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Related Questions
Distribute to create an equivalent expression with the fewest symbols possible.
\dfrac12(2a - 6b+ 8) =
2
1
(2a−6b+8
Answers
The equivalent expression for 1/2(2a - 6b+ 8) will be a - 3b + 4
How to calculate the equivalent expression?Expressions that are equivalent do the same thing even though they have different appearances. When we enter the same value(s) for the variable, two algebraic expressions that are equivalent have the same value (s).
When two expressions can be reduced to a single third expression or when one of the expressions can be written in the same way as the other, they are said to be equivalent. When values are substituted for the variable and both expressions yield the same result, you can also tell if two expressions are equivalent.
This will be:
1/2(2a - 6b+ 8)
= a - 3b + 4
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Complete question
Distribute to create an equivalent expression with the fewest symbols possible 1/2(2a - 6b+ 8) =
The following is a list of various costs of producing sweatshirts. Classify each cost as either a variable, fixed, or mixed cost for units produced and sold.a. Electricity costs of $0.025 per kilowatt-hour.b. Warehouse rent of $6,000 per month plus $0.50 per square foot of storage used.c. Thread.d. Lubricants used to oil machinery.e. Janitorial costs of $2,000 per month.f. Advertising costs of $10,000 per month.g. Sales salaries. Color dyes for producing different colors of sweatshirts.h. Salary of the production supervisor.i. Straight-line depreciation on sewing machines.j. Patterns for different designs. Patterns typically last many years before being replaced.k. Maintenance cost with sewing machine company. The cost is $2,000 per year plus $0.001 for each machine hour of use.l. Property taxes on factory, building, and equipment.m. Cotton and polyester cloth.n. Hourly wages of sewing machine operators.Variable Cost:Variable cost is the cost incurred in the production of goods or services and changes with the level of output produced by an organization. It includes costs directly linked with production, like material cost.
Answers
Following are the answers to all the asked questions for classifying types of cost.
a. Electricity costs of $0.025 per kilowatt-hour - variable cost
b. Warehouse rent of $6,000 per month plus $0.50 per square foot of storage used - mixed cost
c. Thread - variable cost
d. Lubricants used to oil machinery - variable cost
e. Janitorial costs of $2,000 per month - fixed cost
f. Advertising costs of $10,000 per month - fixed cost
g. Sales salaries - fixed cost
h. Color dyes for producing different colors of sweatshirts - variable cost
i. Salary of the production supervisor - fixed cost
j. Patterns for different designs. Patterns typically last many years before being replaced - fixed cost
k. Maintenance cost with sewing machine company. The cost is $2,000 per year plus $0.001 for each machine hour of use - mixed cost
l. Property taxes on factory, building, and equipment - fixed cost
m. Cotton and polyester cloth - variable cost
n. Hourly wages of sewing machine operators - variable cost
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Which of the following situations satisfies all the conditions of a binomial setting? (These conditions are: we know the number of repetitions, the outcome of each trial can be considered either a success or a failure, we know the probability of success or failure of any trial, and the probability doesn't change from trial to trial.)
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A binomial setting is one in which there are a fixed number of trials, the outcome in each trial is either a success or a failure, the probability of success or failure is known, and the probability doesn't change from trial to trial.
A binomial setting is one in which we know the number of repetitions (n=20), the outcome of each trial can be considered either a success or a failure (p=0.4, q=1-p=0.6), and the probability of success or failure of any trial does not change from trial to trial (p=0.4, q=1-p=0.6).
For example, if we toss a coin 20 times, and we know the probability of success (head) is 0.4 and the probability of failure (tail) is 0.6, then this is a binomial setting. We can calculate the probability of getting exactly 10 heads in 20 tosses using the binomial formula: P(X=10) = (20C10) * (0.4^10) * (0.6^10) = 0.1775.
