Based only on the information given in the diagram, which congruence
theorems or postulates could be given as reasons why AABC= ALMN?
Check all that apply
O A. LL
O B. ASA
I C. LA
D. HL
E AAS
Answers
3 Answers:
Choice A. LLChoice D. HLChoice F. SAS==========================================================
Explanation:
Let's go through the answer choices one by one.
A) This can be used because LL = leg leg, and this means we have two pairs of congruent legs. Those pairs are AC = LN and CB = NM. The LL theorem only applies to right triangles.B) This cannot be used. We don't have info about two pairs of angles. We only know that one pair of angles are the same (those 90 degree angles). So we can't form the second "A" in "ASA". This idea will come up again in choice C and choice E.C) This cannot be used. Why not? Because the "A" of "LA" refers to "acute angle". But unfortunately we don't know anything about the acute angles (whether they are congruent or not). The LA theorem can only be applied to right triangles.D) This can be used. We can use the HL (hypotenuse leg) theorem because we see that AB = LM are the pair of congruent hypotenuses, and you can use any of the congruent leg pairs to form the L of HL. Similar to LL and LA, the HL theorem only works for right triangles.E) This cannot be used. Like with choice B, we can't form the second "A" of "AAS".F) This can be used because we have two pairs of congruent sides, with a pair of congruent angles between those sides. Those angles being the marked 90 degree angles. It turns out that LL theorem is a special case of the SAS theorem.In short, we can use choice A, choice D, choice F. We can't use the other three choices because we lack the info about any other pairs of angles.
The congruence theorem or postulate that we can use to show that triangle ABC is congruent to triangle LMN is LL (Side-Side-Side), the correct option is A.
What are congruent triangles?Suppose it is given that two triangles ΔABC ≅ ΔDEF
Then that means ΔABC and ΔDEF are congruent. Congruent triangles are exact same triangles, but they might be placed at different positions.
The order in which the congruency is written matters.
For ΔABC ≅ ΔDEF, we have all of their corresponding elements like angle and sides congruent.
Thus, we get:
[tex]\rm m\angle A = m\angle D \: or \: \: \angle A \cong \angle D \angle B = \angle E\\\\\rm m\angle B = m\angle E \: or \: \: \angle B \cong \angle E \\\\\rm m\angle C = m\angle F \: or \: \: \angle C \cong \angle F \\\\\rm |AB| = |DE| \: \: or \: \: AB \cong DE\\\\\rm |AC| = |DF| \: \: or \: \: AC \cong DF\\\\\rm |BC| = |EF| \: \: or \: \: BC \cong EF[/tex]
(|AB| denotes length of line segment AB, and so on for others).
We are given that;
Sides are equal
Now,
Based only on the information given in the diagram, we can use the following congruence theorems or postulates to show that triangle ABC is congruent to triangle LMN:
A. LL (Side-Side-Side): This theorem states that if three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent. In this case, we know that AB = LM, AC = LN, and BC = MN, so we can use LL to show that triangle ABC is congruent to triangle LMN.
B. ASA (Angle-Side-Angle): This theorem states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent. In this case, we do not know any angle measures, so we cannot use ASA to show that the triangles are congruent.
Therefore, by the congruent triangles the answer will be LL (Side-Side-Side).
Learn more about congruent triangles here:
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Related Questions
Please help me. if I don’t complete my course I’m getting sent back to my parents house, and I need to complete this course
This is similar polygons, and the lessons I get don’t help
Answers
For real though, I’m hoping you don’t get sent back there. I’m assuming you dislike it there, so good luck with your course. I’m here to help if you need it.
DJVJNNSMKAJABJSHSNSB
Answers
Independent Practice
Find the first, fourth, and eighth terms of the sequence.
an=0.5 · 3n−1a subscript n baseline equals 0.5 times 3 superscript n minus 1 baseline
A.
0.667; 4.5; 364.5
B.
3; 0.375; 0.0234375
C.
0.5; 13.5; 1093.5
D.
0.5; 121.5; 280.5
Answers
Answer:
C.
0.5; 13.5; 1093.5
Step-by-step explanation:
Answer hurry which one 1 2 3 or 4?
