Analyze the figure and the two-column proof.
Triangles A F C and D E B overlap and intersect at point X. Point B of triangle D E B is on side A C of triangle A F C. Point C of triangle A F C is on side B D of triangle D E B. Angles A F C and B E D are right angles. Sides F A and E D are congruent. Line segments A B and C D are congruent.
Which statement/reason pair can be used when proving FC ≅ EB?
♣: Δ ≅ ΔAFC
♦:
Answers
Answer:
1st one: DEB
2nd one: HL
Step-by-step explanation:
By segment addition property, the lengths of the hypotenuse side of both
triangles ΔAFC and ΔDEB are equal.
Response:
A statement/reason pair that can be used when proving [tex]\overline{FC}[/tex] ≅ [tex]\overline{EB}[/tex] is presented as follows: Statement; ΔAFC ≅ ΔDEB, reason; HL Method used to obtain the above responsePlease find attached the diagram representing the triangles
ΔAFC and ΔDEB overlap
Point B is located on side [tex]\mathbf{\overline{AC}}[/tex]
Point C is located on side [tex]\mathbf{\overline{BD}}[/tex]
∠AFC = ∠BED = 90°
[tex]\overline{FA}[/tex] ≅ [tex]\overline{ED}[/tex]
[tex]\overline{AB}[/tex] ≅ [tex]\overline{CD}[/tex]
A statement and reason pair that can be used to prove that [tex]\overline{FC}[/tex] ≅ [tex]\overline{EB}[/tex] is given as follows;
Statement [tex]{}[/tex] Reasons
[tex]\overline{FA}[/tex] ≅ [tex]\overline{ED}[/tex] [tex]{}[/tex] Given
ΔAFC and ΔDEB are right triangles[tex]{}[/tex] Definition of right triangles
[tex]\overline{AB}[/tex] = [tex]\overline{CD}[/tex] [tex]{}[/tex] Definition of congruency
[tex]\overline{BC}[/tex] ≅ [tex]\overline{BC}[/tex] [tex]{}[/tex] Reflexive property
[tex]\overline{BC}[/tex] = [tex]\overline{BC}[/tex] [tex]{}[/tex] Definition of congruency
[tex]\overline{AB}[/tex] + [tex]\overline{BC}[/tex] = [tex]\overline{CD}[/tex] + [tex]\overline{BC}[/tex] [tex]{}[/tex] Substitution property
[tex]\overline{BD}[/tex] = [tex]\overline{AC}[/tex] [tex]{}[/tex] Substitution and segment addition property
ΔAFC ≅ ΔDEB [tex]{}[/tex] Hypotenuse leg (HL) rule of congruency
[tex]\overline{FC}[/tex] ≅ [tex]\overline{EB}[/tex] [tex]{}[/tex] CPCTC
CPCTC is the acronym for Corresponding Parts of Congruent Triangles are Congruent
A statement/reason pair that can be used is therefore;
ΔAFC ≅ ΔDEB / Hypotenuse leg (HL) rule of congruencyLearn more about congruency theorem here:
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Related Questions
In the figure, angle D measures 31° and angle A measures 27°.
Answers
Answer:
Well, if the figure is a triangle than the missing side would be 122 degrees, if it is a square, then it would be 302 degrees.
Step-by-step explanation:
Hope this helps!
What is the quotient of m^6/5/5/m^2? Assume m0.
Answers
Answer:
m^8/25
Step-by-step explanation:
Answer:first option
Step-by-step explanation:
right on edge
2 right triangles have identical angle measures but different side lengths. The first triangle has side lengths of 6, 10, 8 and the second triangle has side lengths of 3, 5, 4. Which transformation maps the large triangle onto the small triangle? dilation reflection rotation translation
Answers
Answer:
Dilation
Step-by-step explanation:
The transformation maps the large triangle onto the small triangle will be dilation. Then the correct option is A.
What is a transformation of geometry?A spatial transformation is each mapping of feature shapes to itself, and it maintains some spatial correlation between figures.
Dilation does not change the shape, but changes the size of the geometry.
2 right triangles have identical angle measures but different side lengths.
The first triangle has side lengths of 6, 10, 8 and the second triangle has side lengths of 3, 5, 4.
