Mathematics High School

## Answers

**Answer 1**

A **composite function **is a type of function that is made up of two or more other functions. It is created by combining two or more functions together. The resulting function can be written as a single **expression**, or as a composition of multiple functions.

A** composite function** is a type of function that is formed by combining two or more other functions. It is created by combining two or more functions together using the mathematical operations of addition, subtraction, multiplication, division, or composition. The resulting function can be written as a single expression, or as a composition of multiple functions. A composite function is often used to simplify a **complex problem**, or to manipulate and** analyze data. **For example, if a data set contains two sets of data, a composite function could be used to combine the two sets of data into a single **expression**. Additionally, composite functions can be used to solve problems that involve multiple variables, as the resulting function can be used to represent the relationship between the variables. Furthermore, composite functions can be used to create graphs, which can be used to further analyze the data.

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## Related Questions

How do you determine if the given point is a solution of each linear inequality?

### Answers

To determine whether the point [tex](1,2)[/tex] is a **solution of inequality** [tex]3x - 2y - 6 > 0[/tex], we substitute the point in the inequality and if the result is True, then it will be the solution .

What is an **Inequality **?

The Inequality is defined as a relationship between two expressions or values that are not equal to each other .

The inequality in the question is given as : [tex]3x - 2y - 6 > 0[/tex] ;

the **point **is ⇒ [tex](1,2)[/tex] ,

to check the solution , we **substitute **the values in the inequality as [tex]x=1[/tex]and [tex]y=2[/tex] ;

we get , [tex]3(1) -2(2) - 6 > 0[/tex]

= [tex]3-4-6 > 0[/tex]

= [tex]3-10 > 0[/tex]

= [tex]-7 > 0[/tex],

But we know that , [tex]-7 < 0[/tex] , So , the given point is **not the solution** of the given inequality .

The given question is incomplete , the complete question is

How do you determine if the given point (1,2) is a solution of each linear inequality 3x - 2y - 6 > 0 ?

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What is the domain of the logarithmic function f/x )= LOGB X?

### Answers

The **domain** of the given **function** would be x > 0.

**What is a function?**

In mathematics, a **function** from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the **domain** of the **function** and the set Y is called the **codomain** of the **function**.

The given function is f(x) = logb(x)

The domain of the logarithmic function [tex]f(x) = log_b(x)[/tex] is the set of all positive real numbers x such that x > 0. This is because the logarithm of a non-positive number is undefined.

Hence, the **domain** of the given **function** would be x > 0.

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The **domain** of the given **function** would be x > 0.

**What is a function?**

In **mathematics**, a **function** from a set X to a set Y assigns to each element of X exactly one **element** of Y. The set X is called the **domain** of the **function** and the set Y is called the **codomain** of the function.

The given function is f(x) = logb(x)

The domain of the logarithmic function [tex]f(x)=log_b(x)[/tex] is the set of all positive real numbers x such that x > 0. This is because the logarithm of a non-positive number is undefined.

Hence, the **domain** of the given **function** would be x > 0.

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the product of 12 and the number n

### Answers

**Answer:**

12n is the answer because 12 is and n if we multiply both of them it will be 12n.

**Answer & Step-by-step explanation:**

1. 3n= 12 divided 3 on both sides

n= 4

2. 6n=12 divide 6 on both sides

n= 2

3. 12n=12 divide 12 on both sides

n= 1

4. 5n = 12 divided 5 on both sides

n = 1.4

5. 8n=12 divide 8 on both sides

n= 1.5

Whats 3x+1? for in high school its really hard to solve none of my friend cant do it

### Answers

As per the **zeros of the function,** the value of the function 3x + 1 is **x = -1/3.**

Zeros of the function in math is defined as the values of the **variable **of the function such that the function **equals 0.**

Here we have given the function 3x + 1.