Answers
Answer:
Option: 1Step-by-step explanation:
Let,
Footprints that Adele will find be = f
So, Footprints that Yumiko finds = 2f = f + f
Since,
As given that,
Yumiko finds 16 Footprints so it will be,
2f = f + f = 16
And,
f = 16 / 2
= 8
Which is half of Footprints found by Yumiko.
So the bar model 1 represents it correct.
Answer:
option 1
Step-by-step explanation:
i did the quiz
#What is the value of the discriminant for the quadratic equation –3 = –x2 + 2x?
Discriminant = b2 – 4ac
–8
4
8
16
Answers
Answer:
16
Step-by-step explanation:
the quadratic equation –3 = –x2 + 2x can be changed into :
x²-2x-3= 0
a=1, b= -2 , and c = -3
so, the discriminant = (-2)²-4(1)(-3)
= 4 + 12 = 16
Triangle ABC is a right triangle.
Triangle A B C. Angle A is x degrees, B is 90 degrees, C is (x minus 10) degrees. The exterior angle to angle C is (2 x + 40) degrees.
Which equations can be used to find the value of x? Check all that apply.
x + 90 + (x minus 10) = 180
x + 90 + (2 x + 40) = 180
2 x + 80 = 180
x + 90 = 2 x + 40
(x minus 10) + 90 = 2 x + 40
Answers
Answer:
x + 90 + (x minus 10)= 180° can be used to find the value of x.
Answer:
A) X+90+ (x-10) - 180
C) 2x+80 = 180
D) x+90 = 2x+40
Step-by-step explanation:
Rhombus LMNO is shown with its diagonals.
Rhombus L M N O is shown. Diagonals are drawn from point L to point N and from point M to point O and intersect at point P. All sides are congruent.
Angle MNO measures 112°. What is the measure of angle LMN?
Answers
Answer:
hope this help
Step-by-step explanation:
Answer:
90
51
10
Step-by-step explanation:
need help asap pls !
Answers
Answer:
L={∅}
Step-by-step explanation:
Monica makes tomato sauce with the plants she grows in her garden. She uses 3 basil leaves in her sauce for every 8 tomatoes. She is making a big batch of sauce with 32 tomatoes from her garden.
Answers
Answer: 12 Basil leaves
Step-by-step explanation:
Given
Monica uses 3 basil leaves for every 8 tomatoes
For 32 tomatoes she needs
[tex]\Rightarrow 3\ \text{basil leaves}\equiv8\ \text{Tomatoes}\\\\\Rightarrow 4\times 3\ \text{basil leaves}\equiv4\times 8\ \text{Tomatoes}\\\\\Rightarrow 12\ \text{basil leaves}\equiv 32\ \text{Tomatoes}[/tex]
Thus, she needs 12 basil leaves.
Find the volume of a rectangular solid that
is 9 ft. by 12 ft. by 8 ft.
Help please
Answers
Answer:
864 ft³ is the volume
Step-by-step explanation:
Volume = width · height · length
= 12 · 9 · 8
= 864
Answer:
Step-by-step explanation:
Volume of rectangular solid = length * width * height
= 9 * 12 * 8
= 864 ft³
Complete the table for the given rule.
Rule: y=2x
Answers
5 - 10
1 - 2
Work —
First line:
y = 2 (9)
y = 18
Second line:
10 = 2x
5 = x
Third line:
y = 2 (1)
y = 2
Answer:
1. y=18
2. x=5
3. y=2
Step-by-step explanation:
y=2x
1.
As you have x, substitute (replace) x for 9 to find y.
2×9=18 (We times 2 by 9 because, in algebra, when a number is next to a letter, it means to times).
So, y=18
2.
As we know that y=10, do the same thing and substitute.
10=2x
Isolate x by dividing:
10÷2=5
So, x=5
3.
Substitute x:
2×1=2
So, y=2
Hope this helps :)
What is the reminder? Help
Answers
Answer:
6
Step-by-step explanations:
The remainder is what is left over after dividing whatever from d. So if you add one to d, then the remainder would increase from 5 to 6.
Hope this helps.
Mr. Wilkerson bought frozen treats for 34 children. Each child picked either a popsicle or an ice cream bar. Each popsicle cost $2 and each ice cream bar cost $5. If Mr. Wilkerson spent a total of $128, how many of each type of treat did he buy?
