The conversion is 0.785 radian = 141.3 degree.
What is Unit Conversion?The same attribute is expressed using a unit conversion, but in a different unit of measurement. For instance, time can be expressed in minutes rather than hours, and distance can be expressed in kilometres, feet, or any other measurement unit instead of miles.
A conversion factor is a value or a number that is used to multiply or divide one set of units into another.
Given:
We have to convert 0.785 rad to pi format.
As, we know Radians = Degrees × π/180'
and, 0.785 rad = 0.785 x 180
= 141.3 Degree
Hence, the conversion is 0.785 radian = 141.3 degree.
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Hey scale drawing of an nfl goal post uses a scale of 2 inches equal 5 feet if the actual width of the goalposts is 18 1/2 feet what is the width of the goal post on the drawing
A scale drawing of an NFL goal post uses a scale of 2 inches equal 5 feet if the actual width of the goal posts is 18 1/2 feet what is the width of the goal post on the drawing.
If 3 inches on the scale drawing represents 5 feet in actuality, determine the actual area of a kitchen if the area of the scale drawing is 45 inches 3 inches to 5 feet is 1:20
From the question asked you cannot determine the area. (No width given) You state the measurement is 45 inches (not square inches) 45 inches at 20:1 = 900 inches or 75 feet (linear)
Hence the answer is 75 ft.
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Answer:
75 ft
Step-by-step explanation:
Given a∥b , and c is not parallel to a or b, which statements must be true?
Select each correct answer.
Responses
m∠1=m∠8
m∠1=m∠12
m∠3=m∠7
m∠5=m∠9
Answer: first one
Step-by-step explanation:
An unopened sweet packet contains red and yellow sweets in the ratio 1:1.
A child opens the packet and eats six of the red sweets.
The ratio of red to yellow sweets in the packet is now 4:5.
How many sweets are still in the packet?
Answer:
Step-by-step explanation: The number of yellow sweets is 28. Step-by-step explanation: Ratio of red to yellow sweets is 3:7. Total sweet is 40. total ratio is 3 + 7 = 10.
use factoring to write two expressions equivalent to 56x^2 - 88x
Answer:
Step-by-step explanation:
well 56^2 is 56*56, 56*56= 3136
1. 3136x-88x
2. 3048x+88x
help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The amount owed by the debtor is $10865
How to determine the amount owed in six years?The given parameters about the compound interest are
Principal Amount, P = $5300
Interest Rate, R = 8%
Time, t = 6 years
To calculate the amount owed, we make use of the following formula
A = P + CI
Where
Compound interest, CI = P(1 + R)^t - P
So, the equation becomes
A = P + P(1 + R)^t - P
Evaluate the like terms
A = P(1 + R)^t
In this question, the formula is given as
A = P(1 + r/n)^nt
Where
n = 12, i.e compounded monthly
Substitute the known values in the above equation
A = 5300 * (1 + 8%/12)^(6*12)
Express 8% as decimal
A = 5300 * (1 + 0.08/12)^(6*12)
Evaluate the sum
A = 5300 * (1.01)^(6*12)
Evaluate the exponent
A = 5300 * 2.05
Evaluate the product
A = 10865
Hence, the value of the amount after 6 years is $10865
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What is the solution set of the inequality for X?.
The solution set of the inequality |x-1| ≤ 5 is found to be [-4,6] by simplifying the inequality.
What do math inequalities mean?An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The most frequent application is to size-compare two numbers on a number line.Relationships between two expressions that aren't equal to one another are known as inequalities. Inequalities are represented by the symbols <, >, ≤, ≥ and ≠.Given inequality is given as:
|x-1| ≤ 5
Simplifying this inequality we get,
-5 ≤ x-1 ≤ 5
Adding 1 on both sides, we get,
-5+1 ≤ x-1 ≤ 5+1
-4 ≤ x ≤ 6
Therefore, the solution set of the inequality |x-1| ≤ 5 is found to be [-4,6] by simplifying the inequality.
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NOTE: The given question is incomplete on the portal. Here is the complete question.
QUESTION: What is the solution set of the inequality |x-1| ≤ 5?
PLEASE HELP!!!!