Now, we have to **equate **the function with zero, in order to solve it, then we get,

=> 3x + 1 = 0

Now, we have to subtract 1 on both sider to individualize the x value then we get the rewritten **expression **as,

=> 3x = -1

Now, we have to **divide **each side by 3, then we get the value of x as,

=> x = -1/3

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A straw is placed inside a rectangular box that is 2 inches by 1 inches by 3 inches, as shown. If the straw fits exactly into the box diagonally from the bottom left corner to the top right back corner, how long is the straw? Leave your answer in the simplest radical form.

### Answers

The **length **of the **straw **is 3.74 inches.

**What is mean by Rectangle?**

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Given that;

In **rectangular **box,

Length (l) = 2 inches

Width (w) = 1 inches

Height (h) = 3 inches

Here, The **straw **is said to fit into the box **diagonally **from the bottom.

So, the length (s) of the straw is calculated as:

⇒ s = √ l² + w² + h²

⇒ s = √ 2² + 1² + 3²

⇒ s = √ 4 + 1 + 9

⇒ s = √ 14

⇒ s = 3.74 inches

Thus, The **length** of straw = 3.74 inches

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The length of the straw will be 3.7416 inches long in radical form.

What is Length of diagonal in cuboid?

If a **cuboid** has length = l units, breadth = b units, and height = h units, then we can evaluate the length of the diagonal of a cuboid using the **formula :** X²=l²+b²+h²

Here,

As per the question the length of the straw is equal to length of the diagonal of Rectangular box.

l= 3 inch , b= 2 inch , h= 1 inch

Let us consider the length of the straw be 'x'.

As, Diagonal of Cuboid is,

X²=14

X=√14

i.e. X=3.7416

We get, X= 3.7416 (in radical form)

Hence, the length of the straw will be 5.91607 inches.

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Suppose a historian wants to estimate the true mean number of children per household in New York City in 1900. The historian randomly selects 200 household census records from New York City. She records the number of children residing in each household. The historian then computes the mean number of children per household among these 200 households.

### Answers

The **data** which is given by the **historian** is used to find the **population**, variable, **parameter**, sample, data, and **statistic**. He estimated the mean number of **children** per **household** in New York City in 1900.

**Population** - all of the **households** in New York City in 1900.

**Variable** - a quantity **equivalent** to the number of children in a randomly selected household

**Parameter** - the mean **number** of children per household in New York City in 1900

**Sample** - the 200 households selected by the **historian**

**Data** - the 200 records **collected** by the historian

**Statistic** - the **mean** number of children per household in the historian's **sample**.

Complete question:

Suppose a historian wants to estimate the true mean number of children per household in New York City in 1900. The historian randomly selects 200 household census records from New York City. She records the number of children residing in each household. The historian then computes the mean number of children per household among these 200 households. Classify each description as one of a parameter, variable, population, sample, data, or statistic.

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Park rangers plan to expand the area of a park to 506 square miles. Currently, the length of the park is 18 miles and the width is 17 miles. They want to extend the length and the width by the same number of miles. If they are successful, what will the new dimensions of the park be? Explain and I need this before tomorrow

### Answers

As 200 is not a perfect** **square it is** not possible **to increase the dimensions of the park by the same number of miles.

What are the area and perimeter of a rectangle?

The area of a rectangle is the product of its length and width.

The perimeter of a rectangle is the sum of the lengths of all the sides.

We know the area of a rectangle is (**length×width**).

Given, Park rangers plan to expand the area of the park to 506 square miles.

Currently, the park has an area of (18×17) = 306 square miles.

Therefore, The amount of square miles they need to increase is (506 - 306)

= 200 miles.

Now, They also want to increase the length and the width by the same amount but 200 is not a **perfect square **so it is not possible to increase the dimensions by the same amount.

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Lisa and Jen left home at the same time, only Lisa biked to school at a speed of 10 mph while Jen just walked at a speed of 4 mph.

How far apart are the school and house?

