How long is 1/3 of 3 hours

2. The area of the cabin's window is 196 square inches.

3. The area of the doghouse is  32.5 square ft.

4. The farmer should purchase 2 begs of soil.

5. The artist needs 161.5 square in material to make the kite.

What is a trapezoid?

A polygon with only one set of parallel sides is called a trapezoid. The parallel bases of a trapezoid are another name for these parallel sides. Trapezoids have two additional sides that are not parallel and are referred to as their legs.

Trapezoids are defined differently by different people. A trapezoid can have one and only one pair of parallel sides, according to one school of mathematics, while another contends that a trapezoid can have multiple pairs of parallel sides. If we take into account the second definition, then a parallelogram is also a trapezoid by that definition. However, the first definition excludes parallelograms from the definition of a trapezoid since it is one of the quadrilateral types that we have already mentioned.

2. The formula for the area of a trapezoid is 1/2 × (sum of parallel side) × height.

The length of one parallel side is 10 inches. The length of the other parallel side is (10+4+4) inches = 18 inches.

The height of the trapezoid is 14 inches

The area of the trapezoid is 1/2 ×(10 + 18) × 14

= 196 square inches.

3.

The formula for the area of a trapezoid is 1/2 × (sum of parallel side) × height.

The length of one parallel side is 5 ft. The length of the other parallel side is (5+3) ft = 8 ft.

The height of the trapezoid is 5 ft.

The area of the trapezoid is 1/2 ×(5 + 8) × 5

= 32.5 square ft.

4.

The area of a parallelogram is the product of height and base.

The length of the base is (2.5 yards + 6.5 yard) = 9 yards

The height of the parallelogram is 6 yards.

The area of the parallelogram is 9 yards × 6 yards

= 54 square yards

Each beg can cover 40 square yards field.

The number of begs that the farmer need is 56/40 = 1.4  ≈2

5.

The area of the kite is half of the product of diagonals.

The length of diagonals are (8.5 in + 8.5 in) = 17 in and (6 in  + 13 in) = 19 in

The area of the kite is (17×19)/2 = 161.5 square in.

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Regression is a statistical procedure for determining the linear relationship between a number of variables. A simple regression model has one dependent variable and one independent variable [tex](y)[/tex]

It is used to forecast the amount of a dependent variable according to the results of one independent variable. [tex](x)[/tex]

The estimated least-squares line has the following shape :[tex]y=bo+b1x[/tex].

In this case, the dependent variable is, the independent variable is, the intercept is, and the slope coefficient is.

The slope of a linear regression describes how a unit change in x changes the y value.

When, the intercept represents the expected mean value of Y. When X never equals zero, the intercept has no intrinsic meaning.

Step  (1) The process of estimating the linear relationship between two or more variables is known as regression. Only if there is a linear relationship between both variables can a regression equation be used to predict future.

Linear regression is the most fundamental a kind of regression and is the most widely used proposed model. A regression line can be used to predict dependent variables based on independent variables.

Step: (2) Outliers have a significant impact on the slope of the regression line. Influential points are also referred to as outliers in regression analysis.

Outliers can have a significant impact on the regression equation, so remove any outliers that are recognized errors. Consider the effects of any known inconsistencies that are outliers.

Step 3: Because outliers can have a large impact on the regression line, they are also referred to as important and powerful points.

An outlier is a data point that is located far away first from remaining pieces of data. These are additionally known as influencing points. Outliers have a significant influence on the slope of something like the regression line.

For linear associations, regression models can be utilized.

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The conversion of the unit centimeters to feet is written as 147 centimeters = 4.82283 feet.

Relation between centimeter and feet is equal to :

One centimeter is equal to 0.0328084 feet.

Now substitute the required converted value centimeter to feet we have,

⇒ 147 centimeters = ( 147 ) × ( 0.0328084 ) feet

⇒ 147 centimeters = ( 4.8228348 ) feet

⇒  147 centimeters = ( 4.82283 ) feet ( Round upto four decimals )

Therefore, the converted units centimeter to feet as per the measurements is equal to  ( 4.82283 ) feet ( Round upto four decimals ) .