Evaluate f(x)=5x−8 when x=−3,0, and 4.
f(−3)=
f(0)=
f(4)=
Solve for x
x =
A
C
E
4
D
3
x
B
4
A
After solving the value of x = 1/2.
From the figure:
AB = 4 ,BD = 3,DE = 4
AD = AB + BD
= 4+3
= 7
ADE is a right angle triangle.
AE^2 = AD^2+DE^2
= 7^2 + 4^2
= 49 + 16
= 65
AE = [tex]\sqrt{65}[/tex]
AC = AE/2
= [tex]\sqrt{65}[/tex]/2
ABC is a right angle triangle.
AC^2 = AB^2+BC^2
[tex](\sqrt{65}/2)^2[/tex]= 4^2+x^2
65/4 = 16 + x^2
65/4 - 16 = x^2
65 - 16*4 / 4 = x^2
1/4 = x^2
x = [tex]\sqrt{1/4}[/tex]
x = 1/2
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the number defects per part from an aging machine is shown below. number of defects (x) per part 0 1 2 3 4 5 probability p(x) 0.15 0.20 0.30 0.10 0.20 0.05 what is the mean of the data?
The mean of the following data is 0.1800
What is mean?In mathematics and statistics, the concept of mean is crucial. The most typical or average value among a group of numbers is called the mean.It is a statistical measure of a probability distribution's central tendency along the median and mode. It also goes by the name "expected value."There are different ways of measuring the central tendency of a set of values. There are multiple ways to calculate the mean. Here are the two most popular ones:Arithmetic mean is the total of the sum of all values in a collection of numbers divided by the number of numbers in a collection.acc to our question-
100C5 * .05^5 *.95^95 ~ 18.00%hence,The mean of the following data is 0.1800
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people with type o- blood are universal donors. that is, any patient can receive a transfusion of o- blood. only 7.2% of the american population has o- blood. if 10 people appear at random to give blood, what is the probability that at least 1 of them is a universal donor?
The probability that at least 1 of them is a universal donor 20.1%
What is a probability simple definition?A probability is a numerical representation of the possibility or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
What are probability and types?Mathematics' study of random events is known as probability, and there are four primary forms of probability: axiomatic, classical, empirical, and subjective. Since probability is the same as possibility, you might argue that it is the likelihood that a specific event will occur.
According to the given equation:-
The probability that at least one of every three is O-negative is 20.1%
Note that the question is unfinished. The following question is similar:
Type O-negative individuals can donate blood to anyone. In other words, O-negative blood can be transfused to any patient. Only 7.2% of Americans have blood that is O-negative. What is the likelihood that at least one of the ten Americans we randomly choose donating blood is a universal donor?
Detailed explanation:
7.2%, or 0.072, of the population has O-negative blood.
Probability of not being O-negative is equal to 1 - P(O-negative), which is 1 - 0.072, or 0.928.
Using the multiplication rule, calculate the likelihood that 10 persons are O-negative.
Probability that 10 is not zero = (P (not O-negative) ¹⁰ = (0.928) (0.928) ¹⁰ =0.4737
Therefore, the probability that at least one is O-negative is given by the formula: 1 - P(not O-negative) = 1 - 0.4737 = 0.5263.
P(at least 1 in 10 being O-negative) = 52.63% in percentage
to 3 arbitrary donors
likelihood of 3 not - (P) negative (not O-negative) ³ = (0.928) (0.928) ³ = 0.7991
As a result, the likelihood that at least 1 is O-negative is equal to 1 - P(3 not O-negative) = 1 - 0.7991 = 0.2009.
P(at least 1 out of 3 being O-negative) = 20.1% in percentage
Examine all related responses
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9)Two boys age 12 years and 7 years shared 108 naira in the ratio of their age .how much will each get of them receive??
Answer:
68.21 and 39.79
Step-by-step explanation:
When it says that they are going to "share" it means that the number (108) is going to be divided amongst the two of them. So you are going to do an addition problem which is 12+7=19. So you are going to do 12/19*108=68.21. Then to find the second number it's 7/19*108=39.79.
7. A. Write a second equation so that the system will have no solutions. B. Write a second equation so that system
will have infinitely many solutions. 2x - 4y = 22
A) The second equation is 2x - 4y +20=0, this system has no solutions.
