Mathematics High School

## Answers

**Answer 1**

The total **amount **the customer will be **charged **per month is $123.93

An expression with a variable is referred to as an **algebraic expression**. We employ the letter "**variable**" to stand in for an unknowable value. For instance, the variable x makes the expression 3x + 2 an algebraic expression. Algebraic expressions can be used to illustrate circ*mstances in which you lack certain knowledge.

For the first 3 **phone lines**, the customer will be charged $19.99 per line, which is a total of 3 * $19.99 = $59.97.

For the remaining 4 lines, the customer will be charged $15.99 per line, which is a total of 4 * $15.99 = $63.96.

Therefore, the total amount the customer will be **charged **per month is $59.97 + $63.96 = $123.93.

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## Related Questions

Tyrone had some milk. He used 1 ⅙ cups of milk to make hot chocolate. Now, Tyrone has 3 ⅓ cup of milk. How much milk did Tyrone have to start?

### Answers

**Answer:**

4 1/2 cups of milk

**Step-by-step explanation:**

To find the answer, we need to add what we used with what we have left over.

This equation would be:

1 1/6 + 3 1/3 = ?

to properly add 1/6 and 1/3, we change the 1/3 to 2/6:

1 1/6 + 3 2/6 = 4 3/6

Simplify:

4 1/2 cups of milk

How much money will there be in an account at the end of 9 years if $18000 is deposited at 7% interest compounded semi-annually? (Assume no withdrawals are made.)

### Answers

There will be $33434.8 in the **account **after 9 years

How much money will there be in an account

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

**Principal**, P = 18000

Time = 9 years

Rate = 7%

Number of times = 2

The formula for calculating the **amount** in an **account **is

A = P * (1 + r/2)^(2t)

So, the amount in the **account **after 9 years will be:

A = $18000 * (1 + 0.07/2)^(2 * 9)

Evaluate

A = $33434.8

Hence, after 9 years there will be $33434.8 in the account.

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What are the factors of 25?

### Answers

**Answer:**

1, 5, 25

**Step-by-step explanation:**

1x25=25

5x5=25

what is the slope? please answer

### Answers

**Answer:**

slope is 1

y = x + 2

**Step-by-step explanation:**

For all integers k, let k* be defined as k* = k(k-1). What is the value of 5*?

### Answers

**Answer: 20**

Work Shown:

k* = k(k-1)

5* = 5(5-1)

5* = 5(4)

5* = **20**

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here we go ~

As per the given information,

[tex]\qquad \sf \dashrightarrow \: k {}^{*} = k(k-1)[/tex]

we need to find the value of k* when k = 5 ~

So, simply plug in the value ~

[tex]\qquad \sf \dashrightarrow \: 5 {}^{*} = 5(5-1)[/tex]

[tex]\qquad \sf \dashrightarrow \: 5 {}^{*} = 5(4)[/tex]

[tex]\qquad \sf \dashrightarrow \: 5 {}^{*} = 20[/tex]

So, our required value is 20 ~

Gavin was disappointed when his favorite basketball player only scored 20 points in last night's game. Gavin had expected him to score 50% more than that. How many points did Gavin expect his favorite player to score?

### Answers

**Answer:**

Im pretty sure that's 30

**Step-by-step explanation:**

20x50%=x

20+x

A linear function goes through the points (-3,1) and (1,-3). What are the coordinates for the y-intercept of this function?

### Answers

The coordinates for the y-intercept of this function is at (0, -2)

What is the point-slope form?

Mathematically, the **point-slope** form of a straight** line** can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

m represents the slope.x and y are the points.

From the information provided above, we have the following slope and data points on the **line**:

Points on the x-axis = (-3, 1).Points on the y-axis = (1, -3).

At data point (-3, 1), a linear function of this line can be calculated in **point-slope** form as follows:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

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

y - 1 = -x - 3 + 1

y = -x - 2

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1a. Explain why chess is not a static game of complete information?

### Answers

**Chess **is not a **static game **of complete information for several reasons. Firstly, the game is **dynamic**, meaning that the position of the pieces on the board changes constantly throughout the game.

