Answers
The length of line EF is proved to be parallel to the length of line EF.
What is the prove that EF// BD?To prove that EF is parallel to BD, we need to show that the opposite interior angles are equal.
Let's denote the center of the circle as O, and the intersection point of BD and AE as X. Since ABCD is a square, we have:
AD = AB, andBD is a diagonal, so BD passes through the center of the circle O.From the above information, we can deduce that:
∠ABD = 45°, and
∠OBD = 90°.
Since line_AF = line_AE, we can also deduce that:
∠FAE = ∠FEA.
Now, let's consider the triangle AFE. We have:
∠AFE + ∠FAE + ∠FEA = 180° (sum of angles in a triangle)
∠AFE + 2∠FAE = 180° (substituting ∠FEA with ∠FAE)
∠AFE = 180° - 2∠FAE
Also, in triangle AXε, we have:
∠AXε + ∠AEX + ∠XAE = 180° (sum of angles in a triangle)
∠AXε + ∠AEX + ∠FAE = 180° (substituting ∠XAE with ∠FAE)
∠AXε + ∠FAE + ∠FAE = 180° (rearranging terms)
∠AXε + 2∠FAE = 180°
Now, let's consider the quadrilateral ABXE. We have:
∠ABX + ∠AXε + ∠AEB = 360° (sum of angles in a quadrilateral)
∠ABX + ∠AEX + ∠AEB = 360° (rearranging terms)
∠ABX + ∠FAE + ∠AEB = 360° (substituting ∠AEX with ∠FAE)
∠ABX + 2∠FAE = 360° (substituting ∠AEB with ∠FAE)
∠ABX = 360° - 2∠FAE
Finally, let's consider the triangle BDE. We have:
∠BDE + ∠BED + ∠EBD = 180° (sum of angles in a triangle)
∠BDE + ∠AEB + ∠EBD = 180° (substituting ∠BED with ∠AEB)
∠BDE + ∠FAE + ∠EBD = 180° (substituting ∠AEB with ∠FAE)
∠BDE + 2∠FAE = 180° (since ∠FAE = ∠FEA)
∠BDE = 180° - 2∠FAE
From the above equations, we can see that:
∠ABX = ∠BDE (since both are equal to 360° - 2∠FAE)
∠ABD = ∠EBD (since both are equal to 45°)
Therefore, by the angle-angle (AA) criterion for similarity, we have:
triangle ABD is similar to triangle EXD.
This implies that:
BD/AD = XD/ED (by the property of similar triangles)
Since AD = BD (since ABCD is a square), we have:
BD/BD = XD/ED
1 = XD/ED
XD = ED
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Related Questions
The chart below shows conversion between gallons and fluid Ounces. Conversion Chart Gallons Fluid Ounces 2 256 3 384 4 512 6 What is the missing value in the table? O 128 O 640 O 768 896
Answers
Answer:
b
Step-by-step explanation:
between gallons and Fluid Ounces.because The chart below shows the conversion
Answer: B
Step-by-step explanation:
square root of 12321 by prime factorization
Answers
12321-3x3x37x37
(3)^2×(37)^2
square root = 3×37=111
Hope it helps you..!!
solve the equation
a) y''-2y'-3y= e^4x
b) y''+y'-2y=3x*e^x
c) y"-9y'+20y=(x^2)*(e^4x)
Answers
Answer:
a) To solve the differential equation y''-2y'-3y= e^4x, we first find the characteristic equation:
r^2 - 2r - 3 = 0
Factoring, we get:
(r - 3)(r + 1) = 0
So the roots are r = 3 and r = -1.
The general solution to the homogeneous equation y'' - 2y' - 3y = 0 is:
y_h = c1e^3x + c2e^(-x)
To find the particular solution, we use the method of undetermined coefficients. Since e^4x is a solution to the homogeneous equation, we try a particular solution of the form:
y_p = Ae^4x
Taking the first and second derivatives of y_p, we get:
y_p' = 4Ae^4x
y_p'' = 16Ae^4x
Substituting these into the original differential equation, we get:
16Ae^4x - 8Ae^4x - 3Ae^4x = e^4x
Simplifying, we get:
5Ae^4x = e^4x
So:
A = 1/5
Therefore, the particular solution is:
y_p = (1/5)*e^4x
The general solution to the non-homogeneous equation is:
y = y_h + y_p
y = c1e^3x + c2e^(-x) + (1/5)*e^4x
b) To solve the differential equation y'' + y' - 2y = 3xe^x, we first find the characteristic equation:
r^2 + r - 2 = 0
Factoring, we get:
(r + 2)(r - 1) = 0
So the roots are r = -2 and r = 1.