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fill in the blank with a whole number with how many significant figures are in the following: a) 0.04550 b) 5.0003 c) 1.000 x 105 d) 0.00002 e) 1.01 x 10-2 f) 7
Answers
a) 0.04550 has four significant figures.
b) 5.0003 has four significant figures.
c) 1.000 x [tex]10^5[/tex] has four significant figures.
d) 0.00002 has one significant figure.
e) 1.01 x [tex]10^{-2}[/tex] has three significant figures.
f) 7 has one significant figure.
Significant figures are the digits in a number that are known with certainty, including one uncertain digit. In general, any non-zero digit is considered a significant figure, and zeros between non-zero digits are also significant figures.
Leading zeros before the first non-zero digit and trailing zeros after the last non-zero digit are not considered significant figures.
For example, in the given number 5.006, there is four significant number,
since all zeros between integers are always significant.
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Una granja tiene q
cerdos, 2 caballos.
y 4 vacas. ¿Cuantos
animales hay ahi?
animales
Answers
Answer: letra “q” no es un número
Step-by-step explanation:
find the center of mass (relative to (0,0)) for the spheres with the following masses and locations: m1
Answers
The center of mass is (2,1) since m1 has a mass of 10 and is located at (4,2). The center of mass is the average of the locations of the masses, weighted by the masses.
We can calculate the center of mass of these two spheres by using the formula c = (m1*L1 + m2*L2) / (m1 + m2). m1 is the mass of the first sphere, and L1 is the location of the first sphere. In this case, m1 is 10, and L1 is (4,2). We assume that m2 is 0 and L2 is (0,0). Plugging these values into the formula, we get c = (10*(4,2) + 0*(0,0)) / (10 + 0), which is (2,1). This is because the center of mass is the average of the locations of the masses, weighted by the masses. In this case, the only mass is 10, and it is located at (4,2). Therefore, the center of mass is simply (4,2) since it is the only mass that contributes to the calculation.
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The complete question: find the center of mass (relative to (0,0)) for the spheres with the following masses and locations: m1 = 10, L1 = ( 4,2)
Type the missing numbers.
Answers
The missing numbers are -80 and -20.
What is Number Line?A number line is a straight line drawn horizontally where the numbers are placed at an equal intervals.
There is a number line in the question.
In a number line, numbers are arranged in equal intervals.
The constant interval here = -40 - -60 = 20
x - -100 = 20
x + 100 = 20
x = 20 - 100
x = -80
First missing number is -80.
y - -40 = 20
y + 40 = 20
y = 20 - 40
y = -20
Hence the numbers missing are -80 and -20.
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Nicole gets paid $2,900 per month. She pays $638 a month for rent. What percent of her monthly pay goes to rent?
Answers
21.931% of Nicole's monthly pay goes to rent.
percent = (638/2900) x 100
percent = 0.21931 x 100
percent = 21.931%
y÷15= 6 R 8
314÷y= 18 R8
What is y how can I solve this on my own for other problems?
Answers
Step-by-step explanation:
y÷15 or y/15 = 6
let's ignore the remainder for a moment.
y/15 = 6
y = 6×15 = 90
now, what does "remainder" mean ?
it means after a clean division there is a result, and there is still this additional remainder left.
the actual result of
a/b is
a/b = c + remainder/b
where c is an integer, and remainder is also an integer.
so, a = b×c + b×remainder/b = b×c + remainder
therefore,
y = 6×15 + 8 = 98
to check
98/15 = 6 remainder 8
so, it is correct
314÷y = 18 remainder 8
314 = 18y + 8
306 = 18y
y = 306/18 = 17
check
314 / 17 = 18 remainder 8
so, it is correct.
