Determine whether angle-angle-angle (AAA) is a valid means for establishing triangle congruence. If it is a valid criterion, explain why. If it is not valid, use GeoGebra to create a counterexample demonstrating that it doesn't work and give an explanation. If you construct a counterexample, take a screenshot of your work, save it, and insert the image in the space below. !! I just write in a box!!
Answers
A triangle is a fundamental form in geometry. The AAA property can not be used to prove if the triangles are congruent.
What is a triangle?A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry.
The property angle-angle-angle (AAA), is used for similar triangles. It can not be used to prove that two triangles are congruent triangles. Therefore, it is not a valid criterion.
Now, this can be proved using two triangles having the same angle measurement as 60°. The two triangles given below has the same angle measurement although, their sides have different measurement, thus, the two triangles are not equal.
Hence, the AAA property can not be used to prove if the triangles are congruent.
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Answer: A triangle is a basic geometric shape. Triangle congruence cannot be established using the AAA property. A triangle is a polygon having three vertices and three edges. It is a fundamental geometric figure. For comparable triangles, the property angle-angle-angle (AAA) is employed. It cannot be used to establish the congruence of two triangles. As a result, it is an invalid standard. Now, this may be demonstrated using two triangles with angles equal to or greater than 60°. The two triangles shown below are not equal because they have different side measurements despite having the same angle measurement. The triangles' congruence cannot therefore be established using the AAA property.
Step-by-step explanation:
Related Questions
What are the roots of the equation x² + 6x-9 = 07
Answers
Answer:
x1 =-3+3[tex]\sqrt{2}[/tex] and x2=-3-3[tex]\sqrt{2\\}[/tex]
Step-by-step explanation:
x² + 6x-9 = 0
-6±[tex]\sqrt{6^{2}-4(1)(-9) }[/tex] / 2
-6±[tex]\sqrt{72}[/tex] /2
so
x1 = -6+[tex]\sqrt{72[/tex] /2
x1 =-3+3[tex]\sqrt{2}[/tex]
and
x2 = -6-[tex]\sqrt{72[/tex] /2
x2=-3-3 [tex]\sqrt{2\\}[/tex]
Find the area of the window
Answers
Answer:
Area = 1250cm²
Step-by-step explanation:
Area of a kite = pq/2
where p and q are diagonals
p = 25+25 = 50
q = 30+ 20 = 50
Area of a kite = pq/2
Area = (50*50 ) / 2
Area = 1250cm²
A tennis ball is launched straight up from a height of 4 feet with an initial velocity of 64 feet per second. Use the
equation h(t) = -16ť² + vot+h, to determine when the tennis ball will be 52 feet in the air. Select all that apply.
01 second
2 seconds
3 seconds
5 seconds
6 seconds
Answers
When the ball hits the ground,
h=0
vt�16t^2=0
64t-16t^2=0..
t(64-16t)=0
t=0 (reject, not reasonable)
or
64-16t=0
16t=64
t=64/16=4
How long will it take for the ball to hit the ground? 4 seconds
4 Answer:
xy is a
a. monomial
b. binomial
c. trinomial
5 Answer:
k2 is a
a. monomial
b. binomial
c. trinomial
6 Answer:
x2y + xy2 + -5 is a
a. monomial
b. binomial
c. trinomial
7 Answer:
n2 + 4n + 4 is a
a. monomial
b. binomial
