Find the value of the variable that results in congruent triangles. Complete the explanation.
F
30°
30°
9 in.
9 in.
(2x) in.
(x + 4) in.
А
B
D
E
AC is congruent to DF, because AC
DF = 9 in. 2C is congruent
to ZF. EF
must correspond to BC. The triangles (select) » congruent by the (select) Triangle
Congruence Theorem only when x = |
Answers
Answer:
[tex] \overline{AC} [/tex] is congruent to [tex] \overline{DF} [/tex], because [tex] \overline{AC} = 9in [/tex], [tex] \overline{DF} = 8 in [/tex]. <C is congruent to <F. [tex] \overline{EF} [/tex] must correspond to [tex] \overline{BC} [/tex]. The triangles are congruent by the SAS Triangle
Congruence Theorem only when x = 4.
Step-by-step explanation:
From the figures given, ∆ABC and ∆DEF have an included corresponding angles measuring 30° each (<C and <F), and also a given corresponding side length of 9 in each (side AC and side DF). The other given as am expression, and hence the length is unknown. For these two ∆s to be considered congruent, using the SAS Triangle Congruence Theorem, we must have two sides and an included angle of ∆ABC equal to the corresponding sides of and an included angle of ∆DEF.
We already know that 1 of the given side corresponding side lengths are equal and also the include angles are equal, to find out what value of x that will make both unknown corresponding lengths equal, in other for the SAS to be true, set 2x equal to (x + 4) to solve for x.
Thus:
2x = x + 4
Subtract x from both sides
2x - x = 4
x = 4
Substituting x = 4 into 2x and x + 4 will give us equal lengths of 8 in respectively. Therefore, if x = 4, both triangles will be congruent based on the SAS Triangle Congruence Theorem.
The answer is:
[tex] \overline{AC} [/tex] is congruent to [tex] \overline{DF} [/tex], because [tex] \overline{AC} = 9in [/tex], [tex] \overline{DF} = 8 in [/tex]. <C is congruent to <F. [tex] \overline{EF} [/tex] must correspond to [tex] \overline{BC} [/tex]. The triangles are congruent by the SAS Triangle
Congruence Theorem only when x = 4.
Related Questions
Bethany is playing a game with her sister. Each player starts with 3 shuffled decks of cards turned upside down in 3 separate
piles so they don't know what order the cards are in. At each turn they draw 2 cards, 1 from the top of 2 piles of their
choosing
Bethany has the last play, and to win the game, she needs 2 face cards. She has paid attention to which cards have been
played from each pile, and she knows what cards are remaining in each pile. The cards remaining in each pile are shown
below.
Pile 1 = (10C, 5D, 9H, 9D, JD, 8D)
Pile 2 - (8D, QC, 45, 4D, AD, JS, 4H)
Pile 3 = {4C, KS, 6S, 10D, 4H}
Which 2 piles should Bethany draw from to have the best chance of winning the game?
Note: The last letter in the lists above gives the suit: Club, Diamond, Heart, or Spade. The first number or letter is the card
value. Jacks, Queens, and Kings are face cards.
Lo
Answers
Answer: its b
Step-by-step explanation:
The following two pile should Bethany draw to have the best chance of winning the game are;
Pile 1 = (10C, 5D, 9H, 9D, JD, 8D)
Pile 2 - (8D, QC, 45, 4D, AD, JS, 4H)
What is the combination?In mathematics, Combination is a term which tells us how many ways there are for the selection of a few things without considering their order.
Formula for selection of a objects from the n objects,
N = ⁿCₐ
Given that,
Bethany is playing a game with her sister,
Each player starts with 3 shuffled decks of cards turned upside down in 3 separate piles
At each turn they draw 2 cards, 1 from the top of 2 piles of their
choosing
Which 2 piles should Bethany draw from to have the best chance of winning the game = ?
Following combination of piles should be selected:-
Pile 1, has 2 face cards (Jack of Diamonds, Queen of Clubs) and pile 2 has 2 face cards (Jack of Spades, Ace of Diamonds), so by drawing from these two piles, Bethany has a total of 4 face cards to choose from.Pile 3 only has 1 face card (King of Spades), so drawing from this pile alone would give her a lower chance of winning the game.To have the best chance of winning the game, Bethany should draw from piles 1 and 2.
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IS THIS A FUNCTION, AND WHY
Answers
Answer:
Yes, it is a function
Step-by-step explanation:
It is a function because for every y value there is a different x value. We can also use the vertical line test to see if there are two points on the same line.
find the value of X for which m is parallel to n .
Answers
Answer:
x = 42
Step-by-step explanation:
the angles are considered congruent so the equation would be 4x-27 = 3x+15
add 27 to both sides: 4x= 3x +42
subtract 3x from both sides: x= 42
If 500x =500 then x equals?
Answers
Answer:
x=1
Step-by-step explanation:
Help, I’m stuck. Lol.