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a. The subtοtal is $23.45, the tip is $4.22, and the tοtal cοst οf their meal is $27.67.

b. Each persοn wοuld pay $13.84.

The additiοn is a basic arithmetic οperatiοn that cοmbines twο οr mοre quantities intο a single sum. It is οne οf the fοur basic οperatiοns in arithmetic, alοng with subtractiοn, multiplicatiοn, and divisiοn.

In additiοn, the quantities being cοmbined are called addends, and the result οf the additiοn οperatiοn is called the sum. The additiοn is represented using the plus sign (+), which is placed between the addends. Fοr example, the additiοn expressiοn "3 + 5" means that we are adding 3 and 5 tοgether tο get a sum οf 8.

Fοr example, tο add the numbers 34 and 56, we start by adding the digits in the οne's place, which gives us 4 + 6 = 10. We write dοwn the 0 and carry the 1 οver tο the tens place. Then we add the digits in the tens place, which gives us 3 + 5 + 1 = 9. The final answer is 90.

a: Subtοtal = Hamburger + Guacamοle + Cheeseburger + Fries + Sοda + Milk

Subtοtal = $7.99 + $1.00 + $8.99 + $2.49 + $1.99 + $0.99

Subtοtal = $23.45

Tip = 18%×Subtοtal

Tip = 0.18 × $23.45

Tip = $4.22 (rοunded tο the nearest cent)

Tοtal = Subtοtal + Tip

Tοtal = $23.45 + $4.22

Tοtal = $27.67 (rοunded tο the nearest cent)

Therefοre, the subtοtal is $23.45, the tip is $4.22, and the tοtal cοst οf their meal is $27.67.

b: If Sue and her friend split the final cοst equally, each persοn wοuld pay half οf the tοtal cοst:

$27.67 / 2 = $13.84 (rοunded tο the nearest cent)

Therefοre, each persοn wοuld pay $13.84.

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25.44cm^2 is the area of the composite figure,

A composite shape is a shape that is made up of two or more figures.

The given shape is made up of circle and triangles. The area of the shaded region is expressed as:

Area = area of semicircle - area of triangle

Area of semicircle = πr²/2

Area of semicircle = 3.14(6)²/2

Area of semicircle = 3.14 * 18

Area of semicircle = 56.62 cm^2

For the triangle;

Area of triangle = 1/2absin60

For the value of a;

a/12 = cos60

a/12 = 1/2

a = 6

Area of triangle = 1/2(12)(6) sin60

Area of triangle = 31.17cm^2

Area of the shaded portion = 56.62 - 31.17

Area of the shaded portion = 25.44cm^2

Hence the area of the shaded portion is 25.44cm^2

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Answer:

45.01

Step-by-step explanation:

You round to the nearest hundredth so since seven is big enough you add a 1 to the hundredth place

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation: (This is to show the equation of the Pythagorean Theorem.)

Remember the Pythagorean theorem is A^2 + B^2 = C^2. To find out a part of a right triangle using the Pythagorean theorem, you would find either A, B, or C. As an example, let us say that A is equal to 10, and B is equal to 8. How we find C^2, is we add A and B, but we square both numbers.

(10^2) + (8^2) = (C^2). We square 10 by itself, and we get 100 as our A. We also square 8 by itself as well, and we get 64 as our B. C does not have any number representing the variable, so we leave it as it is. 100 + 64 = 164 for C. We have to square root 164, since we're using exponents. (Please note that all my equations won't be a complete whole number, I'm using random numbers to show.) To find B or A, we find this equation. Let us keep our own variable, but C is equal to 15. To find B, we make the equation (10^2) + (B^2) = (15^2) or (A^2) + (8^2) = (15^2). To find B, We square 10 by itself to get 100, like from the last equation, but B doesn't have any number for the variable, so we keep it the same. We square 15 to get 225. After we get our 2 numbers, we subtract {100 + (B^2) = 225} ->

{(100 - 100) + (B^2) = (225 - 100)} -> {B^2 = 125}. We square root 125 to get our answer.