c. trinomial
8 Answer:
(2x +3) + (4x + 8) = _____
9 Answer:
(5x2 + 9) + (7x2 + -8) = _____
10 Answer:
(5s + t) + (-3s + 4t) = _____
11 Answer:
(3n2 + 4n) + (n2 + n) = _____
12 Answer:
(2a + 3b + c) + (a + 3b + -4c) = _____
13 Answer:
(7t2 + 3t + -9) + (2t2 + 6) = _____
14 Answer:
(5a + 7b) - (3a + 2b) = _____
15 Answer:
(5c2 + 7c) - (2c2 + 6c) = _____
16 Answer:
(6r + 3s) - (4r + 2s) = _____
17 Answer:
(7xy + 8y) - (3xy + 2y) = _____
18 Answer:
(8a + 2b + 5c) - (2a + b + c) = _____
19 Answer:
(9r2 + 3r + 8) - (2r2 + 7) = _____
20 Answer:
2(n + 7) = _____
21 Answer:
5(3j + -6) = _____
22 Answer:
6n(4n + 6) = _____
23 Answer:
5a(3a + -2) = _____
24 Answer:
8(2w2 + w + -9) = _____
25 Answer:
-4(4d2 + 3d + 2) = _____
26 Answer:
18r + 6
——————— = _____
3
27 Answer:
-15w2 + 10w
——————————— = _____
5w
28 Answer:
2t2 + 8t
———————— = _____
2t
29 Answer:
14z2 + 6z + 8
————————————— = _____
2
30 Answer:
18b3 + 12b2 + 6b
———————————————— = _____
6b
31 Answer:
21x2 + 14xy + -35x
—————————————————— = _____
-7x
32 Answer:
Solve: b + 2(b + 1) = 5 b = _____
33 Answer:
Solve: 3r + 5(r - 1) = 27 r = _____
34 Answer:
Solve: 2y + 2(y + 1) = -6 y = _____
35 Answer:
Solve: 2n + 2(n + 7) + 1 = 39 n = _____
36 Answer:
Solve: -3t + 2(t - 2) + 6 = -3 t = _____
37 Answer:
Solve: -6x + 3(x + 9) - 12 = 27 x = _____
38 Answer:
Solve: 3k + 4(k - 3) + 10 = -58 k = _____
39 Answer:
Solve: -4n + 2(n - 6) + 8 = 10 n = _____
40 Answer:
Solve: 2j + 4(j - 3) - 4 = -16 j = _____
41 Answer:
Solve: 2(x + 3) + 4(x - 2) = -32 x = _____
42 Answer:
Solve: 5(d + 2) + 2(d + 7) = 3 d = _____
43 Answer:
Solve: 6(w + 3) + 2(w - 4) + 10 = -4 w = _____
44 Answer:
Solve: -4z + 2(z + 1) + 3(z - 2) = 7 z = _____
45 Answer:
Solve: 3t + 2(t + 1) + 3(t - 1) = 15 t = _____
46 Answer:
Solve: -6a + 2(a - 3) + 3(a - 5) - 11 = -32 a = _____
47 Answer:
Select the equation that solves this problem:
Eight coins (dimes and nickels) are worth 60 cents. How many dimes are
there?
a. 10d + 25(11 - d) = 170
b. 10d + 25(8 - d) = 170
c. 10d + 5(8 - d) = 60
d. 10d + 5(11 - d) = 60
48 Answer:
Solve: Eight coins (dimes and nickels) are worth 60 cents. How many
dimes are there? _____
49 Answer:
Select the equation that solves this problem:
Eight coins (dimes and quarters) are worth 170 cents. How many dimes are
there?
a. 10d + 25(11 - d) = 170
b. 10d + 25(8 - d) = 170
c. 10d + 5(8 - d) = 60
d. 10d + 5(11 - d) = 60
50 Answer:
Solve: Eight coins (dimes and quarters) are worth 170 cents. How many
dimes are there? _____
51 Answer:
Select the equation that solves this problem:
Eleven coins (dimes and nickels) are worth 60 cents. How many dimes are
there?
a. 10d + 25(11 - d) = 170
b. 10d + 25(8 - d) = 170
c. 10d + 5(8 - d) = 60
d. 10d + 5(11 - d) = 60
52 Answer:
Solve: Eleven coins (dimes and nickels) are worth 60 cents. How many
dimes are there? _____
53 Answer:
Select the equation that solves this problem:
Eleven coins (dimes and quarters) are worth 170 cents. How many dimes
are there?
a. 10d + 25(11 - d) = 170
b. 10d + 25(8 - d) = 170
c. 10d + 5(8 - d) = 60
d. 10d + 5(11 - d) = 60
54 Answer:
Solve: Eleven coins (dimes and quarters) are worth 170 cents. How many
dimes are there? _____
Answers
Find the factor of each ff.
