Mathematics High School

## Answers

**Answer 1**

**Answer:**

25% and 75%

**Step-by-step explanation:**

**Answer 2**

**Answer:**

**Step-by-step explanation:**

i dontk

## Related Questions

From January through June, 46200 immigrants applied for citizenship. During this same period last year, 12000 immigrants applied. What is the percentage of decrease?

### Answers

The **percentage decrease** of the given population of immigrants at the different times of the year is; 61.5%

What is the percentage decrease?

When an initial value is greater than a more recent value, it means that there will exist a **percentage decrease** from that initial value to the more recent value. Therefore, the formula for percent decrease is simply equal to the change in the value divided by the **original value.**

We are given;

Number of immigrants who applied for citizenship for the first six months this year, = 46,200

Number of immigrants who applied for citizenship for the first six months last year = 120,000

Thus, the **percentage decrease** is;

Percentage decrease = [(120000 - 46200)/120000] * 100%

Percentage decrease = 61.5%

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Total Number of Boys 58 Number of boys who can roll their tongues 40 Total Number of Girls 78 Number of girls who can roll their tongues 62 What percentage of the class members can roll their tongues? Record your answer and fill in the bubbles on your answer grid. Be sure to use the correct place value.

### Answers

The **percentage** of the **class members** can roll their **tongues** is 75%

**What is the percentage?**

It's the **ratio** of two **integers **stated as a **fraction** of a **hundred parts.** It is a **metric** for comparing two sets of **data**, and it is expressed as a **percentage** using the **percent** symbol.

Total class members = Total Number of Boys + Total Number of Boys

= 58 + 78

= 136

Total class members who can roll their tongues

= Number of boys who can roll their tongues + Number of girls who can roll their tongues

= 40 + 62

= 102

Percentage of the class members can roll their tongues

= (Total class members who can roll their tongues ) / (Total class members )

= 102/136

= 0.75

= 75%

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Which is an equation of a direct proportion?

### Answers

An** equation **of a direct **proportion** is y=−2x, y=4x

**What is direct proportion?**

By definition, an equation of **direct proportion** has the following form: y=k x

Where k is the constant of proportionality.

The **equation** of the line y=m x+b, where m is the slope and [tex]$\mathrm{b}$[/tex] the [tex]$\mathrm{y}$[/tex] intercept.

When b=0, means that the line passes through the origin. Therefore, it would be:

y=m x

(which is similar to y=k x )

Then, the **slope** of the line would be the constant of proportionality.

By definition, the slope can be positive or negative.

Keeping on mind the information above, you can see that the equation that have that form are:

y=-2 x

y=4 x

**Complete question: **Which is an equation of a direct proportion? y=−2x y=12x−2 y=−2x+3 y=4x

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Is sphere and circle the same?

### Answers

No, a **sphere **is a three-dimensional object, while a **circle **is two-dimensional.

A **sphere **is a three-dimensional object with a curved surface made of points equidistant from its center. It is the three-dimensional equivalent of a circle. A sphere is round and has no edges or vertices, like a circle, but it also has a thickness, like a solid **object**. The circumference of a sphere is the same as the circumference of a circle with the same radius. It is possible to calculate the surface area and volume of a sphere using the formula for the area and volume of a circle.A circle is a two-dimensional shape with a curved line that is equidistant from its center. The circumference of a **circle **is the length of its curved line. It is possible to calculate the area and circumference of a circle using the formula for the area and circumference of a circle. Unlike a sphere, a circle does not have a thickness, and it has no **edges **or vertices.

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help

Choose all of the pairs that are included in the set of solutions for the equation y=12x+32when plotted in the coordinate plane.

Responses

A (3, 3)(3, 3)

B (2, 3)(2, 3)

C (−4, −1)(−4, −1)

D (−5, −1)(−5, −1)

E (7, 5)

### Answers

The **pairs** that are included in the **set of solutions** for y = 1/2x + 3/2 are: (3, 3), (−5, −1), and (7, 5).

