Answer:
The correct answer is option D: 4x² - 13x + 3.
Step-by-step explanation:
To expand the expression (4x - 1)(x - 3), we use the distributive property of multiplication.
Let's multiply each term of the first expression (4x - 1) by each term of the second expression (x - 3):
(4x - 1)(x - 3) = 4x(x) - 4x(3) - 1(x) - 1(-3)
Now, simplify each term:
= 4x^2 - 12x - x + 3
Combining like terms:
= 4x^2 - 13x + 3
Therefore, the expanded form of (4x - 1)(x - 3) is 4x^2 - 13x + 3.
The correct answer is option D: 4x² - 13x + 3.
a graph that uses images to symbolize the data that appears on the graph is known as a
A graph that uses images to symbolize the data that appears on the graph is known as a pictograph.
A pictograph is a type of chart that represents data using images or symbols. Each symbol on the pictograph represents a specific quantity, and the quantity is determined by the number of times the symbol appears on the chart. Pictographs are used to present data in a visually appealing and easy-to-understand manner, especially when the data is complex or there are multiple variables involved. Pictographs can be useful for a wide range of applications, from presenting sales figures to illustrating demographic information. They are often used in advertising, marketing, and educational materials to make data more engaging and memorable.
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In the parallelogram above, if DH = 13, find the length of DF.
Type your answer...
it will be 26 cm as diagonals bisect each other
Please help with this i need this quick
Answer:
x = 11.0
Step-by-step explanation:
Since this is a right triangle, we can find the measure of x using one of the trigonometric ratios.
If we allow ∠A to represent the reference angle, we see that BC is the opposite side and AB is the hypotenuse. Thus, we can use the sine ratio, which is sin (reference angle) = opposite/hypotenuse.We can plug in everything into the sine ratio and solve for x:sin (27) = BC / AB
sin (27) = 5 / x
x * sin (27) = 5
x = 5 / sin (27)
x = 11.01344632
x = 11.0
Given the functions f(x) = 2x −1 and g(x) = 2x + 4, which operation results in the largest coefficient on the x term? (1 point)
Addition
Subtraction
Multiplication
Two operations result in the same coefficien
Answer:
The answer is Multiplication.
Step-by-step explanation:
The coefficient of the x term in f(x) is 2, and the coefficient of the x term in g(x) is 2. When we add or subtract the two functions, the coefficient of the x term remains 2. However, when we multiply the two functions, the coefficient of the x term becomes 4. Therefore, multiplication results in the largest coefficient on the x term.
Here is the solution for each of the operations:
Addition: f(x) + g(x) = (2x −1) + (2x + 4) = 4x + 3
Subtraction: f(x) - g(x) = (2x −1) - (2x + 4) = -5
Multiplication: f(x) * g(x) = (2x −1) * (2x + 4) = 4x^2 + 6x - 4
As you can see, the coefficient of the x term in f(x) * g(x) is 4, which is larger than the coefficients of the x terms in f(x) + g(x) and f(x) - g(x). Therefore, multiplication results in the largest coefficient on the x term.
Compare the rates of change of the following items.
y = 0.6z
6
8
00
2
4
OB. The rate of change of item I is equal to the rate of change of item II.
I
II
OA. The rate of change of item II is greater than the rate of change of item I
y
OC. The rate of change of item I is greater than the rate of change of item II
0.6
1.2
1.8
2.4
The rate of change of item I is greater than the rate of change of item II
The rate of change of item I is 0.6
Let us find the rate of change of item II
Rate of change = 1.2-0.6/4-2
=0.6/2
=0.3
So rate of change of item II is 0.3 which is lesser than rate of change of I
the rate of change of item I is greater than the rate of change of item II
Hence, the rate of change of item I is greater than the rate of change of item II
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4. a) Verify that DEF is a right triangle.
E(-2, 2)
D(1,4)
F(3,1)
b) Describe another method that you could
use to answer part a).