49x²-63x+7
Answers
Answer:
7(7x²-9x +1)
Step-by-step explanation:
49x²-63x+7
7(7x²-9x +1)
Please help I'll give 100 points to whoever is correct
Answers
Answer:
110.5 yd²
Formula's:
Area of triangle:
1/2 × base × height
Area of rectangle:
length × width
Area of the figure:
= area of triangle + area of rectangle's
= 1/2 × 11 × 7 + 3 × 4 + 5 × 3 + 5 × 2 + 7 × 5
= 110.5 yd²
Answer:
110.5 yd²
Step-by-step explanation:
Separate the figure into 1 triangle and 3 rectangles.
(see attached image)
Area 1
Area of a triangle = 1/2 × base × height
= 1/2 × (7 + 2 + 2) × 7
= 1/2 × 11 × 7
= 38.5 yd²
Area 2
Area of a rectangle = width × length
= 3 × (5 + 2 + 2)
= 3 × 9
= 27 yd²
Area 3
Area of a rectangle = width × length
= 5 × (5 + 2)
= 5 × 7
= 35 yd²
Area 4
Area of a rectangle = width × length
= 2 × 5
= 10 yd²
Total Area
Area 1 + Area 2 + Area 3 + Area 2 = 38.5 + 27 + 35 + 10
= 110.5 yd²
if(x) = a^x passes through the point (2, 1/16) the base a is
Answers
Answer:
1/4
Step-by-step explanation:
y = a^x
1/16 = a^2
so the answer is 1/4
Given the following GPA for 4 students: 2, 3, 3, 4. Age of students are: 10, 11, 12, 15. There are 10,000 total students. Average GPA: Unknown, Standard Deviation of GPA: 0.02 and it's Normal. a. Find the mean and standard deviation for GPA. (10 points) b. Calculate a 95% confidence interval for the populations mean GPA. (5 points) c. Use Correlation formula to find r between GPA and Age. (10 points) d. Find Regression Line Equation. (5 points)
Answers
The mean and standard deviation for the GPA of the students will be 3 and 0.8165.
How to calculate the mean?The mean simply means the average of a given set of numbers. The mean will be:
= 12/4
= 3
The standard deviation will be:
= ✓2/3
= 0.8165
The 95% confidence interval for the populations mean GPA will be 1.70 < U < 4.30. The interval lower limit is:
= 3.00 - 1.299.l
= 1.70
The interval upper limit will be;
= 3.00 + 1.299
= 4.30
Also, the regression line is Y = -1.2857 + 0.3571x.
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If 8 packets of fudge cost R 30,80 what will the price of 14 packets be?
Answers
Answer:
53.90
Step-by-step explanation:
30.80/8=3.85 (price per pack)
3.85 x 14 = 53.90
The two formats used in an observation checklist are:
A. Performance profiles and Tallies
B. Tallies and video recording
C. Video recording and audio recording
D. Performance profiles and SMART Targets
Answers
The two formats used in an observation checklist are: D. Performance profiles and SMART Targets.
What is observation checklist?Observation checklist can be defined as the process of observing and evaluating a person or group of people performance.
When carrying out an observation checklist endeavors to make sure that the checklists are dated.
Observation checklist includes Performance profiles and SMART Targets. Where SMART stands for:
S=Specific
M=Measurable
A=Achievable
R=Relevant
T= Time-Bound
Therefore the correct option is D.
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Which is an equation of the line passing through (-2,3) and perpendicular to the line
5x-y=12?
Answers
Answer:
y = -1/5x + 2.6
Step-by-step explanation:
Put the equation into slope intercept form:
5x - y = 12
-y = -5x + 12
y = 5x - 12
The slope of a perpendicular line will be the opposite reciprocal.
So, the slope of the new line will be -1/5
Then, plug this slope and the given point into the equation y = mx + b to find b
y = mx + b
3 = -1/5(-2) + b
3 = 0.4 + b
2.6 = b
So, the equation will be y = -1/5x + 2.6
What is the first step you would take to solve the equation ?
Answers
Like terms are those terms that are having the same variables, also the variables are of the same order as well. The first step to solving an equation is to rearrange the like terms.
What are Like terms?Like terms are those terms that are having the same variables, also the variables are of the same order as well.
for example, 25x and 5x are like terms; 30xy and 7xy are like terms, 9x³ and 4x² are not like terms, etc.
To solve an equation the first step is to rearrange the equation such that like terms are together.
Hence, the first step to solving an equation is to rearrange the like terms.
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Which of the following are statistical questions? Select all that apply.
How many books did the students at this school read over the summer?
What is your favorite ice cream flavor?
How many letters are in the first name of each person in this class?
How many hours do the students in this class sleep each night?
How many hours a night do you spend on homework?
How many chocolate chip cookies were made in the bakery last week?
Answers
amusement on a particularly boring transatlanfic fight one of the authors am used himseft by counting the heads of the people in the seats in front of him. He noticed that all 37 of them either had black hair or had a whole row to themselves or both. Of this total 33 had black hair and 6 were fortunate enough to have a whole row of seats to themselves. How many black haired people had whole rows to themselves?
Answers
A card is drawn at random without replacement. A second card is then drawn. Determine the probability of getting a number greater than 9 and a number less than 4 if cards are selected at a random
Answers
Step-by-step explanation:
it does not say what the card deck consists of, and how many cards of what type there are.
so, I assume a standard playing card set of 52 cards (no jokers) with 4 suits of
Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K
in that ranking of value.
so there are 4 cards of each of the 13 different types.
a card with a number greater than 9 means a 10, a J, a Q, or a K.
so, in total there are 4×4 = 16 such cards in the deck.
a card with a number less than 4 means an Ace, a 2, or a 3.
so, in total there are 4×3 = 12 such cards in the deck.
to get a number greater than 9 and a number less than 4 is a combination of the first card being greater than 9 and the 2 card being less than 4 OR the first card being less than 4 and the second card being greater than 9.
an "and" operation (without overlap) we represent by a multiplication, and an "or" operation (without overlap) by an addition.
remember, a probability is always
"desired cases / total possible cases".
so, the probability to draw a first card greater than 9 is
16/52 = 4/13
the probability to draw a second card greater than 9 (after a first card less than 4) is
16/51
because we still have all the large cards, but one of the smaller ones is now gone.
the probability to draw a first card less than 4 is
12/52 = 3/13
the probability to draw a second card less than 4 (after a first card greater than 9) is
12/51.
so, the complete probability of the scenario is
4/13 × 12/51 + 3/13 × 16/51 = 48/663 + 48/663 = 96/663 =
= 32/221 = 0.14479638...
if my assumptions about the cards are wrong, please adapt the numbers accordingly. but the basic structure of the calculation is the same.
A contalner holds 44 cups of water. How much is this in gallons?
Write your answer as a whole number or a mixed number in simplest form. Include the correct unit in your answer.
Answers
Answer:
5 1/4 gallons
Step-by-step explanation:
Hope this helps and have a nice day
Subtract the radical expression. Simplify if needed.
Answers
Answer:
7[tex]\sqrt{7}[/tex]
Step-by-step explanation:
Take 9 out of [tex]\sqrt{63}[/tex]
You get 3[tex]\sqrt{7}[/tex]
Take 4 out of [tex]\sqrt{28}[/tex]
You get 2[tex]\sqrt{7}[/tex]
So, 3(3[tex]\sqrt{7}[/tex]) - 2[tex]\sqrt{7}[/tex]
= 9 [tex]\sqrt{7}[/tex] - 2[tex]\sqrt{7}[/tex]
=7[tex]\sqrt{7}[/tex]
Write an equation in slope-intercept form for the line with -intercept -2 and slope2
.
Answers
hope this helps
Solve the radical equation.
x + 4 =√x + 10
What is the extraneous solution to the radical equation?
O The solution -1 is an extraneous solution.
O Both -1 and -6 are true solutions.
O The solution -6 is an extraneous solution.
ONeither -1 nor -6 is a true solution to the equation.
Answers
The solution -1 is an extraneous solution
Neither -1 nor -6 is a true solution to the equation.
Option D is the correct answer.
What is a solution?Solutions are the values of an equation where the values are substituted in the variables of the equation and make the equality in the equation true.
We also find the solution in a system of equations using the substitution or elimination method.
Example:
2x + 4 = 8
The solution is x = 2.
We have,
To solve the equation x + 4 = √(x + 10), we need to isolate the radical term on one side of the equation and then square both sides to eliminate the radical.
