The standard form of the number [tex](1.5*10^(13))^2[/tex] is 2.25×[tex]10^(26)[/tex] .
What is standard form of a number ?
An equation, an expression, or a set of integers can all be written in standard form using the standard form approach. It is possible to express a number in a way that adheres to certain standards by writing it in its standard form. Standard form refers to any number between 1.0 and 10.0 that may be expressed as a decimal number and multiplied by a power of 10. The term "standard form" in this context refers to the act of condensing a particularly big expanded form of a number.
Here given is ,
=> [tex](1.5*10^(13))^2[/tex]
=> [tex]1.5^2[/tex] × [tex]10^(13)^2[/tex]
=> 2.25×[tex]10^(26)[/tex]
Therefore standard form of the number is 2.25×[tex]10^(26)[/tex].
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(03.05 HC)
Belinda is thinking about buying a car for $18,500. The table below shows the projected value of two different cars for three years:
Number of years 1 2 3
Car 1 (value in dollars) 17,390 16,346.60 15,365.80
Car 2 (value in dollars) 17,500 16,500 15,500
Part A: What type of function, linear or exponential, can be used to describe the value of each of the cars after a fixed number of years? Explain your answer. (2 points)
Part B: Write one function for each car to describe the value of the car f(x), in dollars, after x years. (4 points)
Part C: Belinda wants to purchase a car that would have the greatest value in nine years. Will there be any significant difference in the value of either car after nine years? Explain your answer, and show the value of each car after nine years. (4 points)
HELP!!!!!!!
a. The functions are classified as follows:
Car 1: Exponential.Car 2: Linear.b. The functions are given as follows:
Car 1: c(t) = 17390(0.94)^t.Car 2: c(t) = 17500 - 1000t.c. She should purchase Car 1, as it will have a higher value in nine years.
How to classify the functions?The functions are classified depending if there is an equal factor or an equal difference between consecutive terms, as follows:
Equal factor: exponential.Equal difference: linear.Hence the functions in this problem are classified as follows:
Car 1: Exponential, as there is an equal factor of 16346.6/17390 = 0.94.Car 2: Linear, as there is an equal difference of 1000.Hence the functions are given as follows:
Car 1: c(t) = 17390(0.94)^t. -> initial value multiplied by the equal factor elevated to time.Car 2: c(t) = 17500 - 1000t. -> Initial value subtracted by the equal difference multiplied by time.After nine years, the values are as follows:
Car 1: 17390(0.94)^9 = $9,964.Car 2: 17500 - 9(1000) = $8,500.More can be learned about exponential functions at https://brainly.com/question/25537936
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Answer:
That's right
Step-by-step explanation:
The table below shows Bentley's earnings on the job.
Time (hours) Earnings (dollars)
16
20
22
$243.20
$304
$334.40
What is the constant of proportionality between earnings
and time in hours?
Constant of Proportionality = 15.20
What's proportionality?
Suppose there are two amounts. Proportionality indicates that if there's a change in the value of one number, the value of other number also changes but maintaining a constant ratio
Proportionality can be direct or inverse
Direct proportion
Two amounts are said to be in direct proportion if on increasing the value of one number, the value of other number also increases and vice versa.
For illustration cost of a commodity and volume of a commodity are in direct proportion
Inverse proportion
Two amounts are said to be in inverse proportion if on increases the value of one number, the value of other volume diminishes and vice versa.
For illustration Number of men and number of days taken by those men to complete a job
From the table, we can calculate the constant of proportionality
Constant of Proportionality =
[tex]\frac{304 - 243.20}{20 -16}\\\frac{60.80}{4}\\15.20[/tex]
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I need help ASAP!!!!!!!!!!!!!
It’s due today!