How to Find the Solution of an Equation?

If a point is located on a line of an **equation**, then the ordered **pair** of that point is defined as belonging to the **set of solutions** for the **equation**.

Given the **equation**, y = 1/2x + 3/2, the **graph** is plotted on a coordinate plane as shown below. It has a slope of 1/2, and a y-intercept of 3/2.

The **graph** shows that the following **pair** of the points are located on the **line** of y = 1/2x + 3/2:

(3, 3)(−5, −1)(7, 5)

Therefore, it is concluded that the **pairs** that are included as the **solution** to y = 1/2x + 3/2 are: (3, 3), (−5, −1), and (7, 5).

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3/5(x - 7/10) = -3 1/4 enter answer as mixed number in simplest form

### Answers

**Answer:**

x=-4 43/60

**Step-by-step explanation:**

3/5(x - 7/10) = -3 1/4

3/5(x - 7/10) = -(3 1/4)

3/5(x - 7/10) = -(3 + 1/4)

3/5(x - 7/10) = -(12/4 + 1/4)

3/5(x - 7/10) = -13/4

3x/5 - (3/5)*(7/10) = -13/4

3x/5 - (3*7)/(5*10) = -13/4

3x/5 - 21/50 = -13/4

30x/50 - 21/50 = -13/4

(30x-21)/50 = -13/4

50*(30x-21)/50 = 50*(-13/4)

30x-21=-650/4

30x-21+21=21-650/4

30x=21*4/4 - 650/4

30x=84/4 - 650/4

4*(30x=84/4 - 650/4)

120x=84-650

120x=-566

x=-566/120

x=(-566/2)/(120/2)

x=-283/60

x=-(43+240)/60

x=-43/60 - 240/60

x=-4 - 43/60

x=-(4 + 43)/60

**x=-4 43/60**

X= -4 43/60 have a good day

How to find the missing side of a triangle Pythagorean Theorem?

### Answers

By using** a² + b² = c² **this formula we can find the missing side of a triangle.

A triangle is right-angled if one of the three angles is 90°, i.e., any two sides are perpendicular.

If we know two other sides of the right triangle, all you need to do is apply the **Pythagorean theorem:**

a² + b² = c²

If leg a is the missing side, then transform the equation to the form where a is on one side and take a square root:

**a = √(c² - b²)**

If leg b is unknown, then:

**b = √(c² - a²)**

For hypotenuse c missing, the formula is:

**c = √(a² + b²)**

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Please help guys this is due and I don’t know how to do it :( do any problem you would like, it would help so much!

### Answers

12. The **time taken** by Joseph alone to clean the room is 9.3 hours.

What is th**e time taken by **Joseph alone to clean the room?

Let the** time** taken by both to clean the room = A = 4hours.

Let the time taken by Isaac alone to clean the room = B = 7 hours

Let the time taken by Joseph alone to clean the room = C

Applying the **time and work** formula,

[tex]C=\frac{AB}{B- A} \\\\=\frac{7 *4 }{7 - 4} \\\\=\frac{28}{3} \\\\= 9.3[/tex]

Thus ,the time taken by Joseph alone to clean the room is 9.3 hours.

What is the time and work concept?Time and work concept is concerned with the amount of time it takes a person or a group of people to complete a task and the effectiveness of the work performed by each of them. What one person can accomplish in a day is referred to as the efficiency of work that is expressed in the form of percentage. The relationship between time and work is inverse.Work is described as something that makes an impact or produces a result, frequently the one that is expected or wanted. The fundamental idea of Time and Work is the same across all areas in arithmetic.

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charlie went to the playground. he played on the swings for 20 minutes and went on the slide for 30 minutes. it was 4:05 p.m. when charlie left the playground. what time was it when charlie arrived at the playground?

### Answers

Charlie played 50 **minutes **at the **playground**. He arrived at the playground at 3.10 pm.

Steps to translate a word problem into an** algebraic expressions **or to **equations**:

- Highlight the important things

- Use mathematic operators plus, minus, divide, times, equal to, inline with the text.

