Answer:
Step-by-step explanation:
Let f(x) = 4x + 3 and g(x)=x²-x+1. Perform the function operation and then find the domain.
g(x)-f(x)
g(x)-f(x) = (Simplify your answer.)
The domain of g(x) - f(x) is all real numbers, or (-∞, ∞).
What is the domain?
The domain of a function is the set of all possible input values (x-values) for which the function is defined and produces a valid output (y-value). In other words, it is the set of values for which the function is valid and can be used without producing any errors or undefined results.
To perform the function operation g(x) - f(x), we need to subtract the function f(x) from the function g(x).
g(x) = x² - x + 1
f(x) = 4x + 3
g(x) - f(x) = x² - x + 1 - (4x + 3)
g(x) - f(x) = x² - 5x - 2
The domain of a function is the set of all possible input values (x-values) for which the function is defined and produces a valid output (y-value).
For the function g(x) - f(x) = x² - 5x - 2, there are no restrictions on the input values, meaning that any value of x can be plugged into the function to produce a valid output.
Therefore, the domain of g(x) - f(x) is all real numbers, or (-∞, ∞).
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The function y = f (x) is graphed below. What is the average rate of change of the function f(x) on the interval - 1 ≤ x ≤ 3?
For the function y = f (x), the average rate of change on the interval - 1 ≤ x ≤ 3 is -2.
What is a function?
In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.
The graph of the function f(x) is graphed and the graph is given.
The average rate of change is a measure of how much the function changed per unit, on average, over that interval.
For a function f(x) at interval [a,b], the average rate of change is given as -
[f(b) - f(a)]/(b - a)
The interval values is given as - [-1,3]
The value for f(a) as seen in the graph is - 4.
The value for f(b) as seen in the graph is - -4.
Substitute the values in the equation -
Average rate of change = [f(b) - f(a)]/(b - a)
A = (-4 - 4)/[3 - (-1)]
A = -8/(3 + 1)
A = -8/4
A = -2
Therefore, the value for average rate of change is -2.
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A representative sample is one that accurately reflects a larger a) control group. Correct Response b) population. c) correlation coefficient. d) dependent variable.
The statement would e: A representative sample is one that accurately reflects a larger population.
The correct answer is an option (b)
We know that the sampling is used to find insights and observations about a population group.
A representative sample is nothing but a sample / a subset of a population that accurately reflect the characteristics of the larger group.
For example, consider a class of 50 students with 25 girls and 25 boys.
We can generate a representative sample that might include ten students: five girls and five boys.
As we know the samples contain smaller, manageable versions of the larger group, they are useful in statistical analysis when population size is large.
Thus, a representative sample is used for obtaining insights and observations of the targeted population group.
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The complete question is:
A representative sample is one that accurately reflects a larger
a. dependent variable.
b. population.
c. control group.
d. correlation coefficient.
The area of this rectangle is at most 400 square centimeters, Write and solve an inequality to represent the possible values for the height, h, for this triangle. Show all steps of your work.
16cm h
An inequality to represent the possible values for the height, h, for this triangle is 1ft≤h≤25ft
The area of a rectangle is expressed as;
Area = Length * height
A = Lh
If the area of a rectangle is at most 400 square centimeters, this is expressed as;
A ≤400
≤ means at most that the area of the rectangle cannot be greater than 400
Substitute the given value into the inequality expression
Lh ≤ 400
Given
L = 16
16h ≤ 400
Divide both sides by 16
16h/16 ≤ 400/16
h ≤ 400/16
h ≤ 25
Hence the possible values of the height are within the range 1ft≤h≤25ft since we cannot have a negative value for the dimension.
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If the playing surface of a carom bored is a square of length 28 inches, what is the diagonal length of the playing surface?
Answer:
To find the diagonal length, you can use the Pythagorean theorem.