Answer:
Step-by-step explanation:
Help me I can’t do this
Answer:
[tex]y = -\frac{7}{20}x + 1[/tex]
Step-by-step explanation:
We have to find the equation of the line that would be made by the stars
This line is parallel to the one already given
Gradients of both lines will be the same
Find out the gradient of the line already given
chose 2 coordinates of the line, I'll choose (0,0) and (-10,3.5)
use the formula
[tex]\frac{y2 - y1}{x2 - x1}[/tex]
[tex]\frac{3.5-0}{-10-0}[/tex]
[tex]-\frac{3.5}{10}[/tex]
-7/20 is the gradient
the star crosses the y axis at y = 1 so the y intercept is 1
y = mx + c
[tex]y = -\frac{7}{20}x + 1[/tex]
Find the number of cube of ide 3cm which can be put into a box which ha internal meaurement of 54cm 40cm and 8 cm
A total of 640 cubes of 3cm size can fit into a box with internal dimensions of 54, 40, and 8 cm.
By using volume, et’s assume that ’n’ cubes can be cut out from the cuboid. The volume of n cubes will be equal to the total volume of the cuboid.
The volume of 1 cube of side 3 cm is (3)^3 = 27 c.c. [volume of a cube of side 'a' is (a)^3]
Now, the volume of cuboid from which the cubes will be cut is 54 X 40 X 8 = 17280 c.c. [volume of a cuboid is length X breadth X height].
Now, the number of cubes that can be cut out from the cuboid (n) = (volume of cuboid)/(volume of 1 cube) => n = 17280/27 = 640.
Hence, a total of 640 cubes of side 3cm can beput into a box which had internal measurement of 54cm 40cm and 8 cm
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you read in a book about bridge that the probability that each of the four players is dealt exactly one ace is about 0.11. this means that
the probability that each of the four players is dealt exactly one ace is about 0.11. this means that in a very large number of bridge deals, the percentage of deals on which each player has one ace will be very close to 11%
The probability of each of the four players is dealt exactly one ace is about 0.11
so,
the probability is always approximately the corresponding percent obtained for very large samples.
Hence it means that in a very large number of bridge deals, the percentage of deals on which each player has one ace will be very close to 11%
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22÷(−2)
solve and show how you solved
the length of a rectangle is 11 less than three times the width, and the area of the rectangle is 42. find the dimensions of the rectangle.
The dimensions of the rectangle are length and width are 6 and 11.6 respectively.
L = 3w - 11 ,
where,
L = length of the rectangle and
W =width of the rectangle
A=LW
Here A is Area of the Rectangle which is product of its dimensions i.e., length and breadth.
LW = 42
substituting for l:-
(3W-11)W= 42
3W^2 - 11W - 42 = 0
(3W + 10)(W - 6) = 0
W = 6 or -10/3 (ignore the negative root)
So the width is 6 and the length is 70/6= 11.6
The rectangle's length and width are therefore 6 and 11.6, respectively.
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The perimeter of the parallelogram is 102 feet. Find m. Write your answer as a decimal or mixed number.
If the perimeter of the parallelogram is 102 feet, then the value of m is 12.75
The perimeter of the parallelogram = 102 feet
The perimeter of the parallelogram = 2(l + w)
Where l is the length and w is the width of the parallelogram
The length of the parallelogram = 3m
The width of the parallelogram = m
Substitute the values in the equation of the perimeter
102 = 2(3m + m)
102 = 2(4m)
102 = 8m
m = 102 / 8
Divide the terms
m = 12.75
Hence, if the perimeter of the parallelogram is 102 feet, then the value of m is 12.75
The complete question is:
The perimeter of the parallelogram is 102 feet. Find m. Write your answer as a decimal or mixed number.
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A cylindrical can without a top is made out of metal material with a total area of 1500π cm2. Find the dimensions that will maximize the volume held by the can.
The dimensions of the cylinder will be r = 8.92 cm and h = 17.86 cm.
What is dimensions ?
Dimensions refer to the length or width of an area, region, or space in one direction.