### Answers

The **distance** between the school and the house is 1.6 miles.

What is distance?

Distance is the sum of an object's **movements**, regardless of direction. Distance can be defined as the amount of **space** an object has covered, regardless of its starting or ending position.

Let the distance between the school and the house be x miles.

Given that:

Lisa:

Rate = 10mph

Time = t hours

Distance= x

According to distance formula we have:

x = 10 *t [ equation 1]

Jen:

Rate = 4mph

Time = t hours

Distance= x-1 miles

According to the distance formula we have:

x-1 = 4*t [equation 2]

Substitute the value of equation 1 in equation 2 we have:

10t -1 = 4t

6t =1

t = [tex]\frac{1}{6}[/tex]

Now substitute the value of t in equation 1.

[tex]x = 10 * \frac{1}{6}[/tex]

x= 1.6 miles.

Hence the distance between the school and the house is 1.6 miles.

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road to white house Math

### Answers

The **value **of f(4) - g(-5) if **function **f(x) = 3 / 2x + 2 and g(x) = 2x² - 3 is -39.

What is function?

An **expression**, rule, or law in mathematics that specifies the relationship between an **independent **variable and a **dependent **variable (the dependent variable). In **mathematics **and the sciences, functions are **fundamental **for constructing physical relationships.

**Given**:

f(x) = 3 / 2x + 2 and g(x) = 2x² - 3

Calculate the value of f(4) and g(-5) as shown below,

f(4) = 3 / 2 × 4 + 2

f(4) = 12 / 2 + 2

f(4) = 6 + 2

f(4) = 8

g(-5) = 2 × (-5)² - 3

g(-5) = 2 × 25 - 3

g(-5) = 50 - 3

g(-5) = 47

Now, calculate the value of f(4) - g(-5) as shown below,

f(4) - g(-5) = 8 - 47

f(4) - g(-5) = -39

Thus, the value of f(4) - g(-5) is -39.

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which of the following phrases translate to the expression y+7 ?

### Answers

The required phrase to translate the **expression **x + 7 is, A number increases by 7 or an Addition of number and 7.

What are equation models?

The **equation model **is defined as the model of the given situation in the form of an equation using **variables **and **constants**.

Here,

Given expression x + 7,

The expression can be translated as a number increase by 7 or the Addition of the number and 7.

Thus. the required phrase to translate the expression x + 7 is, A number increases by 7 or an Addition of number and 7.

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The number of rats living in an abandoned building increases each year. The total number of rats can be described by this sequence: 2, 6, 18, 54, 162, ...

What is the explicit formula?

What is the recursive formula?

Please help with the recursive formula the most if you can!

### Answers

**Answer: The explicit formula for this sequence is given by the expression a_n = 3^n, where n is the position in the sequence (starting from n=1 for the first term).**

**The recursive formula for this sequence is given by the expression a_n = 3a_(n-1), where n is the position in the sequence (starting from n=1 for the first term) and a_(n-1) is the previous term in the sequence.**

**Here's how you can use the recursive formula to find the terms of the sequence:**

**a_1 = 2**

**a_2 = 3a_1 = 3 * 2 = 6**

**a_3 = 3a_2 = 3 * 6 = 18**

**a_4 = 3a_3 = 3 * 18 = 54**

**a_5 = 3a_4 = 3 * 54 = 162**

**and so on.**

**To find the explicit formula, you can try to find a pattern in the terms of the sequence. For example, you might notice that each term is simply the previous term multiplied by 3. This pattern can be expressed using the recursive formula a_n = 3a_(n-1). To find the explicit formula, you can then solve for a_n in terms of n:**

**a_n = 3a_(n-1)**

**a_n / 3 = a_(n-1)**

**a_n / 3 = (3a_(n-2)) / 3**

**a_n / 3 = 3^(n-2)**

**a_n = 3^n**

**Therefore, the explicit formula for this sequence is a_n = 3^n.**

**Step-by-step explanation:**

simplify 2√12+3√48-√75

### Answers

**Answer:**

11√12

**Step-by-step explanation:**

√12 = 2√3

2√12

= 2 * 2√3

= 4√3

√48 = 4√3

3√48

= 3 * 4√12

= 12√12

√75 = 5√3

2√12 + 3√48 - √75

= 4√3 + 12√12 - 5√12

= 16√12 - 5√12

= 11√12

**Answer: My answer is 11√3**

**Step-by-step explanation:**

Pull terms out from under the radical, assuming positive real numbers.

