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
What is the value of the x-coordinate that is 9 units to the left of (4, -7)?
Answers
Answer:
-5
Step-by-step explanation:
If cheese costs $4.50 per pound, what will be the total cost of 3.5 pounds of cheese?
Answers
Answer: 15.75
To find the answer to the question, we have to multiply.
4.50 x 3.5 = 15.75
So, the answer to the question is 15.75.
Hope this helps!
Lisa is collecting data by interviewing people on the streets. She
interviewed 21 people in 3 hours.
At this rate, what is the total number of the people she interviewed if
she works for an additional 2 hours?
Answers
Answer:35 you are welcome
Step-by-step explanation:
Alexandria High School scored 37 points in a football game. Six points are awarded for each touchdown. After each
touchdown, the team can earn one point for the extra kick or two points for a 2-point conversion. The team scored one
fewer 2-point conversions than extra kicks. The team scored 10 times during the game. How many touchdowns were
made during the game? Write and solve a system of equations to get your answer.
Answers
Answer:
Five touchdowns were made in the game
Step-by-step explanation:
Here, we want to know the number of touchdowns made during the game.
We proceed as follows;
Let the number of touch downs be x
So the total points earned through touchdowns is 6 * x = 6x
The number of scores is 10 times
Let the number of extra kick be y which means that the number of conversions will be (y-1)
So the total number of score times will be ;
x + y + y-1 = 10
x + 2y = 11 •••••••••(i)
Now let’s work with points
Touch down points = 6 * x = 6x
Points from extra kick = 1 * y = y
Points from 2-point conversions = 2(y-1) = 2y - 2
So;
6x + y + 2y -2 = 37
6x + 3y = 37 + 2
6x + 3y = 39
divide through by 3
2x + y = 13 •••••••(ii)
So now solve simultaneously
From ii, y = 13 - 2x
Put this into i
x + 2(13-2x) = 11
x + 26 - 4x = 11
x -4x = 11-26
-3x = -15
x = -15/-3
x = 5
There are five touchdowns in the game
There are Five touchdowns were made during the game.
Here,
Alexandria High School scored 37 points in a football game. Six points are awarded for each touchdown.
After each touchdown, the team can earn one point for the extra kick or two points for a 2-point conversion.
The team scored one fewer 2-point conversions than extra kicks. The team scored 10 times during the game.
We want to know the number of touchdowns made during the game.
What is system of equations?
A system of equations is a collection of two or more equations with a same set of unknowns.
Now,
Let the number of touch downs be x
So, the total points earned through touchdowns is;
6 * x = 6x
The number of scores is 10 times
Let the number of extra kick be y which means that the number of conversions will be (y-1)
So, the total number of score times will be ;
x + y + y - 1 = 10
x + 2y = 11 •••••••••(i)
Now let’s work with points
Touch down points = 6 * x = 6x
Points from extra kick = 1 * y = y
Points from 2-point conversions = 2(y-1) = 2y - 2
Hence;
6x + y + 2y -2 = 37
6x + 3y = 37 + 2
6x + 3y = 39
divide through by 3
2x + y = 13 •••••••(ii)
So, now solve this;
From ( ii ), y = 13 - 2x
Put this into ( i )
x + 2(13-2x) = 11
x + 26 - 4x = 11
x -4x = 11-26
-3x = -15
x = -15/-3
x = 5
Hence, There are Five touchdowns were made during the game.
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What is the equation of the line?
Answers
Answer:
y = 1/2x + 2
Step-by-step explanation:
The y-intercept is 2 because it passes through the y axis at (0,2) and the slope if 1/2
Hope that helps and have a great day!
Answer:
[tex]y=\frac{1}{2}x+2[/tex]
Step-by-step explanation:
To find the equation for the line, lets try to find the slope and y-intercept of the line.
From looking at the graph, we can see that the line intersects the y-axis at y = 2. So the y-intercept would be 2.
The slope of the line would be the rise divided by the run. Looking at the graph, we can see that for every 2 the line moves in the x-direction, it moves 1 in the y-direction. This means that the rise is 1 and the run is 2. So the slope would be 1/2.
So we now know that the slope is 1/2 and the y-intercept is 2, we can now plug the information into the slope-intercept form.
Slope-intercept form is:
y = mx + b
where m is the slope and b is the y-intercept.
Plugging in we get
[tex]y=\frac{1}{2}x+2[/tex]
And now we have the equation of the line.
I hope you find my answer and explanation to be helpful. Happy studying.
a company took 59 employees to a management conference across the country. Each round trip plane ticket cost $799. What was the total amount needed to take the employees to the conference?
Answers
Answer:
47,141
Step-by-step explanation:
I'm pretty sure that's right. Hope I helped <3
Answer:
Its this $47,141
Clare and Han have summer jobs stuffing envelopes for two different companies.