B) The second equation is x-2y-11=0, this system has infinite number of solutions.
What is meant by an equation?An equation is a mathematical formula that expresses the equality of two expressions by connecting them with the equals sign =. The term equation and its cognates in various languages may have subtle changes in meaning.
Solving an equation with variables includes determining which variables' values result in equality. The variables for which the equation must be solved are also known as unknowns, and the unknown values that satisfy the equality are known as equation solutions. There are two sorts of equations: identities and conditional equations. An identity holds true for all variable values.
Given equation is,
2x - 4y = 22
A) Let the second equation be
2x - 4y +20=0
∴a₁/a₂=1
b₁/b₂=1
c₁/c₂=-11/10
Therefore, a₁/a₂=b₁/b₂≠c₁/c₂
Hence, the system has no solution.
B) Let the second equation be,
x-2y-11-0
Therefore, a₁/a₂=b₁/b₂=c₁/c₂=2/1
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The graph shows how many gallons of gas are used by a boat when it travels how many gallons of gas would the boat use to travel 24 miles
To travel 24 miles of distance it require 16 gallons of gas
Ratio :
A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
Proportion :
A proportion is an equation in which two ratios are set equal to each other,
From the graph,
We are observing that,
The boat uses 4 gallons to travel 6 miles. Traveling 4 times as far is expected to require 4 times the gas.
In 4 gallons of gas travelling 6 miles,
that is,
In simple word,
4 gallons = 6 miles
Multiply both side by 4 we get,
4 x 4 gallons = 6x4 miles
16 gallons = 24 miles
Thus we can say,
To travel 24 miles of distance it require 16 gallons of gas
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You bought 5 tickets for $30. How many tickets could you purchase for $90?
15
5 t = 30$
1t = 30/5
= 6$ per ticket
then, 90$/6 = 15 tickets
A baseball team sells for two games. the ratio of sold tickets to unsold tickets for the first game was 7 : 3. for the second game, the ratio was 13 : 2. there were 24 unsold tickets for the second game. how many tickets were sold for the first game?
1260 tickets were sold on the first game
For the second game, the ratio of the number of sold tickets to number of unsold tickets is 13:2
Total ratio = 13+2 = 15
There were 240 unsold tickets for the second game. Let total number of tickets for the second game be x
This means that
240 = 2/15 × x
2x/15 = 240
2x = 15 × 240= 3600
x = 3600/2 = 1800
1800 tickets were sold for the second game. Assuming total number of tickets for the first game is equal to total number of tickets for the second game. Therefore,
Total number of tickets sold for the first game is 1800
The ratio of sold tickets to unsold tickets for the first game was 7:3.
Total ratio = 7+3 = 10
Number of sold tickets for the first game would be
7/10 × 1800 = 12600/10
= 1260 tickets
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if using the method of completing the square to solve the quadratic equation x2-9x-26=0, which number would have to be added to complete the square (pls quickkkk!!)
The numbers would have to be added to complete the square is x = [tex]\frac{9+\sqrt{185} }{2}[/tex] and x = [tex]\frac{9-\sqrt{185} }{2}[/tex]
The quadratic equation is
[tex]x^2[/tex] - 9x - 26 = 0
Add both side of the equation by 26
[tex]x^2[/tex] - 9x - 26 + 26 = 26
[tex]x^2[/tex] - 9x = 26
[tex]x^2[/tex] - 2(9/2)x = 26
Take the coefficient of x and take square of the term and add both side of the equation
[tex]x^2[/tex] - 2(9/2)x + 81/4 = 81/4 + 26
Add the terms
[tex]x^2[/tex] - 2(9/2)x + 81/4 = 185/4
Form the left side of the equation in the form of [tex](a-b)^2[/tex]
Then the equation will be
[tex](x-\frac{9}{2} )^2[/tex] = 185/4
x - 9/2 =± [tex]\frac{\sqrt{185} }{2}[/tex]
x = [tex]\frac{\sqrt{185} }{2}[/tex] + 9/2
x = [tex]\frac{9+\sqrt{185} }{2}[/tex]
Then
x = - [tex]\frac{\sqrt{185} }{2}[/tex] + 9/2
x = [tex]\frac{9-\sqrt{185} }{2}[/tex]
Hence, the numbers would have to be added to complete the square is x = [tex]\frac{9+\sqrt{185} }{2}[/tex] and x = [tex]\frac{9-\sqrt{185} }{2}[/tex]
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A construction crew has just built a new road. They built the road at a rate of 31.25 kilometers per week. They worked for 5 weeks. How many kilometers of road did they build?
the tortoise and the hare are in a race. The hare has run 315 feet, while the tortoise has traveled 70 feet.