what size bands would result from cutting the following plasmid using hind iii, eagi and smai? the plasmid has a total of 5541 base pairs
Answers
The size of the bands that would result from cutting the plasmid with Hind III, Eco RI and Sma I would be 5530
The size of bands resulting from cutting a plasmid with Hind III, EagI and SmaI can be determined using the following formula:
Size of Band = Plasmid Size - (Hind III + EagI + SmaI)
The size of the bands that would result from cutting the plasmid with Hind III, Eco RI and Sma I can be calculated using the following formula:
For this example, the plasmid has a size of 5541 base pairs. After cutting with Hind III, EagI and SmaI, the size of the bands will be:
Size of Band = 5541 - (6 + 4 + 4)
Size of Band = 5527 base pairs
Band size = Total base pairs - [size of sites (Hind III + Eco RI + Sma I)] + 1
In this case, the band size would be calculated as follows:
Band size = 5541 - (6 + 6 + 4) + 1
Band size = 5530 bp
Therefore, the size of the bands that would result from cutting the plasmid with Hind III, Eco RI and Sma I would be 5530
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Complete question:
What size bands would result from cutting the following plasmid using Hind III, EcoRI and SmaI? The plasmid has a total of 5541 base pairs.
Suppose we want to choose letters, without replacement, from distinct letters. (a) If the order of the choices does not matter, how many ways can this be done? (b) If the order of the choices matters, how many ways can this be done?
Answers
The number of ways to choose 6 letters from a set of 13 is given as follows:
a) Order does not matter: 1716.
b) Order matters: 1,235,520.
When to use permutation and when to use combination?A combination is used when the order does not matter, hence, for item a, the number of ways is obtained as follows:
C(13,6) = 13!/(6!7!) = 1716.
A permutation is used when the order matters, hence, for item b, the number of ways is obtained as follows:
P(13,6) = 13!/7! = 1,235,520.
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When calculating simple interest, what must you do if you want to invest for months or weeks instead of years? a. Simple interest only pays yearly, so you should find another investment. b. The simple interest calculation does not use those units, so you should just calculate as normal. c. The units have changed, so the interest formula switches to I·t=P·r. d. Interest rates are annual, so you must convert the units into years. Please select the best answer from the choices provided A B C D
Answers
When calculating simple interest, if we want to invest for months or weeks instead of years we must convert the interest rate units into years.
Option D is the correct answer
What is simple interest?It is the interest calculated on the principal at a given rate for a time period.
We have,
The formula for simple interest.
SI = PRT/100
P = principa
R = rate
T = time
Now,
Time is in years when we are calculating the simple interest.
Example:
If time is in months.
T = 4 months
T = 4/12 = 1/3 years.
Thus,
We must convert the units into years.
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In how many months the amount of Rs1000 at the rate of 10%will be RS1200
Answers
Answer: To determine how many months it will take for an initial investment of Rs1000 to grow to Rs1200 at a 10% interest rate, we can use the formula:
Time = (ln(final value / initial value)) / (ln(1 + interest rate))
where ln is the natural logarithm function.
Plugging in the given values:
Time = (ln(1200/1000)) / (ln(1 + 0.10))
Time = (ln(1.2)) / (ln(1.10))
Time = 0.18232 / 0.09531
Time = 1.913 months
It will take approximately 1.913 months for an investment of Rs1000 to grow to Rs1200 at a 10% interest rate.
Step-by-step explanation:
A farmer is building a cylinder-shaped grain bin. The bin will be 10 feet tall and have a diameter of 12 feet. What is the surface area of the grain
bin in square feet? Use x = 3. 14. Round to the nearest hundredth if necessary.
Answers
Answer: 602.88 square feet
Equation for surface area of cylinder:
A = 2πrh+2πr^2
r = 6, because radius is half of the diameter
h = 10
A = 2(3.14)(6)(10) + 2(3.14)(6)^2
A = 376.8 + 226.08
A = 602.88 square feet
Sorry you can’t see the photo clearly, I know it’s a reduction but what is the scale factor?
Answers
Answer:
1/2
Step-by-step explanation:
Triangle XYZ has endpoints (0,0) (0,8) and (4,6)
Triangle X'Y'Z' has endpoints (0,0) (0,4) and (2,3)
As you can see, all the coordinates from Triangle XYZ are halved to get the coordinates of Triangle X'Y'Z', so the scale factor is 1/2.
You get a personal loan of $5,000 with 12% simple interest to be paid over 30 months. What is your monthly payment?
