Find the exact lengths of the sides of quadrilateral ABCD with vertices A(4, 5), B(-3, 3), C(-6,-13) and D(6,-2).

Answer:

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The terms a0, a1, a2, and a3 of the sequence {an} in each case are as follows:

a. a0 = 0, a1 = 3, a2 = 6, a3 = 9

b. a0 = 0, a1 = 2, a2 = 12, a3 = 72

c. a0 = 0, a1 = 0.5, a2 = 1, a3 = 1.5

d. a0 = 0, a1 = 1, a2 = 2, a3 = 3

a. 2n + n

a0 = 2*0 + 0 = 0

a1 = 2*1 + 1 = 3

a2 = 2*2 + 2 = 6

a3 = 2*3 + 3 = 9.

b. n(n+1)!

a0 = 0(0+1)! = 0

a1 = 1(1+1)! = 2

a2 = 2*(2+1)! = 12

a3 = 3(3+1)! = 72

c. [n/2]

a0 = [0/2] = 0

a1 = [1/2] = 0.5

a2 = [2/2] = 1

a3 = [3/2] = 1.5

d. [n/2] + [n/2]

a0 = [0/2] + [0/2] = 0

a1 = [1/2] + [1/2] = 1

a2 = [2/2] + [2/2] = 2

a3 = [3/2] + [3/2] = 3

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On solving the provided question, we can say that the equations are 3x+4y=6 and 8x-4y=5 => x = 1 and y = 3/4

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

the equations are

3x+4y=6

8x-4y=5

adding both equation

11x = 11

x = 1

y = 3/4

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The translation in the form (x,y) is  (-3, -10)

In geometry, translation is a type of transformation that moves each point of a figure to a new location, while preserving the shape and size of the figure. A translation is defined by a displacement vector, which specifies the direction and magnitude of the movement.

T is the initial position of the object and T' is the image (new position) of the object after translation. We can use this equation:

T + translation = T'

translation = T' - T

translation = (6, -2) - (9, 8)

translation = (6-9, -2-8)

translation = (-3, -10)

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The length of the third side could be 5.26 inches.

The Pythagoras theorem states that the square of the longest side must be equal to the sum of the square of the other two sides in a right-angle triangle.

[tex]|AC|^2 = |AB|^2 + |BC|^2[/tex]

There are 2 possible triangles that can arranged one being the 8 the longest side, and another one being the 5 and 8 the sides of the triangle

Given that triangle has two side lengths of 3.5 inches and 7.75 inches.

Using the pythagorean theorem to solve.

3.5² + 7.75² = x²

x² = 12.25 + 15.5

x² = 27.75

x = 5.26

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Answer:

PR = 288.75 feet

Step-by-step explanation:

There are two triangles that we need to consider:
ΔPRE and ΔPOC

These triangles are similar since
m∠PRE = m∠POC = 90°
∠PRE ≅ ∠POC

∠RPE ≅  ∠OPC (common angle)

AA Similarity theorem..
If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.  

∴ ΔPRE ≅ ΔPOC

If two triangles are similar, the ratios of the corresponding sides must be equal

⇒ [tex]\dfrac{PO}{PR} = \dfrac{OC}{PE}\\\\[/tex]    (1)

PO = PR + RO
PR is the width of the river that is to be determined
Let PR = x

Then
PO = x + 165

OC = 330, RE = 210

[tex]\dfrac{PO}{PR} = \dfrac{OC}{PE}\\\\\Rightarrow \dfrac{x + 165}{165} = \dfrac{330}{210}\\\\[/tex]

Left side:
[tex]\dfrac{x+165}{x} = \dfrac{x}{x} + \dfrac{165}{x} = 1 + \dfrac{165}{x}[/tex]

Simplify  [tex]\dfrac{330}{210}[/tex]   by dividing both numerator and denominator by 30

=>
[tex]\dfrac{330}{210} = \dfrac{11}{7}\\\\[/tex]

Therefore
[tex]\dfrac{PO}{PR} = \dfrac{OC}{PE}\\\\\Rightarrow 1 + \dfrac{165}{x} = \dfrac{11}{7}\\[/tex]

Subtract 1 from both sides:
[tex]\dfrac{165}{x} = \dfrac{11}{7} - 1\\\\\dfrac{165}{x} = \dfrac{4}{7}\\\\[/tex]

Cross-multiply
[tex]165 \times 7 = 4x\\\\\Rightarrow 4x = 165 \times 7\\\\\Rightarrow x = \dfrac{165 \times 7 }{4} = 288.75\;feet[/tex]

Answer:

Step-by-step explanation:

da fact that it sometimes get me wrong but it do works ngl

The required area of the washer is  8πr - 16π square millimeter.

