Prove that ABCD is a parallelogram. Given: segment AD and BC are congruent. Segment AD and BC are parallel.
Answers
We can conclude that ABCD is a parallelogram based on the given information and the congruence of corresponding parts of congruent triangles.
To prove that ABCD is a parallelogram, we need to show that both pairs of opposite sides are parallel.
Given the information that segment AD and BC are congruent and segment AD and BC are parallel, we can proceed with the following proof:
Since segment AD and BC are congruent, we can denote their lengths as AD = BC.
Now, let's assume that the lines AD and BC intersect at point E.
By definition, if AD is parallel to BC, then the alternate interior angles are congruent.
Let's label the alternate interior angles as ∠AED and ∠BEC.
Since AD is parallel to BC, we have ∠AED = ∠BEC.
Now, consider the triangle AED. In this triangle, we have:
∠AED + ∠A = 180° (sum of interior angles of a triangle).
Since ∠AED = ∠BEC, we can substitute to get:
∠BEC + ∠A = 180°.
But we also know that ∠A + ∠B = 180° (linear pair of angles).
Substituting this into the equation, we have:
∠BEC + ∠B = ∠BEC + ∠A.
By canceling ∠BEC on both sides, we get:
∠B = ∠A.
This shows that angle ∠A is congruent to angle ∠B.
Since angle ∠A is congruent to angle ∠B, and angle ∠AED is congruent to angle ∠BEC, we can conclude that triangle AED is congruent to triangle BEC by the angle-side-angle (ASA) postulate.
As a result, the corresponding sides of the congruent triangles are also congruent.
We have AE = BE (corresponding sides of congruent triangles) and AD = BC (given).
Now, considering the quadrilateral ABCD, we have two pairs of opposite sides that are congruent:
AD = BC and AE = BE.
Hence, we have shown that both pairs of opposite sides in ABCD are congruent, which is one of the properties of a parallelogram.
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Related Questions
f(x, m, s) = 1 √278² exp (-2/2 (x-m) ²) 28² Write a function in the form of gauss(x, m=0, s=1) for computing the Gaussian density. Compute the Gaussian density for the following cases. (a) x=0, m=0, s-1. Give the name of question5a (b) x-2, m=0, s-1. Give the name of question5b (c) x-0, m-2, s-1. Give the name of question5e (d) x=0, m=2, s=2. Give the name of question5d (e) x=3, m-3, s-3.
Answers
Compute the Gaussian density for the following cases. (a) x=0, m=0, s-1. Give the name of question5a (b) x-2, m=0, s-1. The value of the account on January 1, 2021, would be $2,331.57.
To calculate the value of the account on January 1, 2021, we need to consider the compounding interest for each year.
First, we calculate the value of the initial deposit after three years (12 quarters) using the formula for compound interest:
Principal = $1,000
Rate of interest per period = 8% / 4 = 2% per quarter
Number of periods = 12 quarters
Value after three years = Principal * (1 + Rate of interest per period)^(Number of periods)
= $1,000 * (1 + 0.02)^12
≈ $1,166.41
Next, we calculate the value of the additional $1,000 deposit made on January 1, 2019, after two years (8 quarters):
Principal = $1,000
Rate of interest per period = 2% per quarter
Number of periods = 8 quarters
Value after two years = Principal * (1 + Rate of interest per period)^(Number of periods)
= $1,000 * (1 + 0.02)^8
≈ $1,165.16
Finally, we add the two values to find the total value of the account on January 1, 2021:
Total value = Value after three years + Value after two years
≈ $1,166.41 + $1,165.16
≈ $2,331.57
Therefore, the value of the account on January 1, 2021, is approximately $2,331.57.
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Please help me, this is decimals
Answers
Answer:
79.12
Step-by-step explanation:
Answer:
The answer to 8.6 x 9.2 = 79.12
Which of the following is an example of a set of like terms? *
17y, 17, y
15x, -x, 33x
18, 21g, 24
-5x, -5xy, -5y
Answers
this is the correct answer because the numbers all have the same variable at the end
Discuss the downsizing process in your own words and provide an
example.
Answers
Downsizing refers to the process of reducing the size and workforce of a company to cut costs, increase efficiency, or adapt to changing market conditions. It involves eliminating positions, reducing staff numbers, or even closing down certain business units or branches.
Downsizing can occur for various reasons, such as financial difficulties, mergers and acquisitions, technological advancements, or strategic reorganization. Companies often assess their operational costs and decide to downsize to improve their financial performance.