(a) what is the ratio of the distance the hare traveled to that of the hare? express as a unit rate.
The ratio of the distance the hare traveled to that of the tortoise is 9 : 2 and expressing it in the unit rate it will be 4.5 miles per miles
What is unit rate?
A unit rate is a cost for only one of anything. Unit rate is expressed as a ratio with a denominator of 1. For instance, if you covered 70 yards in 10 seconds, you did so at an average speed of 7 yards per second. Although both of the ratios—70 yards in 10 seconds and 7 yards in one second—are rates, only the latter is a unit rate.
Solution Explained:
For the ratio of the distance:
Try to reduce the ratio further with the greatest common factor (GCF).
The GCF of 315 and 70 is 35
Divide both terms by the GCF, 35:
315 ÷ 35 = 9
70 ÷ 35 = 2
The ratio 315 : 70 can be reduced to lowest terms by dividing both terms by the GCF = 35 :
315 : 70 = 9 : 2
Now, to express it as a unit rate
This is a fraction equal to
315 miles ÷ 70 miles
We want a unit rate where
1 is in the denominator,
so we divide top and bottom by 70
[tex]\frac{315}{70} / \frac{70}{70}[/tex]
= 4.5 miles per miles
Therefore, in unit rate the ratio of the distance the hare traveled to the tortoise is 4.5 miles per miles.
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Elliot takes a roast out of the oven when the internal temperature of the roast is 165°F. After 12 minutes, the temperature of the roast
drops to 140°F.
The temperature of the room is 70°F.
How long does it take for the temperature of the roast to drop to 125°F?
Use the Newton's Law of Cooling equation, T(t)=TA+ (To-TA) e-kt
Enter your answer in the box. Round your answer to the nearest minute.
minutes
Answer:
21.475 minutes
(Rounded) 21 minutes
Step-by-step explanation:
T(t) = TA + (T0 - TA)e^(-kt)
We know that after 12 minutes...
140 = 70 + ( 165 - 70)e^(-k* 12)
1 ) Simplify and subtract 70 from both sides
70 = ( 95)e^(-12k)
2 ) Divide both sides by 25
70/95 = e^(-12k)
3 ) Take the Ln of both sides
Ln (70/95) = Ln e^(-12k)
and we can write Ln (70/95) = (-12k) Ln e
[ Ln e =1, so we can ignore this ]
4 ) Divide both sides by -12
Ln (70/95) / -12 = k ≈ .02545
So...
5 ) We want to find this 125 = 70 + ( 165 - 70)e^(-.02545t)
6 ) 55 = (95)e^(-.02545*t)
7 ) 55/95 = e^(-.02545*t) take the Ln of both sides
8 ) Ln (55/95) = Ln e ^(-.02545 *t)
9 ) Ln (55/95) = (-.02545 * t) * Ln e
10 ) Ln (55/95) = -.02545 * t
11 ) Ln (55/95) / (-.02545) = t ≈ 21.475 minutes
12 ) If we are rounding then it would be 21 minutes
Hope this helps! :)
avery sets up a passcode on her tablet, which allows only nine-digit codes. a spy sneaks a look at avery's tablet and sees her fingerprints on the screen over nine numbers. what is the probability the spy is able to unlock the tablet on his first try? express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
The probability to unlock the tablet on his first try is [tex]P=\frac{1}{10^{9} }[/tex].
According to the statement
We have to find that the probability to unlock the tablet on his first try.
For this purpose, we know that the
Probability is the the ratio of the number of outcomes to the total number of possible outcomes.
And
The desired outcomes is the 1 because only 1 password is the correct.
And the total outcomes is the
Nine-digit codes.so,
[tex]T=10^{9}[/tex]
Because For each digit, there are 10 possible outcomes.
And the probability is the
[tex]P=\frac{1}{10^{9} }[/tex].