Answer:To verify whether triangle DEF is a right triangle, we can use the slope formula and the perpendicularity criterion.
a) Verification of DEF as a right triangle:
Calculate the slopes of the two sides:
Slope of DE = (y2 - y1) / (x2 - x1) = (4 - 2) / (1 - (-2)) = 2 / 3
Slope of EF = (y2 - y1) / (x2 - x1) = (1 - 2) / (3 - (-2)) = -1 / 5
Check if the product of the slopes is -1 (perpendicular lines):
(Slope of DE) * (Slope of EF) = (2 / 3) * (-1 / 5) = -2 / 15
Since the product of the slopes is not -1, the sides DE and EF are not perpendicular. Therefore, triangle DEF is not a right triangle.
b) Another method to determine if triangle DEF is a right triangle:
Another method to answer part a) is by calculating the lengths of the three sides DE, EF, and DF. Then, we can check if the Pythagorean theorem holds true.
Calculate the lengths of the sides:
Length of DE = sqrt((x2 - x1)^2 + (y2 - y1)^2) = sqrt((1 - (-2))^2 + (4 - 2)^2) = sqrt(9 + 4) = sqrt(13)
Length of EF = sqrt((x2 - x1)^2 + (y2 - y1)^2) = sqrt((3 - 1)^2 + (1 - 4)^2) = sqrt(4 + 9) = sqrt(13)
Length of DF = sqrt((x2 - x1)^2 + (y2 - y1)^2) = sqrt((3 - (-2))^2 + (1 - 2)^2) = sqrt(25 + 1) = sqrt(26)
Apply the Pythagorean theorem:
If DF^2 = DE^2 + EF^2, then triangle DEF is a right triangle.
DF^2 = (sqrt(26))^2 = 26
DE^2 + EF^2 = (sqrt(13))^2 + (sqrt(13))^2 = 13 + 13 = 26
Since DF^2 equals DE^2 + EF^2, the Pythagorean theorem holds true, indicating that triangle DEF is a right triangle.
Therefore, the two methods of verification provide conflicting results. One method (using the perpendicularity criterion) suggests that DEF is not a right triangle, while the other method (using the Pythagorean theorem) suggests that it is a right triangle. In such cases, it is important to double-check the calculations and verify the accuracy of the given points to resolve the discrepancy.
Step-by-step explanation:
The distance required for an automobile to stop is directly proportional to the square of its velocity. If a car can stop in 1800 meters from a velocity of 30 kph, what will be the required distance at 28 kph?
Two angles, ∠A and ∠B, are complementary. If sin A = 4/7, what is cos B?
A. 74
B. 47
C. 37
D. √44/7
The Value of cos B is,
⇒ cos B = 0.64
We have to given that;
Two angles, ∠A and ∠B, are complementary.
And, sin A = 4/7
Now, We can simplify as;
sin A = 4/7
A = sin⁻¹ 4/7
A = 39.8°
Since, Two angles, ∠A and ∠B, are complementary.
Hence, We get;
∠A + ∠B = 90°
39.8° + ∠B = 90°
∠B = 90 - 39.8°
∠B = 50.2°
Thus, Value of cos B is,
⇒ cos B = cos 50.2° = 0.64
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Compute the following surface area.
A pyramid has base edges that measure 6 meters, and a slant height of 7.5 meters. What is its surface area?
__________sq. meters
Answer:
126 sq metres
Step-by-step explanation:
area of triangle = 0.5 X base length X height
surface area = base square + 4 (triangles)
= (6X6) + 4(0.5 X 6 X 7.5)
= 36 + 4(22.5)
= 36 + 90
= 126 (sq metres)
x and y intercept for x-2y=32
Answer:
The x-intercept is (32, 0),The y-intercept is (0, -16).------------------------
Set one variable to 0 and solve for the other.
For the x-intercept, set y = 0 and solve for x:
x - 2(0) = 32 x = 32For the y-intercept, set x = 0 and solve for y:
0 - 2y = 32 -2y = 32 y = -16The x-intercept is (32, 0) and the y-intercept is (0, -16).
Given the least squares regression equation, Ŷ = 1,202 + 1,133X, when X = 3, what does Ŷ equal?
Multiple Choice
a.5,734
b.8,000
c.4,601
d.4,050
when X = 3, Ŷ equals 4,601. The correct answer is (c) 4,601.