The transformation maps the large triangle onto the small triangle will be
6 / 3 = 10 / 5 = 8 / 4 = 2
Then the small triangle is dilated by 2.
Then the correct option is A.
More about the transformation of geometry link is given below.
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what is the sum 3/x^2-g + 5/x+3
Answers
======================================================
Work Shown:
[tex]\frac{3}{x^2-9} + \frac{5}{x+3}\\\\\frac{3}{x^2-9} + \frac{5(x-3)}{(x+3)(x-3)}\\\\\frac{3}{x^2-9} + \frac{5x-15}{x^2-9}\\\\\frac{3+5x-15}{x^2-9}\\\\\frac{5x-12}{x^2-9}\\\\\frac{5x-12}{(x+3)(x-3)}\\\\[/tex]
The idea is to get the denominators to be the same to the LCD (lowest common denominator). Note in step 2, I multiplied top and bottom by (x-3) to get this done. Then in step 3, I used the difference of squares rule to get x^2-9. Afterward, we can combine the fractions and like terms.
Is (3, 2) a solution of -8x – 2y < 6?
Answers
Answer:
yes
Step-by-step explanation:
To determine if the point is a solution, substitute the coordinates into the left side of the inequality, evaluate and compare with right side.
- 8(3) - 2(2) = - 24 - 4 = - 28 < 6
Thus (3, 2) is a solution
Answer:
Yes.
Step-by-step explanation:
Let's substitute x = 3 and y = 2 into the inequality:
-8(3) - 2(2) = -28 which is less than 6 so it is a solution.
A Weather Forecaster, predicts that there is a 25% chance of rain on Saturday and a 40% chance of rain on Sunday. If these probabilities are correct, what is the probability that it will rain both days?
32.5%
10%
12%
65%
Answers
Answer:
10%.
Step-by-step explanation:
These 2 probabilities are independent so we multiply them:
Prob(It rains both days) = 0.40 * 0.25
= 0.10
= 10%.
=
Find the value of X
X=
Part B
Find the measure of RPS
A. 45
B. 36
C. 60
D. 64
Answers
Answer:
x=8
RPS = 36
Step-by-step explanation:
QPS = 180
The two angles that form QPS
QPR + RPS = 180
7x+88 + 3x+12 = 180
Combine like terms
10x+100 =180
Subtract 100 from each side
10x = 180-100
10x = 80
Divide by 10
x =80/10
x = 8
RPS = 3x+12
= 3(8)+12
24+12
36
Edward has $8000 in a savings account, has $2500 invested in the stock
market, owns home worth $30,000, has $20,000 left on his student loan
payment, and he has a $600 outstanding credit card debt. What is Edward's
total net worth?
A.19,900
B. 30,000
C. 20,600
D. 40,500
Answers
Answer:A 19900
Step-by-step explanation:
Answer:
A.19,900
Step-by-step explanation:
hope this helps!!
A telescope costs $98. It is on sale for 35% off. What is the cost of the telescope after the discount?
Answers
Answer:
To solve this equation first we need to find out how much is 35% of $98.
The percentage of a number is found by multiplying the percentage by the number:
35% x $98 = $34.3
So the 35% off the telescope equals a discount of $34.30.
Now let’s find the price after the discount.
We need to subtract the discount price from the original price:
$98 - $34.30 = $63.70
So we know that the price of the telescope after the discount is $63.70
plzzz mark me brainliest if this helped :)
I need 3 more brainliests to become an expert
Are there more 3-digit numbers that can be divided by at least one of the numbers 4, 7, or 9, or 3-digit numbers that cannot be divided by either one of them? I need ASAP! HELP! please provide an explanation.
Answers
Answer:
Yes there are more 3-digit numbers that can be divided or not divided by 4, 7, or 9
Step-by-step explanation:
Any real number can be divided by those numbers but you may get decimals as well.
There are less 3-digit real numbers that can be divided by at least one of the numbers 4, 7, or 9. Therefore, it's false.
How to compute the number?It should be noted that for a number to be divisible by 9 and 7, it has to be divisible by 63. Therefore, we have all the three digit multiple of 63.
In this case, there are less 3-digit real numbers that can be divided by at least one of the numbers 4, 7, or 9.
