Mathematics High School

## Answers

**Answer 1**

The **volume **of coal is **42.41 cubic meters **when a pile of coal is stored in a barrel-shaped bin whose base has a **radius **of 3 meters, and the height of the pile measures 1.5 meters.

The cylinder is a** three-dimensional** shape having a circular base. A cylinder can be seen as a set of circular disks that are stacked on one another.

The **volume **of a cylinder **V= b*h **

where b is the area of the base

h is the height of the cylinder.

And since the **area **of a circle is **πr²**, we have this **equation **for the volume of a cylinder

**V = π×r²×h **

Now **substitute**, the known values for r and h, then calculate the result:

V = π×r²×h

V = 3.14159×3²×1.5

V = 3.14159×9×1.5

V = 42.411465

**V = 42.41 **

So the volume of the coal pile is 42.41 cubic meters.

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## Related Questions

question 18 the study method used to evaluate mother-child attachment is best described as: a. experimental. b. observational. c. inferential. d. statistical.

### Answers

The study method used to evaluate **mother-child** attachment is best described as option A: **experimental**.

Children who refuse food by acting negatively or in opposition seem to be a common theme in **feeding** interactions between depressed mothers and their kids. The purpose of this study was to examine parenting behaviours in the setting of feeding in moms who were suffering from serious **depression** from an attachment theory perspective. The easiest way to sum up the research design used to assess mother-child attachment is option A: experimental.

The idea of sensitive responsiveness was developed by **attachment** theory to measure a mother's capacity to empathetically recognise and respond to her child's signals. Their attitudes and **behaviours** when providing care may be badly impacted by this distress, which may be pervasive.

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The value of a ring ($1000) increases exponentially so that it has a value of $3,000 after 5 years. Find the rate.

### Answers

**Answer: **[tex]\sqrt[5]{3}-1[/tex]

**Step-by-step explanation:**

Let the annual rate of increase be [tex]r[/tex].

[tex]3000=1000(1+r)^5\\\\3=(1+r)^5\\\\\sqrt[5]{3}=1+r\\\\r=\sqrt[5]{3}-1[/tex]

Austin's brother loaned him $20 and asked him to pay him back in 3 months. He's going to charge 4% interest. Austin is excited about all extra money he will make in interest. Is is correct to be excited?

### Answers

**Answer:**

**Step-by-step explanation:**

Yes, it is correct for Austin to be excited about the extra money he will make in interest. Interest is a common form of compensation for loaning money to another person, and it is generally expected to be paid back along with the principal amount. In this case, Austin will earn 4% interest on the $20 loan over the course of 3 months, which works out to be a total of $0.80. This is a relatively small amount, but it is still money that Austin would not have had if not for the loan. Therefore, it is reasonable for Austin to be excited about the opportunity to make a little extra money.

Can you guys help me to figure out the area and explain to me pls

### Answers

**Answer:**

123.2

**Step-by-step explanation:**

First find area of the square ABCD, then the triangle AMN.

Find CD:

sin30 = CD/20

CD = 20(sin30) = 10

CD = AD = 10

Find MD:

cos30 = MD/20

MD = 20(cos30) = 17.32

AM = MD - AD = 17.32 - 10 = 7.32

Area of ABCD = (10)(10) = 100

Find height of triangle AMN: AN

cos30 = AN/7.32

AN = cos30(7.32) = 6.34

Area of triangle ANM = 1/2(7.32(6.34) = 23.2

Total Area of the shape = 100 + 23.2 = 123.2

Holly's garden is divided into 5 equal sections. She will fence the garden into 3 areas by grouping some equal sections together. What part of the garden would each fenced area be? please help I forgot how to do it for my lil brother just answer E

### Answers

There are two ways to **fence** the garden in 3 areas with some **equal** sections.

2/5, 2/5, 1/5 and 3/5, 1/5, 1/5.

**Fraction** definition

A fraction depicts a **segment** or component of the **whole**. It represents the equal parts that make up the whole. A fraction is made up of two parts: the numerator and the denominator. The number at the top is the numerator, and the number at the bottom is the denominator. The denominator specifies the total number of equal parts in the whole, whereas the numerator specifies the number of equal parts that are taken.