If the least squares regression equation is Ŷ = 1,202 + 1,133X, we can find the value of Ŷ when X = 3 by substituting X = 3 into the equation and solving for Ŷ:
Ŷ = 1,202 + 1,133(3)
Ŷ = 1,202 + 3,399
Ŷ = 4,601
what is equation?
An equation is a mathematical statement that shows that two expressions are equal. It typically consists of two sides separated by an equals sign (=). The expressions on either side of the equals sign can be numbers, variables, or combinations of both, connected by arithmetic operations such as addition, subtraction, multiplication, and division, as well as more advanced operations such as exponents, logarithms, and trigonometric functions.
An equation can be either true or false, depending on the values of the variables and constants involved. Equations are used in a wide variety of mathematical contexts, from basic arithmetic to advanced calculus, physics, and engineering.
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the slope of line that passes through the points (20,30) and (40,14) is
a) -5/4
b) -4/5
c) 4/5
d) 5/4
Answer:
B
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (20, 30 ) and (x₂, y₂ ) = (40, 14 )
m = [tex]\frac{14-30}{40-20}[/tex] = [tex]\frac{-16}{20}[/tex] = - [tex]\frac{4}{5}[/tex]
In California, each automobile license plate consists of a single digit followed by three letters, followed by three digits. How many distinct license plates can be formed if the first number cannot be zero and the three letters cannot form "DOG"?
Answer: How many distinct license plates can be formed if the first number cannot be zero and the three letters cannot form "DOG"?
Step-by-step explanation:
Since the first digit cannot be 0, there are 9 choices for the first digit.
For the three letters, there are 26 choices for the first letter, 26 choices for the second letter, and 25 choices for the third letter (since we cannot use "D", "O", or "G").
For the last three digits, there are 10 choices for each digit.
Therefore, the total number of distinct license plates can be formed is:
9 x 26 x 26 x 25 x 10 x 10 x 10 = 16,290,000
So there are 16,290,000 distinct license plates that can be formed if the first number cannot be zero and the three letters cannot form "DOG".
{I Hope This Helps! :)}
Triangle ABC has vertices at A(−3, 3), B(0, 4), and C(−3 , 0). Determine the coordinates of the vertices for the image if the preimage is translated 4 units down. A′(−3, −1), B′(0, 0), C′(−3, −4) A′(−3, 7), B′(0, 8), C′(−3, 4) A′(−7, 3), B′(−4, 4), C′(−7, 0) A′(1, 3), B′(4, 4), C′(1, 0)
The answer is correct, we can plot both triangles on a Coordinate plane and visually inspect the result. If we plot triangle ABC with vertices A(-3, 3), B(0, 4), and C(-3, 0), and then plot the image triangle A'B'C' with vertices A'(-3, -1), B'(0, 0), and C'(-3, -4), we can see that the image is a translation of the original triangle down by 4 units.
To determine the coordinates of the vertices of the image of triangle ABC after being translated 4 units down, we need to subtract 4 from the y-coordinates of each vertex. This is because a translation is a type of transformation that moves each point of a figure a certain distance in a certain direction.
So, starting with the preimage of triangle ABC with vertices at A(-3, 3), B(0, 4), and C(-3, 0), we can find the image by subtracting 4 from the y-coordinates:
A'(-3, 3 - 4) = A'(-3, -1)
B'(0, 4 - 4) = B'(0, 0)
C'(-3, 0 - 4) = C'(-3, -4)
Therefore, the coordinates of the vertices for the image after the translation are A'(-3, -1), B'(0, 0), and C'(-3, -4).
So, the correct option is A) A′(−3, −1), B′(0, 0), C′(−3, −4).
To check if the answer is correct, we can plot both triangles on a coordinate plane and visually inspect the result. If we plot triangle ABC with vertices A(-3, 3), B(0, 4), and C(-3, 0), and then plot the image triangle A'B'C' with vertices A'(-3, -1), B'(0, 0), and C'(-3, -4), we can see that the image is a translation of the original triangle down by 4 units.