Main Body:
Volume of cylinder = πr²h
Surface area = 2πr² + 2πrh
Given surface area = 1500 cm²
1500 = 2πr²+2πrh
h= (750/πr)-r ----(1)
V= πr²{(750/πr)-h}
V =750r - πr³
V' = 750- 3πr²
Put V' =0
0 = 750 - 3πr²
r≈ 8.92 cm
substituting the value of r in equation (1)
we get h= 17.86 cm
Hence the dimension of cylinder are r = 8.92 cm and h = 17.86 cm
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how many sequences of 's and 's of length are there that begin with a , end with a , contain no two consecutive 's, and contain no three consecutive 's?
After any particular a, the next a in the sequence must appear exactly 2 or 3 positions down the line. In this case, we start at position b and end at position 19. answer is 65
i.e. we move a total of 18 positions down the line. Therefore, we must add a series of c's and d's to get 18. There are several ways to do this:
Case 1: nine c's - there is only 1 way to arrange them.
Case 2: two d's and six c's - there are 28 ways to arrange them.
Case 3: four d's and three c's - there are 35 ways to arrange them.
Case 4: six c's - there is only 1 way to arrange them.
Summing the four cases gives 1+28+35+1 = 65
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I thought of a three digit number. Each digit i the quare of the digit to the right. What i my number
The three digit number you thought of is 111.
We now have:
According to the question:
N = a*100 + b*10 + c.
where:
b = c^2
a = b^2.
Let's now assign values to c. (here we can start with zero).
If c = 0, then b = 02 = 0 and a = 02 = 0 are the results.
Then N = 0*100 + 0*10 + 0 = 0 (this is not a 3-digit number) is the expression
If c = 1, then b = 12 = 1, then a = 12, and so on.
N = 1*100 + 1*10 + 1 = 111
If c = 2, then b = 2 2 4 a = 4 2 16 will follow.
111 is the only viable choice in this case.
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Kristen lost 30 pounds in
12 weeks. She lost the same
amount of weight per week.
What is the unit rate of weeks to
pounds?
The unit rate of weeks to pounds is 2.5 pounds in just 12 weeks, Kristen shed 30 pounds. Every week, she lost the same amount of weight.
Given that,
In just 12 weeks, Kristen shed 30 pounds. Every week, she lost the same amount of weight.
We have to find how many weeks are there in a pound.
What is unit rate?A rate is a ratio that is utilized to compare the quantities of several commodities. A unit rate is a rate with one as the denominator. Whenever a rate's denominator, such as the price per unit of a certain number of items, is not 1.
So, we can write has
This is the fraction of the number of pounds and number of weeks.
=30pounds / 12 weeks
=2.5 pounds
Therefore, The unit rate of weeks to pounds is 2.5 pounds in just 12 weeks, Kristen shed 30 pounds. Every week, she lost the same amount of weight.
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A baseball used by a professional baseball team must have a diameter that is between 2.86 inches and 2.94 inches. which of the following could be the diameter of a baseball used by a professional baseball team? A. 2 7/8 inches
The option that could be the diameter of a baseball used by a professional baseball team is A. 2 7/8 inches.
How to calculate the diameter?From the information, the baseball used by a professional baseball team must have a diameter that is between 2.86 inches and 2.94 inches.
In this case, 2 7/8 inches to decimal is 2.875
2 7/9 inches will be 2.778
2 8/10 will be 2.8
2 9/11 inches will be 2.818
Therefore, the correct option is A as it fits tye value given.
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Complete question
A baseball used by a professional baseball team must have a diameter that is between 2.86 inches and 2.94 inches. which of the following could be the diameter of a baseball used by a professional baseball team?
A. 2 7/8 inches
B 2 7/9 inches
C 2 9/11 inches
D. 2 8/10 inches.
Determine the degree measure of one angle of a 30-sided regular polygon. 5,400° 5,040° 180° 168°
To determine the degree measure of one angle of a 30-sided regular polygon.
The degree measure of one angle of a 30 sided regular polygon is 168°.
What is a regular polygon?
A two-dimensional geometric shape with a finite number of sides is called a polygon. A polygon's sides or edges are made up of segments of straight lines that are joined end to end to create a closed shape.
The intersection of two lines is referred to as a vertex or corner, and an angle is created as a result. Regular polygons are those that have sides that are congruent.