Given The garden is **divided** into 5 equal pieces, each of which is 1/5 of the total garden size.

By arranging some equal parts together, she will fence the garden into three sections. There are two ways to do this.

(1/5 +1/5) = 2/5

(1/5 +1/5) = 2/5

1/5

these are the 3 areas 2/5, 2/5, 1/5.

and

(1/5 +1/5 + 1/5) = 3/5

1/5, 1/5

these are 3 areas = 3/5, 1/5, 1/5.

Hence there are only **two ways** to fence the garden into three areas by grouping some **equal** sections.

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Is dividing by 1 2 the same as 2?

### Answers

No, dividing by 1/2 is not the same as dividing by 2. Dividing by 1/2 means to take a **number**, and then divide it by 1/2. For example, 8 **divided** by 1/2 would be 16.

Dividing by 1/2 means to take a number, and then divide it by 1/2. For example, 8 divided by 1/2 would be 16.

Dividing by 2 means to take a number, and then divide it by 2. For example, 8 divided by 2 would be 4.

Dividing by 1/2 involves taking a number and dividing it by one half of itself. For example, if you were to divide the number 8 by 1/2, the result would be sixteen. On the other hand, dividing by 2 means taking a number and dividing it by two. If you were to divide the number 8 by 2, the **result** would be four. Both **operations** involve division, but the results are not the same. Dividing by 1/2 involves taking a number, doubling it, and then dividing the result by two, while dividing by 2 involves taking a **number** and **simply** dividing it by two. The difference in results can be seen when comparing 8 divided by 1/2, which is 16, and 8 divided by 2, which is 4. Consequently, these two operations are not the same.

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if 1,000,000 people are exposed to 10 msv, then what is the expected number of radiation induced cancers according to the linear no threshold model of cancer induction

### Answers

The expected number of **radiation **induced cancers according to the linear no threshold model of cancer induction is **500**

Radiation is defined as the energy that comes from a source and travels through space at the** speed of light.**

Here we have given that 1,000,000 people are exposed to 10 msv and here we need to find the the expected number of radiation induced cancers according to the **linear **no threshold model of cancer induction.

As we all know that the amount of **dose **depends on the type of x-ray examination. A CT examination with an effective dose of 10 milli Sieverts

And it may be associated with an increase in the possibility of fatal cancer of approximately 1 chance in 2000.

therefore, here we have the **total **number as 1,000,000

Then the **expected **number if calculated as,

=> 1,000,000/2000

=> 500

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The scatter plot above shows the average rent (in dollars) for a 111-bedroom apartment in New York City each year between 200020002000 and 201320132013. Which of the following is the best estimate of the average change in rent each year

### Answers

The best estimate of the **average change** in rent each** year** include the following: C. $40.

How to determine the average change in rent each year?

Mathematically, the **rate **of change is also referred to as slope or gradient and it can be calculated by using this formula;

Rate of change, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

**Rate **of change, m = (y₂ - y₁)/(x₂ - x₁)

Next, we would determine the **rate **of change of the value of y with respect to the value of x on the **scatter plot**, which represents a line that is passing through the points (0, 800) and (10, 1200):

Rate of change, m = (1200 - 800)/(10 - 0)

Rate of change, m = 400/10

**Rate** of change, m = 40.

Based on the **scatter plot**, we can reasonably infer and logically deduce that the average **rate **of change in rent each year is equal to 40 dollars.

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Complete Question:

The scatter plot below shows the average rent (in dollars per month) for a 1-bedroom apartment in New York City each year between 2000 and 2013.

Which of the following is the best estimate of the average change in rent each year?

answer choices

$0.5

$1

$40

$400

Below is a multiple correlation table. Based on the correlation values, which predictor would lead to the least prediction error in predicting happiness using simple regression

### Answers

From the correlation table , based on the correlation values , then **the predictor** that would lead to least prediction error in predicting happiness using simple regression is **stats class** .

What is **Predictor Variable** ?

The predictor variable is used to predict the future outcome based on some given circ*mstances. The Other names by which predictor variable is known as "criterion variable" and "explanatory variable" .

the best predictor from the given **correlation table **is the highest value in the table ; irrespective of the sign .