- Identify the unknown

- Assign the unknowns to **variables**

- To solve the equations, isolate the variables.

In given problem:

He played on the swings for 20 minutes and went on the slide for 30 minutes.

The word "and" can be translated as** addition**. Hence,

Total time Charlie at the playground = 20 minutes + 30 minutes

= 50 minutes

Let x = time when Charlie arrived at the playground.

Hence,

x + 50 minutes = 4.05 pm

To use mathematic operators on clocks, write 4.05 pm and 50 minutes as:

4.05 = 3.65

50 minutes = 0.50

x + 0.50 = 3.65

x = 3.65 - 0.50 = 3.10

Therefore, Charlie arrived at the playground at 3.10 pm.

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What is the additive inverse of 7 /- 12?

### Answers

The **additive inverse **of 7/(-12) is 7/12.

What is Additive Inverse?

To get a result **equal **to 0, add the **original **number and the **additive **inverse by simply **changing **the **sign **of the **integer**. On the basis of negation of the original number, the characteristics of additive inverse are listed below. For **instance**, if x is the starting number, then -x is x's additive inverse.

Given:

7/-12

Usually in additive inverse we have to **changing **the **sign** of the number and **adding** it to the original number to get an answer **equal **to 0.

As, x + (-x)= 0 here (-x) is the **additive **inverse of x.

Now, 7/(-12) can be written as (-7/12).

**Additive inverse **of (-7)/12 is +(7/12)

So, -7/12+ 7/12 = 0

Hence, the **additive inverse** of 7/(-12) is 7/12.

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What does dilate mean for a triangle?

### Answers

It mean** the measure** of the height, the apothem and the base of the triangle are** change**. It also mean, the circumference and the area of the triangle are change ,but** the angle** of the triangle **did not **change from the original triangle.

**What is dilatation?**

**Dilatation** is a process to change the size of the object whether it is to reduce or to enlarge it but did not change it shape. The follow methods use to in dilatation:

Starting from the center of dilatation, measure the horizontal and vertical distances ;Create a scale factor and calculate the horizontal and vertical distances;Starting from the center of dilatation, put the point to the number that you gain from the step 2

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Is 2xy 2 a monomial?

### Answers

2xy is monomial.

2a is monomial.

As they contains only one** terms**.

What is monomial?

A mathematical **expression** that only contains one term.

Monomial for 2xy:

The exponents of all the **variables** are added to determine a monomial's degree. It is always an** integer** that is not zero.

For instance, the monomial 2xy has a degree of 2.

Variable 'x' has an** exponent** of 1, variable 'y' has an exponent of 1.

The result of adding all these exponents is 1 + 1 = 2. Let's use a different example to demonstrate how to determine a monomial's** degree.**

Hence, the Equation 2xy is Monomial.

Monomial for 2a:

The exponents of all the variables are added to determine a monomial's degree. It is always an integer that is not **zero**.

For instance, the monomial 2a has a degree of 1.

Variable 'a' has an exponent of 1.

The result of adding all these exponents is 1 . Let's use a different example to demonstrate how to determine a monomial's degree.

Hence, the **Equation** 2a is Monomial.

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4(4 - 2p) - p = -3(3p + 5)

a. 13

b. -1

c. 15

d. no solution

### Answers

The** equation** has no solution because p cannot be found. Therefore, the answer is option d.

How to solve an equation?

An **equation** is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.

We have to find he variable of the equation p.

A **variable** is a number represented with a letter in an equation.

Therefore, let's find the variable p in the equation.

4(4 - 2p) - p = -3(3p + 5)

open the bracket

8 - 8p - p = -9p - 15

8 - 9p = -9p - 15

add 9p to both sides of the equation

8 - 9p = -9p - 15

8 - 9p + 9p = -9p + 9p - 15

8 = -15

Therefore, the** equation** has no solution.