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Express each of the following as a rational number: 7/12 - 5/6 + 1/8 - 5/8
Answer:
The answer is -0.75
Step-by-step explanation:
7/12-5/6+1/8-5/8
find Lcm of 12 and 8 is 24
7/12-5/6+1/8-5/8
-------------------------
24
2(7)-4(5)+3(1)-3(5)
-------------------------
24
14-20+3-15
-----------------
24
= -18
-----
24
=-3/4
= -0.75
PLEASE HURRY!! Which angle is adjacent to DFE
The adjacent angle is BFD.
We are given to find the adjacent angle to angle DFE in the figure.
The two angles that have a common vertex and a common side are called adjacent angles.
We can see that angles DFE and AFB have a common vertex F but they do not have a common side. So, the angles are not adjacent.
We can see that angles DFE and AFC have a common vertex F but they do not have a common side. So, the angles are not adjacent.
We can see that angles DFE and BFD have a common vertex F and a common side FD. So, the angles are adjacent.
Hence,
∠BFD adjacent angle.
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The solution is (-6,0). Which statement best describes the flaw in David's reasoning? (В D David's answer is correct, but he should have graphed the lines. David's answer for x should be 0 because x - x (in line two of his work) is 0. David should have stopped when he calculated -6=-6. This means there are no solutions because the slopes are equal. David should have stopped when he calculated -6=-6. This means there are an infinite number of solutions because it is a true statement.
Answer:
Step-by-step explanation:
the anser is 16
Answer all these questions for ratio and rate
1. We can buy 15 cans of green beans for $10.
2. The jet could fly 959 miles in 7 hours at same speed.
3. Its take 4 days for the car manufacturer to produce 800 cars.
How many cans can be bought for $10?A proportion refers to an equation in which two ratios are set equal to each other.
To get how many cans of green beans you can buy for $10, we will set up a proportion:
9 cans / $6 = x cans / $10
By cross-multiplying, we get:
9*($10) = 6x
90 = 6x
x = 90 / 6
x = 15.
2. To get distance the jet can fly in 7 hours, we will use [tex]Distance = rate * time[/tex]
Rate = Distance / Time
Rate = 548 miles / 4 hours
Rate = 137 miles per hour
Now we will it to get how far the jet could fly in 7 hours:
Distance = Rate × Time
Distance = 137 miles per hour × 7 hours
Distance = 959 miles.
3. We will set up a proiportion.
1400 cars / 1 week = 800 cars / x days
To solve for x, we cross-multiply and divide
1400 * x = 800 * 7
1400x = 5600
x = 5600 / 1400
x = 4.
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The equation y = 5x + 50 shows the amount of money Emma has in her savings account. How much money will Emma have in her account after 30 weeks?
The amount of money that Emma would have in her account after 30 weeks is $200.
What is the slope-intercept form?In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;
y = mx + c
Where:
m represent the slope or rate of change.x and y are the points.c represent the y-intercept or initial value.Based on the information provided above, a linear equation that models the amount of money Emma has in her savings account is given by;
y = mx + c
y = 5x + 50
By substituting the given parameter (x = 30 weeks), we have the following:
y = 5(30) + 50
y = $200
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Using the slope-intercept form of the linear equation, the amount in her account after 30 weeks is $200
What is a linear equation?An equation that has the highest degree of 1 is known as a linear equation. This means that no variable in a linear equation has a variable whose exponent is more than 1.
In this problem, we are given an equation in the slope- intercept form and which is represented as y = mx + c
In the given equation;
y = 5x + 50
x = number of weeksThe amount in her account after 30 weeks is calculated as;
y = 5(30) + 50
y = 200
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Select the true statement about trend lines.
A. The distance between each point and the line is always the same.
B. The distance from the points to the line should be as small as
possible.
OC. A trend line connects the points.
D. A trend line goes through the first and last points.
The true statement about trend lines include the following: B. The distance from the points to the line should be as small as possible.
What is a trend line?In Mathematics and Statistics, a trend line is sometimes referred to as a line of best fit and it can be defined as a statistical tool which is commonly used in conjunction with a scatter plot, in order to determine whether or not there's any form of correlation (either positive or negative) between a given data.