Answers
Work Shown:
A = P*(1+r*t)
A = 5000*(1+0.12*30/12)
A = 6500
The amount $6500 is what you pay back
Divided over 30 months gives 6500/30 = 216.67 dollars per month.
Side note: The value t is in years, so 30 months = 30/12 years.
are the coordinates of the point on the directed line segment from (-3, -10) to (9, 5) that partitions the segment into a ratio of 1 to 2?
Answers
Answer:
An agency that occurs when a principal and an agent categorically agree to enter into an agency agreement with each other is known as which of the following?
Question 3 Multiple Choice Worth 2 points)
(04.05 MC)
B
A random sample of 75 juniors are asked whether they plan to attend Homecoming. Of these, 62 juniors said they will attend. What is the margin of error at 90% confidence and
its interpretation?
0.072; 90% of the time we will capture the true proportion of juniors who will attend Homecoming within 0.072 of the population proportion
0.072; we are 90% confident that the true proportion of juniors who will attend Homecoming is within 0.072 of the sample proportion
0.086; we are 90% confident that the true proportion of juniors who will attend Homecoming is within 0.086 of the sample proportion
0.086; 90% of the time we will capture the true proportion of juniors who will attend Homecoming within 0.086 of the population proportion
Answers
The margin of error at a 90% confidence level for this sample is approximately 0.086.
What is meant by margin of error?
In statistics, the margin of error is the level of inaccuracy in the findings of surveys using random samples.A wider margin of error in statistics denotes a lower chance of relying on a survey's or poll's findings, i.e., a lower level of confidence in the findings' ability to accurately reflect a population.When 62 out of 75 juniors in a random sample were asked if they would be attending homecoming, the margin of error at 90% confidence was roughly 0.086.This suggests that the true proportion of juniors who will attend homecoming is within 0.086 of the sample proportion, with a 90% confidence level.The standard error of the sample proportion is calculated using the following formula:
Standard error = √((sample proportion * (1 - sample proportion)) / sample size)
Plugging in the values for the sample proportion (62/75) and sample size (75), you get a standard error of approximately 0.072.
Multiplying the standard error by the critical value gives the margin of error:
The margin of error = critical value * standard error
= 1.645 * 0.072
= 0.086
Hence, the margin of error at a 90% confidence level for this sample is approximately 0.086.
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The sides of the rectangle in Fig. 14.4 are given in cm. 4x - y, 4x + 3, x + 6y, 3x + 1 Fig. 14.4 Find x and y and the area of the rectangle.
Answers
Variable x and y for the rectangle is given by
x = (3x + 3)/6 + 1
y = (3x + 3)/6
How to find x and y and the area o the rectangle?Yes that's right. You have to equate the expressions for widths and for the lengths, since left and right widths (and lengths) have the same dimensions.
You may rewrite the equation for y=3x+3÷6 as
y = (3x + 3)/6
And now you have an expression for y, we can substitute it to the other equation you got:
x = y + 1
x = (3x + 3)/6 + 1
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What is the value or x?
Answers
Answer:
x = 25
Step-by-step explanation:
Since the given triangle is a right triangle and we are also given two sides which are opposite (height) = 24 units and adjacent (base ) = 7 units. We can apply the Pythagoras Theorem where:
[tex]\displaystyle{\text{opposite}^2 + \text{adjacent}^2 = \text{hypotenuse}^2}[/tex]
In simpler words, it is:
[tex]\displaystyle{\text{height}^2 + \text{base}^2 = \text{slope}^2}[/tex]
Substitute in given values:
[tex]\displaystyle{24^2+7^2=x^2}[/tex]
Evaluate and solve for x:
[tex]\displaystyle{576+49=x^2}\\\\\displaystyle{625=x^2}\\\\\displaystyle{\sqrt{625}=\sqrt{x^2}}\\\\\displaystyle{\pm \sqrt{625}=x}\\\\\displaystyle{\pm 25=x}[/tex]
However, x is a length value and length's value cannot be negative so x can only be 25.