If one side is 28 inches, and the board is a square, the other side must also be 28 inches.
a = side 1
b = side 2
c = diagonal length
a^2 + b^2 = c^2
(28)^2 + (28)^2 = c^2
784 + 784 = c^2
1568 = c^2
Square root both sides.
c = about 39.6 inches diagonal length
cathy has obtained a sample mean of 0.7 and , but she cannot remember if the sample size was 20 or 25. she accidentally erased the data file. find the correct sample size.
The sample size of the data which has a sample mean of 0.7 is 20.
What is mean?
Mean is a measurement of a probability distribution's central tendency along the median and mode. It also goes by the name "anticipated value."
Given:
Cathy has obtained a sample mean of 0. 7 and, but she cannot remember if the sample size was 20 or 25,
Calculate the sample size as shown below,
As we know that the variance would be positive,
s² ≥ 1 / (n - 1) [Σ xi²-nx²]
0 ≥ 1 / (n - 1) [Σ xi²-nx²]
[10 - n × x × 0.7²] ≥ 0
n × x × 0.7² ≤ 10
n ≤ 10 / (0.7)²
n ≤ 20.408
Thus, the sample size is 20.
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At the local Convenience store William and Sarah are getting snacks for the friends. William buys 3 soft drinks and 2 hot dogs at a cost of $7. 70, while Sarah buys 2 soft drinks and 1 hot dog at cost of $ 4. 55.
Find the cost of 1 soft drink and 1 hot dog.
If at local Convenience store , William buys 3 soft drinks and 2 hot dogs for $7.70, while Sarah buys 2 soft drinks and 1 hot dog at cost of $4.55 , then the cost of 1 soft drink is $1.4 and cost of 1 hot dog is $1.75 .
We will use system of equations to find cost of 1 soft drink and 1 hot dog. let the cost of 1 soft drink is = $x ; and
let the cost of 1 hot dog is = $y ;
So , for William the situation is represented as ;
⇒ 3x + 2y = 7.70 .....equation(1)
and for Sarah the situation is represented as ;
⇒ 2x + y = 4.55 ....equation(2)
we first solve equation(1) for y:
⇒ y = (7.70 - 3x)/2
We can substitute this expression for y in equation (2) and solve for x:
⇒ 2x + (7.70 - 3x)/2 = 4.55
⇒ 4x + (7.70 - 3x) = 4.55×2
⇒ 4x -3x = 9.1 - 7.70
⇒ x = 1.4
So, the cost of 1 soft drink is $1.4 ,
Now , We can use this value of x to find the cost of 1 hot dog:
⇒ y = (7.70 - 3x)/2
⇒ y = (7.70 - 3×1.4)/2
⇒ y = (7.70 - 4.2)/2
⇒ y = 3.5/2 ;
⇒ y = 1.75
So, the cost of 1 hot dog is $1.75 .
Therefore, one soft drink costs $1.4 and one hot dog costs $1.75 .
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Graph the solution to this inequality on the number line.
−4x≥12
Answer:
Solution set for x is x ≤ -3
First option
Step-by-step explanation:
We have the equation
- 4x ≥ 12
Divide both sides by 4:
- x ≥ 12/4
-x ≥ 3
Multiply by -1 to make x positive. When we multiply an inequality by a negative number the inequality sign changes: ≥ becomes ≤
Therefore we get
x ≤ 3
On the number line this is represented by the first choice
Note that the 3rd and 4th choices are easily eliminate since they represent ≥ -3 and > -3
Choice #2 has an unfilled circle at -3. This represents a < inequality
A filled circle represents a ≤ inequality
Answer
Solution set for x is x ≤ -3
First option
pls help me with this equation
In contrast to the pair of following two triangles, the initial two triangles do not share any similarities.
What is meant by similar triangles?Two triangles are considered to be similar if the corresponding sides are proportionate and the corresponding angles are congruent. Or to put it another way, comparable triangles may not necessarily be the same size but they do have a similar shape. The triangles are also congruent if the lengths of their respective sides are the same.
We already know that the ratio of the two triangles' corresponding sides must match for them to be identical triangles.