Generally speaking, the line of best fit or trend line should be very close to the data points as much as possible. This ultimately implies that, a characteristics of a trend line is that the distance from each of the data points to the line must be as small as possible i.e closer to the line.
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one way of solving systems of linear equations is by adding a multiple of one equation to the other. the multiplier for one equation is chosen so that one of the two variables will cancel out in the sum. what should you multiply the equation y
To eliminate one of the variables by adding a multiple of one equation to the other, you should multiply the equation containing the variable you want to eliminate by a suitable multiplier.
Let's assume you want to eliminate the variable y. In this case, you should multiply the equation containing y by a multiplier that will make the coefficient of y in one equation equal to the negative coefficient of y in the other equation. This will ensure that when you add the two equations, the y terms will cancel out.
For example, if the equation you want to eliminate y from is 2x + 3y = 7, and the other equation is 4x + 5y = 9, you would multiply the first equation by -5 and the second equation by 3 to obtain:
-5(2x + 3y) = -5(7) (equation 1 multiplied by -5)
3(4x + 5y) = 3(9) (equation 2 multiplied by 3)
This will result in:
-10x - 15y = -35 (equation 1 after multiplication)
12x + 15y = 27 (equation 2 after multiplication)
Now, when you add the two equations, the y terms will cancel out, and you can solve for the remaining variable x.
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Question 18
YARDWORK Each week Imani and Demond must mow their 4-acre yard. When they use both their 36-inch mower and 42-inch mower, it
takes them 2 hours. When the 36-inch mower is out for repairs, it takes them 3 hours. How long would the job take if the 42-inch mower
were broken?
Answer:
6/12
Step-by-step explanation:
this is because if you do the math it is 6/12
let $s$ be a subset of $\{1,2,3,...,50\}$ such that no pair of distinct elements in $s$ has a sum divisible by $7$. what is the maximum number of elements in $s$?
The maximum number of elements in $s$ is $\boxed{7}$, which we can achieve by choosing one element from each of the residue classes modulo $7$.
To find the maximum number of elements in $s$, we need to consider the elements of $\{1,2,3,...,50\}$ that are congruent to each residue class modulo $7$. There are seven residue classes modulo $7$, namely $\{0,1,2,3,4,5,6\}$. Since the sum of two elements from the same residue class modulo $7$ will also be in the same residue class modulo $7$, we cannot include more than one element from each residue class in $s$.
We can include one element from the residue class $0$, which gives us one element. For the other six residue classes, we can choose at most one element from each of them without violating the condition that no pair of distinct elements in $s$ has a sum divisible by $7$. This gives us a total of $1+6=7$ elements in $s$.
Therefore, the maximum number of elements in $s$ is $\boxed{7}$, which we can achieve by choosing one element from each of the residue classes modulo $7$.
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paperback books cost a total of $. How much change will Prakash get if he buys 3 hardcover books and 5 paperback books, and gives the clerk $20 bills?
If the cost of one paperback book is less than $1, he would receive even more change.
To solve this problem, we need to know the cost of one paperback book. Unfortunately, that information is missing from the question. Without it, we cannot determine the total cost of the 5 paperback books and therefore cannot calculate Prakash's change.
However, we can make an educated guess based on the fact that the question mentions both paperback and hardcover books. Typically, hardcover books are more expensive than paperbacks, so we can assume that the cost of one paperback book is less than the cost of one hardcover book.
Assuming that each hardcover book costs $10, the total cost of 3 hardcover books would be $30. If Prakash gives the clerk $20 bills, he would pay $60 in total. If we subtract the cost of the 3 hardcover books ($30) from the total amount paid ($60), we are left with $30.
This is the maximum amount of change Prakash could receive if each paperback book costs $1.