Unlike in games like Tic Tac Toe or Connect Four, the state of the **game **at any given point is not fixed, and there are a vast number of possible outcomes. This means that players cannot simply memorize the best **moves **and **outcomes** for every situation, as they would in a game of complete information.

Secondly, chess is a game of **imperfect information**, as both players do not know what moves their opponent will make. Even with a complete understanding of the game's rules, players cannot predict with certainty the moves of their opponent, and must instead make **strategic decisions **based on their best assessment of their opponent's likely choices.

Finally, **chess** is a **game** of hidden information, as players do not know what their opponent is thinking or planning. A player may be able to predict their opponent's next move, but cannot know for sure what their long-term strategy is, making it difficult to make optimal decisions.

Overall, chess is a** highly dynamic** and complex game that is not static or complete in terms of information. Players must make strategic decisions based on incomplete and uncertain information, making it a challenging and rewarding game for those who play it.

Chess is a **strategic** board game played between two players, with each player starting with 16 pieces on a 64-square board. The game has been around for centuries and is considered one of the most **popular** and complex games in the world.

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ST:

swer

Consider AQRS .A student correctly proves the three line segments dividing sides

QR and QS are parallel to side RS.

Q

9 cm

9 cm

6 cm

6 cm

R

36 cm

+ x cm

Which proportion could the student write as a step in the proof?

### Answers

To prove that the three line segments dividing sides QR and QS are parallel to side RS, the student can use the **proportion**: QS/QR = (QS - 6)/(QR - x)

What is a proportion?

A **proportion** is a fraction of a total amount, and the measures are related using a rule of three.

The relations between variables, either direct or inverse **proportional**, can be built to find the desired measures in the problem.

We are given thag

MQ = NP = 6 cm, NR = PS = 9 cm, and RP = x cm.

Use the similarity of triangles QSM and QRP to write the proportion:

QS/QR = SM/RP

Use the similarity of triangles QSN and PQN to write the proportion:

QS/QR = (QS - 6)/(QR - NR)

Use the similarity of triangles QSP and MRP to write the proportion:

QS/QR = RP/(QR - x)

Substitute the lengths of the line segments into the three proportions:

QS/QR = 9/(x)

QS/QR = (QS - 6)/(QR - 9)

QS/QR = (x)/(QR - x)

QS/QR = x/(QR - x)

Combine the first and third proportions to get:

9/(x) = x/(QR - x)

9(QR - x) = x^2

QR = (9x)/(x + 9)

Substitute this value of QR into the second proportion to get:

QS/[(9x)/(x + 9)] = [(QS - 6)/9]

QS(x + 9) = 9(QS - 6)x/(x + 9)

QS = (54x)/(8x + 81)

Use this expression for QS to simplify the third proportion:

[(54x)/(8x + 81)]/[(9x)/(x + 9)] = x/(QR - x)

54x(x + 9) = 8x(x + 9)(QR - x)

QR = (9x)/(x + 9)

Therefore the **proportion** will be QS/QR = (QS - 6)/(QR - x).

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write a function area_of_circle(r) which returns the area of a circle of radius r.

### Answers

The **area of circle** is given as 3.14159265359 * r * r.

The function area_of_circle takes one **argument** r, which is the radius of the circle. The function returns the** area of the circle,** which is calculated by multiplying constant value Pi (approximately 3.14159265359) by the square of the radius r.

This formula is a commonly used formula to calculate the area of a circle and is accurate for most practical purposes. The returned result is a **float value **that represents the area of the circle with the given radius.

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find the volume v of the solid obtained by rotating the region bounded by the given curves about the specified line. 2x = y2, x = 0, y = 4; about the y-axis.

V= ?

### Answers

The **volume** of the solid obtained by **rotating** the region about the y-axis is 2048π/5 cubic units.

To find the volume of the solid obtained by rotating the region **bounded** by the curves 2x = y^2, x = 0, and y = 4 about the y-axis, we can use the method of **cylindrical** **shells**.

We can see that the region is bounded below by the x-axis and above by the curve 2x = y^2. To use the method of cylindrical shells, we imagine **slicing** the region into thin vertical strips of width **dx**, and then revolving each strip about the y-axis to form a cylindrical shell.