To find A, A doesn't have any number to fill in for the variable, We square 8 to get 64. We square 15 to get 225. After we get our 2 numbers, we subtract {(A^2) + 64 = 225} -> {A^2 + (64 - 64) = (225 - 64)} -> {B^2 = 161}. We square root 161 to get our answer. For the 3 sides: A and B, near the right triangle are both the "legs" of the triangle, while the slant of the triangle (C), is the hypotenuse.

The total time of the guitar session will be 7¹/₂ hours.

A scatter plot is a plot mathematical chart or graph that depicts the relationships by the use of dots and shows the two numeric variables.

The dots are positioned on each horizontal and vertical value for an individual. They are used for observing the relationship between the variables. The graph shows are positive but nonlinear association.

The total time will be calculated as:-

T = ( 3) x ( 1 / 4 ) + (4) x (1 / 2 ) + ( 5 ) x ( 3 / 4 ) + 1

T = 3/4 + 4 / 2 + 15 / 4 + 1

T = 3 / 4 + 2 + 15 / 4 + 1

T = 18 / 4 + 3

T = 15 / 2

T = 7¹/₂ hours.

Therefore, the total time will be 7¹/₂  hours.

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Answer:

here is how to solve the math problems with sales tax and discount:

a) To find the total bill, we need to add the purchase price and the sales tax. To find the sales tax, we need to multiply the purchase price by the sales tax rate. The purchase price is the sum of the prices of the two pairs of shoes, which is $37 + $42 = $79. The sales tax rate is 7%, which as a decimal is 0.07. So, the sales tax is 0.07 x 79 = $5.53. The total bill is 79 + 5.53 = $84.53.

b) To find the discounted price, we need to subtract the discount from the original price. To find the discount, we need to multiply the original price by the discount rate. The original price is the same as the purchase price in part a, which is $79. The discount rate is 25%, which as a decimal is 0.25. So, the discount is 0.25 x 79 = $19.75. The discounted price is 79 - 19.75 = $59.25. To find the total bill with the coupon, we need to add the sales tax to the discounted price. The sales tax rate is still 7%, which as a decimal is 0.07. So, the sales tax is 0.07 x 59.25 = $4.15. The total bill with the coupon is 59.25 + 4.15 = $63.40.

I hope this helps!

Step-by-step explanation:

The relationship between the lines is (a) parallel

From the question, we have the following parameters that can be used in our computation:

y =-5/6x - 4

-10x - 12y = -18

To determine if the two lines are parallel or not we need to compare their slopes.

Make y the subject

y = -5/6x - 4

y = -5/6x  + 3/2

A linear equation represented as

y = mx + c

...has its slope to be m

Using the above as a guide, we have the following:

Since the slopes are equal, the two lines are parallel.

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68 kilograms is approximately equal to 149.91416 pounds.

A kilogram (symbol: kg) is the base unit of mass in the International System of Units (SI).

It is currently defined based on the fixed numerical value of the Planck constant, h,

Which is equal to 6.62607015 × 10-34 in the units of J·s.

A pound (symbol: lb) is a unit of mass used in the imperial and US customary systems of measurement.

The international avoirdupois pound (the common pound used today) is defined as exactly 0.45359237 kilograms.

To convert 68 kilograms to pounds,

We need to multiply the value in kilograms by 2.20462,

Since one kilogram is approximately equal to 2.20462 pounds.

Therefore,

68 kilograms multiplied by 2.20462 gives us:

68 kg x 2.20462 = 149.91416 pounds

(rounded to five decimal places)

So, 68 kilograms is approximately equal to 149.91416 pounds.

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See below for the steps to find the coordinates

To find the x and y coordinates of a point on a coordinate plane, follow these steps:

Lastly, write down the coordinates as an ordered pair (x, y)

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The equation of the line perpendicular to y = -4x + 4 that contains the point (5, -1) is y = 1/4x - 9/4.