Hence, x = 25 units
Consider the numerical expression: 3 + 6 × (5 + 4) ÷ 3 − 7.
Answers
Answer:
14
Step-by-step explanation:
When solving something like this use Pemdas
hope this help in some way
Data set: 8, 7, 10, 10, 17, 13, 7, 10
How much does the data set above vary?
Answers
Standard Deviation, σ: 3.152
Count, N: 8Sum, Σx: 82Mean, μ: 10.25Variance, σ2: 9.9375What a standard deviation means?The term "standard deviation" (or "σ") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.
Given, Data set: 8, 7, 10, 10, 17, 13, 7, 10
variance:
σ² = Σ(xi - μ)²/N
σ²= ((8 - 10.25)² + … + (10 - 10.25)²)/8
σ²= 79.5/8
σ² =9.9375
σ = √9.9375
σ = 3.1523
The sampling mean most likely follows a normal distribution. In this case, the standard error of the mean can be calculated using the following equation:
σ = σ/√N
σ = 1.114
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help someone please!!!!!
Answers
62.8363 cm is the total circumference of the given circle.
What is Fraction?An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a correct fraction is smaller than the denominator.
Given a circle that has an arc of 165 degrees and also given that arc has a circumference of 28.8cm
Circumference of 165 Degrees arc = 28.8cm
Circumference of 1 Degree arc = 28.8/165
Circumference of 1 Degree arc =0.17454
Since the total angle in a circle is 360 degrees
Thus from the fraction,
Circumference of 360 Degrees arc = 0.17454*360
Circumference of 365 Degrees arc = 62.8363 cm
Therefore, the total circumference of the given circle is 62.8363 cm.
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Mr. Stans bought 4.65 pounds of dog food, 2.28 pounds of cat food, and 1.4 pounds of rabbit food. How many pounds of pet food did Mr. Stans buy?
A. 7.33
B. 7.07
C.6.91
D.8.33
Answers
Explanation: 4.65 + 2.28 + 1.4 equals 8.33
A study found that a student's GPA, g, is related to the number of hours worked each week, h, by the equation g=−0.0007h2+0.018h+3.02. Estimate the number of hours worked each week for a student with a GPA of 2.72.
Answers
After solving the given equation we know that students worked for 17 hours a week.
What are equations?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.
For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
So, the given equation is:
g=−0.0007h+0.018h+3.02
Now, we know that g is 2.72, so we can calculate for h as follows:
2.72=−0.0007h+0.018h+3.02
2.72 = -0.0173h + 3.02
- 0.3 = -0.0173h
h = -0.3/-0.0173
h = 17.34
Rounding off: 17 hours
Therefore, after solving the given equation we know that students worked for 17 hours a week.
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The period (T) of a pendulum is related to the length (L) of the pendulum and acceleration due to gravity (g) by the formula T=2π√L/g. If gravity is 32 ft/s2 and the period is 1 second, find the approximate length of the pendulum. Round to the nearest inch. Note: 12 in. = 1 ft.
Answers
The approximate length of the pendulum is 2 feet.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given that period (T) of a pendulum is related to the length (L) of the pendulum and
acceleration due to gravity (g) by the formula T=2π√L/g.
g=32 ft/s2
t=1 sec
We need to find L
1=2×3.14√L/32
32=6.28√L
32/6.28=√L
5.09=√L
Square on both sides
L=25.9 inches
L=2 feet because 12 inches = 1ft.
Hence, the approximate length of the pendulum is 2 feet.
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6. To play a board game, there must be at least 4 people on each team. You
divide your friends into 3 groups. Write and solve an inequality to represent
the number of friends playing the game.
Answers
The inequality that best represent the expression is x ≥ 12
What is inequality?A relationship between two expressions or values that are not equal to each other is called 'inequality. ' So, a lack of balance results in inequality.
The sign for greater than is >
The sign for less than <
The sign for greater than or equal to is ≥
The sign for less than or equal to is ≤
There must be at least 4 people in the group. This means that a group member must greater or equal to 4. There are 3 groups.