The height of each shell is the difference between the y-coordinates of the **upper **and **lower** curves at the corresponding value of x, which is given by:

height = y - 0 = y

The **radius** of each shell is the distance from the y-axis to the corresponding value of x, which is given by:

radius = x

The **volume** of each cylindrical shell is therefore:

dV = 2πrh dx = 2πxy dx

To find the total volume, we integrate this **expression** over the range of x from 0 to 4, which gives:

V = ∫(0 to 4) 2πxy dx

= 2π ∫(0 to 4) x(y^2/2) dx

= π ∫(0 to 4) y^2 x dx

= π ∫(0 to 16) (y^2/2)(y^2/4) dy (using the equation 2x = y^2)

= π ∫(0 to 16) y^4/8 dy

= π [y^5/40] from 0 to 16

= π (16^5/40)

= 2048π/5.

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if labor costs are $55,000 for concession staff, $82,500 for security, $45,000 for parking lot operations and $49,000 for ticket/usher operations, what percentage of the labor cost is for concessions and parking lot operations?

### Answers

The **labor cost** for **concessions **and parking lot operations is **35.57% **of the **total **labor costs.

**Percentage **is a term used to describe a **portion **of a whole expressed as a **fraction **of 100.

Let's call the **total **labor costs "L". The labor cost for concession staff is 55,000, the labor cost for security is 82,500, the **labor cost **for parking lot operations is 45,000 and the labor cost for ticket/usher operations is 49,000.

L = 55,000 + 82,500 + 45,000 + 49,000

L = 281,500

The labor cost for **concessions **and parking lot operations is 55,000 + 45,000 = 100,000.

To find the **percentage **of L that is represented by the labor cost for concessions and parking lot operations, we **divide **100,000 by 281,500 and multiply by 100:

100,000 / 281,500 * 100 = 35.57%

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The coordinate of point H are (12, -15). In which quadrant i point H located? A. Firt B. Second C. Third D. Fourth

### Answers

The answer is **D. Fourth**. A coordinate plane is a two-dimensional plane with a horizontal x-axis and a vertical y-axis. Points in a coordinate plane can be located by their x and y **coordinates**.

The x-coordinate represents the **horizontal **position and the y-coordinate represents the **vertical **position. The origin (0, 0) is the point where the x and y axes **intersect**.

The coordinate **plane **is divided into four **quadrants**, numbered I through IV, based on the signs of the x and y coordinates. The first quadrant is where the x-coordinate and **y-coordinate** are both positive. The second quadrant is where the** x-coordinate** is negative and the y-coordinate is positive. The third quadrant is where both the x-coordinate and y-coordinate are negative. The **fourth quadrant **is where the x-coordinate is **positive **and the y-coordinate is negative.

To determine in which quadrant a point is located, you simply need to determine the **signs **of the x and y **coordinates**. If both coordinates are positive, the point is in the first quadrant. If the x-coordinate is negative and the y-coordinate is positive, the point is in the second quadrant. If both coordinates are negative, the point is in the third quadrant. If the x-coordinate is **positive **and the y-coordinate is **negative**, the point is in the fourth quadrant.

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Complete question:

The coordinate of point H are (12, -15). In which quadrant is point H located?

A. First

B. Second

C. Third

D. Fourth

For one month Siera calculated her home town’s average high temperature in degrees Fahrenheit. She wants to convert that temperature from degrees Fahrenheit to degrees Celsius using the function C of F = five-ninths (F minus 32) . What does C(F) represent?

the temperature of F degrees Fahrenheit converted to degrees Celsius

the temperature of F degrees Celsius converted to degrees Fahrenheit

the temperature of C degrees Fahrenheit converted to degrees Celsius

the temperature of C degrees Celsius converted to degrees Fahrenheit

{y | y = –7, –6, –2, –1, 0, 1, 3, 9}

### Answers

For given **average **temperatures and °C=5/9°F-32 C represents **temperature unit in celsius**.

What is **average**?