The given equation is y = -4x + 4, which is in slope-intercept form y = mx + b, where m is the slope and b is the y-intercept.

To find the slope of the given line, we can compare it to the slope-intercept form and see that the slope is -4.

Since we want to find the equation of a line that is perpendicular to the given line, we know that its slope will be the negative reciprocal of -4.

The negative reciprocal of -4 is 1/4, so the slope of the perpendicular line is 1/4.

Now we have the slope of the line and a point that it passes through, so we can use the point-slope form of a line to write the equation:

y - y1 = m(x - x1)

where (x1, y1) is the given point and m is the slope we just found.

Plugging in the values, we get:

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

Simplifying this equation, we get:

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

Subtracting 1 from both sides, we get the final equation:

y = 1/4x - 9/4

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To convert watts to horsepower, use the formula 1Hp = 735Watt.

Watt and horsepower are both power units.

Nevertheless, horsepower is a more potent unit of power. We measure the power of electrical instruments such as turbines, motors, and a variety of other devices using horsepower.

Hence, 1 Horsepower is 735 Watt using standard unit conversion rates.

1 Hp = 735 W

As a result, we have the conventional relationship 1Hp = 735 W. We can now simply convert any horsepower provided to the unit of Watt.

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Answer:

Angle 5 is 105 degrees.

Step-by-step explanation:

[tex]180-75[/tex]

[tex]105[/tex]

a)  The electrical potential V (center) at the center C of the circle due to the charges Q1 and Q2 is -2.30 V.

b) The total electrical potential at the point P due to charge Q1 and Q2 , located at a distance of 6.71 cm is -1.78V.

Given that:

Radius of the circle, r = 8.20cm

Charge distributed along one-quarter of the circumference of the circle,

Q1 = +4.20pC

Charge distributed along 3/4th of the circumference of the circle,

Q2 = 25.20pC

Distance of the point from the center, d = 6.71cm

The electric potential at infinity is. V = 0

Using the concept of potential at a point on a thin rod, we can obtain the individual potential due to each charge. The sum of these values ​​can now be used to obtain the desired potential value at the center and at the point, taking into account the distance to the point.

Formula:

The potential due to a point charge at a distance r from the point charge is determined by the equation V = [tex]\frac{1}{4\pi E_0} * \frac{q}{r}[/tex]        ---------------- (1)

The potential due to the collection of point charges is determined by formula:

V = ∑[tex]\frac{1}{4\pi E_0} * \frac{q}{r}[/tex]                 -------------------- (2)

(a) The potential VQ1 at the center C of the circle due to the charge Q1 is determined using equation (i) as:

[tex]V_Q_1 = \frac{1}{4\pi E_0} * \frac{Q_1}{R}[/tex]              --------------------- (3)

Here, R is the radius of circle

The potential VQ1 at the center C of the circle due to the charge Q1 is determined using equation (i) as:

[tex]V_Q_1 = \frac{1}{4\pi E_0} * \frac{Q_2}{R}[/tex]                 ----------------------- (4)

Now the potential V(center) at the center C of the circle due to charges Q1 and Q2 is the sum of the potential due to charge Q1 and the potential due to charge Q2. This is given using equations (a) and (b) in equation (ii) as:

    [tex]V_Center = \frac{1}{4\pi E_0} * \frac{Q_1}{R} + \frac{1}{4\pi E_0} * \frac{Q_2}{R}[/tex]

⇒ [tex]V_Center = \frac{1}{4\pi E_0} *( \frac{Q_1}{R} + \frac{Q_2}{R})[/tex]

⇒ 9.0 × 10⁹Nm²/C₂ ([tex]\frac{4.20*10^-12 C}{0.082m} +\frac{-25.2*10^-12C}{0.082m}[/tex])

⇒ -2.30V

The electrical potential V (center) at the center C of the circle due to the charges Q1 and Q2 is -2.30 V.