Clare's earnings can be seen in the table.
Number of Envelopes Money in Dollars
400 40
900 90
Han earns $15 for every 300 envelopes he finishes.
a. Who would make more money stuffing 1500 envelopes?
How much more would they make? $ more
b. What is the rate of change for each situation.
Clare = per
Hans = per
c. Who gets pair more in their job?
gets paid more.
Answers
Answer:
yes
Step-by-step explanation:
15 x 300 = 7500
Write the ratio 4 to 9 in two different ways
Answers
Answer:
4;9
4 to 9
4/9
or 4 blocks and 9 circles
Step-by-step explanation:
The height of a building is 72 m. Find the angle of elevation from a point on ground level that is 55 m away from the base of the building
Answers
Answer:
52.6 degrees
Step-by-step explanation:
tan^-1(72/55)
Angle of elevation is equals to 52°7'(approximately).
What is angle of elevation?
" Angle of elevation is the angle between the horizontal plane and line of sight from the point of observation."
Formula used
In a right angled triangle,
tanθ = ( opposite side) / adjacent side)
According to the question,
As shown in diagram
Height of the building (AB) = 72m
Distance between base of the building and point of observation
(BC)= 55m
Angle of elevation = θ
Substitute the value in the formula we have,
tanθ = AB / BC
= 72 / 55
⇒ θ = tan⁻¹ (72 /55)
= tan ⁻¹(1.3091)
= 52° 7' (approximately)
Hence, angle of elevation is equals to 52°7'(approximately).
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PLEASE HELP MEE OUTT!!
ILL MARK UR ANSWER AS BRAINLIST
2) Find the midpoints of the line segment with endpoints ( 4 12, 5/2) and ( 10/7, 4/7)
3) suppose you have lunch with five friends and the total check (with tax and tips) is $252. how much should each person pay if you split the check evenly.
Answers
Answer:
you will each pay $50 and 4 cents
Step-by-step explanation:
Answer:
2) (37/42,43,28)
3) $50.40
Step-by-step explanation:
2)
[tex] \frac{4}{12} + \frac{10}{7} = \frac{37}{21} \div 2 = \frac{37}{42} [/tex]
this is for x
[tex] \frac{5}{2} + \frac{4}{7} = \frac{43}{14} \div 2 = \frac{43}{28} [/tex]
this is for y and the midpoint is (37/42,43/28)
3)
[tex]252 \div 5 = 50.40[/tex]
I think this is the answer
guys what is 1 + 1
ive been trying to solve it all day
teachers give IMPOSSIBLE questions!!
Answers
Answer: AHHHHHH I WILL HELP
Step-by-step explanation:The statement which describes the meaning of the slope is " The boiling point decreases by 1.8 degrees as the altitude increases by 1,000 feet " ⇒ D
Step-by-step explanation:
The boiling point of water (measured in degrees), at altitude (measured in feet), is modeled by the function T(a) = −0.0018 a + 212, where
a is the altitude measured in feet
T(a) is the boiling point of water in degree
The form of the linear function is f(x) = mx + b, where m is slope (the rate of change), and b is the y-intercept (the value of f(x) at x = 0)
By comparing between the form of the function and the given function
∴ m = -0.0018 ⇒ degrees per foot
∵ The sign of the slope is negative
∵ The slope = Δf(x)/Δx
- That means T(a) is decreasing function
∴ The boiling point is decreases when the altitude increasing
∵ -0.0018 = degrees per feet
∴ The boiling point decreases by 18 degrees as the altitude
increases by 10,000 feet or the boiling point decreases by 1.8
degrees as the altitude increases by 1,000 feet
The statement which describes the meaning of the slope is " The boiling point decreases by 1.8 degrees as the altitude increases by 1,000 feet "
Learn more:
You can learn more about the linear function in brainly.com/question/9801816
ITS 2
One pound of candies costs $3.50.
How much will we have to pay for 0.2 lb?
Answers
four a number, increased by one , is between seven and thirteen .
Answers
(4x+7)(4x+7) um help pls? idk how to math >~<
the assignments due in like 30 minutes aaaaaa
Answers
Solving Steps:
car A is traveling east at a steady speed of 60 miles per hour after 2 hours, it is 130 miles east of Johnstown. car B is traveling east on the same road. its distance east of Johnstown is represented by the graph.
plzzzzzzzzzzzzzzzzz help mee
Answers
Answer:
There's no numbers on this graph. it you can tell me where it is, ill gladly update my answer. Other than that, I know exactly what they are saying, I just need numbers.