We will use the side-angle relation of a regular polygon with any no. of sides to find total sum of interior angles that is
(Side - 2) × 180°
(30 - 2) × 180°
= 5040°
Measure of each angle of 30-gon
= 5040°/30
= 168°
Thus, the degree measure of One angle of a 30 sided regular polygon is 168°
Hence the answer is, The degree measure of one angle of a 30 sided regular polygon is 168°.
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write the expression in algebraic form. [hint: sketch a right triangle, as demonstrated in example 3.] cos arcsin x - h r
Given trigonometric expression in algebraic form would be,
cos(arcsin(x - h/r)) = ± [√(r² - (x - h)²)]/r
In this question, we need write the expression in algebraic form.
Given trigonometric expression is cos(arcsin(x - h/r))
Let y = arcsin(x - h/r)
so, sin(y) = (x - h)/r
By trigonometric identity,
sin^2(y) + cos^2(y) = 1
we have cos(y) = ±√(1 - sin²y)
cos(arcsin(x - h/r)) = ±√[1 - ((x - h)/r)^2]
= ± [√(r² - (x - h)²)]/r
Therefore, given trigonometric expression in algebraic form would be,
cos(arcsin(x - h/r)) = ± [√(r² - (x - h)²)]/r
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a prism is made up of 120 equal cubes. if the volume of the prism is 25, 920 cm3, what is the length of each cube?
The side of the cube is 6 cm.
What is the Volume of a prism?
The area that a prism takes up is referred to as its volume. A prism is a solid, three-dimensional structure with two identical faces and additional faces that resemble parallelograms. It is a polyhedron whose nomenclature is influenced by the various basic forms. Every prism has a particular base, whether it be a triangular prism (triangular base), square prism (square base), rectangular prism (rectangular base), pentagonal prism (pentagonal base), hexagonal prism (hexagonal base), or an octagonal prism (octagonal base). Consequently, because a prism is a three-dimensional form, its volume likewise exists in a three-dimensional plane. Prisms are measured in terms of their volume in cubic meters, cubic millimeters, cubic inches, or cubic feet. Following are the steps to calculate the prism's volume:
Write down the prism's dimensions as specified in step one.
Step 2: Use the formula V = B H to calculate the prism's volume. V, B, and H stand for the prism's volume, base area, and height, respectively.
Step 3: After obtaining the volume of the prism's value, add the unit of prism volume at the conclusion (in terms of cubic units).
In the question, we have given that:
Prism is made up of 120 equal cubes;
The volume of the prism is 25, 920[tex]cm^{3}[/tex];
So, we can equate the volume of 120 equal cubes with the prism's volume;
⇒ 120 × [tex](a)^{3}[/tex] = 25, 920;
⇒[tex](a)^{3}[/tex] = [tex]\frac{25920}{120}[/tex]
⇒[tex](a)^{3}[/tex] = 216;
So, the value of a is 6 cm;
That is the side of the cube is 6 cm;
Hence, The side of the cube is 6 cm.
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PLS HELP!!!
(Order of Operations with Radicals MC)
Simplify the expression.
-5 (3 - CUBE ROOT of 27 times 2) divide by 3 (or over 3 because it's a fraction)
A. six fifths
B. 5
C. negative six fifths
D. −5
The Simplify the expression is -10, when we use fraction.
What is a fraction?
If the numerator is bigger, it is referred to as an improper fraction and can also be expressed as a mixed number, which is a whole-number quotient with a proper-fraction remainder.
Any fraction can be expressed in decimal form by dividing it by its denominator. One or more digits may continue to repeat indefinitely or the result may come to a stop at some point.
=-5(∛27 *2)/3
=-5(3*2)/3
=-5(6)/3
=-10
Hence the answer will be -10 simplify the expression.