The general solution to the homogeneous equation y'' + y' - 2y = 0 is:
y_h = c1e^(-2x) + c2e^x
To find the particular solution, we use the method of undetermined coefficients. Since 3xe^x is a solution to the homogeneous equation, we try a particular solution of the form:
y_p = (Ax + B)e^x
Taking the first and second derivatives of y_p, we get:
y_p' = Ae^x + (Ax + B)e^x
y_p'' = 2Ae^x + (Ax + B)e^x
Substituting these into the original differential equation, we get:
2Ae^x + (Ax + B)e^x + Ae^x + (Ax + B)e^x - 2(Ax + B)e^x = 3xe^x
Simplifying, we get:
3Ae^x = 3xe^x
So:
A = 1
Therefore, the particular solution is:
y_p = (x + B)e^x
Taking the derivative of y_p, we get:
y_p' = (x + 2 + B)e^x
Substituting back into the original differential equation, we get:
(x + 2 + B)e^x + (x + B)e^x - 2(x + B)e^x = 3xe^x
Simplifying, we get:
-xe^x - Be^x = 0
So:
B = -x
Therefore, the particular solution is:
y_p = xe^x
The general solution to the non-homogeneous equation is:
y = y_h + y_p
y = c1e^(-2x) + c2e^x + xe^x
c) To solve the differential equation y" - 9y' + 20y = x^2*e^4x, we first find the characteristic equation:
r^2 - 9r + 20 = 0
Factoring, we get:
(r - 5)(r - 4) = 0
So the roots are r = 5 and r = 4.
The general solution to the homogeneous equation y" - 9y' + 20y = 0 is:
y_h = c1e^4x + c2e^5x
To find the particular solution, we use the method of undetermined coefficients. Since x^2*e^4x is a solution to the homogeneous equation, we try a particular solution of the form:
y_p = (Ax^2 + Bx + C)e^4x
Taking the first and second derivatives of y_p, we get:
y_p' = (2Ax + B)e^4x + 4Axe^4x
y_p'' = 2Ae^4x +
Look at this square: 8 m 8 m If the side lengths are halved, then which of the following statements about its area will be true? The new area will be 1 of the old area. 4 The new area will be 1 of the old area. 2 The new area will be 1 of the old area. end The new area will be 16 times the old area.
Answers
Answer:The solution is in the attached filefile.Ifilefile.If you still don't understand,I'm ready to explain more
Step-by-step explanation:
Simplify using the order of operations. 2+6*8=
Answers
Answer:
The answer is 50.
Step-by-step explanation:
Use MDAS
Multiplication, Division, Addition and Subtraction
2 + 6 * 8 =
Multiply first then add
2 + 6*8 = ?
= 2 + 48
= 50
Find the approximate radius of a circle with a circumference of 34.48 inches. Use 3.14 for pie. Round to the nearest 100
Answers
Answer:
r = 5.49
Step-by-step explanation:
The formula for the radius of a circle is circumference/2(3.14).
34.48/2(3.14) = 5.49
The radius of the circle is equal to 5.49 inches.
What is the area and circumference of a circle?The circumference (or) perimeter of a circle = 2πr units. The area of a circle = πr2 square units. Where r is the radius of the circle. The circumference of the circle or the perimeter of the circle is the measurement of the boundary of the circle. Whereas the area of the circle defines the region occupied by the circle.
Given here: Circumference as 34.48 inches and π=3.14
Now circumference of the circle is given by
2πr=34.48
r=34.48/2×3.14
r=5.49 inches
Hence, The radius of the circle is equal to 5.49 inches.
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April buys soil for her flowerpots. she uses 9 kilograms of soil for her violets and 4 kilograms of soil for her tulips. she has 3,000 grams of soil left for some daisies (1 kilogram = 1,000 grams) use the drop down menus to show how much soil she bought
Answers
April bought 16 kilograms of soil in total.
To show how much soil April bought
We need to add the amounts of soil she used for her violets and tulips. Since April used kilograms for violets and tulips, we need to convert the 3,000 grams to kilograms before we can add them up.
April bought:
9 kilograms of soil for violets
4 kilograms of soil for tulips
3 kilograms of soil for daisies (since 3,000 grams is 3 kilograms)
Therefore, April bought 16 kilograms of soil in total.
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PLEASE HELP ME 12 POINTS
Answers
Answer:
Streamers cost 2.50 and balloons cost 1.25.
Step-by-step explanation:
Pls mark brainliest.
Answer:
Balloon : $1.25
Streamer : $ 2.50
Step-by-step explanation:
Form simultaneous equations.