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3.1 Complete the following statements so that they are true: 3.1.1The angle between the tangent and chord is ... 3.1.2Opposite angles of a cyclic quadrilateral are ... 3.2In the diagram below, two circles have a common tangent TAB. PT is a tangent to the smaller circle. PAQ, QRT and NAR are straight lines. Let Q = 40°. N B 40° 3.2.1 Determine, with reasons, THREE other angles equal to 40°. 3.2.2 If P₁= A4 prove that PTRN is a parallelogram.
a circle has radius 16 units and a central angle that defines an arc with length . a second circle has radius 5 units and a central angle that defines an arc with length . how do the measures of the 2 angles compare? explain or show your reasoning..
In this problem, we have two circles with different radii and central angles defining arcs with specific lengths. We are asked to compare the measures of the two central angles.
Recall that the length of an arc (arc length) can be calculated using the formula: Arc Length = Radius × Central Angle (in radians). To compare the measures of the central angles, we'll first rearrange the formula to solve for the central angle: Central Angle = Arc Length / Radius.
For the first circle with radius 16 units and an arc length, let's denote the central angle as θ₁. Thus, θ₁ = Arc Length₁ / 16.
For the second circle with radius 5 units and an arc length, let's denote the central angle as θ₂. Therefore, θ₂ = Arc Length₂ / 5.
To compare the central angles θ₁ and θ₂, we can use the ratios of the respective arc lengths and radii. If the ratio of Arc Length₁ to Arc Length₂ is the same as the ratio of 16 to 5, then the central angles are equal. If the ratio is greater, then θ₁ is greater than θ₂, and if the ratio is smaller, then θ₁ is smaller than θ₂.
Without the specific arc lengths, we cannot determine the exact relationship between the central angles, but this method can be used to compare them once the arc lengths are provided.
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Please HELPP!!!!! I badly need this. Math, Geometry, circle unit.
Answer:
36 π and 12 π respectively.
Step-by-step explanation:
To find the area of a circle, we do πr^2. For circumference, we do 2πr, where r is the radius. Since we know the diameter of this circle is 12, and we know the radius is half the diameter, then:
12/2 = 6 = r
knowing r, we can find out the area and the circumference. The area is:
πr^2 = π 6^2, so it is 36π for the area. The circumference is:
2πr = 2 π 6 = 12π.
Brainlest and 10 points!!!!!!!!!
Answer:
1. Yes, 90+45+45=180
2. Yes, adds to 180
3. No
4. No
Step-by-step explanation:
suppose at a certain college we know 80% of the students like chipotle and 65% of the students like papa john's pizza. moreover, of the students that like chipotle we know 69% like papa john's pizza. suppose we randomly select a student. what is the probability that a student likes papa john's, given they do not like chipotle?
Therefore, the probability that a student likes papa john's given they do not like chipotle is approximately 0.275 or 27.5%.
Bayes' theorem allows us to calculate conditional probabilities, which is the probability of an event occurring given that another event has already occurred. In this case, we want to find the probability that a student likes Papa John's pizza given that they do not like Chipotle.
We start by using the given probabilities to calculate the probability that a student does not like Chipotle, which is the complement of the probability that they do like Chipotle. Then, we calculate the probability that a student likes both Papa John's and Chipotle, and use this to find the probability that a student likes Papa John's given that they do not like Chipotle.
Bayes' theorem is a powerful tool that is used in a wide range of fields, including statistics, probability theory, and machine learning. It provides a systematic way to update probabilities based on new information or evidence, which is a crucial aspect of many real-world applications.
P(B) = 1 - 0.8 = 0.2 (the probability that a student does not like chipotle)
P(A|B) = P(A and B) / P(B) = (0.65 - 0.69*0.8) / 0.2 ≈ 0.275
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Find the value of x in the trapezoid below.
C
A
B
X
79° D
x = [?]°
The value of x in the trapezoid that is shown above is calculated as:
x = 101°.
How to Find the value of x in the Trapezoid?The trapezoid in the image shown is an isosceles trapezoid because the two lower base angles are indicated to be congruent to each other, therefore, any of the lower base angle and upper base angle would be supplementary or have a sum of 180 degrees when added together.
Given that angle A and angle D are congruent, therefore:
m<A = 79 degrees.
m<A + m<B = 180 [supplementary angles]
79 + x = 180
x = 180 - 79
x = 101°
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