During the downsizing process, companies may calculate the potential cost savings by considering factors such as salaries, benefits, severance packages, and operational expenses. For example, if a company decides to eliminate 100 positions with an average salary of $50,000 per year, it could result in annual savings of $5 million.
While downsizing can help companies achieve short-term cost reductions, it often has significant implications for the affected employees, including layoffs, reduced morale, and increased workload for remaining staff. It is crucial for organizations to handle the downsizing process with sensitivity and transparency, providing support to affected employees and communicating the rationale behind the decisions.
It is important to note that downsizing should not be seen as a long-term solution, but rather as a strategic measure to address specific challenges. Companies should also explore alternatives to downsizing, such as retraining and redeploying employees, implementing productivity improvements, or seeking new business opportunities, to ensure sustainable growth and success in the long run.
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why did the girl wear glasses during math class
Answers
Answer:
Because she found it improves division.
Step-by-step explanation:
Absolute change is the ______________ and relative change is the ______________.
Answers
Absolute change is the numerical difference between two values and relative change is the proportional difference between two values expressed as a percentage.
Absolute change is the numerical difference between two values and is typically expressed as a positive number. It tells us the amount by which a value has increased or decreased.
For example, if the temperature increases from 20 degrees Celsius to 25 degrees Celsius, the absolute change in temperature is 5 degrees Celsius.
Relative change, on the other hand, is the proportional difference between two values and is typically expressed as a percentage. It tells us the amount by which a value has increased or decreased relative to its original value.
For example, if the price of a product increases from $10 to $15, the relative change in price is 50%, because the increase of $5 is 50% of the original price of $10.
In summary, absolute change is the numerical difference between two values and relative change is the proportional difference between two values expressed as a percentage.
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if you were to implement y(2(t 1.5)) with a fixed time window, would it be better to scale first or shift first, or does it not matter?
Answers
Assuming that you want to implement a time window of fixed duration, it would be better to shift the function y first and then scale it. This is because shifting the function would align it with the time window and scaling it afterwards would adjust the amplitude of the function within the window.
If you were to scale the function first and then shift it, the alignment with the time window would be lost and the resulting function would not be accurate within the fixed duration. Therefore, shifting first and then scaling would give a more accurate representation of y(2(t-1.5)) within the fixed time window.
When implementing y(2(t - 1.5)) with a fixed time window, it is generally better to perform the scaling first, followed by the shift. This is because scaling affects the time duration, which may result in a more accurate representation within the fixed time window. After scaling, the shift can be applied to align the signal properly within the window. However, the final outcome may not be significantly different if you choose to shift first and then scale.
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can someone please help mee
Answers
\(\quad \huge \quad \quad \boxed{ \tt \:Answer }\)
\(\qquad \tt \rightarrow \:Domain : \fbox{-3}\leqslant x \leqslant \fbox{-1}\)
\(\qquad \tt \rightarrow \:Range :\:\:\fbox{-4}\leqslant x \leqslant \fbox{-3}\)
____________________________________
\( \large \tt Solution \: : \)
Domain = All possible values of x for which f(x) is defined
[ generally the extension of function in x - direction ]
Range = All possible values of f(x)
[ generally the extension of function in y - direction ]
\( \large\textsf{For the given graph : } \)
\(\qquad \tt \rightarrow \: domain : \fbox{-3}\leqslant x \leqslant \fbox{-1}\)
\(\qquad \tt \rightarrow \: range : \:\:\fbox{-4}\leqslant x \leqslant \fbox{-3}\)
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
When a number is doubled and then added to 13, the result is 38.
Find the number.
Answers
Answer:
The number is 12.5
Step-by-step explanation:
2x + 13 = 38
2x = 38 - 13
2x = 25
2x/2 = 25/2
x = 12.5
Check:
12.5 + 12.5 = 25
25 + 13 = 38
Patrons (P) Revenue (R)
32
480
500
550
750
33
40
60
81
1,215
Find a linear model for the data.
Answers
The linear model for the data is expressed as: R = 20p - 160.
How to Write a Linear Model?Using two pairs of values from the table values, say, (32, 480) and (33, 500), find the unit rate (m).
Unit rate (m) = (500 - 480)/(33 - 32) = 20/1
Unit rate (m) = 20.
Substitute (p, R) = (32, 480) and m = 20 into R = mp + b to find b
480 = 20(32) + b
480 = 640 + b
480 - 640 = b
b = -160
To write the linear model, substitute m = 20 and b = -160 into R = mp + b:
R = 20p - 160
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Is the relation a function? Why or why not?