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Answer these for award
Answer:
1: Supplementary angle; x = 95
2: Complementary angle; x = 31 [(2x-3)+x]
3: vertical angle; x = 90
4: supplementary angle; x = 92 [x+(x-4)]
Step-by-step explanation:
1: 180-85 = 95 (x)
2: (2x-3)+x = 90 evaluates into x = 31
3: all sides are equal so if one side is 90 then the rest are
4: x+(x-4) = 180 evaluates into x = 92
Let me know if you need any more help.
Please hurry I don't have time needs to be done only h and c and an explanation on how you found them please
Answer:
25 & 37
Step-by-step explanation:
Jim began a 182-mile bicycle trip to build up stamina for a triathlete competition. Unfortunately, his bicycle chain broke, so he finished the trip walking. The whole trip took 5 hours. If Jim walks at a rate of 4 miles per hour and rides at 40 miles per hour, find the amount of time he spent on the bicycle.
Based on the concept of unitary method, the amount of time he spent on the bicycle is 5.6 hours.
Unitary method:
Unitary method is used for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given,
Jim began a 182-mile bicycle trip to build up stamina for a triathlete competition. Unfortunately, his bicycle chain broke, so he finished the trip walking. The whole trip took 5 hours.
Here we need to find the amount of time he spent on the bicycle if Jim walks at a rate of 4 miles per hour and rides at 40 miles per hour.
Let us consider x be the hours on the bike for distance 40x miles.
We know that, he spent 5 - x hours walking for distance 4(5 - x) miles or it can be written as
=> 20 - 4x
And we also know that those two, 40x and 20 - 4x, add to 182 miles
=> 40x + 20 - 4x + 182
=> 36x + 202
=> 36x = 202
=> x = 5.6
And the units calculation is m/h*h=m
If the value of x = 5.6 hours on the bike for 139.5 miles, then 5 - x =0.6 hours walking for 4 miles.
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The janitor at a school discovered a leak in a pipe. The janitor found that it was leaking at a rate of 12 f oz per minute. How fast was the pipe leaking in gallons per hour?
Answer:
5.625 gallons are being leaked per hour.
Step-by-step explanation:
Since every fluid ounce = 0.0078125 of a gallon,
0.0078125 x 12 (the amount of fluid ounces leaked per minute) = 0.09375
Since 0.09375 is the number of gallons leaked per minute, we have to multiply by 60 (because an hour is 60 minutes long).
12 x 60 = 720 (the number of fluid ounces leaked per minute)
0.09375 x 60 = 5.625 (the number of gallons are being leaked per hour)
what is the probability that, of 6 such types of devices, at least 3 will function for at least 15 hours? what assumptions are you making?
The probability that one such device will work at least 15 hours at least 3 among 6 devices is 0.33 approximately.
The cumulative distribution function of X is:[tex]F(x)= 1- 10/x[/tex] ( for x > 10)
X = the entire lifespan of a definite type of electronic device in hours, then the probability function of X,
here we use the cumulative distribution function, which is used to specify random variables,
F(X)= 1 - 10/X is cumulative distribution function,
then the probability that at least 3 devices will work for 15 hours
P(X[tex]\geq[/tex]15)= 1- P(X<15)
= F(15)
= 1- 10/15
=5/15
=0.333
Hence, the probability that one such device will work at least 15 hours at least 3 among 6 devices is 0.33 approximately.
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How do i find the area if the x is 25. i broke the shape into a rectangle and a triangle, the area of the smaller rectangle is 40 and the area of the bigger rectangle is 250. I am trying to find the area of the whole complex figure
Answer:
See the picture below
Step-by-step explanation:
Evaluate 4-0.25g+0.5h4−0.25g+0.5h4, minus, 0, point, 25, g, plus, 0, point, 5, h when g=10g=10g, equals, 10 and h=5h=5h, equals, 5.
The equation, 4 - 0.25g + 0.5h, will be evaluated as equal to: 4.
How to Evaluate an Equation?To evaluate an equation, plug in the values of the variables in the equation and solve to get the simplified value.