A =  π r², where r is the circle's radius, is the formula for calculating a circle's surface area. The square unit, such as m², cm², in², etc., is the unit of area.

Circle Area Formulas;

Area is equal to  π r², where r stands for radius.

Area is equal to ( π /4) d², where d stands for diameter.

Area is equal to C²/4 π  where C stands for circumference.

The area of a washer with outer radius "r" and inner radius "r-4" can be found as follows:

Area = π * (outer radius² - inner radius²)

= π * (r² - (r-4)²)

= π * (r² - r² + 8r - 16)

= 8πr - 16π square millimeter.

Thus, required area  of washer is 8πr - 16π,Option(B) is correct.

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In a case whereby It was recently estimated that domestic vehicles out number foreign vehicles by about seven to five. If there are 4152 vehicles in a county, the number of them that are domestic is 2422  domestic vehicles.

The concept that will be used here is simplification.

From the question, we were told that there are 7x domestic vehicles  as well as 5x foreign vehicle.

We can see that the x is the unknown number, which we need to find out,  

Then  we can make an equation as:

7x + 5x =  4152

12x= 4152

x=4152/12

=346

Hence we can say that there are  7*346 = 2422  domestic vehicles

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Answer:

Step-by-step explanation:

To calculate the rate at which the water level drops, we need to find the volume of water being lost per second and convert that to a height change. The volume of water being lost is given as 0.05 liters per second. The volume of a cylinder with height h and radius r is given by the formula:

V = πr^2h

We can rearrange this formula to solve for h:

h = V / (πr^2)

Substituting the given values, we get:

h = 0.05 / (π * 20^2) = 0.05 / (π * 400) = 0.05 / 1257.0796

So the rate at which the water level is dropping is approximately 0.04 cm per second.

The program for assigning variable and solving expression 2 * x * y - z is -

def func1(x, y, z):

  return 2*x*y - z

x= int(input("Enter x"))

y= int(input("Enter y"))

z= int(input("Enterz"))

solveEquation=func1(x, y, z)

print (solveEquation)

What is Expression in Code?

Expressions in computer science are written by developers, interpreted by computers, and 'evaluated.' The evaluation yields a result or return. Expressions in code include simple mathematical equations like 2 + 2. They are commonly referred to as arithmetic expressions.

The program for the condition given is -

def func1(x, y, z):

  return 2*x*y - z

x= int(input("Enter x"))

y= int(input("Enter y"))

z= int(input("Enterz"))

solveEquation=func1(x, y, z)

print (solveEquation)

Therefore, the coding has been done.

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The region for A' ∪ B ∩ C' is region III.

A Venn diagram is a visual representation that makes use of circles to highlight the connections between different objects or limited groups of objects. Circles that overlap share certain characteristics, whereas circles that do not overlap do not. Venn diagrams are useful for showing how two concepts are related and different visually.

Given:

So from the Venn diagram, the item represents the regions four, five, six and seven.

We have to find not A union B intersection not C.

A' is the complement of set A.

So, the region is for not A union B is represented by B.

and, then B ∩ C' gives the region B.

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Check the picture below.

Answer:

x=1/3;3/2

Step-by-step explanation:

6x^2-5x+6 = 6x+3

-6                    -6

6x^2 -5x = 6x - 3

+5x            +5x

6x^2 = 11x -3

6x^2 + 11x - 3 = 0

(3x-1)(2x-3)=0

3x-1=0

3x=1

x=1/3

2x-3=0

2x=3

x=3/2

A unit can be used for measurement, and is commonly found in mathematics to describe length, size, etc.

First, because we are dealing with different units here, we need to know how many milliliters are in a litre.

So, an equation we can use is:

If we look at 1.2 litres, we can now convert it to milliliters.

Comparing 1200ml to 140ml, we can see that 1200ml is bigger.

Therefore, 1.2 litres are greater.