We have to predict happiness using the **simple regression** ;

So to find the predictor , we select the row in the **happiness **row ,

we can see that the biggest value for the happiness row is 0.41 , which is the stats class .

Therefore , The predictor that lead to least **prediction error** is Stats Class .

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the student population of school is 480. 85% participate in atleast one extra-curricular activity. how many students participate in at least one extra-curricular activity ?

### Answers

**Answer: 408**

**Step-by-step explanation:**

85% is equal to 0.85 in decimal form.

So, the answer is [tex](480)(0.85)=408[/tex] students.

**Answer:**

408

**Step-by-step explanation:**

In decimal notation, 85% is 0.85.

chord of a circle is 13.2 cm long and circles radius is 9.4 find the angle subtended by the chord at the centre of the circle

### Answers

**Answer:**

To find the angle subtended by a chord at the center of a circle, we can use the formula:

θ = 2 * arcsin (c / 2r)

where θ is the angle subtended by the chord, c is the length of the chord, and r is the radius of the circle.

Step 1: Substitute the given values into the formula

θ = 2 * arcsin (13.2 / (2 * 9.4))

Step 2: Simplify the equation

θ = 2 * arcsin (13.2 / 18.8)

Step 3: Use a calculator or a math table to find the value of arcsin

arcsin (13.2 / 18.8) = 0.636 radians

Step 4: Multiply the value obtained by 2

0.636 * 2 = 1.27 radians

**Final Answer: The angle subtended by the chord at the centre of the circle is 1.27 radians or 72.8 degrees**

**Answer:**

ForTheTriangleABOtofindthelengthr

Wehave

sin(

2

α

)=

hypotenuse

opposite

=

OA

AB

=

9.4

6.6

=0.70212

whereAB=

2

13.2

=6.6cm

2

α

=sin

−1

(0.70212)

thenweoptain=

α=44.6°×2

=89.2°

alberto sold half of his comic books. and then bought nineteen more. he now has 43. with how many did he start with

### Answers

**Answer:**

48

**Step-by-step explanation:**

First you should subtract 43 and 19

then you get a answer 24

Multiply it by 2

you get 48

**Answer:**

no. of books =48 books

**Step-by-step explanation:**

lets say that he started with

x

books so,

(X÷2)-19=43

X÷2=24

X=48

Write an equation in point-slope form of the line that passes through the point (-9, 1) and has a slope of

2/3

### Answers

**Answer:**

y-1=2/3(x+9)

**Step-by-step explanation:**

Sorry cant really explain well but I am positive this is the right answer.

4. you are looking for a deep spot to take a swim in a local river. the width of the river is about the same all along its length, but there are places where the water flows quickly and places where it flows slowly. which is a better choice for a swim?

### Answers

The **best choice** for a deep spot to take a swim is to go to a place in the river where the **cross-sectional area **is larger, and the water flows slower.

If you are looking for a deep spot to take a swim in a local river, the best choice is to go where the water flows slowly. The **speed** of the water is determined by the **formula**:

v=Q/A,

where v is the speed of the water, Q is the discharge rate, and A is the cross-sectional area of the river. As Q is constant for the same river, a slower water flow can be achieved by** increasing A**, which is the cross-sectional area of the river. Therefore, the best choice for a deep spot to take a swim is to go to a place in the river where the** cross-sectional area** is larger, and the water flows slower.

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Cameron and his children went into a movie theater where they sell drinks for $6 each and candies for $5 each. Cameron has $100 to spend and must buy at least 18 drinks and candies altogether. If xx represents the number of drinks purchased and yy represents the number of candies purchased, write and solve a system of inequalities graphically and determine one possible solution.

### Answers

One **possible** **solution** is to have **Cameron** **buying** 18 candies and 6 drinks, this solution is (6,18) and it lies in the **intersection** of **all** **three** **half**-**planes**.