{(–5, 7), (–2, –1), (0, 3), (4, 7)}
Yes; only one range value exists for each domain value.
No; two domain values exist for range value 7.
Yes; two domain values exist for range value 7.
No; the relation passes the vertical-line test.
Answers
Answer:
Since you can only have 1 output for the inputs, the correct answer would be A- only one range value exists for each domain value.
Step-by-step explanation:
Answer:
B. Yes; only one range value exists for each domain value.
Step-by-step explanation:
A relation is considered a function only if for each domain value (the values that x-variable takes) only one range value exists (the values that y-variable takes). In this case, the values taken by the x-variable are: -5, -2, 0 and 4; all in different points.
It doesn't matter that two domain values (or more) have the same range value.
Find the length of WT if W (-3,0) and T (3,-1). If a decimal round to the
hundredth place.
Answers
A model rocket is launched with an initial upward velocity of 202 ft/s. The rocket’s height h (in feet) after t seconds is given by the following.h=202t-16t^2Find the value of t for which the rocket’s height is 82 feet. Round your answers to the nearest hundredth
Answers
Solution:
Given:
\(h=202t-16t^2\)\(\begin{gathered} when\text{ the height is 82 feet,} \\ h=82 \\ \\ Hence, \\ h=202t-16t^2 \\ 82=202t-16t^2 \\ Collecting\text{ all terms to one side to make it a quadratic equation;} \\ 16t^2-202t+82=0 \\ Dividing\text{ the equation all through by 2,} \\ 8t^2-101t+41=0 \\ \\ To\text{ solve for t, we use the quadratic formula;} \\ \frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ where; \\ a=8,b=-101,c=41 \\ Hence, \\ t=\frac{-\left(-101\right)\pm\sqrt{\left(-101\right)^2-\left(4\times8\times41\right)}}{2\times8} \\ t=\frac{101\pm\sqrt{10201-1312}}{16} \\ t=\frac{101\pm\sqrt{8889}}{16} \\ t=\frac{101\pm94.28}{16} \\ t_1=\frac{101+94.28}{16}=\frac{195.28}{16}=12.205\approx12.21s \\ t_2=\frac{101-94.28}{16}=\frac{6.72}{16}=0.42s \end{gathered}\)Therefore, to the nearest hundredth, the value of t for which the rocket's height is 82 feet is;
0.42 seconds or 12.21 seconds.
Please help, it’s not college math!!
Answers
Answer: The first answer choice
AKA: y = -1.74x + 46.6
Step-by-step explanation:
In each part express the vector as a linear combination of P1 = 2 + x + 4x2, p2 = 1 - x + 3x2, and p3 = 3 + 2x + 5x2. (a) -9 - 7x - 15x2 (b) 6 + 11x + 6x2 (c) 0 (d) 7 + 8x + 9x2
Answers
The final expression shows that:
(a) -9 - 7x - 15x2 = (5/6)P1 - (11/6)P2 - (5/6)P3
(b) 6 + 11x + 6x2 = (7/2)P1 - (5/2)P2 + 2P3
(c) 0 = (1/3)P1 - (1/3)P3
(d) 7 + 8x + 9x2 = (-1/2)P1 + (5/2)P2 + (3/2)P3
How to show that the given vectors as a linear combination of given basis vectors?To express the given vectors as a linear combination of P1, P2, and P3, we need to solve a system of equations.
Let's set up the augmented matrix for each vector and row reduce to find the coefficients:
(a) -9 - 7x - 15x2 = c1(2 + x + 4x2) + c2(1 - x + 3x2) + c3(3 + 2x + 5x2)
The augmented matrix for this system is:
[2 1 3 -9]
[1 -1 2 -7]
[4 3 5 -15]
Row reducing this matrix using elementary row operations, we get:
[1 0 0 -3]
[0 1 0 2]
[0 0 1 -1]
So the coefficients for the linear combination are
c1 = -3, c2 = 2, and c3 = -1:
-9 - 7x - 15x2 = -3(2 + x + 4x2) + 2(1 - x + 3x2) - (3 + 2x + 5x2)
Therefore, -9 - 7x - 15x2 = -7 - 7x + 5x2.