In Maths, an average of a list of data is the **expression **of the central value of a set of data. Mathematically, it is defined as the ratio of summation of all the data to the number of units present in the list. In terms of statistics, the average of a given set of numerical data is also called **mean**. For example, the average of 2, 3 and 4 is (2+3+4)/3 = 9/3 =3. So here 3 is the central value of 2,3 and 4. Thus, the meaning of average is to find the mean value of a group of numbers.

**Average = Sum of Values/Number of Values**

Also

Suppose, we have given with n number of values such as x1, x2, x3 ,….., xn. The average or the mean of the given data will be equal to:

**Average = (x1+x2+x3+…+xn)/n**

Now,

Given formula

** °C=5/9°F-32,** C represents where °c is temperature unit in **Celsius **and

°F represents unit of temperature in **Fahrenheit**.

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A botanist wanted to know if the stem lengths of daffodils differed depending on which side of a building they grew on. So she measured all of the flowers on the north, east, south, and west sides of the building and created the following graph:a. For this analysis, what is the explanatory variable? What is the response variable? For

each variable, provide the type and scale.

b. Which building side has the largest range? Which side has the largest IQR?

c. On the south side of the building, the first quartile is 43cm, the median is 46cm, and

the third quartile is 48cm. If she goes to the south side and randomly selects three

daffodils, what is the probability that none of them are between 46cm and 48cm?

### Answers

a. The explanatory and response variable is building side and stem length respectively.

b. East side has the largest IQR and south side has the largest range.

c. The probability that none of the **daffodils** are between 46cm and 48cm is around 0.75.

a. The **explanatory variable** is the building side (North, East, South, West), which is a categorical variable with nominal scale.

The **response variable** is the stem length of the daffodils, which is a continuous variable with interval scale.

b. The **largest range** can be determined by subtracting the minimum value from the maximum value for each building side.

North = 16.5

East = 19.5

South = 14

West = 17

The largest IQR can be determined by subtracting the first quartile from the third quartile for each building side. So from the figure attached, east side has maximum range.

c. To calculate the **probability** that none of the three selected daffodils have a stem length between 46cm and 48cm, we can estimate the proportion of the data that falls outside this interval. Based on the **quartile values**, it can be estimated that around 25-30% of the data falls between 46cm and 48cm. Therefore, the probability of randomly selecting three daffodils with stem lengths outside of this interval would be around 70-75%.

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A chool choir mut practice inging for at leat 175 minute each week. So far thi week they have practiced for 85 minute. Which inequality decribe all the poible number of minute (m) the choir mut practice inging during the remainder of thi week?

### Answers

The** inequality** that describes the possible number of **minutes** the **choir **must practice singing during the remainder of the week is:

85 + m ≥ 175

where m is the number of minutes the choir still needs to practice.

Inequality Describing Choir Practice

To determine the** inequality**, I used the information provided in the problem: "A school choir must practice singing for at least 175 minutes each week."

So, we know that the **total amount** of time the choir must practice singing is 175 minutes.

Then, the problem states that "so far this week they have practiced for 85 minutes."

Therefore, we can use the information to set up the** inequality**:

85 + m ≥ 175,

where m is the number of minutes the choir still needs to practice.

The inequality says that the total number of minutes the choir has practiced so far (85 minutes) plus the number of minutes they still need to practice (m) **must be greater** than or equal to 175, which is the minimum number of minutes they must practice each week.

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Alexander wraps a gift box in the shape of a right rectangular prism. The figure below shows a net for the gift box. 9 m 10 m 9 m 7 m 9 m 9 m How much wrapping paper did he use, in square meters?

### Answers

The **amount** of wrapping paper which Alexander used as described in the task content is; 446 m².

What amount of wrapping paper will Alexander use?

It follows from the task content that the gift is to be wrapped in the shape of a right rectangular prism.

Since the area of a rectangular prism is given by the formula; A = 2 (lw + wh + lh)

where the dimensions of the rectangular prism are 9, 10 and 7 m.

Hence, the **area** of the **prism** as required is;

A = 2 ( (9•7) + (7•10) + (9•10) )

A = 2 ( 63 + 70 + 90 )

A = 446 m².

Ultimately, the **quantity** of wrapping paper he uses is; 446 m².

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Which of the relations given by the following sets of ordered pairs is a function?