Step-by-step explanation:
help me please !! ❤️❤️
Answers
Answer:
Sorry, I don't understand what m and a||b means. If you are able to explain it to me, I can follow up for this question. much appreciated, Accqty.
Step-by-step explanation:
number of your answer choice and the answer itself.
2. The point (5,-9) is the image under the translation (x, y) = (x + 4, y - 2). What is the pre-image?
1) (9,-11)
2) (1, -7)
3) (1, -11)
4) (20, 18)
+ Ac
Pear Deck Interactive Slide
Students, write your response!
Answers
Answer:
Answer: (1,-7)
Step-by-step explanation:
since the translation is under (x + 4, y - 2)
the symbols (+ and -) would change so the translation to use would be
(x - 4, y + 2)
so you plug in (5, -9) to the new translation and you get your answer which is (1,-7)
What is the reverse of "multiply by 4"?
O A. subtract 4
O B. divide by
O C. add 4
O D. divide by 4
Answers
Answer:
D - divide by 4
Step-by-step explanation:
Answer:
D rip I'm late :(.......
11. 11 - a when a = -3
12.x^3 when x =-3
pls helppp step by step
Answers
Answer:
11) 14
12) -27
Step-by-step explanation:
11-a when a=-3
Plug in -3 into the equation
11-(-3)
A negative times a negative becomes a positive
So the equation becomes 11+3
Answer is 14
x³ when x=-3
Plug in -3 into the equation
-3³
Solve, which should give you -27
Juan bought a used bike from his uncle $20.6 each month for 2 years. What was the total amount Juan paid for the bike?
Answers
Answer:
$494.40
Step-by-step explanation:
What was the price of one candle before the sale?
Answers
Answer:
$4.69
Step-by-step explanation:
HOPE THIS HELPEDDDD ❤✨
Answer:
The original price of the candles was $4.69
Step-by-step explanation:
$11.96 (price of 4 candles) ÷ 4 candles = $2.99 (how much each candle costs)
$2.99 (how much each candle costs) + $1.70 (how much the price of the candles lowered) = $4.69 (the old price per candle)
(hope I helped)
Which statement is correct?A. -1.5 < -2, B. 2.5 < -3 ,C, 3.5 <2.5 D, 2<-1
Answers
I don't know the answer
Answers
=(64) + (32)
=96
Hope this helps!
Please help. Only help if you know the answer
Answers
Answer:y-7=-9/8(x-0)
Step-by-step explanation:
Answer:
y -7 = -9/8 (x-0)
Step-by-step explanation:
i hope it help
180 minus what = 45
i really need this answer thank you
Answers
Answer: 135
Step-by-step explanation: All you need to do is 180-45=135.
The 180 minus 135 is equal to 45.
To find the value that, when subtracted from 180, gives a result of 45, set up the following equation:
180 - x = 45
To solve for x, to isolate it on one side of the equation by subtracting 180 from both sides:
180 - 180 - x = 45 - 180
Simplifying:
-x = -135
Now, to solve for x, multiply both sides of the equation by -1 to change the sign:
(-1) × (-x) = (-1) × (-135)
x = 135
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What is one idea that Andre doesn’t understand about rotations?
Answers
Answer:
457367
Step-by-step explanation:
A line passes through the points (8,-1) and (-4, 2).
What is the y-intercept of this line? O-4
O-1
O 1
O 4
Answers
Answer:
04
Step-by-step explanation:
0 -4 zero is just zero so 4 replace
Answer:
4
Step-by-step explanation:
As you walk to your car, you notice that your tire is nearly flat! The initial psi level yesterday was 40 but it is now only 38 today. If this trend continues and the tire keeps losing the same percentage of air, how much should be left at the end of the week rounded to 1 decimal? (7 days later)
Answers
Answer:
Step-by-step explanation:
Given that:
Initial psi yesterday = 40 psi
psi today = 38 psi
If trend continues and tire loses the same percentage of air. How much air will be left in tire at the end of the week
1 week ( 7days)
Total loss after 7 days = (amount lost per day * number of days)
Total psi lost per day= [(40 - 38) = 2
% psi lost = (2/40) * 100
= 5%
Applying the exponential loss functin:
A = I ( 1 - r)^t
t = 7days ; r = 5% = 0.05 ; A = amount left ; I = Initial amount
A = 40(1 - 0.05)^7
A = 40(0.95)^7
A = 40 * 0.69833729609375
A = 27.933
A = 27.9 psi
Evaluate:
a) 53.24 ÷ 9.351
Answers
Answer:
5.693508715645386
Step-by-step explanation:
Answer:
Answer is 5.69350871565
Step-by-step explanation:
3. Translate the triangle 3 units left
and 2 units up. What are the
coordinates of the image?
Answers
Answer:
p: (-2,2)
q: (1,4)
r:(3,3)