(b) 6 + 11x + 6x2 = c1(2 + x + 4x2) + c2(1 - x + 3x2) + c3(3 + 2x + 5x2)
The augmented matrix for this system is:
[2 1 3 6]
[1 -1 2 11]
[4 3 5 6]
Row reducing this matrix using elementary row operations, we get:
[1 0 0 3]
[0 1 0 2]
[0 0 1 -1]
So the coefficients for the linear combination are
c1 = 3, c2 = 2, and c3 = -1:
6 + 11x + 6x2 = 3(2 + x + 4x2) + 2(1 - x + 3x2) - (3 + 2x + 5x2)
Therefore, 6 + 11x + 6x2 = 7 + 2x + 13x2.
(c) 0 = c1(2 + x + 4x2) + c2(1 - x + 3x2) + c3(3 + 2x + 5x2)
The augmented matrix for this system is:
[2 1 3 0]
[1 -1 2 0]
[4 3 5 0]
Row reducing this matrix using elementary row operations, we get:
[1 0 0 0]
[0 1 0 0]
[0 0 1 0]
So the coefficients for the linear combination are
c1 = 0, c2 = 0, and c3 = 0:
0 = 0(2 + x + 4x2) + 0(1 - x + 3x2) + 0(3 + 2x + 5x2)
Therefore, 0 = 0.
(d) 7 + 8x + 9x2 = c1(2 + x + 4x2) + c2(1 - x + 3x2) + c3(3 + 2x + 5x2)
The augmented matrix for this system is:
[
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the growth curve shown depicts growth projections for a single population. a graph plots population size on the y axis and time on the x axis. an exponential curve shows slow population growth at first and then rapid increase over time. what would happen if the birth rate were to decline?
Answers
If the birth rate were to decline in a population, the growth curve would be affected as well. A decrease in the birth rate would cause the population growth to slow down, resulting in a change in the shape of the curve.
Initially, the exponential curve illustrates slow population growth, followed by a rapid increase over time. However, with a declining birth rate, the curve would likely transition into a logistic growth curve. This type of curve is characterized by an initial period of slow growth, followed by a phase of rapid growth, and eventually leveling off when the population reaches its carrying capacity or other limiting factors come into play.
The projections for the population growth would also be impacted by the decrease in the birth rate. Lower birth rates typically lead to slower growth rates, and in some cases, may even result in a population decline if the birth rate falls below the death rate. This change would be reflected in the updated projections for population growth over time.
In summary, if the birth rate were to decline in a population with an exponential growth curve, the curve would likely shift towards a logistic growth pattern, with slower overall growth and eventual leveling off. The projections for population growth would need to be adjusted to account for the changes caused by the reduced birth rate.
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You Walked around a circle which has diameter of hundred metre how far you worked
Answers
Answer:
314.16 metres
Step-by-step explanation:
The answer to this problem is essentially just the circumference of the circle.
The circumference, or perimeter, is denoted by C = 2πr = πd, where r is the radius (and half the diameter) and d is the diameter.
Here, the diameter is 100 metres, so plug this in for d:
C = πd
C = π * 100 ≈ 314.16 metres
The answer is about 314.16 metres.
~ an aesthetics lover
I serious help. a ton
Answers
Answer:
Since BD bisects Angle ABC, Angle ABD = Angle DBC
\(3x+6=7x-18\)
Subtract 6 from both sides:
\(3x+6-6=7x-18-6\)
\(3x=7x-24\)
Subtract 7x from both sides:
\(3x-7x=7x-24-7x\)
\(-4x=-24\)
Divide both sides by -4:
\(\frac{-4x}{-4}=\frac{-24}{-4}\)
\(x=6\)
Angle \(ABD=3x+6=3(6)+6=18+6=24\)
Angle \(CBD=7x-18=7(6)-18=42-18=24\)
Angle \(ABC=ABD+CBD=24+24=48\)
Answer:
m<ABD= 6
m<CBD= -18
m<ABC= -108
Step-by-step explanation:
Need help ASAP!! I'll give brainliest to the correct answer!!!
Answers
One number is 16 more than another number. The two numbers have a sum of 120. Which system of equations could you use to find the two numbers?
A)y=x – 16
y=x + 120
B)y=x + 16
y = x + 120
C)y=x - 16
y=x – 120
D)y= x - 16
y = -x + 120
Answers
Answer: D)y= x - 16
y = -x + 120
Step-by-step explanation:
Let the two numbers be x and y
such that if one number is x , the other number y
Let x be the number which is 16 more than another number , so that it can be expressed as
x= y+16 which can also be written as
y= x - 16
Also, if the two numbers have a sum of 120, then it can be represented as
x+y=120 or
y = -x + 120
Therefore system of equations to find the two numbers are
D)y= x - 16
y = -x + 120
Find the area and perimeter of the rectangle below. Put answers in simplest radical form
Answers
Answer:
Area = 34 - 11√10
Perimeter = 22-4√10
Step-by-step explanation:
Let's do perimeter first bc it's easier.. To find perimeter add up all four sides.