O {(-2,5), (7, 5), (-4, 0), (3, 1), (0, -6)}

O {(1, 3), (1, 1), (1, 1), (1, 3), (1,5)}

O {(1, 2), (2, 3), (3, 4), (2, 1), (1, 0)}

O

1

{(2,8), (6,4), ( – 3, 9), (2, 0), (-5,3)}

### Answers

The relation given by the set of** ordered pair** that is a **function** is;

{(-2,5), (7, 5), (-4, 0), (3, 1), (0, -6)}

How to find the ordered pair?

An** ordered pair** is defined as any pair of numbers for which order is important. Thus, the order of coordinates for a given point is very important for example (6, 3) and (3, 6) represent two very different points on a **coordinate system.**

For any of the ordered pair to be a function, there needs to be one unique value of y for every x.

Looking at the options, the only correct** ordered pair **that shows the law of an ordered pair being a function is Option A.

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Find the equation of the line that pae through the point (-3,0) and (4,-5). Give the equation in lope-intercept form. Do not round-off any numerical value in the equation--only exact decimal or fraction will be accepted. Be ure to click the "preview" button to verify that what you have entered i interpreted correctly

### Answers

The **equation **of the line that **passing **through the point (-3,0) and (4,-5) in slope intercept form is y = -5/7x - 5.

The **line **with m as the slope, m and c as the y-intercept is the graph of the linear **equation **y = mx + c. The values of m and c are real integers in the slope-intercept form of the **linear **equation.

We have two **points **(-3, 0) and (4, -5)

so for finding **slope**,

m = (y2-y1)/(x2-x1)

m = -5/7

m = -5/7

By using the **equation **of line,

y =mx + c

where m is slope and c is y intercept ,

y = -5/7 x -5

Therefore, the **equation **of the line that **passing **through the point (-3,0) and (4,-5) in slope intercept form is y = -5/7x - 5.

The **slope**, m, is a measure of how steep a line is. Sometimes, the gradient of a line is referred to as its slope. A line's y-**intercept**, ab, denotes the y-coordinate of the location where the line's graph crosses the y-axis.

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In a school with 400 students,120 ride the bus to school.What percent of the students ride the bus to school

### Answers

**Answer:**

30%

**Step-by-step explanation:**

120 divided by 400, time 100 = 30%

So, 30% of the students ride the bus to school.

Let's check

30% = 0.3

400 times 0.3 = 120 students

It matches the number given, so 30% is the correct answer.

Ax+3 = 8x + B

What values of A and B will result in an equation with infinite solutions? Enter the answers in the boxes.

A =

B =

### Answers

The **values** of A and B that would result in an **equation** with infinite solutions include the following:

A = 8

B = 3.

What are infinitely many solutions?

In Mathematics, an **equation** is said to have an **infinitely many solution** (infinite number of solutions or infinite solutions) when the left hand side and right hand side of the **equation** are the same or equal.

If the given equation has **infinitely many solutions** (infinite number of solutions or infinite solutions), then:

Ax = 8x

A = 8

Similarly, the value of B is given by:

3 = B

B = 3.

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what is inverse square law

### Answers

The **inverse** **square** **law** is given below.

What is an expression?

An **expression** isa way of writing a statement with more than two variables or numbers with **operations** such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

**Inverse** **square** **law** states that the intensity of the radiation is inversely proportional to the square of the distance.

If **intensity** = I and **distance** = x

Then

I ∝ 1/x²

Thus,

The **inverse** **square** **law** is given above.

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An octopus is 15 meters below the ocean. What is its elevation?

(for any mod who sees this, this isn't for a test)

### Answers

The **elevation **of the **octopus **is -15 meters if An octopus is 15 meters below the ocean.

**What is elevation ?**

Elevation refers to the **height **or altitude of an object or location above sea level or some other reference point. It is usually measured in units of length, such as meters or feet. Elevation can be positive, indicating that the object or **location **is above the reference point, or negative, indicating that it is below the reference point.

Given,

An octopus is** 15** meters **below **the ocean.