A.) In the first pair of triangles,
The first pair of triangles to be similar,
[tex]$\frac{U S}{U D}=\frac{U T}{U E}=\frac{S T}{D E}$$[/tex]
The aforementioned ratio ought to be comparable, however as we can see,
[tex]$$\begin{aligned}& \frac{U S}{U D} \neq \frac{U T}{U E} \\& \frac{39}{16} \neq \frac{40}{16}\end{aligned}$$[/tex]
The two triangles supplied are not identical triangles because, as we can see, the ratio of the triangle's sides is not the same.
B.) In the second pair of triangles,
The second pair of triangles to be similar,
[tex]$\frac{A B}{H G}=\frac{B C}{G F}=\frac{C A}{F H}$$[/tex]
As we can see, the ratio should be comparable to the one above.
[tex]$\frac{72}{12}=\frac{48}{8}=\frac{84}{14}=6$$[/tex]
The two triangles supplied are similar triangles because, as we can see, the ratio of the triangle's sides is the same.
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for how many values of the constant k will the polynomial x2 kx 36 have two distinct integer roots?
There are 2 values of k, 12 and -12, for which the polynomial x^2 + kx - 36 has two distinct integer roots.
The polynomial x^2 + kx - 36 has two distinct integer roots if and only if its discriminant is a perfect square.
The value of the discriminant is given by:
b^2 - 4ac = k^2 + 4 * 36 = k^2 + 144
So, for the polynomial x^2 + kx - 36 to have two distinct integer roots, k^2 + 144 must be a perfect square.
We know that the difference of two consecutive perfect squares is equal to an odd number, so we can start testing values of k by incrementing k by 1 and checking if k^2 + 144 is a perfect square.
Starting with k = 0, we have k^2 + 144 = 144, which is not a perfect square. For k = 1, k^2 + 144 = 145, which is also not a perfect square.
For k = 2, k^2 + 144 = 148, which is still not a perfect square.
We keep incrementing k and checking until we find a value of k such that k^2 + 144 is a perfect square.
When k = 12, we have k^2 + 144 = 168, which is a perfect square (12^2).
Therefore, the polynomial x^2 + 12x - 36 has two distinct integer roots.
We can repeat this process for negative values of k to see if the polynomial has two distinct integer roots for those values.
We find that for k = -12, the polynomial x^2 - 12x - 36 also has two distinct integer roots.
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Brittany opened a checking account with $50 she received for her birthday. She deposits $5 of her allowance each week.
the coordinates of three points are (2, 2), (4, 2), and (3, 3). what is the area of the triangle formed by connecting these three points?
The area of the triangle formed by connecting the three points is 6 square units. The result is obtained by using the determinant method.
How to find the area of a triangle in coordinate geometry?The area of a triangle in coordinate geometry can be found by using the determinant formula.
[tex]Area \: of \: triangle = \frac{1}{2} \left[\begin{array}{ccc}x_{1}&y_{1}&1\\x_{2}&y_{2}&1\\x_{3}&y_{3}&1\end{array}\right][/tex]
The three points of a triangle are:
(x₁, y₁) = (2, 2)(x₂, y₂) = (4, 2)(x₃, y₃) = (3, 3)Using the determinant formula, the area of the triangle is
[tex]= \frac{1}{2} \left[\begin{array}{ccc}2&2&1\\4&2&1\\3&3&1\end{array}\right][/tex]
= ½ |2(2-(3)) - 4(2-(3)) + 3(2-2)|
= ½ |2(-6) - 4(-6) + 0|
= ½ |-12 + 24|
= ½ |12|
= 6 square units
Hence, the area of the triangle is 6 square units.
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a swimming pool can be filled using either a pipe, a hose, or both. using the pipe alone it takes 12 hours. using both it takes 8 4/7 hours. how long does it take using the hose alone?
It takes 30 hours using the hose alone to fill the swimming pool.
How to add and subtract fractions?Step 1: Make denominators the same
Step 2: Add or Subtract the numerators (keeping the denominator the same)
Step 3: Simplify the fraction
To add or subtract unlike fractions, the first step is to make denominators the same so that numerators can be added just like we do for like fractions.
