.

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Rotation is the rigid type of transformation which is equivalent to the two reflections across intersecting lines.

Therefore, the rigid type transformation which is equivalent to two reflection across the intersecting lines is called rotation.

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Answer: 0.48 m,  480 mm

Step-by-step explanation:

1 m = 100 cm

So take 48 divided by 100 = 0.48m, so this is correct.

1 cm = 10 mm

So take 48 times 10 = 480 mm, so this is correct

The equivalent expression will be;

B) -2 +4 (x+3) and 4x + 10

C) 3x+5(x - 1) and 8x - 5

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

There are some expressions.

Now,

From option (A),

⇒  2 (x+3) + 2x and 4x + 3

Solve as;

⇒ 2 (x + 3) + 2x = 2x + 6 + 2x

                         = 4x + 6

Which is not equal to 4x + 3.

From option (B),

⇒ -2 +4 (x+3) and 4x + 10

Solve as;

⇒ - 2 + 4 (x + 3) = - 2 + 4x + 12

                        = 4x + 10

Hence, This is equivalent expression.

From option (C),

⇒ 3x+5(x - 1) and 8x - 5

Solve as;

⇒ 3x + 5 (x - 1) = 3x + 5x - 5

                      = 8x - 5

Thus, This is equivalent expression.

From option (D),

⇒ 5x² (x + 4) and 3x + 8

Solve as;

⇒ 5x³ + 20x²

Thus, This is not correct.

From option (E),

⇒ 4-5 (x+2) and 5x - 6

Solve as;

⇒ 4 - 5 (x + 2) = 4 - 5x - 10

                      = - 5x - 6

Thus, This is not correct.

Therefore, The value of equivalent expression is;

⇒ -2 +4 (x+3) and 4x + 10

⇒ 3x+5(x - 1) and 8x - 5

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Jelly beans are $1.5/lb and trail mix is $2.063/lb, according to the data.

A heterogeneous mixture would be a trail mix. When the components of a combination are dispersed unevenly across the mixture, the mixture is said to be heterogeneous. As a mixture of nuts, raisins, and other seeds, trail mix cannot have an evenly distributed dispersion of its ingredients.

t = trail mix, j = jelly beans

3t + 8j = 21

5t + 2j = 18

Solving the first for t

2t = 6j - 3

t = (6j - 3)/2

Substituting

5(6j - 3)/2 + 2j = 18

j = 51/34

j = 1.5, Jelly beans cost $1.5/lb

now,

8t + 3(1.5) = 21

8t = 16.5

t = 2.0625, trailmix costs $2.063 dollars/lb

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Answer:

Step-by-step explanation:

1/5y+3/20

plug in 1/4 for y

1/5(1/4)+3/20

1/20+3/20

4/20

1/5

Answer:

It is not possible to determine the amount of ingredients needed to make 1 quart of cereal without knowing the specific recipe being used. Different types of cereal require different ingredients and proportions of those ingredients, so the amount needed to make 1 quart of cereal will vary depending on the recipe being followed.

In general, most cereals are made from a mixture of grains, such as wheat, corn, oats, or rice, which are ground into flour or meal and mixed with other ingredients such as sweeteners, flavorings, and preservatives. The exact proportions of these ingredients will depend on the type of cereal being made and the specific recipe being used. To determine the amount of ingredients needed to make 1 quart of cereal, you would need to consult a specific recipe and follow its instructions.

Step-by-step explanation:

The graph of the system of inequalities is given by the image shown at the end of the answer.

The system of inequalities in this problem is defined as follows:

Then the graph of the system of inequalities is the region between these two curves.

The function y > 4x - 3 means that the lower bound of the interval is the line y = 4x - 3, which has an intercept of -3 and a slope of 4.

In standard format, the second line is defined as follows:

3y - x ≤ 9.

In slope-intercept format, it is defined as follows:

3y ≤ 9 + x

y ≤ x/3 + 3.

Which means that the upper bound of the graph is the linear function with a slope of 1/3 and an intercept of 3.

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