Given the equation, 4 - 0.25g + 0.5h, where:
g = 10
h = 5
Substitute g = 10 and h = 5 into the equation 4 - 0.25g + 0.5h, then evaluate:
4 - 0.25(10) + 0.5(5)
Simplify
= 4 - 2.5 + 2.5
= 4 + 0
= 4
Therefore, if g = 10 and h = 5, the equation 4 - 0.25g + 0.5h, is evaluated as: 4.
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The Question:
Evaluate 4 - 0.25g + 0.5h when g = 10 h = 5.
If y varies directly with x when y=68 and x-6, find the value of y when x=24.
The value of y when x = 24 is 272.
What is proportionality?Proportionality indicates that two quantities or variables are related linearly.
Given that, y varies directly with x when y = 68 and x = 6
y/x = 68/6 = 34/3
Therefore, the proportion is 34/3
when x = 24
34/3 = y/24
y = 272
Hence, y = 272 when x = 24
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Line m passes through the points ( 2, -7 ) and ( 4 , -9 ) . Line m is parallel to which of the following lines ?
Answer: 6 -3
Step-by-step explanation: i just took the test
Answer:
(-6,3) (5,-9)
Step-by-step explanation:
Solve the system of equations. 8x-3y = 3 3x - 2y = -5
The solution of the system of equations is x = 1 and y = -1.
What is a two-variable linear equation?
If an equation is written in the form ax + by + c=0, where a, b, and c are real integers and the coefficients of x and y, i.e., a and b, respectively, are not equivalent to zero, it then is said to be a linear equation in 2 factors. Examples of two-variable linear equations are 10x+4y = 3 and -x+5y = 2.
SOLUTION TO WORK OUT
the equations are resolved
8x + 3y = 5 & 3x − 2y = 5
EVALUATION
The equations in the given system are
8x + 3y = 5 - - - - - - - (1) (1)
3x − 2y = 5 - - - - - - - (2) (2)
Equation 1's two sides multiplied by two gives us
16x + 6y = 10 - - - - - - (3) (3)
Equation 2's two sides are multiplied by three to get
9x - 6y = 15 - - - - - - (4) (4)
Equation 3 and Equation 4 together give us
25x = 25
⇒ x = 1
Equation 1 is completed when x = 1.
8 + 3y = 5
⇒ 3y = 5 - 8
⇒ 3y = - 3
⇒ y = - 1
FINAL RESPONSE
Consequently, the needed answer is x = 1 and y = - 1.
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briefly explain the goal for defining and measuring variability. a measure of variability describes the degree to which the scores in a distribution are . variability also measures the .
Variability provides a quantitative measure of the differences between scores in a distribution and describes the degree to which the scores are spread out to clustered together. The purpose for measuring variability is to obtain an objective measure of how the scores are spread out in a distribution
What is variability ?Variability also measure how accurately individual score or sample represent the entire population
When the standard deviation is 0 , the scores have no variability.
Variability describes how far the data points are from each other and from the center of the distribution. In addition to measures of central tendency, measures of variability provide descriptive statistics that summarize the data.
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Complete the two-column proof below. The ‘reasons’ are already given, so only the mathematical ‘statements’ need to be completed.
Given: ∠A and ∠B are complementary angles. ∠B and ∠C are complementary angles.
Prove: ∠A ≅ ∠C
Statements
Reasons
1. Given
2. Definition of complementary angles
3. Substitution property of equality
4. Subtraction property of equality
5. Angles that have equal measure are congruent.
The blanks in this two-column proof should be completed (filled) as follows:
Statements Reasons_______________
∠A and ∠B are complementary angles. Given
∠B and ∠C are complementary angles.
m∠A + m∠B = 90° Definition of complementary angles
m∠B + m∠C = 90°
m∠A + m∠B = m∠B + m∠C Substitution property of equality
m∠A = m∠C Subtraction property of equality
∠A ≅ ∠C Angles that have equal measure are congruent.
What is a complementary angle?In Mathematics, a complementary angle can be defined as two (2) angles or arc whose sum is equal to 90 degrees (90°).
Mathematically, a complementary angle can be represented by using this mathematical expression:
Q + R = 90°
Where:
Q and R are measure of the angles subtended.
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