Exact Form:

11√3

Decimal Form:

19.05255888…

What is the length of PQ

### Answers

Check the picture below.

[tex]\sin(30^o)=\cfrac{\stackrel{opposite}{PQ}}{\underset{hypotenuse}{4}}\implies 4\sin(30^o)=PQ\implies 4\left( \cfrac{1}{2} \right)=PQ\implies 2=PQ[/tex]

Work out

m

and

c

for the line:

2

y

−

4

x

=

2

### Answers

**Answer:**

General equation : y = mx + c

2y - 4x = 2

2y = 4x + 2

y = 2x + 1

Therefore m = 2 and c = 1.

The point (0, 5) lies on a circle with the center at (0, 0). What is the area of the circle?

### Answers

A = 2*pi*r^2

A = 2*pi*5^2

A = 2*pi*25

A = 50pi or 157.1

Determine if the expression -3z2 is a polynomial or not. If it is polynomial, state

the

type and degree of the polynomial.

### Answers

Therefore, the equation that best fits these **scatter plot** facts as the answer to this problem is y=661-0.1x.

Describe a scatter plot.

The term "scatter plot" refers to a particular sort of **graph **in which the x- and y-axes are used to represent the values of two **variables**, with the dots that arise indicating any association between the data.

Given the correlation between the data at this moment and the graph provided in the question, y=661-0.1x is an equation that best captures the scatterplot's line of best fit.A scatter plot is a specific type of graph in which the x- and y-axes are used to represent the values of two variables, with the dots that appear showing any associations between the data.

y=661-0.1x is the equation whose solution best fits this data.

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How many dimes are in 4.72

### Answers

**Answer:**

There are 47 dimes and 2 pennies.

**Step-by-step explanation:**

10¢ = 1 dime

$4.70 = 470 ¢

470 dimes = 47 dimes

and 2 pennies

What does f âˆ˜ G mean?

### Answers

F âˆ˜ G is a **mathematical operation **that is used to find the composite of two functions, f and G. This operation is also known as **function **composition or composition of functions.

**Function **composition (also known as function composition of functions) is a mathematical operation that allows one to combine two or more functions into a single, larger function. This operation is symbolized by F âˆ˜ G. The composite of two functions, f and G, is defined as the composite of two functions f and G, which is a new function h, such that h(x) = f(G(x)) for all x in the **domain **of the function. This means that the output of G is the input of f and the output of f is the output of h. Function **composition **is a useful tool for combining functions in order to create more complex functions. It can also be used to simplify and shorten existing functions, as well as to simplify an **equation **by reducing the number of operations that need to be performed.

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What is the equation of a line with a slope of 3 and y-intercept equal to 5?

### Answers

The** equation of a line** is given by y = mx + b, where m is the slope and b is the y-intercept. Given that the slope is 3 and the** y-intercept **is 5, the equation of the line is y = 3x + 5.

The equation of a line is a** mathematical expression** of the form y = mx + b, where m is the slope and b is the y-intercept. This equation can be used to describe the relationship between the **x-coordinate** and y-coordinate of points on a line. In this specific equation, the slope is 3 and the y-intercept is 5, which means that the line passes through the point (0, 5) and has a **slope** of 3. Substituting 3 for m and 5 for b in the equation, we get y = 3x + 5, which is the equation of the line with a slope of 3 and a y-intercept of 5. We can use this **equation** to determine the y-coordinate of any given point on the line, provided we know the x-coordinate of the point. It is important to note that this equation is only applicable to straight lines, and not curves.