Learn more about real number on:
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Using Identity, find the value:
i) 203 x 205
Plss I NEED HELP!!! T^T
Answers
Step-by-step explanation:
203*205
(200+3)*(200+5)
200²+200(5+3)+15
40000+3000+15
403015
Which equation best represents the data given in the table ?
Answers
Answer:
B
Step-by-step explanation:
The equation that satisfies the above table is y = 8[tex](\frac{1}{2})^{x}[/tex]
Given,
Table between x and y .
Here,
To get the equation between x and y first justify the data given in the table.
So,
When,
x = -3 , y = 64
x = -2 , y = 32 .
In the equation y = 8[tex](\frac{1}{2})^{x}[/tex] substitute the values of x and check for y .
Put x = -3 ,
y = 8[tex](1/2)^{-3}[/tex]
y = 8 * 8
y = 64
Thus it satisfies the value given in the table .
So the correct equation will be Option B .
Know more about equations,
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The graph of f(x) = (xl is reflected across the y-axis and
translated to the left 5 units. Which statement about the
domain and range of each function is correct?
Answers
Answer:
The range is different. (Last option)
Step-by-step explanation:
Since the graph was reflected, the range will change since it is no longer a minimum amount but a maximum amount that it will reach. The domain will continue to stay the same because the x values it will reach are still all real numbers.
Choose the right answer.
Which year had a decrease in profit between months 3 and 4?
Last year
This year
Answers
Step-by-step explanation: last year
Answer:
Last Year
Step-by-step explanation:
If you take a look at the red and blue lines in between the numbers 3 and 4 at the bottom of the graph, you can see that the profit for the red line (last year) is decreasing while the profit for the blue line (this year) is increasing. Last year (red line) had a decrease in profit between months 3 and 4.
what’s the answer to this ?
Answers
Answer:
1.43cm
Step-by-step explanation:
I hope it helps :)
360/9 (x is 9) is 40
Then we multiple that number by the radius
40 x 9.1 is 364
Then we multiply that by 2pi
Arc length = 1.42
Create a list of steps, in order, that will solve the following equation.
3(x+2)^2=48
Answers
Answer:
Start with the given equation.
%28x-2%29%5E2=%2848%29%2F%283%29 Divide both sides by 3.
%28x-2%29%5E2=16 Reduce.
x-2=%22%22%2B-sqrt%2816%29 Take the square root of both sides.
x-2=sqrt%2816%29 or x-2=-sqrt%2816%29 Break up the "plus/minus" to form two equations.
x-2=4 or x-2=-4 Take the square root of 16 to get 4.
x=2%2B4 or x=2-4 Add 2 to both sides.
x=6 or x=-2 Combine like terms.
Step-by-step explanation:
Steps: Divide both sides by 3
- Then take square root of both sides
- Separate the equation like this:
x+2= -4
x+2= 4
- Solve for x:
To get -6 subtract -4 and 2
To get 2 subtract 4 and 2
x= -6
x= 2
Simplify (2^3)^–2. 70 points
a. -1/64
b. 1/64
c. 2
d. 64
Answers
Answer:
1/64
Step-by-step explanation:
(2^3)^-2
= 1/((2^3)^2)
= 1/2^6
= 1/64
---
Hope this helps! :) If so, please mark my answer as brainliest!
The right answer is 1/64
please see the attached picture for full solution
Hope it helps.....
omg please help meee fastttt
Answers
Answer:
Jill will make less money if they both work 3 hours
Step-by-step explanation:
Trust me. I hope this helps :)
The last option(D)
I need answer, help
Answers
Answer:
60 percent
Step-by-step explanation:
(30/50)=60%
A scale drawing of a square has a side length of 6 millimeters. The drawing has a scale of 1 mm : 7 km. Find the actual perimeter and area of the square.
Answers
P=168km
An actual square will ALWAYS have the same lengths on each of the 4 sides. Therefore it will be 6mm all around the square. There are different ways to solve this type of problem but we’ll go with this one.
First you want to understand that the scale is a ratio or a fraction. With fractions you multiply the numerator or denominator, but if you multiply or divide with one, you must with the other. In this case the ratio (we can put it in fraction form) is 1/7. Now you want to make it to where the 1 (because it is a mm) becomes 6 because that’s how many mm we have on each side. To do that you need to find what times 1 is equal to 6 (which is 6 itself).