Answers in bold

[tex]\begin{array}{|c|c|} \cline{1-2}\text{Term} & \text{Coefficient}\\\cline{1-2}\text{x}^2 & \boldsymbol{1}\\\cline{1-2}\boldsymbol{-3\textbf{x}} & -3\\\cline{1-2}2 & \boldsymbol{2}\\\cline{1-2}\end{array}[/tex]

Explanation:

The given expression [tex]\text{x}^2-3\text{x}+2[/tex] is the same as [tex]\text{x}^2+(-3\text{x})+2[/tex]

This leads to the three terms as shown in the table above. Each term is separated by a plus sign.

The coefficient is the number to the left of the variable. Think of [tex]\text{x}^2[/tex] as [tex]1\text{x}^2[/tex] and think of [tex]2[/tex] as [tex]2\text{x}^0[/tex]

In other words, [tex]\text{x}^2-3\text{x}+2[/tex] is the same as [tex]1\text{x}^2+(-3\text{x})+2\text{x}^0[/tex]

The measures of the angles are:

n = q = j = 57°

m = l = p = k = 123°

Remember that vertical angles have the same measure, then:

n = 57°

And if the two horizontal lines are parallel, then the values in the correspondent quadrants are the same ones, then:

q = 57°

j = 57°

And adjacent angles add up to 180°, them:

57° + m = 180°

m = 180° - 57°

m = 123°

Then:

m = l = p = k = 123°

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The solution is, Total estimated living expenses = $53,900.

In mathematics, multiplication is 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,

Estimated expenses for next 2 years:

Rent = 1100 * 12 * 2 = 26,400

Gym membership = 450 * 2 = 900

Gym monthly fee = 40 * 12 * 2 = 960

Renter's insurance = 60 * (12 * 2 / 6) = 240

Groceries = 300 * 12 * 2 = 7200

Eating out & entertainment = 175 * 52 * 2 = 18,200

Total estimated living expenses = $53,900

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We can see that matching each formula on the left side to an equivalent formula on the right side, we have:

A = BC + D ------ B = A - D/C

A = B + CD ------ B = A - CD

A = BD - C ------- B = A + C/D

A = CD - B ------- B = CD - A

A formula is a mathematical expression that represents a set of instructions for solving a specific problem or calculating a desired value. It often uses symbols and variables to represent values, and can include operations such as addition, subtraction, multiplication, and division.

Formulas can be used in a variety of fields, including physics, chemistry, finance, and engineering.

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Answer:

see explanation

Step-by-step explanation:

(a)

let ∠ QRS = x then ∠ PQR = x and

∠ QPS = [tex]\frac{6}{7}[/tex] x and ∠ PSR = [tex]\frac{4}{7}[/tex] x

the sum of the 4 angles in a quadrilateral = 360°

sum the 4 angles and equate to 360

x + x + [tex]\frac{6}{7}[/tex] x + [tex]\frac{4}{7}[/tex] x = 360 ( multiply through by 7 to clear the fractions )

7x + 7x + 6x + 4x = 2520

24x = 2520 ( divide both sides by 24 )

x = 105

then

∠ QRS = 105° , so

∠ PSR = [tex]\frac{4}{7}[/tex] × 105° = 4 × 15° = 60°

(b)

∠ QPS = [tex]\frac{6}{7}[/tex] × 105° = 6 × 15° = 90° ← a right angle

Using the box method, the expression is solved as: 4x³ + 8y² - 19y - 35 (see image below).

The box method, also known as the grid method or area model, is a visual technique for multiplying two expressions or expanding algebraic expressions. Here are the steps to expand an algebraic expression using the box method:

The box method shows how the expression has been expanded, thus, combining like terms, we have:

4x³ + 8y² - 19y - 35

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the food needed for 10 cats will be 80 pounds.

What is the arithmetic operation?

The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem. Arithmetic is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers

An animal shelter needs to buy 8 pounds of cat food for every cat

they have.

So per pound, it food needed for 10 cats will be 8*10 = 80 pounds.

Hence the food needed for 10 cats will be 80 pounds.

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The sample standard deviation of the given data will be 10.058.

It is the measure of the dispersion of statistical data. Dispersion is the extent to which the value is in a variation.

[tex]\rm \sigma = \sqrt{\dfrac{\Sigma (x_i - \mu)^2}{n}}[/tex]

The table is given below.