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An employee records the number of minutes it takes each team to complete the escape room

this week. The dot plot shows the data.

How many teams completed the escape room

this week?

teams

●

Escape Room

40 41 42 43 44

45 46

45 46 47

Time to Complete (min)

47 48 49 50

### Answers

To begin, our game organizer will introduce participants to the escape **game instructions **and backstory. Teams will have 60 minutes to complete their chosen quest

What is escape room?

An escape room, also known as an escape game, puzzle room, exit game, or riddle room is a game in which a team of players discover clues,** solve puzzles,** and accomplish tasks in one or more rooms in order to accomplish a specific goal in a limited amount of time. The goal is often to escape from the site of the game.

Once you’re ready to start the game, your team will watch a mission video. This video explains the world your team is now a part of, what you’re trying to accomplish, and why you only have 60 minutes to do so!Some missions are about escaping the room, like in a prison break room. Other missions might not be centered around **escaping**, but instead, you might be completing a heist or launching a martian spaceship.Here’s an example of the type of mission video that plays at the beginning of a game. This one is from The Escape Game’s The Heist!

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**Answer:21 teams **

**Step-by-step explanation:because if you cont the black dots and read the question that would be the answer **

GEOMETRY:

I might just be slow but I don't understand what this question is asking at all. Can someone help?

### Answers

**Answer:**

[tex]b = 90[/tex]

[tex]d = 100[/tex]

[tex]c = 80[/tex]

**Step-by-step explanation:**

The problem is asking for the values of the variables [tex]b[/tex], [tex]c[/tex], and [tex]d[/tex] in the given parallelogram with angles [tex]d\textdegree[/tex], [tex]c\textdegree[/tex], [tex](b-10)\textdegree[/tex], and [tex](b+10)\textdegree[/tex].

To solve for these variables, we can construct three equations using the knowledge that any two adjacent angles of a parallelogram are supplementary (their measures add to 180º).

The first equation shows that the top two angles are supplementary:

[tex]d\textdegree + c\textdegree = 180\textdegree[/tex]

The second equation shows that the bottom two angles are supplementary:

[tex](b-10)\textdegree + (b+10)\textdegree = 180\textdegree[/tex]

The third equations shows that the left two angles are supplementary:

[tex]d\textdegree + (b-10)\textdegree = 180\textdegree[/tex]

First, we can solve for [tex]b[/tex] in the second equation using simple algebraic manipulation.

[tex](b-10)\textdegree + (b+10)\textdegree = 180\textdegree[/tex]

[tex](b+b)\textdegree + (10-10)\textdegree = 180\textdegree[/tex]

[tex]2b\textdegree = 180\textdegree[/tex]

[tex]b\textdegree = 90\textdegree[/tex]

[tex]b = 90[/tex]

Using this [tex]b[/tex]-value, we can solve for [tex]d[/tex] by rewriting the third equation, plugging [tex]90[/tex] in for [tex]b[/tex]:

[tex]d\textdegree + (b-10)\textdegree = 180\textdegree[/tex]

[tex]d\textdegree + (90-10)\textdegree = 180\textdegree[/tex]

[tex]d\textdegree + 80\textdegree = 180\textdegree[/tex]

[tex]d\textdegree = 100\textdegree[/tex]

[tex]d = 100[/tex]

Finally, we can solve for [tex]c[/tex] in the first equation by plugging [tex]100[/tex] in for [tex]d[/tex]:

[tex]d\textdegree + c\textdegree = 180\textdegree[/tex]

[tex]100\textdegree + c\textdegree = 180\textdegree[/tex]

[tex]c\textdegree = 80\textdegree[/tex]

[tex]c = 80[/tex]

Olivia owns a pastry shop, and needs to fill an order for 700 cupcakes

She already has 15 cupcakes made, and she can make 137 cupcakes

hour. How many hours does Olivia need to fill the order?