Answers
Answer:
a. height = 12
b. area = 228
Step-by-step explanation:
a. To find the height, we can use the triangle formed by the side that measures 15, the side that measures 9. and the height. The hypotenuse of the triangle(the longest side opposite of the right angle), is 15. We can then use the Pythagorean Theorem, which states that [tex]a^2+b^2=c^2[/tex], where c is the hypotenuse, and a and b are the two other sides. In this case, we need to find a leg of the triangle, not the hypotenuse. What do we do? We can first call the height a, and rearrange the Theorem into [tex]c^2-b^2=a^2[/tex]. [tex]15^2=225, 9^2=81,[/tex] and [tex]225-81=\sqrt{144}[/tex]=12. Therefore, the height of the parallelogram is [tex]\boxed{12}[/tex]
b. To find the area of the parallelogram, we can use the area formula, which is Base*Height. The base is the flat side. We can find the base by adding 9+10=19, and [tex]19\cdot12=\boxed{228}[/tex]
5 = 4a -7 please help me
Answers
Answer:3
Step-by-step explanation:
Answer:
3
Step-by-step explanation:
CLT
5+7= 4a
12=4a
Divide through by 4
12÷4= 3
Solve for x in the following triangle.
Answers
Answer:
x = 12
Step-by-step explanation:
The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
8 + 6x is an exterior angle of the triangle, thus
8 + 6x = 30 + 4x + 2 = 4x + 32 ( subtract 4x from both sides )
8 + 2x = 32 ( subtract 8 from both sides )
2x = 24 ( divide both sides by 2 )
x = 12
The probability of rain for Monday is 40%. The probability of rain on
Friday is 20%.
What is the probability that it rains both days?
Answers
52 percent as 0.4 + 0.2 - 0.08 = 0.52
Answer:
52% is that an answer?
Step-by-step explanation:
What is the missing addend?
52,835 +
= 87,216
Answers
Answer: 34,381
Step-by-step explanation:
You have to subtract 52,835 by the sum 87,216 which will get you the answer of 34,381
The missing addend is 34,381.
87,216-52,835=34,381
2. Ilang kontinente ang bumubuo sa daigdig?
A. 5
B. 6
C. 7
D. 8
D
Answers
Answer:
C.7
Step-by-step explanation:
Ang mundo ay gawa sa tuluy-tuloy na dami ng lupa.
Ang mga lupaing ito ay nahahati sa mga rehiyon na tinutukoy namin bilang mga kontinente ng mundo.
Mayroong 7 mga kontinente sa mundo at ang mga ito ay:
1) Asya
2) Africa
3) Hilagang Amerika
4) Timog Amerika
5) Antarctica
6) Europa
7) Australia.
the perimeter of the triangle below is 38 units. Find the length of side WX. Write your answer without variables
Answers
Answer:
5.5
Step-by-step explanation:
Add each side of the triangle.
3z+z+1+4z-3 = 8z - 2
8z - 2 is equivalent to the perimeter.
Since you know the perimeter is 38 units, you can set 8z-2 to 38.
8z-2 = 38
Solve for z. Subtract 2 from each side.
8z = 36
Divide each side by 8.
z = 4.5
Now solve for side WX.
WX = z + 1
WX = 4.5 + 1
WX = 5.5
Camelia misses 8 points on the first math test. She misses 5 points on the second math test. What integer represents the number of points Camelia misses on the first two test?
Answers
7. The cost of a hotel room during Lacy's trip is
$325. The hotel room tax in the city she is in
is 10.5%. What is the total cost of the hotel
room? (Example 2)
Answers
Answer:
355.95
Step-by-step explanation:
i am going with my heart that this is correct.
In parallelogram JKLM, what is the relationship between angle j and angle k?
j° + k° = 180°
j° = k°
j° = -k°
j° - k° = 180°
1 of 4
Answers
Answer:
since j&k are interior angles if I added they should come up to 180° so j + k is equals to 180° yeah that's the answer
You can run 1/5mi in 2 min how long will it take you you run 2mi
Answers
Answer:
20 minutes
Step-by-step explanation:
evulate a^2 - b^2 if a=4 and b= -2
Answers
Answer:
20
Step-by-step explanation:
4^2 = 16
-2^2 =-4
16 -(-4) =20
Please help me solve step by step
solve V = lwh for w
1.
2.
3.
4.
Answers
Here are two similar rectangles.
4 cm
4.8 cm
7 cm
Work out the area of the larger rectangle.
Answers
Answer:
[tex]40.32cm^{2}[/tex]
Step-by-step explanation
4*1.2=4.8
7*1.2=8.4
8.4*4.8=40.32
A rectangle is a two-dimensional shape where the length and width are different.
The length and width of the larger rectangle are 4.8 cm and 8.4 cm.
The area of the larger rectangle is 40.32 cm².