We can write a **system** of **inequalities** to represent the situation as follows:

6x + 5y ≥ 90 (because Cameron must spend at least $90 on drinks and candies)

x + y ≥ 18 (because Cameron must buy at least 18 drinks and candies altogether)

x ≥ 0, y ≥ 0 (because Cameron can't buy negative number of drinks or candies)

To **graphically** represent the **solution** set of this system, we can plot the **inequalities** on a coordinate plane. We can start by drawing the line representing the first inequality: 6x + 5y = 90. To find the slope-intercept form of this equation we can subtract 90 from both sides, 6x + 5y - 90 = 0, and we get: 6x + 5y = 90.

The **second** **inequality** is x + y ≥ 18 which is a boundary line.

The **third inequality** is x ≥ 0 and y ≥ 0 which means that both x and y should be non-negative.

The solution set of this system of **inequalities** is the intersection of the half-planes defined by the inequalities. This is the set of all points that lie in all three half-planes. One possible solution is to have Cameron buying 18 candies and 6 drinks, this solution is (6,18) and it lies in the intersection of all three half-planes.

Therefore, One **possible** **solution** is to have **Cameron** **buying** 18 candies and 6 drinks, this solution is (6,18) and it lies in the **intersection** of **all** **three** **half**-**planes**.

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To support a triangular kite, Hana

attaches thin strips of wood from each vertex

perpendicular to the opposite edge. She

then attaches the kite's string at the point

of concurrency. To calculate the point of

concurrency, she determines the coordinates

of each vertex on a coordinate plane. What

are the coordinates where the wood strips

cross? Round your answer to the nearest

hundredth.

### Answers

The slope of the** line parallel** to BC is 18/7 * (x + 0) is 18/7 y. the orthocenter is where concurrency occurs.

What is the slope of the line parallel to BC ?

Hana fastens tiny wood strips perpendicular to the opposing edge from each vertex. As a result, the orthocenter is where concurrency occurs.

Given: Hana fastens small wood strips** perpendicular **to the opposing edge from each vertex.

As a result, the orthocenter is where concurrency occurs.

Think of the ABC triangle with coordinates.

A(0, 0) B(0, 58), C(36, 44) (36, 44)

first determine the angles of the triangle's two sides.

Formula for slope: (y 2 - y 1)/(x 2 - x 1)

slope of the AB& A(0, 0) matrix side matrix, Slope of BC side B(0,58), B(0, 58) = (58 + 0)/(0 + 0) = 0 C(36,44) = (44 - 58)/(36 + 0) = - 14/36 = - 7/18

Use Equation of the altitude perpendicular to AB's point slope form after that.

The vertex in opposition to AB is point C.

A line perpendicular to AB has a slope of zero.

y-y 1 = m(x-x 1) y-44 = 0(x-36) y = 44

Altitude Equation Perpendicular to BC

The vertex opposite BC is Point A. A line perpendicular to BC has a **slope **of 18/7.

y + 0 = 18/7 * (x + 0)

y = 18/7 * x

Change the value of y in the equation above. y = 18/7 * x 44 = 18/7 * x

x = 17.11 The slope of the line parallel to BC is 18/7 * (x + 0) = 18/7 y.

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15. Lori is 4 years younger than Shawn. Write an expression that represents Lori's age in relation

to Shawn.

### Answers

S-4=L

S stands for Shawn’s age

L stand’s for how old Lori will be

**Answer:**

**Step-by-step explanation:**

You will need to utilise **algebraic expressions** to create an **equation** to show Lori's age in relation to Shawn.

The procedure will be completely described in the sections that follow with step-by-step instructions .

Let us assume that Shawn's age is x and Lori's age is y .Younger denotes negative sign in **algebric expression** ( - ) .If Lori is 4 years younger than Shawn, then Lori is 4 years younger than Shawn.Therefore, an **expression** that represents Lori's age in relation to Shawn can be written as following : **y=x-4**

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For the function f(x) = 9/x-4, find f^(-1)(x).

### Answers

**Answer:**

f

(

x

)

=

9

x

−

4

.

**Step-by-step explanation:**

The inverse of

f

(

x

)

=

9

x

−

4

is a function

g

(

x

)

such that

f

(

g

(

x

)

)

=

(

f

∘

g

)

(

x

)

=

x

but

f

(

g

(

x

)

)

=

9

g

(

x

)

−

4

=

x

Solve for X, Leave in simplest radical form.

### Answers

Hope it helps.

If you have any query, feel free to ask.