(b) From the above figure the r between each charged particle and the point P is given as:

[tex]r = \sqrt{R^{2}+D^{2} }[/tex]                    

In the figure above, r between each charged particle and point P is defined as: ="1662703245948 "

[tex]V_Q_1 = \frac{1}{4\pi E_0} * \frac{Q_1}{\sqrt{R^{2} + D^{2} } }[/tex]                  ------------------ (5)

Again, the electric potential at point P due to charge Q2 is given using equation (i) as follows:
[tex]V_Q_1 = \frac{1}{4\pi E_0} * \frac{Q_2}{\sqrt{R^{2} + D^{2} } }[/tex]                   -------------------- (6)

A The potential at point P due to charge Q2 is determined using equation (i): The potential of charge Q1 and the potential of charge Q2. This is given using equations (c) and (d) in equation (ii) as:

[tex]V_P = 9.0 * 10^9Nm^2/C^2 (\frac{4.20*10^-12C-6(4.20*10^-12C)}{\sqrt{(0.082m)^{2} + (0.082m)^{2} } })[/tex]

= -1.78V

The total electrical potential at the point P due to charge Q1 and Q2 , located at a distance of 6.71 cm is -1.78V.

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The true statement about Graphed Function is:

f(x) > 0 over the interval  (–∞, –4)

A graph is referred to be an interval graph if each of its vertices can be connected to a real line interval in such a way that two vertices are only connected if and only if the connected intervals have a nonempty intersection.

Given:

Our curve has a minimum at (-2.5, -12)

Our curve has a maximum at (0, - 3)  

We know that the curve crosses the x-axis at (-4, 0) and y-axis at (0, -3)

At the value x = -2.5 > (-4) the function is negative.

So, f(-2.5) = -12

f(-4) = 0

As a result, it is clear that the function is negative after f(x) crosses the x-axis at x = -4.

This implies that the function must be positive prior to that point.

Thus, the function > 0 for x values less than -4.

f(x) > 0 if x < -4

From this, we can conclude that in the range (-∞, –4), the function is above the x-axis.

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The mode would not change if the number 24 were added to the set, as it is still the number that appears most frequently in the set.

What is a mode in statistics?

In statistics, the mode is the value that appears most frequently in a set of data. In other words, it is the value that occurs with the highest frequency.

For the set of 5 numbers given: 24 58 24 24 53, the mode is 24 because it appears three times, which is more than any other number in the set.

If the number 24 were added to the set, then the set would become: 24 58 24 24 53 24. In this case, the mode would still be 24 because it still appears most frequently, now occurring four times in the set.

Hence, the mode would not change if the number 24 were added to the set, as it is still the number that appears most frequently in the set.

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The value of E is [tex](-2)^{\frac{n-1}{8n} }[/tex].

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

We have,

[tex]E^{8n}[/tex] = 1 x [tex](-2)^{n -1}[/tex]

8n root on both sides.

E = [tex]((-2)^{n -1})^\frac{1}{8n}[/tex]

E = [tex](-2)^{(n-1)\times\frac{1}{8n}}[/tex]

E = [tex](-2)^{\frac{n-1}{8n} }[/tex]

Thus,

E = [tex](-2)^{\frac{n-1}{8n} }[/tex].

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The difference between the two pots is 4731.761 cm^3

How to determine this?

1 gallon = 3785.41 cm^3

2 gallons = 3785.41 cm^3 *2

= 7570.82 cm^3

And also,

1 quart = 946.353 cm^3

3 quarts = 946.353 cm^3 * 3

= 2839.059 cm^3

So, the difference between the two

= 7570.82 cm^3 - 2839.059 cm^3

= 4731.761 cm^3

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The value of conversion of 100 minutes to hours is equal to  1 ( 2/ 3 ) hours.