Olivia needs

more hours.

### Answers

**Answer:**

5 hours

**Step-by-step explanation:**

Olivia needs to make 700 - 15 = <<700-15=685>>685 cupcakes.

So she needs to work for 685 / 137 = <<685/137=5>>5 hours

5 hours

Explanation below

3x-y=2 and 12x-4y=4 parellel or perpendicular line

### Answers

**Answer:**

They are parallel line.

An elliptical mirror measures 16 inches wide and 20 inches high. The ellipse is centered at (0, 52) on a coordinate plane, where units are in inches. Which equation represents the mirror?

(y - 52)²/400 + x²/256 = 1

(y – 52)²/100+ x²/64 = 1

X²/400+ (y-52)²/256 = 1

x²/100+(y-52)²/64 = 1

### Answers

**Equation **of ellipse is x²/400 + (y-52) ²/256 =1

What is ellipse?

An ellipse is an oval shaped close geometrical figure. Ellipse has two radius, one is horizontal, and the other is vertical. An ellipse can be stretched either horizontal direction or vertical direction.

Which equation represent the mirror?

given, width of elliptical mirror = 16 inches

height of elliptical mirror = 20 inches

the center of ellipse = (0, 52)

as the width of elliptical mirror is less than height so the ellipse has vertical **major** axis.

vertical radius is denoted by b.

and horizontal radius is denoted by a.

as per the question, a = 16 inches and b = 20 inches.

we know the equation of ellipse whose major axis is vertical and center at the origin is shown by

x² / b² + y²/ a² = 1

we are given information about an ellipse having center (0, 52) and vertical radius 20 and horizontal radius 16.

the equation of this ellipse is.

x² / (20) ² + (y -52) ²/ (16)² = 1

x²/400 + (y - 52) ² /256 = 1

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If there are 10 fish in a tank 5 escaped 2 died.

How many are left?

Pls help

### Answers

**Answer: 8**

**Step-by-step explanation:**

Its a fish tank no fish can escape. So 10-2 because 2 fish died and that is 8.

So you have 8 fish.

Hope this helps

Okay so if there’s 10 - 5 - 2 = ?

10 - 5 = 5 since it’s subtracting.

Then you subtract 2 more such as

5 - 2 = 3

The two smaller angles of a right triangle have equal measures. find the measure of all three angles.

### Answers

**Answer:**

**Step-by-step explanation: Because all three angles of the triangle must equal to 180 degrees, the two smaller angles of the right triangle must be 45 degrees. This is because a right angle always is 90 degrees and because you know that the other two angles are the same, and it must all equal to 180, the angles must be 45 degrees, 45 degrees, and 90 degrees.**

**Angle 1: (right angle) 90 degrees**

**Angle 2: 45 degrees**

**Angle 3: 45 degrees**

Rectangle A is similar to rectangle B by scale factor r. The length of rectangle A is 1. 5r+2. 25 units. The length of rectangle B is 3 unite. What is the scale factor

### Answers

The scale factor of the two **rectangles **is 1.5

Describe the rectangle.

According to** Euclidean Plane Geometry**, a rectangle is a quadrilateral with equal opposed sides and four right angles. In other words, a rectangle is a **parallelogram **with a right angle of 90 degrees or an equiangular quadrilateral (i.e., 360°/4 = 90°). A rectangle is referred to as a square if its four sides are all the same length.

The ratio of the matching side lengths of two comparable figures is known as the scale factor. We know that the ratio of the respective side lengths of the two rectangles equals equivalent to r since Rectangle A and Rectangle B are similar to one another by the scale factor r.

We can set up the following ratio to determine the scale factor if the lengths of rectangles A and B are 1.5r+2.25 units and 3 units, respectively.