During a hammer thrower’s practice swings, the 7.1-kg head A of the hammer revolves at a constant speed in a horizontal circle as shown. Knowing that the speed of the hammer is 2.5 m/s and θ = 60°, determine (a) the tension in wire BC, (b) the radius of the circle, rho.

### Answers

(a) The value of the** tension** in wire BC will be = 80.4 N

(b) The value of the **speed** of the hammer’s head will be = 2.30 m/s

Mass of the head of the hammer = 7.1 Kg.

The **speed** at which it is revolving = v

value of ρ=0.93 m

The value of the angle θ=60°

**Tension** is described as the** force** transferred through a rope, string, or wire when pushed by opposing forces. The tension force is directed along the **length** of the wire and draws **energy** evenly on the bodies at the ends.

(a) Now, we will first calculate the value of the tension in wire BC,

First, we will note

[tex]$$a_A=a_n=\frac{v_A^2}{\rho}$$[/tex]

(a)

[tex]$+\Sigma F_y=0: T_{B C} \sin 60^{\circ}-W_A=0$[/tex]

or we can write it as:

[tex]$$\begin{aligned}T_{B C} & =\frac{7.1 \mathrm{~kg} \times 9.81 \mathrm{~m} / \mathrm{s}^2}{\sin 60^{\circ}} \\\end{aligned}$$[/tex]

=> =80.426 N

=>= 80.4 N (approx)

(b) Now calculate the **speed** of the hammer’s head.

[tex]$\quad+\Sigma F_x=m_A a_A: T_{B C} \cos 60^{\circ}=m_A \frac{v_A^2}{\rho}$[/tex]

or

[tex]$$v_A^2=\frac{(80.426 \mathrm{~N}) \cos 60^{\circ} \times 0.93 \mathrm{~m}}{7.1 \mathrm{~kg}}$$[/tex] = 2.30 m/s

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Note: The correct question may be like this:

During a hammer thrower’s practice swings, the 7.1-kg head A of the hammer revolves at a constant speed v in a horizontal circle as shown. If ρ=0.93m and ,θ=60° determine (a) the tension in wire BC, (b) the speed of the hammer’s head.

The needed diagram is attached below

Suppose an and bn are series with positive terms and bn is known to be convergent. (a) If an > bn for all n, what can you say about an? Why? O a n converges if and only if an < 2bn. Oman converges by the Comparison Test. O an diverges by the Comparison Test. We cannot say anything about an. o a n converges if and only if an 5 4bn. (b) If an

### Answers

Nothing that we can say regarding an we are unsure of whether the terms of an are rising or falling, a passes the Comparison Test and **sequence**, Since bn, an also converges.

what is a sequence?

A collection of **numbers**, or "terms," is referred to as a sequence. Examples of terms are 2, 5, and 8. Some sequences can be made endlessly lengthy by taking advantage of a particular **pattern **they follow. Use the example of 2,5,8 and add 3 to continue the sequence.

We are unable to comment on an.

This is due to the fact that bn converges, causing a to exceed bn, and as a result, we are unable to determine whether the terms of an are increasing or decreasing.

What can you say about an if a bn for all n? a passes the Comparison Test and converges.

This is due to the fact that since bn converges and a converges since bn, we may infer that the terms of an are likewise decreasing and that an also sequence since bn based on the comparison test.

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If $m$ is a real number and $2x^2 mx 8$ has two distinct real roots, then what are the possible values of $m$

### Answers

The **possible values** of [tex]$m$[/tex] are all **real numbers** greater than [tex]$\frac{2}{x^2}$[/tex]

A **quadratic equation **is an equation of the form ax² + bx + c = 0, where a, b, and c are real numbers and a ≠ 0. It is called a quadratic equation because the highest degree of its** unknown variable** (x) is two. The solutions of a quadratic equation can be found by solving the equation using the quadratic formula, factoring, or graphing. Quadratic equations are used in many areas of mathematics, from basic algebra to differential equations.

Let [tex]$y = 2x^2mx8$[/tex]

The** two distinct **real roots of the equation imply that y is a quadratic equation with two distinct real roots.