So, The probability to unlock the tablet on his first try is [tex]P=\frac{1}{10^{9} }[/tex].
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what is X,Y, and Z, show work if possible
The values of x, y and z are 74°, 37° and 17° respectively
What is Angles?
An angle is a figure in Euclidean geometry made up of two rays that share a common endpoint and are referred to as the angle's sides and vertex, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. Dihedral angles are these.
Given,
x°, (4z + 6)°, 2y° and 106°
Lets solve,
x° and 106°
From the co-interior angle
x + y = 180°
x° + 106° = 180°
x = 180 - 106
x = 74°
by alternate exterior angle
x = 2y
Since we know about the value of x
we can write it as
74 = 2y
y = 74/2
y = 37°
Now by alternate interior angles
(4z + 6) = x
(4z + 6) = 74
4z = 74 - 6
4z = 68
z = 68/4
z = 17°
Hence, Value of x, y and z is 74°, 37° and 17° respectively
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Cuánto es el resultado de 1326 dividido entre 41
1326 divided by 41 is equivalent to 32.35.
What is Equation Modelling?
Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
Given is 1326 divided by 41.
Assume that 1326 divided by 41 is equivalent to [x].
[x] = 1326/41
[x] = 32.35
Therefore, 1326 divided by 41 is equivalent to 32.35.
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[Question translation in english -
How much is the result of 1326 divided by 41.]
A colony of bacteria double every half hour. How many
new bacteria would there be after 4 hours if there are
60 bacterium to start?
when there are few data, we often fall back on personal probability. there had been just 2424 space shuttle launches, all successful, before the challenger disaster in january 1986. the shuttle program management thought the chances of such a failure were only 11 in 100,000.in 100,000. suppose 11 in 100,000100,000 is a correct estimate of the chance of such a failure. if a shuttle was launched every day, about how many failures would one expect in 300 years?300 years? round your answer to the nearest whole number.
If a shuttle was launched every day, about 1 failures would one expect in 300 years.
What is estimate?Finding an estimate or approximation—a value that can be used for a purpose despite the possibility of incomplete, uncertain, or unstable input data—is the process of estimation. Despite this, the value is still useful because it was created using the most up-to-date data.
Here,
There are about 110,000 days in 300 years, so the expected number of failures is about 10/11 ≈ 1.
This assumes the launch conditions are identical for each of the launches, or that whatever variation there might be has no effect on the probability. These are bad assumptions.
If a shuttle was launched every day, one might anticipate one failure every 300 years.
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5.
8cm
The diagram shows a prism.
9cm
5cm
Not to scale
Work out the volume of the prism.
3cm
10cm
Answer:
9cm r=2x3x9= 54. Find the volume of the cube. Include units. 5cm ... Not to scale. Work out the volume of the prism. Area of front. 3x5=15. 3cm 4x8=32. 10cm.
Step-by-step explanation:
Answer:
470 cm³
Step-by-step explanation:
You want the volume of a prism with an L-shaped base.
VolumeThe volume of a prism is given by ...
V = Bh
where B is the area of the base, and h is the distance between bases.
Base areaThe base is has an L-shape. Its area can be found by extending the horizontal line to divide the figure into two rectangles.
The top rectangle is 4cm × 5cm, so has an area of ...
A = LW = (4 cm)(5 cm) = 20 cm²
The bottom rectangle is 9 cm × 3 cm, so has an area of ...
A = LW = (9 cm)(3 cm) = 27 cm²
Then the total base area is ...
B = (top rectangle area) + (bottom rectangle area)
B = (20 cm²) +(27 cm²) = 47 cm²
Prism volumeThen the volume is ...
V = Bh = (47 cm²)(10 cm) = 470 cm³
The volume of the prism is 470 cm³.
What are area and perimeter of figures?.
Certain figures are explained in both cases in perimeter as well as area,
to illustrate the examples of geometrical figures.
What is Geometrical Figures?Geometrical shapes are shapes that illustrates the shapes of different items. some figures have two dimensions, while others have three. Only the x and y axis are used for two-dimensional structure, whereas the x, y, and z axes are used for three-dimensional structures. The height of the object is displayed in the z-axis.