Conversion of minutes to hours is :

One hour is equal to sixty minutes

⇒ 1 minutes = ( 1 / 60 ) hours

Substitute the required value to convert into hours we get ,

⇒ 100 minutes ( 100 / 60 ) hours

⇒ 100 minutes = 1  40 / 60 hours

⇒ 100 minutes = 1 2 / 3 hours

Therefore, after converting minutes into hours the value of 100 minutes is equal to 1 ( 2 / 3 ) hours.

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Answer:

115m

Step-by-step explanation:

Given

In TriangleXYZ

XZ = 23m

ZY = 19m

In TriangleXVW

WV = 95m

Solution

In Triangles XYZ and XVW

AngleWXV = AngleYXZ as they are Vertically Opposite Angles

AngleXWV = AngleXZY as they are Alternate Angles

Therefore TriangleXYZ and TriangleXVW are Similar Triangles

So,

XY/XV = YZ/VW = XZ/XW as they are Corresponding Sides of Similar Triangles

So,

XZ/XW = YZ/VW

or

23/XW = 19/95

23/XW = 1/5

XW = 23 × 5

XW = 115m

Therefore the distance WX is 115m

To divide polynomials by a monomial written in standard form, you can divide each term of the polynomial by the monomial separately. Applying this to the given expression, we get:

(30c^8d^3 - 3bc^6d^2 + 6c^8d) / (12c^2d)

= 30c^8d^3/(12c^2d) - 3bc^6d^2/(12c^2d) + 6c^8d/(12c^2d)

= 2.5c^(8-2)d^(3-1) - 0.25bc^(6-2)d^(2-1) + 0.5c^(8-2)d^(1-1)

= 2.5c^6d^2 - 0.25bc^4d + 0.5c^6

= 5c^6d^2 - 0.5bc^4d + c^6/2

Therefore, the simplified expression is 5c^6d^2 - 0.5bc^4d + c^6/2.

The value of x in the figure is 5

From the question, we have the following parameters that can be used in our computation:

The double triangles

On the figure, we have

RN = NP

This means that

12x = 60

Divide by 12

12x/12 = 60/12

Simplifying the left side by canceling out the 12s, we get:

x = 5

Hence, the solution to the value of x is x = 5.

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The perimeter and the area for each shape are given below.

For figure (i) there are 11 small square and area of each small square is 1 sq cm.

Area of the given figure =(11×1)cm =11 cm²

Perimeter of the given figure =(18×1)cm=18 cm

For figure (ii) there are 13 and area of each small square is 1 sq cm.

Area of the given figure =(13×1)cm =13 cm²

Perimeter of the given figure =(28×1)cm=28 cm

For figure (iii) there are 13 and area of each small square is 1 sq cm.

Area of the given figure =(13×1)cm =13 cm²

Perimeter of the given figure =(28×1)cm=28 cm.

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The domain and ranges of the relations are;

3. Domain; {3, 5, -10, 9}

Range; {-4, 0, 6}

4. Domain; -2 ≤ x ≤ 4

Range; -2 ≤ y ≤ 4

The domain is the set of the set of the possible input values of the relation and the range is the set of the possible output values of the relation

3. {(3, -4), (5, -4), (3, 0), (-10, 6), (9, 6)}

The above ordered pair are presented in the form (x, y), where, the input values are the x-values and the output values are the y-values

The domain which is the set of the input values is therefore;

The range is therefore;

The x-value of 3 has two different y-values of -4 and 0. therefore, the relation is not a function

4. The relation is location of points on the circumference of a circle.

The input values are the x-values related to the graph, and the output values are the y-values related to the points on the circumference of the circle.

The diameter of the circle parallel to the x-axis extends from (-2, 1) to (4, 1)

The coordinates of locations on the diameter of the circle parallel to the y-axis are; (1, 4), and (1, -2)

The possible x-values, and therefore the domain are; -2 ≤ x ≤ 4

The possible y-values and therefore the range (vertical extension or reach of the circle) are; -2 ≤ y ≤ 4

The x-value of x = 1 has two y-values of -2 and 4, the relation between the x and y-values is therefore not a function.

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2/4 + 4/5

=28/35 is the total distance to her grandfather's house