So,[tex]$y = 0 = 2x^2mx8 \implies 2x^2mx - 8 = 0$[/tex]

Using the **quadratic formula** , [tex]$m = \frac{8}{2x^2x}$[/tex]

The two distinct real roots of the equation imply that the discriminant of the** quadratic equation**, [tex]$\Delta = b^2-4ac$[/tex] is greater than 0.

So, [tex]$\Delta = (2x^2)^2-4(2)(-8) > 0 \implies 4x^4 + 64 > 0$[/tex]

[tex]$4x^4 > -64 \implies x^4 > -16$[/tex]

So, [tex]$m > \frac{8}{2x^2x} \implies m > \frac{8}{2x^2(-4)} = \frac{2}{x^2}$[/tex]

Hence, the possible values of m are all real numbers greater than [tex]$\frac{2}{x^2}$[/tex]

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Write an expression that represents the height of a tree that begins at 6.7 feet and increases by 2.9 feet per year. Let t represent the number of years.

### Answers

An **expression **that represents the height of a tree is 6.7 + 2.9.

What is an expression?

Mathematical expressions consist of at least two numbers or **variables**, at least one arithmetic operation, and a statement. It's possible to **multiply**, divide, add, or subtract with this mathematical operation.

Here, we have

Given

The initial height of the tree is 6.7 feet

The increase in height per year = 2.9 feet

Thus,

The expression will be = 6.7 + 2.9t,

Here t represents the number of years.

Hence, an expression that represents the height of a tree is 6.7 + 2.9.

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howard collected data from a random sample of 600 people in his town asking whether or not they attend church. based on the results, he reports that 48% of the people in his state attend church. why is this statistic misleading?

### Answers

This **statistic** is **misleading** because Howard surveys only his department and not **members** of all the **departments** that the company has.

When **studying** anything from a **population**, it is usual practice in statistics to **identify** a sample of that **group**.

However, the **sample** has to be **representative**.

For **example**: I want to estimate the **proportion** of New York state residents who are Buffalo Bills fans. So I ask, let's say, 1000 randomly selected Buffalo residents whether they are Buffalo Bills fans, and expand this to the entire **population** of New York State residents. This is not representative of all New York State residents, just Buffalo **residents**.

**Howard** wants to know the **proportion** of **employees** of a company who use the company's **healthcare**. He asks only his **department**. However, a company as multiple departments, which leads to the **statistics** found in Howard's **survey** being **misleading**.

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Please assist with C ii

Solve the equation 1-2/x^2 = -x-1

x = ?

### Answers

The **value **of x in the expression 1 - (2/x²) = - x - 1 is ± √2, 4.

What is a factor of a polynomial?

We know that if x = a is one of the roots of a given polynomial x - a = 0 is a factor of the given polynomial.

To confirm if x - a = 0 is a factor** **of a polynomial we **replace **f(x) with f(a) and if the remainder is zero then it is confirmed that x - a = 0 is a factor.

Given, An **expression **1 - (2/x²) = - x - 1.

- (2/x²) + x = 2.

Multiplying each term by x².

- 2 + x³ = 2x².

x³ - 2x² = 2.

x²(x - 2) = 2.

x² = 2 ⇒ x = ± √2 Or x - 2 = 2 ⇒ x = 4.

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The sum of the present ages of two teachers is 54 years. If the age of one teacher is 4 years more than the other, find their present ages. Algebra. please give full answer .

### Answers

The **present ages** of the teachers are 25 and 29 years old.

What is the unitary method?

The unitary method is a method for **solving **a problem by the first value of a single unit and then finding the value by multiplying the single value. **Unitary method** is a technique by which we find the value of a single unit from the value of multiple devices and the **value **of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.

Given that **sum **of the present ages of two teachers is 54 years. If the age of one teacher is 4 **years **more than the other, then;

Let the **ages **of teachers are x and y

x + y = 54

x = 4 + y

So, 4 + y + y = 54

4 + 2y = 54

y = 25

x = 29

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2. Divide $7200 into four parts proportional

to 1:2:3:4. How much is each part?