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john randomly selects a ball from a bag containing different colored balls. the odds in favor of his picking a red ball are 3:11. what is the probability ratio for john picking a red ball from the bag? 3 over 8 3 over 14 3 over 11 3 over 10

### Answers

The** probability** ratio for **John **picking a **red ball** from the bag is 3/14

How to determine the probability ratio for john picking a red ball from the bag?

**Probability** is a measure of the likelihood of an event occurring, expressed as a number between 0 and 1. An event with a probability of 1 is certain to occur, while an event with a probability of 0 is impossible to occur.

The probability ratio for **John** picking a** red ball** from the **bag** is 3:11, which means that there are 3 outcomes in favor of John picking a red ball and 11 outcomes against John picking a red ball. Thus:

Odd ratio = 3:11

Number of red balls = 3

Total number of **balls** = 3 + 11 = 14

Probability of** picking** red ball = 3/14

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At a large museum, there are 80 people in each group use this info to fill in the table then plot the (ordered pairs) given by the table. Thanks to whoever awsners

### Answers

There are 160 people in 2 tours, 320 people in 4 tours, and 720 people in 9 tours. The **ordered pair** is plotted on the graph attached.

Based on the information provided, there are 80 people in each group. The number of people in given number of tours is given by: No of people = 80 x No of tour

No of tour = 2

No of people = 80 x 2 = 160

No of tour = 4

No of people = 80 x 4 = 320

No of tour = 9

No of people = 80 x 9 = 720

Hence, the **ordered pair** described by the data is (2, 160), (4, 320), and (9, 720). An ordered pair refers to a composition of the **x coordinate **(abscissa) and the **y coordinate **(ordinate), having two values written in a fixed order within parentheses. It helps to locate a point on the **Cartesian plane** for better visual comprehension. Plot the ordered pair on the graph

Note: The question is incomplete. The complete question is attached.

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Solve

X^4 + x³ + 4x² + 4x = 0.

A 0,-1, +or - 2i

B. 0, 1, +or- 2i

C. O, -1, +or- 2

D. 0, 1, +or- 2

### Answers

The **solution** for the given **equation** would be 0, -1, ±2i.

Option (A) is correct.

**What are quartic polynomials?**

**Quartic** is **polynomials** whose highest **degree** is **four**. There is no special formula for finding the **roots** of **quartic** **functions**, but there are three mathematical methods that could help find the roots.

The given equation is [tex]x^4 + x^3 + 4x^2 + 4x = 0.[/tex]

Multiplicity: 1, x1=−1

Multiplicity: 1, x2=−2i=−2.0i

Multiplicity: 1, x3=2i=2.0i

Multiplicity: 1, x4=0

Hence, the **solution** for the given **equation** would be 0, -1, ±2i.

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How do you find an equation with a point and undefined slope?

### Answers

Any line with an unknown slope is a **vertical line **with no y-intercept. As a result, the equation of a line with an unknown **slope **is x = a, where a = the x-intercept. Here **a = 1.**

Because the **slope **of a vertical line is indeterminate, neither the slope-intersect form nor the point-slope form can be used to construct the equation of a vertical line. However, the **conventional **form can be used.

Because the line with an unknown slope is a **vertical line**, all x -coordinates will be the same regardless of the y -coordinate. When a line is vertical, it has an indeterminate slope. A vertical line lacks the **horizontal distance **required to have a positive, negative, or neutral value.

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at a water park, there are several different attractions. the following table displays data on the most popular rides. ride type speed (mph) tunnel maximum weight (lbs) number of riders big drop thrill 20 no 250 single-rider dark chute family 20 yes 275 4-person tube river rapids family 15 no 300 single-rider wild thunder thrill 18 no 250 double tube splash shoot kids 15 yes 150 single-rider what is the number and type of variables?

### Answers

4 categories and 2 **numerical variables** make up the total number of factors.

What is numerical and categorical variable?

A category or type is a **categorical variable**. For instance, hometown or hair color are both examples of categorical values. Gender, species, and method of therapy are all categorical variables.