Let [tex]x\\[/tex] represent the swimming pool be filled with hose alone.
Given that using the pipe alone it takes 12 hours. using both it takes 8 4/7 hours. According to given condition,
[tex]\frac{1}{x} + \frac{1}{12} = \frac{1}{8\frac{4}{7} } \\\frac{1}{x} = \frac{1}{\frac{60}{7} } - \frac{1}{12}[/tex]
[tex]\frac{1}{x} = \frac{7}{60} - \frac{1}{12}\\\\ \frac{1}{x} = \frac{7}{60} - \frac{5}{60}\\\\\frac{1}{x} = \frac{2}{60}\\\\ x = \frac{60}{2}\\\\\\ x= 30[/tex]
It takes 30 hours using the hose alone to fill the swimming pool.
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You started a project on 9/29/2019. the project ended on 08/01/2022. how many working days did you have for the entire project?
a. 741 b. 1037 c. 1287 d. 832
To avoid using the variable "vi", which of the following equations should you use?
A) v² = v² + 2aAx
B) Ax = (v₁ + v₁)t
C) Vf = V₁ + at
D) Ax = vft – ⁄at²
In order to avoid using the variable "Vi", the equation which you should use include the following: D) Ax = Vft – 1/2at².
What is the second equation of motion?In Mathematics, the third equation of motion is represented by this mathematical expression:
Ax = Vit + ½at² ......equation 1.
Where:
Ax represents the distance travelled or covered.t represents the time.Vi represents the initial velocity.a represents the acceleration.From the first equation of motion, we have:
Vf = Vi + at
Making Vi the subject of formula, we have:
Vi = Vf - at ......equation 2.
Substituting the equation, we have:
Ax = (Vf - at)t + ½at²
Ax = Vft - at² + ½at²
Ax = Vft + ½at²
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Complete the stem-and-leaf plot of the data.
The stem-and-leaf plot for the data in this problem is given as follows:
0|5 8 91| 2 2 3 4 5 82|1 5.3|0.How to build the stem-and-leaf plot?The measures that are less than 10 are given as follows:
5, 8 and 9.
Hence they go on the plot as follows:
0|5 8 9
The measures that are between 10 and 19 are given as follows:
12, 12, 13, 14, 15, 18.
Hence they go on the plot as follows:
1| 2 2 3 4 5 8
The measures that are between 20 and 29 are given as follows:
21 and 25.
Hence they go on the plot as follows:
2|1 5.
The remaining measure is given as follows:
30.
Which goes on the plot as follows:
3|0.
Missing InformationThe problem is given by the image presented at the end of the answer.
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i need helppp
HELLPP!!!!!!!!!!!
√131 lies between 11 and 12.
What are whole numbers?The numbers that include natural numbers and zero are called whole numbers.
Given is the square root of 131.
We can write the square root of 131 as -
√131 = 11.45
We can write the whole numbers as -
11 < 11.45 < 12
Therefore, √131 lies between 11 and 12.
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Dan and Matt's ages add up to 56. Dan is 13 times older than Matt. How old are they?
Dan is 52 years old and Matt is 4 years old.
What are their ages?The first step is to form a system of equations using the information provided in the question:
a + b = 56 equation 1
a = 13b equation 2
Where:
a = Dan's age
b = Matt's age
The substitution method would be used to determine the values.
Substitute for a in equation 1 using equation 2:
13b + b = 56 equation 3
14b = 56
b = 56 / 14
b = 4
Substitute for b in equation 2:
a = 13(4)
a = 13 x 4
= 52
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can you answer this? please
[tex]55 \times 35 = [/tex]
On multiplying 55 × 35, the answer is 1925.
The simplest way to start teaching multiplication is to establish the relationship between the concept and addition, which your pupils should already be familiar with. Make sure your students understand the first principle of multiplication—that it is just repeated addition—before continuing on.
Your youngster can learn that multiplication is actually just a means to repeatedly add multiple groups of the same number by using objects like blocks and small toys. For instance, ask your youngster to arrange the blocks into six groups of three by writing the issue 6 x 3 on a sheet of paper.