M                  f                  Mf                         M²f

15                 8                 120                       1,800

25                18                450                      11,250

35                20               700                     22,050

45                13                585                     26,325

55                 7                 385                      21,175

The variance is given as,

Var = 1 / (66 - 1) [82600 - 2240² / 66]

Var = 101.16

Then the standard deviation is given as,

SD = √ Var

SD = √101.16

SD = 10.058

The sample standard deviation of the given data will be 10.058.

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The value of x that makes MBUL a kite is given as follows:

x = 6.

For MBUL to represent a kite, the following lengths have to be congruent:

BA and AL.

The lengths for this problem are defined as follows:

As the sides are congruent, the equation is given as follows:

BA = LA.

Hence the value of x that makes MBUL a kite is obtained as follows:

3x - 1 = 17

3x = 18

x = 18/3

x = 6.

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The size input which ABC's computer can execute in one minute for each algorithm for the following growth rates are given below:

For a growth rate of "n", it means the execution time increases linearly with the size of the input. In this case, XYZ's computer takes 1 minute to execute an input size of "n".

Company ABC claims that their computer is 100 times faster, so they can execute an input size of 100n in one minute.

For a growth rate of "2^n", it means the execution time increases exponentially with the size of the input.

In this case, if we double the input size, the execution time increases two times. So, if XYZ's computer takes 1 minute to execute an input size of "n", it would take 2 minutes to execute an input size of "2n".

Company ABC claims that their computer is 100 times faster, so to execute an input size of "2n" in 1 minute, the input size must be log2(100n).

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Answer:

40 hours

Step-by-step explanation:

This is an example of a work-rate-time problem

Since the experienced roofer can finish the job in 24 hours, his rate of work would be 1/24 (of the roof) per hour

Let the time taken by the trainee alone be x hours

His rate of work = [tex]\dfrac{1}{x}[/tex]

Together they finish the roof in 15 hours
So combined work rate = [tex]\dfrac{1}{15}[/tex]

Since combined rate = sum of individual rates we get

[tex]\dfrac{1}{24} +\dfrac{1}{x} = \dfrac{1}{15}[/tex]

Move 1/24 to the right side:
[tex]\dfrac{1}{x} = \dfrac{1}{15} - \dfrac{1}{24}[/tex]

[tex]\dfrac{1}{x} =\dfrac{24 - 15}{24\cdot 15} = \dfrac{9}{360}\\\\[/tex]

Taking reciprocals on both sides

[tex]x = \dfrac{360}{9} = 40 \;hours[/tex]

Answer:

y = x + 1

Step-by-step explanation:

Since we have two points, we can find the equation of the line in slope-intercept form or y = mx + b, where m is the slope and b is the y-intercept.

We can find the slope using the slope formula, which is:

[tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex], where y2 and x2 are one point on the line and y1 and x1 are the other point on the line:

Thus, we have:

[tex]m=\frac{7-26}{6-25}\\ m=\frac{-19}{-19}\\ m=1[/tex]

Now that we have the slope, we choose one of the points and plug in the slope to find the y-intercept:

[tex]26=1(25)+b\\26=25+b\\1=b[/tex]

timer--;  //This statement uses the auto-decrement operator to decrease the value of the variable timer by 1.

The auto-decrement operator -- is used to decrease the value of a variable by 1. In this case, the variable is called timer. The statement which uses the auto-decrement operator is timer--;. This statement will take the current value of the timer variable and decrease it by 1. For example, if the current value of timer is 5, the statement timer--; will decrease the value to 4. This is a very useful and efficient way to decrease a variable's value by 1. It is also much shorter than having to write out a statement such as timer = timer - 1;. The auto-decrement operator can be used with other types of variables as well, such as strings or characters.

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The correct answer is: The study is an experiment that uses random assignment to assign volunteers to experimental conditions (treatments).

A sample is an analytic subset of a larger population in statistics. The utilization of samples enables researchers to conduct investigations with more manageable data and more quickly. Randomly chosen samples exhibit little bias if they are large enough, but obtaining such a sample can be costly and time-consuming.

Here,

A study that uses random assignment to assign volunteers to experimental conditions (treatments) is considered the best design to establish cause-and-effect relationships. In this type of study, researchers can control the variables and minimize extraneous factors that could confound the results. By using random assignment, the volunteers in the experimental and control groups are similar on average, making it more likely that any observed differences between the groups are due to the treatments.

The correct answer is: The research is an experiment in which volunteers are randomly assigned to experimental settings (treatments).

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