Any variable where the measurement or number has a numerical value is referred to as a numerical variable. For instance, the amount of rain measured in inches, the heart rate, and the number of cheeseburgers eaten in an hour are all numerical values.

For statistical purposes, a categorical variable can be written as a number, but these numbers don't signify the same thing as a numerical value.

For instance, if I were researching how three different pharmaceuticals affect a disease, I might use the names Medicine 1, Medicine 2, and Medicine 3. However, medicine three is not more effective than medicine one, nor is it any faster. These figures don't imply anything.

Hence, 4 categories and 2 **numerical variables** make up the total number of factors.

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Check all of the solutions to the original equation.

x^-9 - 6x^3 + 6 = 0

### Answers

The **solutions** of the **original** **equation** are x = -1.5, 1.5, 1/√[3].

To **solve** this equation, we can factor the l**eft-hand side** as follows:

x^-9 - 6x^3 + 6 = (x^-3 - 2)(x^6 + 3x^3 + 3) = 0

We can then **solve** for the **roots** of the equation by **setting** **each** **factor** **equal** to **zero**:

x^-3 - 2 = 0 -> x^-3 = 2 -> x = 2^(-1/3) = 1/√[3]

x^6 + 3x^3 + 3 = 0 -> x^6 + 3x^3 = -3 -> (x^3)^2 + 3(x^3) = -3 -> x^3 = (-3 ± √[9 - 4])/2 = -1.5, 1.5

Thus, the **roots** of the **original** **equation** are x = -1.5, 1.5, 1/√[3].

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What is 24/240 as a decimal

### Answers

**Answer:**

0.1

**Step-by-step explanation:**

Just take 24/24 which is 1 and move the decimal one place to the left because there is an extra 0 on the denominator

The table shows the difference between the actual volumes of some bottled teas and the average volume of a bottled tea. Piyush opens a bottle of tea and finds that it has 0.75 ounce more than the average tea volume. Between what two bottles is the volume of the bottle that Piyush opened?

### Answers

By using **fractions** and **decimals**, it can be calculated that

Between bottle 2 and bottle 4 is the** volume** of the bottle that Piyush opened

**What is fraction and decimal?**

Suppose there is a **collection **and a part of **collection** has to be taken. The** part** which is taken is called **fraction**. In other words, **part **of a **whole **is called **fraction**.

The upper part of the** fraction** is the **numerator **and the lower part of the **fraction **is the **denominator.**

This is a word problem of **fraction **and **decimal**

For bottle 1

Difference between the **actual volumes** and the** average volume** = [tex]\frac{9}{10}[/tex] = 0.9 oz

For bottle 2

Difference between the **actual volumes **and the** average volume** = -1.1 oz

For bottle 3

Difference between the **actual volumes** and the** average volume** = [tex]1\frac{1}{4}[/tex] = 1.25 oz

For bottle 4

Difference between the **actual volumes** of some bottled teas and the **average volume** = -0.4 oz

Now 0.75 oz lies between -0.4 and 0.9

Between bottle 2 and bottle 4 is the **volume** of the bottle that Piyush opened

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Choose an equivalent system of equations to the following system: (1 point)

Fx + Gy = H

Qx + Ry = S 3Fx + 3Gy = 3H

Qx + Ry = S

Choices:

3Fx + Gy = 3H

Qx + 3Ry = S

3Fx + 3Gy = 3H

Qx − Ry = S

Fx + 3Gy = 3H

Qx + Ry = S

### Answers

An **equivalent** system of **equations** to the given system equations are 5Fx+5Gy=5H and Qx+Ry=S. Therefore, option C is the correct answer.

What are equivalent system of equations?

**Equivalent system** of equation is that system of equations in which **solution** does not change. If a constant multiplied on both sides of an equation then solution of **equation** remain same.

The given **system** of equations are Fx+Gy=H and Qx+Ry=S.