In Mathematics area and perimeter of certain figures are known,
Rectangle
Perimeter of a Rectangle = 2(a+b)
Area of Rectangle = a × b
Square
Perimeter of a Square = 4a
Area of a Square = a²
Triangle
Perimeter of a triangle = a + b +c , where a, b and c are the three different sides of the triangle.
Area of a triangle = 1/2 b × h; where b is the base and h is the height of the triangle.
Circle
Circumference of Circle = 2πr
Area of Circle = πr²
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Identify the domain of the function shown in the graph -6 < x < 6
The domain of the function shown on the graph is given by the following option:
B. All real numbers.
What is the domain of a function?The domain of a function is the set composed by all the input values that are assumed by the function.
On a graph, the meaning of each variable is given as follows:
Values of x -> horizontal axis -> input values.Values of y -> vertical axis -> output values.Hence, considering the graph of the function, the domain of the function is the set that contains all the values of x of the function.
From the image given at the end of the answer, the line continues to left and to right, meaning that it has no spaces in it's definition, and thus the function is defined for all real values and the correct option is given by option b.
Missing InformationThe problem containing the graph of the function and the options is given by the image presented at the end of the answer.
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Find the perimeter and area of the rectangle with coordinates (3,7), (3,-2), (-6.-2) and (-6,7)
The area of the rectangle 81 square units and the perimeter of the rectangle is 36 units.
In this question, we have been given the rectangle with coordinates (3,7), (3,-2), (-6.-2) and (-6,7)
We need to find the perimeter and area of the rectangle.
Using distance formula we find the length and width of the rectangle.
d1 = √(-2 - 7)² + (3 - 3)²
d1 = √(-9)²
d1 = 9
And d2 = √(-2 + 2)² + (-6-3)²
d2 = √(-9)²
d2 = 9
d3 = √(7 + 2)² + (-6 + 6)²
d3 = 9
This means, the length and width of rectangle are equal i.e., 9 units.
So, perimeter would be,
P = 4 * 9
P = 36 units
And the area would be,
A = 9 * 9
A = 81 square units
Therefore, the area of the rectangle 81 square units and the perimeter of the rectangle is 36 units.
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Arithmetic Sequence - Identify the first term and common difference
i) The first term, a is 3 and the common difference, d, is 2
ii) The first term, a is 18 and the common difference, d, is -5
iii) The first term, a is 8 and the common difference, d, is 11
iv) The first term, a is -15 and the common difference, d, is -4
v) The first term, a is 4.5 and the common difference, d, is 0.8
Arithmetic sequence: Determining the first term and the common differenceFrom the question, we are to determine the first terms and the common differences of the arithmetic sequences.
The first term, a, is the first number in the sequence and the common difference, d, is the value of the difference between the second term and the first term.
That is,
Common difference = Second term - First term
i) 3, 5, 7, 9, ...
a = 3
d = 5 - 3
d = 2
ii) 18, 13, 8, 3, ...
a = 18
d = 13 - 18
d = -5
iii) 8, 19, 30, 41, ...
a = 8
d = 19 - 8
d = 11
iv) -15, -19, -23, -27, ...
a = -15
d = -19 - (-15) = -19 + 15
d = -4
v) 4.5, 5.3, 6.1, 6.9, ...
a = 4.5
d = 5.3 - 4.5
d = 0.8
Hence, the first term is 4.5 and the common difference is 0.8
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2log (10/9) + 3log(81/30)= 2log(25/24)+log 2 give answers after solving
After solving the equation we get to know LHS = RHS
What is an equation ?
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated by the symbol "equal."
LHS
7 log(10/9) - 2log(25/24) + 3 log( 81/80)
= 7log{(2*5)/3²} - 2log{5²/ (2^3 *3)} + 3log{(3^4/(2^4*5)}
= 7( log 2 + log5 - 2log3) -2 (2log 5- 3log2-log3) + 3(4log3 - 4log2–log5)
= 7log2+ 7log5- 14log3 - 4log5 + 6log2 + 2log 3 + 12log3 - 12log2 - 3log 5
= (7log2+ 6log2 -12log2 ) + (7log5 - 4log5–3log5)
= 13log2 - 12 log2 + 3log5 - 3log5
= log2
= RHS
∴ LHS = RHS
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