P = (3-√10 )+ (8-√10)+(3-√10 )+ (8-√10)
add all the 3s and 8s.
P = 22-√10-√10-√10-√10
combine all the √10s
P = 22 - 4√10
Area is just length × width. If you know how to multiply binomials (like (x-3)(x-7) for example) you will do it the same way. You may have learned an area model or an algorithm called FOIL. You can use these methods. Basically it's just an amped up version of distributive property. To find the area, it takes four multiplications :
A = length × width
= (8-√10)(3-√10)
= 24 - 8√10 - 3√10 + 10
= 34 - 11√10
Solve the right triangle.
Round your answers to the nearest tenth.
Answers
Answer:
20.8
Step-by-step explanation:
tan = opposite/ adjacent
opposite = tan * adjacent
opposite = 1,482561 * 14 = 20,755854
Answer:
20.8 =x
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta = opp / adj
tan 56 = x/ 14
14 tan 56 =x
20.75585356 =x
To the nearest tenth
20.8 =x
please I need help.
Part of a stained glass window is shown at the right. Each square in the grid is 1 in. long. Find the perimeter and area of the dark gray parallelogram.
Answers
Answer:
Perimeter: 5 in
Area: 9 in^2
Step-by-step explanation:
express 0.3°8° in form a/b where by b#0
Answers
Answer:
0.3° = 0.3π/180
8° = 2π/45
Multiplying both
0.3π/180×2π/45
3/10π/180 × 2π/45
You will get
π/300 × π/45
= π²/13500 where a = π² b= 13500
Hope this helps.
AD is the median of a TRIANGLE ABC, prove that AB+BC+CA>2AD
Answers
hope this helps!!
What is the completely factored form of 3x5 – 7x4 + 6x2 – 14x?
Answers
Given:
The expression is:
\(3x^5-7x^4+6x^2-14x\)
To find:
The complete factor form of the given expression.
Solution:
We have,
\(3x^5-7x^4+6x^2-14x\)
Tanking out the GCF, we get
\(=x(3x^4-7x^3+6x-14)\)
\(=x(x^3(3x-7)+2(3x-7))\)
\(=x(x^3+2)(3x-7)\)
Therefore, the complete factor form of the given expression is \(x(x^3+2)(3x-7)\).
(-4c2+7cd+8d)+(-3d+8c2+4cd)=
Answers
Answer:
4c² + 11cd + 5d
Step-by-step explanation:
To add monomials, you have to look at the variables that are accompanied by their coefficients. In the given problem, (–4c2 + 7cd + 8d) + (–3d + 8c2 + 4cd), you can combine both cd ut nt cd and c² and cd and d and d and c² because they have different variables.
(–4c2 + 7cd + 8d) + (–3d + 8c2 + 4cd)
(-4c² + 8c²) + (7cd + 4cd) + (8d - 3d)
4c² + 11cd + 5d
Answer:
4,11,5
Step-by-step explanation:
The second term is 5 the fourth term is 12 and the seventh term is 22. 5 what is the first term?
Answers
Answer:
3.5
Step-by-step explanation:
each jump will increase 3.5
order: 2 3 4 5 6 7
num: 5 8.5 12 15.8 19 22.5
What is the standard deviation and its meaning given this population of customer ages? 45, 76, 30, 22, 51, 40, 63, 66, 41
Answers
The standard deviation is 16.54 if the population of customers ages is 45, 76, 30, 22, 51, 40, 63, 66, and 41.
What is the standard deviation?It is defined as the measure of data disbursement, It gives an idea about how much is the data spread out.
\(\rm SD = \sqrt{\dfrac{ \sum (x_i-X)^2}{N}\)
SD is the standard deviation
xi is each value from the data set
X is the mean of the data set
N is the number of observations in the data set.
It is given that:
The data set:
45, 76, 30, 22, 51, 40, 63, 66, 41
From the formula:
∑(x(i) - X)² = 2463.55
N = 9
SD = √(2463.55/9)
SD = 16.54
Thus, the standard deviation is 16.54 if the population of customers ages is 45, 76, 30, 22, 51, 40, 63, 66, and 41.
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Write an explicit formula for an, the nth term of the sequence 24, 30, 36, ....
Answers
Answer: an = a1 + d(n-1) or an = 24 + 6(n-1)
Step-by-step explanation: