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
Which descriptions are true of the function shown in the table? Check all that apply.
Quadratic
Linear
Rational
Y= 5x+10
Y=5x^2+10
Y=5/x+10
Answers
9514 1404 393
Answer:
LinearY = 5x+10Step-by-step explanation:
As x-values increase by 1, y-values increase by 5. This means the function is linear and has a slope of 5/1 = 5. The appropriate choices are ...
Linear
Y = 5x+10
Answer:
b & d
Step-by-step explanation:
yw
place holder for the question
Answers
Answer:
The area of the trapozoid would be 192 inches.
Step-by-step explanation:
Here are the steps on how to find the area of a trapozoid.
Add the two bases together. 14 + 18 = 32Divide that by 2. 32/2 = 16Then lastly multiply that by the height. 16 x 12 = 192.I hope I helped
brainliest would be appreciated.
What is the y-intercept of this function?
f(x) = 2(x - 7)2 - 32
(0,-32)
(0,66)
(0,-7)
(0,17)
Answers
Answer:
(0, 66 )
Step-by-step explanation:
To find the y- intercept, let x = 0 and solve for y
f(0) = 2(0 - 7)² - 32
= 2(- 7)² - 32
= 2(49) - 32
= 98 - 32
= 66
The coordinates of the y- intercept are (0, 66 )
Simplify the expression -1/2 (-5/6 + 1/3)
A. -5/12 + 1/3
B. 5/12 - 1/6
C. -5/12 + 1/6
D. 5/12 + 1/3
Answers
Answer:
5/12 - 1/6
Step-by-step explanation:
-1/2( -5/6+1/3)
Distribute
-1/2*-5/6 -1/2*1/3
5/12 - 1/6
Simplify the following expression
x^9*x^-4=x^n
Answers
Answer:
x^5 = x^n
Step-by-step explanation:
x^9*x^-4=x^n
x^5 = x^n
Tomas selects one of these garments at random. Let AAA be the event that he selects a blue garment and let BBB be the event that he chooses a shirt.
Please help!!!
Answers
Answer:
can u explain it more lol
Step-by-step explanation:
1)The probability of choosing a blue garment is 1/2
2)The probability of choosing a shirt is 1/3.
Thomas has 1 blue shirt
Thomas has 1 green shirt
Thomas has 1 blue hat
Thomas has 1 green scarf
Thomas has 1 blue pair of pants
Thomas has 1 green pair of pants
So, number of blue garments = 3
Number of shirts = 2
Total garments =6
What is probability?Probability is the measure of the likelihood of an occurrence.
P(event) = Favorable outcomes / Total outcomes
P(blue garment) = 3/6 =1/2
P(shirt) = 2/6 =1/3
Hence, 1)The probability of choosing a blue garment is 1/2
2)The probability of choosing a shirt is 1/3.
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What is the point-slope form of a line with slope -3 that contains the point
(10,-1)?
A. y+ 1 = 3(x + 10)
B. x + 1 = -3(y-10)
C. y + 1 = -3(x-10)
D. y + 1 = 3(x-10)
Answers
Answer:
C
Step-by-step explanation:
Since we have a point and a slope, we can use the point slope formula.
The point slope formula is:
[tex]y-y_{1} =m(x-x_{1})[/tex]
where m is the slope, and (x1, y1) is the point given.
We know that the slope is -3, and the point given is (10, -1)
Therefore, our m is -3, x1 is 10, and y1 is -1.
y- -1 = -3(x-10)
y--1 is the same as y+1
y+1= -3(x-10)
Therefore, choice C is correct.
answer the question below in the image
Answers
Answer:
c 100%
Step-by-step explanation:
polynomial division
(4x^2 +7x +6) ÷(x+ 2)
Answers
Answer:
4x2 + 7x - 6
————————————
x - 2
Step-by-step explanation:
Answer:
Step-by-step explanation:
There are many methods but I give you the factorisation:
[tex]4x^{2} +7x+6= 4x^{2} + 8x - x - 2 +8= (4x^{2} + 8x )- (x + 2) +8\\= 4x(x+2)-(x+2) -8\\=(x+2)(4x-1) +8[/tex]
So
[tex]\frac{4x^{2} +7x+6}{x+2}=\frac{(x+2)(4x-1)+8}{x+2} =\frac{(x+2)(4x-1)}{x+2}+\frac{8}{x+2}\\ \\=4x-1 +\frac{8}{x+2}[/tex]
That means the quotient is 4x-1 and the remainder is 8.
A restaurant added a new outdoor section that was 40 ft'. It
was 4 feet wide. How long is their new section?
Answers
Answer: 10
Step-by-step explanation:40 ft is the height and 4is the width so divide 40 by 4 and 10 is your answer
Morgan works at a store that sells clothing accessories. The supply function
for baseball caps is p= Q-4, where Pis the price and Q is the quantity of
baseball caps. If Morgan sells the baseball caps for $18 apiece, how many
baseball caps will the store supply?
A. 18 baseball caps
B. 22 baseball caps
C. 26 baseball caps
D. 4 baseball caps
Answers
Answer:
The number of supply of base balls is 22
Step-by-step explanation:
Given
P = Q - 4
Price = $18
Required
Number of supply
The relationship between price and quantity is given to be P = Q - 4 where price is represented by P and Q represents the quantity.
To get the quantity supply when price is $18, all you need to do is to substitute 18 for P in the above equation;
Thus, giving:
18 = Q - 4
Make Q the subject of formula
Q = 18 + 4
Q = 22 quantities
Hence, the number of supply of base balls is 22
Answer:
B. 22 baseball cap
Step-by-step explanation:
P=Q-4
Make Q the subject of the formula
P+4=Q
Therefore,
Q=p+4
If Morgan sells the baseball cap for $18
Q=18+4
Q=22
Morgan store will supply 22 baseball caps
MARKING BRAINLIEST!!! PLSS HELP ASAPP!! Plz show all work!!!
Answers
Answer:
CCCC IDK the type of vehicle but its c
Step-by-step explanation:
43.2+ 4 x 2.8 + (4.4 x 4 x 1/2) = 63.2
Please! I need brainliest
Mark had 45 football cards. Josh had twice as many football cards as Mark. Jo
then bought 5 more football cards. Which equation can be used to find f, the
number of football cards Josh has now?
A 2 x 45 + 5 = f
B 2 x 45-5 = f
C 2 + 45 x 5 = f
D 2 + 45 + 5=f
can someone help me please
Answers
Answer:
I think It will be A. I’m trying my best to help
Step-by-step explanation:
Find the area of the un-shaded region. The perimeter of the square is 16 feet. ( with explanation)
Answers
Answer:
12.56
The answer is 12.56 since the radius if the circle is 2². Multiply 2 by 2 since it is squared. Then multiply that product (4) by pi. 4 x π = 12.56
Will give brainliest answer
Answers
Answer:
Step-by-step explanation:
Diameter is 7cm
radius is diameter/2 = 7cm/2 = 3.5cm
Answer:
[tex]diameter = 7 \: \: cm \\ radius = 3.5 \: \: cm[/tex]
Step-by-step explanation:
[tex]d = 7 \: \: cm[/tex]
[tex]r = \frac{d}{2} \\ r = \frac{7}{2} \\ r = 3.5cm[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
Malik scores 24 goals in 8 soccer games. At that rate, how many goals will he sore in 15 games?
Answers
Answer:
45 goals
Step-by-step explanation:
You have the fraction 24/8
After you simplify it you get 3/1 (that’s the percentage of goals/games)
Supposing goals = x,
x/15 = 3/1
x= 45 goals
The lines shown below are parallel. If the green line has a slope of 5, what is
the slope of the red line?
Answers
Answer:
D
Step-by-step explanation:
By definition, any two lines that are parallel must have the same slope, since they are angled the same amount (they travel the same amount up over a certain sideways distance). Hope this helps!
The required slope of the red line is equal to 5. Option D is correct.
What is the slope of the line?The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.
Here,
The slope of the parallel line is always equal, so as of the given condition if green and red lines are parallel then the slope of the red line is equal to the slope of the green line.
The slope of the red line = slope of the green line
The slope of red line = 5
Thus, the required slope of the red line is equal to 5, Option D is correct.
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3. Find the value of X in degrees
Answers
180-64-45= 71. Angle x amd the interior angle create a 180 degree line. And 180-71= 109; the sum of the 2 angles in the triangle are equivalent to the exterior angle
On the beach, a cable is attached to the pier. The line formed by the cable has a slope of 3/5. Is the triangle formed by the pier, the beach, and the cable similar to the triangle formed by the boat, the parasailer, and the rope?
Answers
Answer:
That's kinda hard bro u sure ur in middle school
Step-by-step explanation:
Solve for the following system of equations by using the substitution method for x-y=0 and x-y-2=0
Answers
Answer:
The picture doesn't pop up.
Step-by-step explanation:
I need help pleaseee
Answers
Answer:(0,7)(1,42/5)
Step-by-step explanation:
Put one dot on (0,7), the other on (1,42/5)
The quadratic function d = –3x^2 + 16 models a skateboarder’s distance, in feet, from the bottom of a hill x seconds after the skateboarder starts moving down the hill. After how many seconds is the skateboarder 8 ft from the bottom of the hill?
Answers
Answer:
To find the solution, plug in 8 for d
d=-3x2+16
8=-3x2+16 Subtract 8 from both sides
0=-3x2+8
Now, use the quadratic equation to solve for x
a=-3
b=0
c=8
x=1.63 or
C. 1.6s
Step-by-step explanation:
The skateboarder is 8 feet from the bottom of the hill after 1.633 seconds.
What are Quadratic Functions?Quadratic functions are polynomial functions consisting of variables and exponents and the degree of the variable is 2.
The general form of a quadratic function is f(x) = ax² + b x + c.
Given that,
Quadratic function which models a skateboarder’s distance, in feet, from the bottom of a hill x seconds after the skateboarder starts moving down the hill is,
d = –3x² + 16
We have to calculate after how many seconds is the skateboarder 8 ft from the bottom of the hill.
d = 8 feet. Substitute it.
–3x² + 16 = 8
–3x² = 8 - 16
3x² = 8
x² = 8/3
x = √(8/3) seconds
≈ 1.633 seconds
Hence the time is approximately 1.633 seconds.
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Simplify each side of the equation.
6-4 = k-3k
Answers
Answer:
k = -1
Step-by-step explanation: 6-4 = k-3k
subtract: 2 = -2k
divide both sides by -2: k = -1
simplifying is easy! we simply add or subtract like terms on each side.
6-4=2
1-3=-2 and then add k which is the variable so -2k
The equation would be 2=-2k and then we can divide both sides by -2 to isolate the variable to get -1=k
Graph the equation of the line y=3x+4 and use it for your reference to find:
c
Quadrants in which this graph is in. (Use the numbers 1−4)
Answers
Answer:
The line is quadrants 1 2 and 3
Step-by-step explanation:
remember top right is 1
top left is 2
and bottom left is 3
Evaluate the expression.
-66/(-3) + (-4) - (-5)
Answers
Answer:
23
Step-by-step explanation:
Simplify the following:
(-66)/(-3) - 4 - -5
The gcd of -66 and -3 is -3, so (-66)/(-3) = (-3×22)/(-3×1) = (-3)/(-3)×22 = 22:
22 - 4 - -5
-(-5) = 5:
22 - 4 + 5
22 + 5 = 27:
27 - 4
| 2 | 7
- | | 4
| 2 | 3:
Answer: 23
22+-4=22-4=18
18 - -5=18+5=23
im having a crisis
2] Simplify: √3∙√6
A. √18
B. 3√2
C. 9√2
D. 4.24
3] 2√5∙4√5
Response: __________
4) The simplified form of √1749 is √177.
A. True
B. False
5) Simplify: √24√6
A. cannot be determined
B. √1446
C. 2
D. √6
6) Solve: 3x2 + 12 = 12
Response: __________
Answers
3. False
4.False
5. D
6. 18
Eric needs a $1,500 loan in order to buy a drone. Which loan option would cost him the MOST in interest?
A) A 24-month loan with a 6.25% annual simple interest rate.
B) A 30-month loan with a 6.00% annual simple interest rate.
C) A 36-month loan with a 4.00% annual simple interest rate.
D) A 42-month loan with a 3.75% annual simple interest rate.
Answers
Answer:
Pretty sure its A
Step-by-step explanation:
wait hold on im wrong
how do you delete an answer
24 months- 6.25% x 2 = 12.5%
30 months- 6.00% x 2.5 = 15%
36 months- 4.00% x 3 = 12%
42 months- 3.75% x 3.5 = 13.125%
Find the value of x. Will mark brainliest.
Answers
Answer:
x = 8
Step-by-step explanation:
Melanie's bedroom floor has length equal to 6x + 5 and width equal to 9x – 2 points
4. What equation represents the area of the floor?
Answers
Answer:
(6x+5)(9x-2)
Step-by-step explanation:
Area = Length x Width
Answer:
54[tex]x^{2}[/tex] +33x - 10
Step-by-step explanation:
you have to use F.O.I.L. First Outter Inner Last
(6x + 5)(9x - 2)
First (6x)(9x) = 54 [tex]x^{2}[/tex]
Outter (6x)(-2) = -12x
Inner (5)(9x) = 45 x
Last (5)(-2) = -10
combine middle terms
54[tex]x^{2}[/tex] +33x - 10
Simplify the expression
Answers
Answer:
x^(3)y^(4)\sqrt(2)
Step-by-step explanation:
