In the triangles, Line segment B C is-congruent-to line segment D E and Line segment A C is-congruent-to line segment F E. Triangles A B C and F D E are shown. The lengths of sides A C and F E are congruent. The lengths of sides B C and D E are congruent. If m Angle C is greater than m Angle E, then Line segment A B is ________ Line segment D F. Congruent to longer than shorter than the same length as
Answers
Answer:
Longer than
Step-by-step explanation:
The lengths of sides A C and F E are congruent. The lengths of sides B C and D E are congruent. Therefore:
AC = FE, BC = DE
Also m∠C is greater than m∠E
∠C is the angle opposite to line AB and ∠E is the angle opposite to line DF. Since AC = FE, BC = DE and m∠C is greater than m∠E. The length of a side of a shape is proportional to its opposite angle, since the opposite angle of AB is greater than the opposite angle of DF therefore AB is greater than DF
From the given two triangles under the given conditions of congruency, we can say that;
Line segment AB is longer than Line segment FD.
CongruencyThe image showing both triangles is missing and so i have attached it.
From the attached image, we see that BC is congruent to DE and AC is congruent to FE. Thus, if Angle BCA was congruent to angle DEF, then the it means that both triangles would be congruent as well, because it would satisfied the Side Angle Side (SAS) congruence postulate.Therefore, we can say that line AB and line FD do not have the same length.
Now, we see that angle BCA is larger than angle DEF, and as such we can say that the line segment AB is longer than line segment FD.
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Related Questions
67) Interest on a Loan: Jeff Hubbard borrowed $800 from his brother for 2 years. At the end of 2 years, he repaid
the $800 plus $128 in interest. What simple interest rate did he pay?
Answers
Answer:
0.08%
Step-by-step explanation:
2 years,
the $800 plus $128 in interest. What simple interest rate did he pay?
128/2
$64 a year
64/800=0.08
so 0.08%
Is △FHK similar to △GHJ? If so, which postulate or theorem proves these two triangles are similar? △FHK is similar to △GHJ by the SSS Similarity Theorem. △FHK is similar to △GHJ by the SSA Similarity Theorem. △FHK is similar to △GHJ by the SAS Similarity Theorem. △FHK is not similar to △GHJ.
Answers
Answer:
ΔFHK and ΔGHJ are the similar triangles by SAS similarity theorem.
Step-by-step explanation:
Picture for the given question is missing; find the picture attached.
If [tex]\frac{\text{FH}}{\text{GH}}=\frac{\text{HK}}{\text{HJ}}[/tex] and ∠H ≅ ∠H
Then ΔFHK ~ ΔGHJ
[tex]\frac{\text{FH}}{\text{GH}}=\frac{\text{HK}}{\text{HJ}}[/tex]
[tex]\frac{(12+10)}{10}=\frac{(15+18)}{15}[/tex]
[tex]\frac{22}{10}=\frac{33}{15}[/tex]
[tex]\frac{11}{5}=\frac{11}{5}[/tex]
Since, [tex]\frac{\text{FH}}{\text{GH}}=\frac{\text{HK}}{\text{HJ}}[/tex] and ∠H ≅ ∠H [By reflexive property]
Therefore, ΔFHK and ΔGHJ are the similar triangles by SAS similarity theorem.
Option (3) will be the answer.
Answer:
ΔFHK and ΔGHJ are similar triangles by the SAS similarity theorem.
Step-by-step explanation:
Verified correct with test results.
What is the radical equivalent for 197^7/8?
Answers
Answer:
[tex]\sqrt[8]{197^{7} }[/tex]
Step-by-step explanation:
[tex]\sqrt[8]{197^{7} }[/tex]
is the measure of how much the values in a data set vary, or deviate, from the mean; it tells us how spread out the data is from the mean.
Answers
Answer:
Standard deviation
Step-by-step explanation:
The standard deviation provides a measure of the overall variation in a data set. The standard deviation is always positive or zero. The standard deviation is small when the data are all concentrated close to the mean, exhibiting little variation or spread.
Which expressions are equivalent to 2(b+3c)2(b+3c)2, left parenthesis, b, plus, 3, c, right parenthesis ?
Choose all answers that apply:
Choose all answers that apply:
(Choice A)
A
3(b+2c)3(b+2c)3, left parenthesis, b, plus, 2, c, right parenthesis
(Choice B)
B
(b+3c)+(b+3c)(b+3c)+(b+3c)left parenthesis, b, plus, 3, c, right parenthesis, plus, left parenthesis, b, plus, 3, c, right parenthesis
(Choice C)
C
2(b)+2(3c)2(b)+2(3c)2,
Answers
Answer:
B. (b+3c)+(b+3c) C. 2(b)+2(3c)Step-by-step explanation:
Given this expression 2(b+3c), its equivalent expression is derived by simply opening up the bracket as shown below;
Open the parenthesis by multiplying the constant outside the bracket with all the variables in parenthesis.
= 2(b+3c)
= 2(b)+ 2(3c)
= 2b +2*3*c
= 2b +6c
It can also be written as sum of b+3c in 2 places i.e (b+3c)+(b+3c) because multiplying the function b+3c by 2 means we are to add the function by itself in two places.
Hence the equivalent expression are (b+3c)+(b+3c) and 2(b)+2(3c) or 2b+6c
Increase 150 by 120%
O A. 330
OB. 180
O c. 300
OD. 200
Answers
Answer:
C
Step-by-step explanation:
Find 120% of 150
1.2 x 150 = 180
Increase to 150
180 + 150 = 330
Hope that helped!!! k
How many minutes will it take a caterpillar to go seven feet if it travels 24 inches per minute? To travel seven feet, it will take the caterpillar a0 minutes.
Answers
Answer:
3 and and half minutes--> 7ft
Step-by-step explanation:
If it travels 24 inches aka 2ft per minute
then it has to travel 12 inches aka 1ft in 30secs
SO
3mins and 30secs to travel 7ft
24inches--- 2ft---- per minute
4ft--- 2 mins
6ft---- 3mins
7ft--- 3minutes and 30 seconds
PLEASE - Select the correct answer.
Answers
Answer:
D
Step-by-step explanation:
Find the equation of a line given the point and slope below. Arrange your answer in the form y = mx + b, where b is the constant. (1, 3) m = 2
Answers
Answer:
y= 2x+1
hope it helps...........
Solve for x. 23x +2=15x+48x+6
Answers
Answer:
[tex]x = - \frac{1}{10} [/tex]Step-by-step explanation:
23x +2 = 15x+48x+6
To solve for x group like terms
That's
Send the constants to the right side of the equation and those with variables to the left side
We have
23x - 15x - 48x = 6 - 2
Simplify
- 40x = 4
Divide both sides by -40
[tex] \frac{ - 40x}{ - 40} = \frac{4}{ - 40} [/tex]We have the final answer as
[tex]x = - \frac{1}{10} [/tex]Hope this helps you
Multiply the input by 2. Then add 4 to the result to get the output.
Answers
Answer:
2x +4
Step-by-step explanation:
The Expression for "Multiply the input by 2 and then add 4 to the result to get the output" is 2x+ 4.
What is expression?A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:
An absolute numerical number is referred to as a constant.Variable: A symbol without a set value is referred to as a variable.Term: A term can be made up of a single constant, a single variable, or a mix of variables and constants multiplied or divided.Coefficient: In an expression, a coefficient is a number that is multiplied by a variable.Given:
Multiply the input by 2.
let the input be x.
So, 2x
Now, add the result to 4
Then, 2x+ 4
Hence, the expression is 2x+ 4.
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There are a total of two hundred students and chaperones going on a
field trip. Each bus can hold 60 passengers. How many buses will be
used for the field trip? Explain why your answer is reasonable.
Answers
Answer:
4 bus is required for field trip to carry 200 passengers.
Step-by-step explanation:
Total no . of passengers = 200
let the be x bus required to carry 200 passengers
capacity of 1 bus = 60 passengers
capacity of x bus = 60*x passengers = 60x passengers
Thus,
60x = 200
x = 200/60 = 3 2/3
thus, 3.66 bus is required , but no. of bus cannot be in fraction hence we take integral value greater than 3.66 which is 4
Thus, 4 bus is required for field trip to carry 200 passenger.
determine if the following set of ordered pairs represents a quadratic function explain (5,7),(7,11),(9,14),(11,18)
Answers
Answer:the pairs are not a quadratic eqation
Step-by-step explanation:
The differences between the differences of the y value are not consistent
The set of ordered pairs (5,7),(7,11),(9,14),(11,18) does not represents a quadratic function
What is a function?A relation is a function if it has only One y-value for each x-value.
Given,
The set of ordered pairs
(5,7),(7,11),(9,14),(11,18)
We have to determine whether the (5,7),(7,11),(9,14),(11,18) is quadratic function or not.
Start by representing the function as an x-y table
x:- 5 || 7 || 9 || 11
y:- 7 || 11 || 14 || 18
The difference between the y values is not same
11-7=4
14-11=3
18-14=4
For the function to be quadratic, the above difference must be the same and since they are not, then the function does not represent a quadratic function.
Hence, the set of ordered pairs (5,7),(7,11),(9,14),(11,18) does not represents a quadratic function
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factorize
2ab+abk-2m-mk
Answers
Answer:
=2ab +abk -2m- mk
= ab(2+k) -m(2+k)
=(2+k)(ab-m)
Step-by-step explanation:
3. When Antoine or Adriane is halfway to the top of the Ferris wheel, what is his or her elevation? (Use the
diameter of the Ferris wheel to determine the correct vertical shift for your modeling function.) (1 point)
Answers
Answer: 70
Step-by-step explanation:
Antoine's elevation when he is halfway to the top is 70. You cut the diameter (120) in half which gets you 60 and you add the height of the stand holding the wheel (10) which gets you 70.
The his or her elevation should be 70.
Calculation of the elevation:Since the diameter is 120 And, elevation of Antoine should be halfway to the top so here we split the diameter into half i.e. half of 120 is 60 and there is the height for stand holding the wheel i.e. 10
So, the elevation should be
= 60 + 10
= 70
Therefore, The his or her elevation should be 70.
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1)Sheyna drive to the lake and back. It took two hours less time to get there than it did to get back. The average speed on the trip there was 60 mph. The average speed on the way back was 36 mph. How many hours did the trip there take?
Answers
Answer:
8 hours
Step-by-step explanation:
Given:
Sheyna drives to the lake with average speed of 60 mph and
[tex]v_1 = 60\ mph[/tex]
Sheyna drives back from the lake with average speed of 36 mph
[tex]v_2 = 36\ mph[/tex]
It took 2 hours less time to get there than it did to get back.
Let [tex]t_1[/tex] be the time taken to drive to lake.
Let [tex]t_2[/tex] be the time taken to drive back from lake.
[tex]t_2-t_1 = 2[/tex] hrs ..... (1)
To find:
Total time taken = ?
[tex]t_1+t_2 = ?[/tex]
Solution:
Let D be the distance to lake.
Formula for time is given as:
[tex]Time =\dfrac{Distance}{Speed }[/tex]
[tex]t_1 = \dfrac{D}{60}\ hrs[/tex]
[tex]t_2 = \dfrac{D}{36}\ hrs[/tex]
Putting in equation (1):
[tex]\dfrac{D}{36}-\dfrac{D}{60} = 2\\\Rightarrow \dfrac{5D-3D}{180} = 2\\\Rightarrow \dfrac{2D}{180} = 2\\\Rightarrow D = 180\ miles[/tex]
So,
[tex]t_1 = \dfrac{180}{60}\ hrs = 3 \ hrs[/tex]
[tex]t_2 = \dfrac{180}{36}\ hrs = 5\ hrs[/tex]
So, the answer is:
[tex]t_1+t_2 = \bold{8\ hrs}[/tex]
Which expression is equivalent 6+7n+4+8n?
Answers
Answer: 5(2+3n)
Step-by-step explanation:
Answer:
15n + 10 should be your answer.
Step-by-step explanation:
in scientific notation
1.6 x 10^3/ 8 x 10^7
Answers
Answer:
Step-by-step explanation:
[tex]\frac{1.6*10^{3}}{8*10^{7}}=\frac{1.6}{8}*10^{3-7}\\\\\\=0.2*10^{-4}\\\\\\=2.0*10^{-5}[/tex]
[tex]\frac{a^{m}}{a^{n}}=a^{m-n}[/tex]
what is the angle taken in anticlockwise direction between (1) North-east and south- west
Answers
Answer:
Step-by-step explanation:
North-east has a bearing of 45 degrees
South-west has a bearing of 225 degrees.
Taken anticlockwise,
angle = south-west - north-east
= (225-45)
= 180 degrees
answer
hope this helps....
If f(x)= 5x+4 and g(x)= -2+1...... 1) f(6) + g(-8) = ? 2) g(4)= ? 3) f(-2)= ? PLZ PLZ PLZ HELP ME I AM SOOOOO CONFUSED!!!!!!!!!!!
Answers
Answer:
See below.
Step-by-step explanation:
So we have the two functions:
[tex]f(x)=5x+4\text{ and } g(x)=-2x+1[/tex]
1)
First, find the values of each function:
[tex]f(x)=5x+4\\f(6)=5(6)+4\\f(6)=30+4=34[/tex]
[tex]g(x)=-2x+1\\g(-8)=-2(-8)+1\\g(-8)=16+1=17[/tex]
Therefore:
[tex]f(6)+g(-8)\\=(34)+(17)=51[/tex]
2)
Plug in the number into the function:
[tex]g(x)=-2x+1\\g(4)=-2(4)+1=-8+1=-7[/tex]
3)
Like the last one:
[tex]f(x)=5x+4\\f(-2)=5(-2)+4=-10+4=-6[/tex]
HELP! answer if you can !!
Answers
You can find the area of a triangle by using this formula. A=bh/2.
Basically what you do is you multiply the base by the height, and then divide that by 2 to get your area.
Answer:
The formula for ABC Triangle
(AB×AC)/2
= (4.7×2.4)/
= 11,28/2
= 5,64 in²
MP Find the Error Katrina states that
3.5 X 104 is greater than 2.1 x 106 because
3.5 > 2.1. Explain her mistake and correct it.
Answers
Answer:
3.5 X 10^4 < 2.1 x 10^6
Step-by-step explanation:
3.5 X 10^4 < 2.1 x 10^6
The first thing we look at is the exponent
10 ^4 is less than 10^6
10000 < 1000000
If the exponents are the same, then we look at the numbers out front
A rectangle has a perimeter of 26 feet. Twice its length is one foot more than three times its width (w). What is
the length of the rectangle, in Thet?
Answers
Answer:
The length of the rectangle is 13
Step-by-step explanation:
13 times 2 its equal 26
Winning the jackpot in a particular lottery requires that you select the correct five numbers between 1 and 35 and, in a separate drawing, you must also select the correct single number between 1 and 45. Find the probability of winning the jackpot.
Answers
Answer:
1 / 14608440
Step-by-step explanation:
Given the following :
Winner has to select the five correct numbers between 1 and 35
Then, a single correct number between 1 and 45
Step1:
Number of ways to select 5 corre t numbers between 1 and 35; selecting 5 things from a total of 35 = 35C5
nCr = n! ÷ (n-r)!r!
35C5 = 35! ÷ (35-5)!5!
35C5 = 35! ÷ (30)!5!
= (35 * 34 * 33 * 32 * 31) / (5 * 4 * 3 * 2 * 1) = 324632 ways
Then find number of ways of selecting 1 correct number between 1 and 45:
45C1
45C1 = 45! ÷ (45-1)!1!
45C1 = 45! ÷ (44)!1!
45C1 = 45 ÷ 1 = 45
35C5 * 45C1 = 324632 * 45 = 14608440
Therefore, probability of winning the jackpot :
Required outcome / Total possible outcomes
= 1 / 14608440
Is 7/12 rational or irrational
Answers
Answer:
7/12 is a rational
Step-by-step explanation:
because it is containing a quantity which are expressible
Convert 5280 vodas to pivos. Show three significant figures for your answer.
1 pivo = 3.1416 molokos
1 moloko = 2.71828 vodas
Answers
(5280 vodas) * (1/2.71828 moloko/voda) * (1/3.1416 pivo/moloko) ≈ 618 pivos
(because 5280 has 3 significant digits)
If P = (3,4), Find: Rx=1 (P)
Answers
Answer:
-1, 4
Step-by-step explanation:
Answer:
Step-by-step explanation:
answer is (-1,4)
The table below shows one doctor's patients who got the flu and whether or not they took a vitamin each day. What is P(took a vitamin | got the flu)? (Note: If your fraction will reduce, you need to reduce it.)
Answers
Answer:
1/4
Step-by-step explanation:
25 people took a vitamin and still got the flu and the total number is 100 so the fraction is 25/100 which can be reduce to 1/4
The P(took a vitamin | got the flu) will be 1/4.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Here, the table below shows one doctor's patients who got the flu and whether or not they took a vitamin each day.
We need to find the P(took a vitamin | got the flu).
Now, 25 people took a vitamin and still got the flu.
The total number is 100.
So, the fraction is 25/100 which can be reduce to 1/4.
P(took a vitamin | got the flu) = 25/100
P(took a vitamin | got the flu) = 1/4
Therefore, the P(took a vitamin | got the flu) will be 1/4.
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Please help
A) y< 2x+4
B) y< 1/2x+3
C)y> 1/2x+3
D) y> 2x+3
Answers
Answer:
B
Step-by-step explanation:
if it is shaded under than it is <
the slope is 1/2x so that is the answer
Apply
48. Think About a Plan A lumberjack cuts 7 pieces of equal length
from a log, as shown at the right. What is the change in the log's
length after 7 cuts?
• What operation can you use to find the answer?
• Will your answer be a positive value or a negative
value? How do you know?
49. Farmer's Market A farmer has 120 bushels of beans for sale at a farmer's market.
dau what is the change in the
Answers
Answer:
you can use a median method of counting and eliminating each side being each cut but the difference would it would be an equal number as the central off number cut divides one piece of wood into an even number.
Another operation is subtracting the cuts from the pieces you have 7 - 6 = 1 whole. Meaning the answer is correct if you are left with 1
If the cuts were even then you would have an a number of pieces that amount to an odd number.
So with 7 they are even and positive.
With counter checking they are positive as you always start with one piece of wood.