A) 5Fx+5Gy=5H

First equation is multiplied by 5 but the **value** remains same as original equation Fx+Gy=H

Second equation Qx−Ry=S is not same as original equation Qx+Ry=S

B) First equation 5Fx+Gy=5H is not same as original equation Fx+Gy=H

Second equation Qx+5Ry=S is not same as original equation Qx+Ry=S

C) First equation 5Fx+5Gy=5H is **multiplied** by 5 but the value remains same as original equation Fx+Gy=H

Second equation Qx+Ry=S is **same** as the original equation Qx+Ry=S

D) First **equation** Fx+5Gy=5H is not same as original equation Fx+Gy=H

Second equation Qx+Ry=S is same as the original equation Qx+Ry=S

An **equivalent** system of **equations** to the given system equations are 5Fx+5Gy=5H and Qx+Ry=S. Therefore, option C is the correct answer.

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"Your question is incomplete, probably the complete question/missing part is:"

Choose an equivalent system of equations to the following system:

Fx+Gy=H

Qx+Ry=S

A. 5Fx+5Gy=5H

Qx−Ry=S

B. 5Fx+Gy=5H

Qx+5Ry=S

C. 5Fx+5Gy=5H

Qx+Ry=S

D. Fx+5Gy=5H

Qx+Ry=S

e In a company, 85% of the workers are men. If 540 people work for the company who aren't men, how many workers are there in all? Use pencil and paper. Show two different ways that you can solve this problem.

### Answers

The number of **workers **in all, in the **company**, given the percentage that are men and the number who are not, is 3, 600 workers

How to find the number of workers ?

The **percentage **of **workers **who are men is 85 % which means that the percentage who aren't men is :

= 100 % - 85 %

= 15 %

The number of workers in the **company **is therefore :

= Number of workers who aren't men / Percentage who aren't men

= 540 / 15 %

= 3, 600 workers

Another way to find the number of workers is:

x = 85%x + 540

x - 0.85x = 540

0.15x = 540

x = 540 / 0.15

x = 3, 600 workers

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to win at lotto in a certain state, one must correctly select 6 numbers from a collection of 50 numbers (one through 50.) the order in which the selections is made does not matter. how many different selections are possible?

### Answers

There are 15890700 different **selections** to win at lotto at a certain state.

To find the number of different **selections **that are possible, you can use the **combination **formula. The combination formula is:

C(n , r) = n! / (r! × (n - r)!)

where C(n , r) represents the number of combinations, n represents the total number of items, and r represents the number of items being chosen at a time.

In this case, n is 50 and r is 6, so the number of different selections is:

C(50 , 6) = 50! / (6! × (50 - 6)!) = 50!/6!44! = 15890700

Therefore, there are 15890700 different selections that are possible.

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Observe the two scenarios involving electrically charged objects. Predict what will happen when you bring the objects close together.

1

Soda

Scenario #1

Scenario #2

O The balloon will attract the soda can, while the two balloons will repel each other.

O The balloon will attract the soda can, while the two balloons will do nothing.

O The balloon will repel the soda can, while the two balloons will also repel each other.

O The balloon and soda can will do nothing, while the two balloons will repel each other.

### Answers

From the both **scenarios**, when the objects are brought close together, the **balloon** will attract the **soda can,** while the two balloons will repel each other. That is **option A.**

What is Electrical charge?

**Electrical charge** is defined as the force experienced by a particle when placed in an electric or magnetic field.

An electrical charge can either be positive or a negative charge.

When a **positive charged** particle and a **negative charged** particle are placed in a field, they both attract each other.

But when two objects bearing the same charges are placed in a field, they repel each other.

Therefore, in **scenario 1,** the balloon and soda can bears different charges that's why they attract each other; while in **scenario 2 **the two balloons bear the same charges so they repel from each other.