5 5
× 3 5
------------
2 7 5
+ 1 6 5 ×
--------------
1925
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To make mango smoothie, Fritzi mixed some mango and water in the
ratio of 3:4. She made 2800 ml of such smoothie. How many milliliters of water
did she use? A. 1600 B. 1500 C. 1400 D. 1300
Please complete. Due today
3 (n+7)
Answer:
3(n+7) =
(3)(n) + (3)(7) =
3n + 21
Step-by-step explanation:
I hope this helps you :D
One angle of a triangle measures 35°. The other two angles are in a ratio of 10:19. What are the measures of those two angles?
95 and 50 are the measures of those two angles.
What are the properties of triangle?The properties of the triangle are: The sum of all the angles of a triangle (of all types) is equal to 180°. The sum of the length of the two sides of a triangle is greater than the length of the third side. In the same way, the difference between the two sides of a triangle is less than the length of the third side.
given, One angle of a triangle measures 35°. The other two angles are in a ratio of 10:19.
Let second angle of the triangle is "x"
Thus, third angle of triangle will be = 10/19x
Since, sum of the three angles of triangle is 180 degrees
35 + x + 10/19x = 180
29x/19 = 145
x = 5 *19
x = 95
So, Second angle of triangle = x = 95
Third angle of triangle = 10/19x = 50
therefore, the measures of those two angles are 95 and 50.
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In △feg , point h is between points e and f, point j is between points f and g, and hj¯¯¯¯¯∥eg¯¯¯¯¯ . eh=14 , hf=26 , and fg=60 . what is fj ? enter your answer in the box. fj =
The value of FJ is 39 units.
See the attached figure to better understand the problem
We know that
If two triangles are similar, then the ratio of their corresponding sides is proportional and their corresponding angles are congruent.
According to this problem,
△FEG is similar to △FHJ ( by AA Similarity Theorem)
so
[tex]\frac{FE}{FH} = \frac{FG}{FJ}[/tex]
We have,
FE = HF + EH = (26 + 14 ) units
FE= 40 units
FH = HF = 26 units
FG = 60 units
substitute the given values,
[tex]\frac{40}{26} = \frac{60}{FJ}[/tex]
[tex]FJ = \frac{26 * 60}{40}[/tex]
FJ = 39
So, the value of FJ is 39 units.
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NEW ASSESSMENT QUESTION:
BASIC EDUCATION CERTIFICATE
SECTION A: OBJECTIVES
1. Divide 2.646 by 0.9. Give your answer to 1
d.p.
On applying the arithmetic operation of division, the expression 2.646 / 0.9 gives a result of 2.9.
What is arithmetic operation?
A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.
The expression given is -
2.646 / 0.9
The expression is given in decimal form.
Use the arithmetic operation of division.
First remove the decimal points.
Multiply the numerator and denominator by 1000 as there are three decimal points in the numerator -
(2.646 × 1000) / (0.9 × 1000)
Now divide the expression -
2646 / 900
= 2.94
Rounding off to one decimal point gives 2.9.
Therefore, the value is obtained as 2.9.
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What is the value of 4.3x10^5
Answer: The value of 4.3x10^5 is 430000.
Step-by-step explanation:
To find the value of 4.3x10^5, you need to multiply 4.3 by 10 raised to the power of 5. This can be written as 4.310^5.
The value of 4.310^5 is 430000.
the graph of a twice-differentiable function f is shown below(in image). if f(2)=0, which of the following is true
A) f(2)
B) f’’(2)
C) f’(2)
D) f(2)
E)f’’(2)
Answer:
The correct answer is C f(2)
a study that surveyed a random sample of otherwise healthy high school students found that they are more likely to get muscle cramps when they are stressed. the study also noted that students drink more coffee and sleep less when they are stressed. (a) what type of study is this? observational experiment correct: your answer is correct. (b) can this study be used to conclude a causal relationship between increased stress and muscle cramps? yes no correct: your answer is correct. (c) state possible confounding variables that might explain the observed relationship between increased stress and muscle cramps. (select all that apply.) extra-curricular activities caffeine lack of sleep classes
This is because a survey of healthy high school students who were chosen at random revealed that stress is more likely to produce muscle cramps.