(1.5r+2.25) / 3 = r

Solving for r, we get:

r = (1.5r + 2.25) / 3

multiply both sides of the equation by 3

3r = 1.5r + 2.25

Subtract 1.5r from both sides

1.5r = 2.25

divide both sides by 1.5

r = 2.25/1.5

r = 1.5

Therefore, the scale factor of the two rectangles is 1.5.

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Give an example of a quadratic function that has a maximum value. How do you know that it has a maximum value?

### Answers

An example of a **quadratic **function that has a maximum value is the **parabola **defined by the equation y = -(x-3)^2 + 4.

What is quadratic function?

A quadratic function is a type of **polynomial **function that can be written in the form y = ax^2 + bx + c, where a, b, and c are constants and x is the variable. The graph of a quadratic function is a parabola, which can either open upward or downward depending on the value of the leading **coefficient **(a).

What is equation?

An equation is a mathematical statement that asserts the equality of two expressions. It is usually written with an "=" sign between the two expressions, such as y = 2x + 3 or x^2 + y^2 = 1. Equations can be used to model real-world situations, and solving an equation means finding the values of the variables that make the equation true.

We can determine that this function has a maximum value by looking at the leading coefficient of the quadratic term (x^2). In this case, the coefficient is -1, which means that the parabola opens downward. Therefore, since the parabola opens downward, the vertex of the parabola is the highest point of the parabola, which means that it is a maximum point.

Also we can find the vertex of the parabola by using the formula x = -b/2a, in this case x= -0 / 2*-1 = 3/2 =1.5, and using this value in the function, we get the y value which is 4, so the vertex is (1.5,4) which confirms that the function has a maximum value at (1.5,4)

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Sport

Soccer

Jogging

Walking

Skiing

Football

Total

Hrs

5

20

10

5

10

50

Calculate the

portion for jogging

in degrees

[?]

20 hrs.

Total Sport Hours

### Answers

The portion for walking in degrees when Soccer take 5 hours, Jogging take 20 hours, Walking take 10 hours, Skiing take 5 hours and Football take 10 hours of the total 50 hours of **sport hours** is 72 degrees.

Therefore the answer is 72°.

To calculate the portion of **walking** in degrees, we first need to find the total amount of time spent walking. In this case, it is 10 hours.

Next, we need to find the total amount of** time** spent on all sports, which is 50 hours.

Now we can calculate the portion of walking by taking the amount of time spent walking (10 hours) and dividing it by the total amount of time spent on **sports** (50 hours).

This gives us the fraction of time spent walking which is

10/50

= 1/5

Finally, we can convert this fraction to **degrees** by multiplying it by 360 (the number of degrees in a full circle).

So the portion of walking in degrees is

(1/5) × 360

= 72 degrees

--The question is incomplete, complete question is given below--

"Calculate the portion for walking in degrees when Soccer take 5 hours, Jogging take 20 hours, Walking take 10 hours, Skiing take 5 hours and Football take 10 hours of the total 50 hours of sport hours."

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Arlene buys a phone case and charging cord for 15% off. The original cost of the phone case is $18. Her total discount is $4. 20.

Write and solve an equation to find the original price of the charging cord, x

### Answers

The **equation** to find the original price of the charging chord is 0.15x + 0.15y = 4.20 and the original price of the charging cord is $10.

Let the price of the phone case is x.

And the price of the charging cord is y.

Discounted price for phone case: 15% of x = 0.15x

Discounted price for charging cord = 0.15y

Now, according to the question, the **total discount** is $4. 20

⇒0.15x + 0.15y = 4.20

⇒0.15 * 18 + 0.15y = 4.20

⇒2.7 + 0.15y = 4.20

⇒0.15y = 4.2 - 2.7

⇒y = 1.5/0.15

⇒y = $10

Therefore the equation to find the original price of the cord is 0.15x + 0.15y = 4.20 and the **original price **of the charging cord is $10.

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