The octopus is 15 meters below the ocean, which **means **it has a **negative **elevation. If we consider the ocean to be at sea level (0 meters), then the **elevation **of the octopus would be:

**Elevation = 0 meters - 15 meters **

**= -15 meters**

Therefore, the elevation of the octopus is** -15 meters.**

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Find the volume of a cone with a diameter of 4.2 meters and a height of 5 meters. Leave your answers in terms of pi

### Answers

**Answer: 7.35pi meters**

**Step-by-step explanation:**

Formula to find the volume of a cone is V = (1/3) x (pi) x (r^2) x (h)

diameter = 2r

4.2 = 2r -> r = 2.1 meters

plug in the height and radius in the formula

V = (1/3) x pi x (2.1)^2 x (5)

V = 7.35pi meters

**Answer:**

7.35 pi meters cubed

**Step-by-step explanation:**

The formula for the volume of a cone is V=πr^2*h/3. You substitute the values you know and then solve as normal, but don't get rid of the pi. You are left with 7.35 pi meters cubed.

4-3 practice solving quadratic equations by factoring write a quadratie equation in standard form with the given root). 1. 7.2 4. -7.-8 7. 1.1/2x2 - 9x + 14 =0 x2 - 15x + 56 =0 2x2 - 3x + 1 =02. 0.3 5. -6.-3 8. 1/3.2x3 - 3x =0 x3 - 9x + 18 =0 3x3 - 7x + 2 =03. -5.8 6. 3.14 9. 0.-7/2x2 - 3x + 40 =0 x2 + x - 12 =0 2x3 - 7x =0factor each polynomial. 10. r2 + 3r2 - 54r 12. e2 - 49 14. 16r2 - 169r(r +9)(r - 6) (c - 7)(c + 7) (4r + 13)(4r - 13)11. 8a2 + 2a - 6 13. x8 + 8 15. b2 - 81

2(4a - 3 )(ra + 1) (x + 2)(x2 - 2x + 4) (b2 + 9)(b + 3)(b - 3)

### Answers

**Quadratic** Equations: 1. [tex]x^{2} -15x+56=0[/tex], 2. [tex]x^{2} +x-12=0[/tex], 3. [tex]x^{2} -11x+28=0[/tex] **Factored** Polynomials:10. (r + 9)(r - 6), 12. (c - 7)(c + 7), 14. (4r + 13)(4r - 13), 11. 2(4a - 3)(ra + 1), 13. (x + 2)[tex](x^{2} -2x+4)[/tex], 15. (b + 3)(b - 3)

The given problem asks to write the **quadratic** equation in standard form given the roots and then factor the polynomials.

A quadratic equation in **standard** form is written as [tex]ax^{2} +bx+c=0[/tex], where a, b, and c are constants.

To write the equation in standard form, we can use the sum and product of the roots of the equation. The sum of the roots can be found by adding the given roots, and the product of the roots can be found by multiplying them. We then use these values in the equation [tex]ax^{2} +bx+c=0[/tex] as follows:

b = -(sum of roots)c = product of roots

Once we have the equation in standard form, we can factor it by finding two binomials whose product is equal to the equation.

For example, let's consider the equation [tex]x^{2} -11x+28=0[/tex] with roots 7.2 and -5.8.

sum of roots = 7.2 + -5.8 = 1.4product of roots = 7.2 * -5.8 = -41.76

So, b = -(sum of roots) = -1.4 and c = product of roots = -41.76. Hence, the equation in standard form is [tex]x^{2} -11x-41.76=0[/tex]. To factor the **polynomial**, we look for two **binomials** that multiply to give the equation. We can find these by inspection or by using a formula. In this case, the factorization is (x - 7.2)(x + 5.8) = 0.

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Find the length of PM. Leave the answer in simplest radical form.

The length of PM is

### Answers

The **length** of PM is √74.

What is the Pythagorean theorem?

**Pythagorean** **theorem** states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

We have,

ΔPMK is a **right** **triangle**.

So,

PM² = PK² + MK²

PM² = 5² + 7²

PM² = 25 + 49

PM² = 74

PM = √74

Thus,

PM is √74.

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What is the range of the function f(x) = -4|x + 1| − 5?

O A.

(-∞, -5]

B.