Now that you found what the numerator will be, we need to also multiply 7 by 6 because what you do with one side you must do to the other. So 7*6 will be 42. Your new fraction (or ratio) is 6/42.
Finally you should know that since a square has 4 sides you need to multiply what one side length of the square is by 4 for the perimeter. Because 6mm is 42km (because of the ratio) then do 42*4 which is 168.
Finding the area is much simpler with the already known lengths, area is l*w, which in this case for the square is just two side lengths times eachother. 42*42= 1764.
Elene and abbi are in a race. Elene can run 3 meters per second and abbi can run 2 meters per second. Elene gives abbi a 10 meter head start. How long will it take for elene to catch abbi?
Answers
Answer:
10 Seconds
Step-by-step explanation:
Speed of Elene = 3m/s
Speed of Abbi = 2m/s
Let the time be t seconds taken by Elene to catch abbi.
Distance for any speed S and time is calculated by formula given below
Distance = speed * time
distance covered by Elene in time t = 3m/s * t = 3t m -->equation Adistance covered by Abbi in time t = 2m/s* t = 2t m --> equation BSince it is given that Elene has given abbi 10 m head start it means that
Elene has to run extra 10 meters than Abbi to catch abbi.
Thus we can say that
distance run by Elene = 10 m + distance run by Abbi
Substituting that value distance run by Elene from equation A
and distance run by Abbi from equation B
we have
3t = 2t +10
=>3t - 2t = 10
=> t = 10
Therefore it will take 10 second for elene to catch abbi.
From the moment the first car started how many hours will it take the second car to catch up to the first
Answers
Answer:
HELP
Step-by-step explanation:
1. A space figure with two parallel and congruent bases can be any of these except a
A cone
B prism
c cylinder
Dcube
Answers
Answer:
C. cylinder
Step-by-step explanation:
i hope this help
-1 3/7 • (-3 2/5)
Find the product simplify if possible
Answers
Answer:
6 4/5
Step-by-step explanation:
-1 3/7 • (-3 2/5)
Let's turn them both into fractions with no whole numbers to make this easier:
-10/7 • -17/5
Now we can multiply straight across much easier!
170/35 (the negatives canceled each other out)
34/5 (simplified)
6 4/5 (answer)
Hope this helps! Please mark Brainliest :)
choose the function whose graph is given by:
Answers
Answer:
Option C
(would really, reallly appreciate the brainliest)
Step-by-step explanation:
plotted with desmos (free online math tool)
The function whose graph is given is y = 0.5cosx
What is a function?A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
Given that, a graph we need to find its function,
To analyze the given graph let us,
compare the given to a known, standard functiontake maxima and minima points from the graph and analyze them.From the given graph we can pick the points which can tell us about the nature of the cosine function we took,
It is clear from the graph that the function plotted is equal to the standard function i.e. cos(x)
in cos(x) ⇒ we have minima at (-π, 1)
in the given graph, the function has a maximum and touches the y-axis at (0, 0.5)
Therefore, 0.5cosx is the function represented in the graph.
Learn more about function click;
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Can some help me thank you
Answers
What is the ratio of the volume of Cylinder A to the volume of Cylinder B? if cylinder a has the height of 4 and radius of 3 and cylinder b has the the height of 3 and radius of 4
Answers
Answer:
3/4
Step-by-step explanation:
Cylinder A
V = πr^2h
V = π(3)^2(4)
V = 36π
Cylinder B
V = π(4)^2(3)
V = 48π
36π/48π
3/4
9) A cooler contains eight bottles of sports
drink: four lemon-lime flavored and four
orange flavored. You randomly grab a
bottle and give it to your friend. Then,
you randomly grab a bottle for yourself.
You and your friend both get lemon-lime.
Are the events independent or dependent?
What is the probability?
Answers
Answer:
dependent. 2/8=1/4
Step-by-step explanation:
help asap will mark brainliest
Answers
Answer:
76
Step-by-step explanation:
Alternate interior angles
Answer:
76
Step-by-step explanation:
Write an equation to represent the following statement.
The product of 12 and k is 84.
Solve for k.
k=
Answers
Answer:
12*k=84
k = 7
Step-by-step explanation:
Product means multiply and is means equals
12*k=84
Divide each side by 12
12k/12 = 84/12
k = 7