Here are the steps:
x + 4 = √(x + 10)
Subtract 4 from both sides:
x = √(x + 10) - 4
Square both sides:
x² = (√(x + 10) - 4)²
Expand the right side using the formula (a - b)^2 = a^2 - 2ab + b^2:
x² = x + 6 - 8√(x + 10)
Move all terms to the left side:
x² - x - 6 + 8√(x + 10) = 0
To solve this equation, we can use a substitution u = √(x + 10):
u = √(x + 10)
Square both sides:
u² = x + 10
Substitute into the original equation:
(u² - 10) + 4 = u
Simplify:
u² - u - 6 = 0
Factor:
(u - 3)(u + 2) = 0
So u = 3 or u = -2.
But u = -2 leads to a negative value under the square root in the substitution u = √(x + 10), which is not allowed.
Therefore, we only consider u = 3, which gives:
√(x + 10) = 3
Square both sides:
x + 10 = 9
Subtract 10 from both sides:
x = -1
So the solution to the original equation is x = -1.
To check if it is extraneous, we need to substitute it back into the original equation:
x + 4 = √(x + 10)
-1 + 4 = √(-1 + 10)
3 = √9
3 = 3
The equation is true, so x = -1 is a valid solution and not extraneous.
Therefore,
Neither -1 nor -6 is a true solution to the equation.
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Find the surface area
Answers
Answer:
A≈9248.85
Step-by-step explanation:
A=2πrh+2πr2=2·π·32·14+2·π·322≈9248.84877
what is the volume of a cylinder, in cubic inches, with a height of 2 inches and a base diameter of 4 inches? Round to the neares tenths place
Answers
Answer:
V≈25.13in³
Step-by-step explanation:
=3.142*4^2/4*2
=25.136 cubic inches
PLEASE HELP!!
Which function, g or h, is the inverse function for function f??
Answers
Answer: The function h because the graphs of f and h are symmetrical about the line y=x.
answer please
need quickly please please
Answers
This is because the slope is -1 and the y-intercept is 2.
Help please!!!!! FIRST CORRECT GETS BRAILIEST
Answers
Answer:
I think it is D, if I am wrong I am sooooo sorry
one third of a number y is 2
Answers
Answer:
y = 6
1/3 indicates that we may have to multiply the number by 3 to get the whole number. Multiply 3 by the part given, 2.
3 × 2 = 6
the perimeter of a rectangle is 26 and the area is 30. what are the dimensions of the rectangle ?
Answers
Answer:
Step-by-step explanation:
PLeaseeeee Help
6. Given the order pairs (2, 3), (4, 5), (4, 7), (5, 10), and (6, 8) find the following. Round all final answers to three decimals places. Be careful not the round to early.
Express the line of best fit in the form of y = mx+b.
(a) The line of best fit. =
(b) Find the coefficient of linear correlation. =
Answers
Answer:
B
Step-by-step explanation:
answer is based on results from the Cartesian plane
if f (1) =5 and f (n) = 5f (n-1) + 5 then find the value of f (3)
Answers
Using the given information, the value of the f(3) is 155
Determining the value of a functionFrom the question, we are to determine the value of f(3)
From the given information,
f(n) = 5f(n-1) + 5
∴ f(2) = 5f(2-1) +5
f(2) = 5f(1) + 5
From the given information,
f(1) = 5
Then,
f(2) = 5(5) + 5
f(2) = 25 + 5
f(2) = 30
Also,
f(3) = 5f(3-1) + 5
f(3) = 5f(2) + 5
∴ f(3) = 5(30) + 5
f(3) = 150 + 5
f(3) = 155
Hence, the value of the f(3) is 155.
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plsss help meeeeeeeeee
Answers
seventeen
Bell shaped would be like the photo attached
Work out the bearing of C from A.
45°
65°
(Look at the picture) please help me
Answers
Answer:
110°
Step-by-step explanation:
if we're looking for the bearing of C from A, the angle should be formed at A
then, starting from the north poles, move in a clockwise direction till you meet the line coming from C . then, sum up the angles involved.
which is = 45°+ 65° = 110°
therefore, the bearing of C from A is 110°