Let streamer be represented by ------------s
Let balloons be represented by ------------b
So the equations will be;
3s + 2b = 10 ----------------i
2s + 1b = 6.25---------------ii
Make the terms with s equal by multiplication
[3s + 2b = 10 ]2
[2s + 1b = 6.25]3
Perform subtraction
6s + 4b = 20
6s + 3b = 18.75
b = 1.25 ---------iii
Use iii in ii as;
2s + 1b = 6.25
2s + 1.25 = 6.25
2s = 6.25 - 1.25
2s = 5.00
s= 5.00 / 2
s= 2.5
Hence ; a balloon is $1.25 and a streamer is $2.5
Jason has a cousin and she is 3 years more than 2 times his age. The sum of their ages is 78. How old is jason and his cousin?
Answers
Answer:
Jason=25 years
Cousin= 53 years
Step-by-step explanation:
Jason's age= x
Jason's cousin= 3+2x
Sum of their ages= 78
--> 3+2x+x=78
--> 3+3x=78
--> 3x=78-3
--> 3x=75
--> x=75/3
--> x=25
Jason's age= x= 25
Jason's cousin= 3+2x=53
Sum of ages= 53+25= 78
Hence, Verified.
5+5 100 points please help I'm in 8th grade and my teacher wants me to answer this
Answers
5+5=55
Hope this helped!
Find the area of the parallelogram.
Answers
Answer:
894
Step-by-step explanation:
Brainliest for whoever if they get this CORRECT.
Answers
c
All the information you need is in the quadratic trinomial ... Read from right to left:
Find factors of 49 which ADD (+) to give 14.
These will be 7 and 7 because: 7 × 7 = 49 and 7 + 7 = 14
The + sign shows that the signs in the brackets will be the SAME, the minus (-) shows that they will be negative:
( x − 7 ) ( x − 7 ) = ( x − 7 ) 2
which alphabet is missing V S P W T P_
Answers
Answer:
E
Step-by-step explanation:
I need help this is due in like 20 minutes
Answers
Answer:
(5,4)
Step-by-step explanation:
Tanya performs two transformations on ABC to form A"B" and C" as shown on the coordinate grid below.
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the transformation ABC is not similar to A”B”C”. hence the statement is false.
How do we know?We say the statement is false because the ratios of the grid squares are not similar.
We notice that the first triangle is up to over 3 and the other triangle is up 4 over 4 so in order for them to be similar the first triangle would have to be up 3 over 3.
A transformation is described as a general term for four specific ways to manipulate the shape and/or position of a point, a line, or geometric figure.
#complete question:
Please help this is due today and I’m so stressed!I will mark Branliest!!!
Tanya performs two transformations on ABC to form A"B"C" as shown on the coordinate grid below.
True or False:ABC is similar to A”B”C”?
Select a personal or professional example of a measurement you use routinely. Convert the measurement either from U.S customary units to metric units, or from metric units to U.S. customary units. You may choose more than one measurement and may choose among weight, length, temperature, etc. Show each step of your conversion and be sure to include all units from the original and converted measurements (for example, yards to meters, degrees Celsius to degrees Fahrenheit).
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A personal example of a measurement I use routinely is converting weight from U.S. customary units to metric units. Let's convert pounds to kilograms.
To convert pounds to kilograms, we use the conversion factor of 1 pound = 0.453592 kilograms.
For example, if I have a weight of 150 pounds, I can calculate the equivalent weight in kilograms as follows:
150 pounds * 0.453592 kilograms/pound = 68.0388 kilograms
Therefore, 150 pounds is approximately equal to 68.0388 kilograms.
In this conversion, we multiply the weight in pounds by the conversion factor to obtain the weight in kilograms. By using the appropriate conversion factor, we can accurately convert weights from U.S. customary units to metric units.
It's important to note that conversion factors may vary slightly depending on the rounding used and the exact value of the conversion factor.
For such more question on metric units
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Write y = 5(x - 8)^2 + 4 in standard form
Answers
Answer:
\(y=5x^2-80x+324\)
Step-by-step explanation:
You win $10 000 in a Best Math Student competition. Being a generous person, you decide to invest the money
You win $10 000 in a Best Math Student competition. Being a generous person, you decide to invest the money in two local businesses to them get off the ground. The businesses are Paul’s Paper and Tiffany’s Tyres. They offer the following annual interest rates return to encourage your investment;
PP – 10% p.a.TT – 5% p.a.The investment’s combined return is $620 after one year. How much was invested in each company?
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Cumulative costs of the investments of a mutual fund you currently hold are the amount invested. Net Investment is one investment action's net amount of inflow.