Represent the value of the number of friends by x
then, x/3 ≥ 4
therefore x ≥ 12
this means that the number of friends must be greater or equal to 12
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Find all the solutions, including imaginary solutions if they exist, of the following equation. x^4+17x^2+16=0
Answers
The solution to the equation is i , -i , 4i , -4i
What is Quadratic Equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.
The roots of the quadratic equations are
x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )
where ( b² - 4ac ) is the discriminant
when ( b² - 4ac ) is positive, we get two real solutions
when discriminant is zero we get just one real solution (both answers are the same)
when discriminant is negative we get a pair of complex solutions
Given data ,
Let the equation be represented as A
Now , the value of A is
x⁴ + 17x² + 16 = 0 be equation (1)
On simplifying the equation , we get
Substitute the value of x² = u
u² + 17u + 16 = 0
The roots of the quadratic equations are
u = [ -b ± √ ( b² - 4ac ) ] / ( 2a )
u = [ -17 ± √ ( 289 - 4 ( 1 ) ( 16 ) ) ] / 2
On further simplification , we get
u = [ -17 ± √ ( 289 - 64 ) ] / 2
u = ( -17 ± √ 225 ) / 2
u = ( -17 ± 15 ) / 2
The two values of u are
u = ( -17 - 15 ) / 2
u = -16
And , u = ( -17 + 15 ) / 2
u = -1
Substitute the value of x² = u , we get
x² = -16
Taking square roots on both sides of the equation , we get
x = ± √ ( -16 )
x = ± 4i
And ,
x² = -1
x = ± i
So , the values of x are i , -i , -4i and 4i
Hence , the equations are solved
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We found the correlation coefficient for the comparison between height and weight in babies to be -0.12. That means
correlation is strong
the taller the baby, the heavier the baby
the taller the baby, the lighter the baby
Height and weight of babies are independent
Answers
The Correlation Coefficient -0.12 shows that The taller the baby, the lighter the baby.
What is Correlation Coefficient?A statistical measure called correlation shows how much two or more variables fluctuate in connection to one another.
A correlation coefficient is a statistical indicator of how well changes in one variable's value predict changes in another. When two variables are positively linked, the value either rises or falls together.
Given:
Correlation Coefficient = -0.12
As, The range of a correlation coefficient ranges from -1 to 1.
When the number is closer to -1 or closer to 1, there is a substantial association, and when the number is closer to 0, there is no link.
The correlation coefficient in this instance is -0.12, indicating a marginally negative correlation. The negative sign indicates that when one component changes, the other decreases, making a baby that is taller and lighter.
Hence, The taller the baby, the lighter the baby.
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Which of the following is a property of an isosceles trapezoid? Choose ALL that apply.
Four right angles
Two pairs of parallel sides
Diagonals are congruent
Diagonals are perpendicular
Answers
The property of an isosceles trapezoid is that the diagonals are congruent. That is option C.
What is an isosceles trapezoid?An isosceles trapezoid is defined as the type of quadrilateral whereby line of symmetry bisects one pair of opposite sides.
The unique characteristics of an isosceles trapezoid include the following:
Only one pair of sides are parallel. Non-parallel sides (legs) are equal in measure.The diagonals are equal in measure. The base angles are equal in measure. The opposite angles are supplementary.Therefore, the property of an isosceles trapezoid that is listed above is that Diagonals are congruent which means that they are equal.
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The properties of isosceles trapezoid are
Two pairs of parallel sides
Two pairs of parallel sides
What are features of Isosceles trapezoid?An isosceles trapezoid has left and right sides that are equal in length or identical in length, therefore the base angles are also equal.
The diagonals are identical because the lengths of the left and right sides are equal and the base angles are equal.
Additional varieties of trapezoids include
There are two right angles on the right trapezoid.It is an isosceles trapezoid because its parallel and non parallel sides are of the same length.It is a scalene trapezoid since neither its angles nor its sides are equal.Generally, all trapezoids have two parallel sides.
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