[-5, ∞)

O C.

[-4, 0)

O D.

(-∞, -4]

What can I do to remember how to easily solve this? Thanks

### Answers

The **range **of the function f ( x ) = -4 | x + 1 | - 5 is ( -∞, -5 )

What are domain and range?

The **domain **of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.

The **range **is the set of outputs of a relation or function. In other words, it's the set of possible y values. Recall that ordered pairs are of the form (x,y) so the y coordinate is listed after the x. The output is listed after the input.

Given data ,

Let the **function **be represented as f ( x )

Now , the value of f ( x ) = -4 | x + 1 | - 5

The vertex of the function is calculated as

The point vertex of the graph is P ( -1 , -5 )

So , **range **is the set of outputs of a relation or function or the possible values of y

And , the **range **of the function is ( -∞, -5 )

Hence , the **range **of the function is ( -∞, -5 )

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A loan in the amount of $14,800 was opened on January 22, at an interest rate of 9%. The maturity value of the loan is $15,799. What is the due date of the loan? Multiple Choice

September 30

September 22

October 31

October 22

### Answers

The **due **date of the loan is **October 22**.

How to determine the due date of a loan?

First we need to calculate the number of **days** between the date it was opened and the date it matures, then add that number of days to the date it was **opened.**

Given that the loan was o**pened **on January 22, the **maturity value** of the loan is $15,799, and the interest rate is 9%, we can use the formula:

L = P * (1 + r * t)

**where **

L is the maturity value of the loan P is the amount of the loan r is the interest rate as a decimal t is the time in years.

We can **rearrange** the formula to find the time in years:

t = (L / P - 1) / r

**Substituting **the values:

t = ($15,799 / $14,800 - 1) / 0.09 = 0.066 years = 245 days

So, 245 days after January 22 is:

January 22 + 245 days = October 22

Therefore, the due date of the loan is **October 22**.

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Figure 4 shows a sketch of part of the curve C with equation Show that the area of R is 46. y=32x^-2+3x-8, x>0. The point P (4, 6) lies on C. The line / is the normal to C at the point P. The region R, shown shaded in Figure 4, is bounded by the line 7, the curve C, the line with equation x = 2 and the x-axis.

### Answers

It has been **proven **that R is 46, below.

How to solve this

Suppose that l: y=kx + b

We know that y = -64/x^3 + 3

So, the **slope **of the curve C at point P is

y (4) = 2

Because the** line l is the normal to C at point P**

So, k.y(4) = -1, k = [tex]\frac{-1}{y(4)}[/tex] = 1/2

So l:y = -1/2 x + b

Because P(4, 6) lies on l, so we have:

6= -1/2 x 4+ b, b= 8

So the **equation of line l**: y = -1/2 x + 8, and the **coordinate** of the point the l intercepts the x-axis is (16,0)

So the **area of R **is equal to

We use **differentiation** here

= (-16-(-26)) + (64- 28)

= 46.

Hence, proven.

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Consider the problem:A shopper buys cat food of 3 Ibs.Her cat eats 3/4 Ib each week.How many weeks does one bag last?a.Draw a diagram to represent the situation and label your diagram so it can be followed by others.Answer the question.b.Write a multiplication or devision equation to present the situation.c.Multiply your answer in the first question (the number of weeks)by 3/4 did you get 3 as a result?If not,revise your previous work.

### Answers

The **solution** is, the total food can be** eaten** by the cat in 4 **weeks**.

What is multiplication?

In mathematics,** multiplication i**s a method of finding the **product** of two or more** numbers.** It is one of the basic** arithmetic **operations, that we use in **everyday life.**

here, we have,

**BODMAS** rule is applicable in basic calculations to get the actual **answe**r.

Thus, the total food can be eaten by the cat in 4 weeks.

Total **weight **of a bag of cat food = 3 lbs.

The **number **of lbs the cat eats the food = 3/4 lbs each** week.**

We need to find the** number** of weeks does one **bag t**hat is 3 lbs last.

Now, the total food we have is 3 and** cats **eat 1/4th of total food each **week.**

Thus, the** total **food can be eaten by the cat in 4** weeks.**

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