What is a rectangle?A rectangle is a two-dimensional shape where the length and width are different.
The area of a rectangle is given as:
Area = Length x width
We have,
Two similar rectangles:
Smaller rectangles:
Length = 4 cm
Width = 7 cm
Larger rectangles:
Length = 4.8 cm
We need to find the width of the larger rectangle.
Since the two rectangles are similar.
4 cm = 4.8 cm
Multiply 7/4 on both sides.
7/4 x 4cm = 7/4 x 4.8 cm
7 cm = 8.4 cm
Now,
Larger rectangle:
Length = 4.8 cm
Width = 8.4 cm
Now,
The area of the larger rectangle:
Area = Length x width
Area = 4.8 x 8.4
Area = 40.32 cm²
Thus,
The area of the larger rectangle is 40.32 cm².
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A certain even integer is 32 less than twice the next even integer. Find the integer.
I know the answer is 28 but I do not know how to get to that answer. I could use help ASAP.
Answers
Answer:well you should have paid more attention in class
Step-by-step explanation:
Laura checked her outdoor thermometer and noticed that the temperature rose from 31 degrees in the morning to 45 degrees in the afternoon. What is the approximate percent increase for the day so far?
Answers
Answer: 45%
So for some reason I need to add at least 20 words? So... yeah... the answer is 45%
Answer: 45%
Step-by-step explanation:
what is the mean of the data set? 61, 38, 40, 53
Answers
Answer:
48Step-by-step explanation:
Mean = Sum of all values/ total no of data
[tex]\frac{61+38+40+53}{4} \\\\= \frac{192}{4} \\\\=48[/tex]
what % is 60 of 45%?????????????????
Answers
Explanation:
a = p% of b
45 = p% of 60
so you basically divide 60 by 45.
45 / 60 = .75
.75 is equivalent to 75%
The answer is 75%
Solve: -3 - (-5) + (-2)
Answers
Answer:
answers 0
Step-by-step explanation:
Answer:
0
Step-by-step explanation:
-3+5=2
2-2=0
Mai’s kitchen table measures 4 cm by 2.5 cm on the scale drawing.
Answers
Answer:
nice
Step-by-step explanation:
Im not sure what I have to solve here....
3 pounds of peanuts for $7.50. How much is the cost per pound
plz put in comments i dont have brainly plus :/
Answers
Answer:
you take 7.50 and divide it by 3 which equals $2.50
F&J Farms sells super egg-laying chickens that historically weigh on average 3 pounds with a standard deviation of 0.4 pounds. However, it has been discovered that the chickens actually weigh twice as much as they used to. What is actual the mean and standard deviation of the chickens?
Answers
Answer:
Mean of chicken = 6 pounds, Standard Deviation of chicken = 0.6 pounds
Step-by-step explanation:
Given : Chickens mean & standard deviation = 3 & 0.4 pounds respectively. Chickens considered weigh twice actually now.
If all numbers in the series are multiplied by a constant, the mean gets multiplied by that constant. So, new mean = 3 x 2 = 6
If all numbers in the series are multiplied by a constant, the standard deviation gets multiplied by that constant. So, new standard deviation = 0.4 x 2 = 0.8
What’s 1 divided by 3
Answers
Answer:
0.3 (3 repeating)
Step-by-step explanation:
Hope this helps!!
Answer:
0.33333333333333333333333333333333
Step-by-step explanation:
Adjust point D so the measure of angle BAD is equal to the measure of angle CAD. Which statements are true? Check all that apply.
AD bisects ∠BAC.
AD bisects BC.
AD forms right angles with BC.
AD is perpendicular to BC.
AD is the perpendicular bisector of BC.
Answers
Answer: AD bisects BC
AD forms right angles with BC
AD is the perpendicular bisector of BC
Step-by-step explanation:
What is 14/20 as a percent
Answers
Remember 'bout :
Percent is /100
So :
14 ×5 70
-------- = ----- -
20×5 100
70 %
Im sorry if im wrong
6x - 2 3x + 7 18. Identify the segment bisector of RS. Then find RS. (Section 1.3) M R S
Answers
Answer:
m is 7
Step-by-step explanation:
The length of RS is 32.
Given,
M is the bisector of RS
RM = 6x - 2
MS = 3x + 7
We need to find RS.
What does it mean to be a bisector point in a line?A bisector point in a line divides the line into two equal halves.
Example:
A_____B_____C
B = midpoint
AB = BC
AC = AB + BC
We have,
R_____M______S
RS = RM + MS
M = bisector
RM = MS
RM = 6x - 2
MS = 3x + 7
6x - 2 = 3x + 7
6x - 3x = 7 + 2
3x = 9
x = 9/3
x = 3
Now,
RS = RM + MS
RS = 6x - 2 + 3x + 7
RS = 9x + 5
RS = 9 x 3 + 5
RS = 27 + 5
RS = 32
Thus the length of RS is 32.
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