### Answers

Let's denote the first part as x. Then, the second part is 2x, the third part is 3x, and the fourth part is 4x. So, x + 2x + 3x + 4x = 10x = $7200. Solving for x, we get x = $720. Hence, the four parts are:

First part: $720

Second part: 2x = 2 * $720 = $1440

Third part: 3x = 3 * $720 = $2160

Fourth part: 4x = 4 * $720 = $2880

**Answer: **720, 1440, 2160, 2880

**Step-by-step: **

Create arbitrary variable a, such that 7200 = a + 2a + 3a + 4a.

Reduce to get 720 = a

and plug in a into the set {a, 2a, 3a, 4a} to get the answer

How many right triangles have integer leg lengths a and b and a hypotenuse of length b 1, where b < 100

### Answers

The possible number of the **right triangle** is 6. Hence option A is the correct option.

**What is the right triangle?**

A right triangle or right-angled triangle, or more formally an orthogonal triangle, formerly known as a** rectangle triangle**, is a triangle with one right angle, i.e. two perpendicular sides. Trigonometry is founded on the relationship between the sides and other angles of a right triangle.

Given that △ABC is a right triangle.

The legs of the △ABC are a and b which are **integers**. The hypotenuse is b+1. Since b is an integer thus b+1 is an integer.

**Pythagorean theorem:**

The sum of the square of the legs of a right triangle is the square of the **hypotenuse**.

According to Pythagorean theorem,

a² + b² = (b+1)²

Applying the **algebraic formula** (a+b)² = a² + b² + 2ab

a² + b² = b² + 2b +1

Cancel out b² from both sides:

a² = 2b + 1

2b is always a **positive number **since 2 is multiplied with b. Thus 2b+1 is an odd number.

Since a² = 2b + 1, thus a² is an **odd number**.

The square of an odd number is an odd number. Thus a is an odd number.

Again given that,

b<100

2b < 200

2b + 1< 201

Putting 2b + 1 = a²:

a² < 201

Now putting a=1 in a² < 201:

1² < 201 (true)

Now putting a=3 in a² < 201:

3² < 201 (true)

Now putting a=5 in a² < 201:

5² < 201 (true)

Now putting a=7 in a² < 201:

7² < 201 (true)

Now putting a=9 in a² < 201:

9² < 201 (true)

Now putting a=11 in a² < 201:

11² < 201 (true)

Now putting a=13 in a² < 201:

13² < 201 (true)

Now putting a=15 in a² < 201:

15² < 201 (false)

If a = 1, 2b+1 = 1 which implies b = 0. The length of a side of a triangle is never zero. Therefore a ≠ 1.

Thus the **possible values **of a are 3,5,7,9,11,13.

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How do I solve this?

### Answers

The evaluation of the **piecewise function **gives:

when x = -3, f(x) = -4; when x = 2, f(x) = 0; and when x = 4, f(x) = 2.

when x = -3, w(x) = 2; when x = 2, f(x) = 5; and when x = 4, f(x) = 5

How to evaluate a piecewise function?

A **piecewise function** is a function that is defined by multiple sub-functions, each of which applies to a certain range of the input (or domain) values.

We want to **evaluate** the piecewise function when x = -3, x =2 and x = 4:

{ -4, x < 2

f(x) = { x-2, -2 ≤ x≤ 4

{0 x > 4

when x = -3:

f(x) = -4 because x < 2 (i.e. -3 < 2)

when x = 2:

f(x) = x-2

f(2) = 2-2 = 0

when x = 4:

f(x) = x-2

f(2) = 4-2 = 2

{ -x - 1, x ≤ -3

w(x) = { 2x + 2, -3 < x < 2

{5, x ≥ 2

when x = -3:

w(x) = -x - 1

w(-3) = -(-3) - 1 = 2

when x = 2:

f(x) = 5

when x = 4:

f(x) = 5

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What is the length of segment AB?

### Answers

50

I attached a pic of my work.

so what I did was find the amount of the other sides of the triangle using their opposite congruent sides. aka, the bottom is 90, which means the top should also be 90. and 90-50 is 40, so the rest of that side (which is one side of the triangle) should be 40.

and then I used the pythagorean theorem, since it is a right triangle (indicated by the squares in the corners).

the theorem states that a^2 + b^2 = c^2

so just plug in the legs (a and b), and you should get the amount of segment AB (which is c)