Invested Amount in PP \(\bold{= \$2400}\)Invested Amount in TT \(\bold{= \$(10000 - 2400) = \$7600}\)Solution:
The formula for calculating the simple interest:
\(\to \text{Simple interest} = principal \times rate \times time\)
Total amount = 10000
Let :
Invested Principle (PP) \(\bold{= r}\) ............................. (i)Invested Amount in TT \(\bold{= 10000 - r}\) ................................. (ii)From both investments total earned interest = $620
\(\to \bold{PP \ investment \ return + TT \ investment\ return = 620}\)
\(\to (r \times 10\% \times 1) + (10000 - r \times 5\% \times 1) = 620\\\\\to (r \times \frac{10}{100} \times 1) + (10000 - r \times \frac{5}{100} \times 1) = 620\\\\\to (r \times 0.10 \times 1) + (10000 - r \times 0.05 \times 1) = 620\\\\\to 0.1r + 500 - 0.05r = 620\\\\\to 0.05r = 620 - 500\\\\\to 0.05r = 120\\\\\to r =\frac{ 120}{0.05}\\\\\to r = 2400\)
Therefore,
Invested Amount in PP \(\bold{= \$2400}\)Invested Amount in TT \(\bold{= \$(10000 - 2400) = \$7600}\)Learn more :
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I need help with #6!!
Answers
The probability of randomly drawing a 10 from the deck is:
P = 1/13
How to find the probability?We want to find the probability of randomly drawing a 10 from the deck.
Remember that there are 4 suits of 13 cards each, so thereare 52 cards in total and 4 of these cards are tens.
The probability of randomly drawing a 10 is equal to the quotient between the number of cards with a 10 on it (4 of these) and the total number of cards in the deck (52).
It is:
P = 4/52 = 1/13
That is the probability.
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what goes in to 18 and 6
Answers
Answer:
Answer us 3
Step-by-step explanation:
3×2=6 3×6=18
Harrison deposits $345 in a savings account that earns 4.2% simple interest paid annually. How long will it take for the total amount in the account to reach $410?
PLEASE ASAP I HAVE THIS QUESTION ON A TEST HELLPP
Answers
The time required for the total amount in Harrison's account to reach $410 is 4.49 years.
What is time required to reached an accrued amount of $410?The simple interest formula is expressed as;
A = P( 1 + rt )
Where A is accrued amount, P is principal, r is interest rate and t is time.
Given the data in the question;
Principal P = $345Interest rate r = 4.2% = 4.2/100 = 0.042Accrued amount A = $410Time t = ?Plug the given values into the above formula and solve for time t.
A = P( 1 + rt )
A/P = 1 + rt
A/P - 1 = rt
t = ( A/P - 1 ) / r
t = ( $410/$345 - 1 ) / 0.042
t = ( 13/69 ) / 0.042
t = 4.49 years
Therefore, the time needed to reach accrued amount is 4.49 years.
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7. AXYZ with X(-2, 2), Y(4,2), and Z(1, -5); rotate 180° clockwise. 73 a. What are the vertices of the image after the transformation? 76 b. Graph the original triangle and its image. у
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The given coordinate of the vertices of triangle XYZ is X(-2,2), Y(4,2) and Z(1,-5).
a). When rotates 180 degrees clockwise the new coordinate of the triangle can be determined as,
\(\begin{gathered} X^{\prime}(2,-2) \\ Y^{\prime}(-4,-2) \\ Z^{\prime}(-1,5) \end{gathered}\)b). The original and the new coordinates of the triangle can be drawn as,
The original and the new triangles can be drawn as,
Please please help me !
Thank you for the help.
Point and brainliest
Answers
1. no
2. no
3. strong
4. positive
this is what i think is right. lmk which is wrong :)
David is traveling to his next weightlifting competition. If he weighs 120.3 kilograms, how much does he weigh in pounds?
Answers
Step-by-step explanation:
120.3×2.2= 264.66
Please can someone answer this I don’t get it!!! 5 points and Brainly:)
Answers
Answer:
the answer will be 39cm yes
Determine the number of zeros of the polynomial function.h(t) = (t − 6)2 − (t + 6)2
Answers
Answer:
Step-by-step explanation:
(t - 6)^2 = t^2 - 12t + 36
(t + 6)^2 = t^2 + 12t +36
(t - 6)^2 - (t + 6) = t^2 - 12t + 36 - (t^2 + 12t + 36)
(t - 6)^2 - (t + 6) = t^2 - 12t + 36 - t^2 - 12t - 36
(t - 6)^2 - (t + 6) = -24t The other 4 terms cancel out.
-24t = 0 Divide by - 24
t = 0
There is one root.
What value does point P represent on the number line given?
–3.9
–3.1
–2.9
–0.3
Number line ranging from negative five to five, with the point P labeled between negative two and three
Answers
Determine whether the polygons are similar, please help.
Answers
Answer:
yes I just checked it
Step-by-step explanation:
What is the area of this triangle?
Answers
Answer:
21 units²
Step-by-step explanation:
A=1/2bh
b=6
h=7
1/2(6)(7)=
1/2(42)=
21 units²
WILL MARK BRAINLY FOR WHO EVER ANSWERS THIS RIGHT
Answers
Answer:
B
Step-by-step explanation:
Hope this helps!