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Geometry help please

### Answers

**Answer:**

b is the correct geometry because there is vertices and coordinates

Help pls

Simplify 7(n+1)-12n+9

### Answers

**Answer:**

-5n+16

**Step-by-step explanation:**

7(n+1)-12n+9

7n+7-12n+9

-5n+7+9

-5n+16

__% of 44 = 161 Round your answer to the nearest whole percent if necessary.

a. 27

b 366

c. 37

d. 316

### Answers

The answer to the nearest **whole percent** is:

366% of 44 = 161 (option b)

**Percent **means per a **hundred**. Percent is equal to a** fraction** of a hundred.

For example, 60% = 60/100.

To convert a fraction into a percent form, find its equivalent fraction with denominator 100.

Example:

3/4 is **equivalent** to 75/100. Hence,

3/4 = 75/100 = 75%

To multiply a percent with a whole number, convert the percent into its equivalent fraction.

In the given problem:

__% of 44 = 161

[tex]\frac{...}{100}\times44=161[/tex]

Let assign the unknown to a variable p

(p/100) x 44 = 161

p = 161 x 100 / 44

p = 365.9 ≈ 366

Hence,

366% of 44 = 161 (option b)

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Circumcenter and incenter if w is the circumcenter of qrs find each measure

### Answers

Applying the **circumcenter theorem** and the **Pythagorean Theorem**, the following measures are calculated as:

a. QR = 50

b. RZ = 41

c. XS = 40

d. ZS = 41

e. WZ = 32.5

**What is circumcenter theorem?**

Based on the** circumcenter theorem** of a triangle, the following holds true given that Z is the circumcenter of triangle QRS:

RZ, QZ, and ZS are equal (circumcenter Z is equidistant from the three vertices of ΔQRS).

The perpendicular** bisectors divides** the three sides, RS, QS, and QR into equal parts each.

Points X, Y, and W are at** right angles.**

Given:

RS = 80

WQ = 25

XZ = 9

a. Find QR:

QR = 2 × WQ = 2 × 25

QR = 50

b. Find RZ in right ΔXRZ:

XZ = 9 (given)

XR = 1/2(RS) = 1/2(80) = 40

Apply Pythagorean Theorem to find RZ

RZ = √(XZ² + XR²)

Substitute

RZ = √(9² + 40²)

RZ = 41

c. Find XS:

XS = 1/2(RS) = 1/2(80)

XS = 40

d. Find RZ:

RZ = ZS = QZ = 41 (equidistant)

ZS = 41

e. Find WZ in right ΔWRZ:

WR = WQ = 25

WR = 25

RZ = 41

Apply** Pythagorean Theorem** to find WZ

WZ = √(RZ² - WR²)

Substitute

WZ = √(41² - 25²)

WZ = 32.5

**Complete question: **Circumcenter and incenter if w is the circumcenter of qrs find each measure

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Use a double integral to find the area of the region. One loop of the rose r = 8 cos(3theta) Incorrect: Your answer is incorrect.

### Answers

The sum of the **areas** of the enclosed regions is 2.004 , and -3.811 the **rate** at which h changes with respect to x when x = 1.8 .

Given : f(x) = 1 + x + e^x^2 - 2x and g(x) = x^4 - 6.5x^2 + 6x + 2

The graphs of y = f(x) and y = g(x) intersect in the first **quadrant** at the points (0, 2), (2, 4), and (A, B) = (1.032832, 2.401108).

(a) the sum of the **areas** of the enclosed regions is given by

Area =

[tex]\int\limits^A_0[[g(x) - f (x)] dx +\int\limits^2_A [f(x) - g(x)] dx[/tex]

= 0.997427 +1.006919

= 2.004

(b) the sum of the **volumes** of the **enclosed regions** is given by

Volume = [[ƒ(x) − g(x)]² dx = 1.283

(c) the **rate** at which h changes with respect to x when x = 1.8

h(x) = f(x) = g(x)

h'(x) = f'(x) - g'(x)

h'(1.8) = f'(1.8) g'(1.8)

=-3.812 (or -3.811)

Hence , the sum of the **areas** of the enclosed regions is 2.004 , and -3.811 the **rate** at which h changes with respect to x when x = 1.8 .

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