(a) What kind of research is this?
"Observational study" is the study's type.
Reason: This is because a survey of healthy high school students who were chosen at random revealed that stress is more likely to produce muscle cramps.
Can this data be used to draw a causal conclusion about the link between elevated stress levels and muscle cramps?
No, an observational study was unable to draw any conclusions about the link between elevated stress levels and muscle cramps. The Chi-square test can be used to determine the relationship between increasing stress and cramps.
(c) Describe any potential confounding factors that could account for the correlation between greater stress and muscle cramps.
Muscle cramps may be impacted by the increased stress.
In this case, the factors under consideration are qualitative variables. Count the number of times that high school students have visited a doctor with a muscular ailment.
Confounding factors for stress may include anxiety over taking the exam, less sleep, spending more time studying, eating less, drinking more coffee, and other factors.
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If EF=8, FD=10, ED=11, IG=24, and HG=26.4, find the perimeter of GHI. Round your answer to the nearest tenth if necessary. Figures are not easily drawn to scale.
The perimeter of the given figure is 79.4 units.
What is perimeter:The perimeter of a polygon is defined as the length of the boundary around the sides of the polygon. The perimeter of a polygon can be calculated by calculating the sum of the lengths of the sides of the polygon.
Perimeter of polygon = Sum of sidesHere we have
EF = 8, FD = 10, ED = 11, IG = 24, and HG = 26.4
As we know,
Perimeter = Sum of all sides
The perimeter of GHI = (EF + FD + ED + IG + HG)
= 8 + 10 + 11 + 24 + 26.4
= 79.4 units
Therefore,
The perimeter of the given figure is 79.4 units.
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Are the linear expressions equivalent? Select from the drop-down menus to correctly complete the statement. The expression 5(x−3)+1 Choose... to the expression 2+5x−16 .
The expression that would render the both the sides equivalent is 3x+2-2
What are like and unlike terms in an expression?In Algebra, the like terms are defined as the terms that contain the same variable which is raised to the same power. In algebraic like terms, only the numerical coefficients can vary. We can combine the like terms to simplify the algebraic expressions.
Given here: The expression 2+8x-16
To find its equivalent we have an incomplete expression 5(x-3)+1
Now 5(x-3)+1=5x-15+1
=5x-14
Thus Adding 3x+2-2 to this expression we get
5x-14+3x+2-2=2+8x-16
Therefore, we can deduce that the missing term must be 3x+2-2
Hence, The missing expression is 3x+2-2
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Which of the following are true about ALL parallelograms? Select each correct
answer.
a. Opposite sides are congruent.
b. Opposite sides are parallel.
c. Opposite angles are congruent.
d. The diagonals bisect each other.
e. The diagonals are congruent.
f. Consecutive angles are congruent.
g. Opposite angles are supplementary.
h. Consecutive angles are supplementary.
following are true about ALL parallelograms are:
a. Opposite sides are congruent.
c. Opposite angles are congruent.
d. The diagonals bisect each other.
h. Consecutive angles are supplementary.
What is parallelogram?
A parallelogram is a straightforward quadrilateral with two sets of parallel sides in Euclidean geometry. A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of similar size.
There are six crucial parallelogram characteristics to be aware of:
Congruent sides are those when AB = DC.Congruent opposite angels are D = B.Consecutive angles are supplementary.All angles are correct if just one of them is.A parallelogram's diagonals cut each other in half.A parallelogram's diagonals divide it into two congruent.A rhombus is what we have when all of the sides of a parallelogram are congruent. Rhombi can use the characteristics of parallelograms.
We have a quadrilateral that is referred to as a trapezoid if just one pair of its sides are parallel. While the nonparallel sides are referred to as legs, the parallel sides are known as bases. We have what is referred to as an isosceles trapezoid if the legs are congruent.
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