Answers
Answer: He bought 20 ice cream bars and 14 popsicle
Step-by-step explanation:
To solve this I used the elimination method, you could use substitution as well
Here are our two equations
x+y=34 Because the total number of ice creams bought must be given to 34 children and no more
2x+5y=128 because that is the cost for each ice cream and the amount he spent
For the elimination method we have to cancel out one of the variables, I decided to cancel out the x, so I multiplied the top equation by -2. So i got -2x-2y=-68
2x+5y=128 Then we get
3y=60 so
y=20
Now we can go back to the first equation and plug in y.
x+20=34
-20 -20
x=14
So he bought 14 popsicles and 20 ice cream bars.
A rectangular bathroom mirror has a perimeter of 22 feet. Its area is 18 square feet. What are the dimensions of the mirror?
Answers
Answer:
The dimensions of the mirror is 9 feet and 2 feet
Step-by-step explanation:
Keep in mind that the area and perimeter of a rectangle is:
Area - length x width
Perimeter - 2 (l + w)
List the factors of 18 (the area of the mirror):
1, 2, 3, 6, 9, 18
POSSIBLE DIMENSIONS OF MIRROR:
1 ft and 18 ft
Area = 18 ft^2
Perimeter = 38 feet
2 ft and 9 ft
Area = 18 ft^2
Perimeter = 22 feet
3 ft and 6 ft
Perimeter = 18 feet
The rectangle with dimensions 2 feet and 9 feet corresponds with the area and perimeter of the mirror mentioned. So those are the correct dimensions.
Hope these helps!
Help anyone can help me do the question,I will mark brainlest.
Answers
Answer:
a) 30
b)600pi
Step-by-step explanation:
For the first questions, since the arc is 240°, the area of the sector and circumference will be 240/360 or 2/3 of the total of the circles'. Therefore 125.6 x 3/2 is the circumference, which is 188.4. When we divide this by 6.28, we get 30
Now, since the area is pi r^2 where we know that r=30, we get 900pi as the area of the whole thing, however since the sector is 2/3 of the whole circle, 2/3 x 900pi = 600pi
HELP ME PLEASEEEE
TAXI RATES A New York City taxi charges $2.50, plus $.40 for each fifth of a
mile if it is not delayed by traffic. Write an expression for the cost of the ride
if you travel x miles in the taxi with no traffic delays.
Answers
Step-by-step explanation:
C(x) = 2.50 + 5(0.40x)
<=> C(x) = 2.50 + 2.00 x
The required expression for the taxi charges is C(x) = $2.50 + 0.4 * x/5.
Given that,
A New York City taxi charges $2.50, plus $.40 for each fifth of a
mile if it is not delayed by traffic. To determine an expression for the cost of the ride, if travel x miles in the taxi with no traffic delays to determined.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
Here,
Let the number of miles be x,
The total charge be C(x)
Now accoding to the condition total charge could be the sum of the cost of every fifth mile and $2.40. So, every fifth mile = x / 5
Now,
C(x) = 2.40 + 0.40 * x/5
Thus, the required expression for the taxi charges is C(x) = $2.50 + 0.4 * x/5.
Learn more about arithmetic here:
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You order CDs for $14.25 each and the website charges $4.50 for each shipment.
The expression $14.25p + $4.50 represents the cost of p CDs. Find the total cost for
ordering 4 CDs.
Answers
Answer:
$61.50
Step-by-step explanation:
14.25(4) + 4.50
= 57.00 + 4.50
= 61.50
using appropriate properties , find 7/5 × 5/12 − 3/12 × 7/5 − 1/15
Answers
Answer:
[tex] \frac{1}{6} [/tex]
Step-by-step explanation:
[tex] \frac{7}{5} \times \frac{5}{12} - \frac{3}{12} \times \frac{7}{5} - \frac{1}{15} = \frac{7}{5} ( \frac{5}{12} - \frac{3}{12} ) - \frac{1}{15} = \frac{7}{5} \times \frac{1}{6} - \frac{1}{15} = \frac{7}{30} - \frac{2}{30} = \frac{5}{30} = \frac{1}{6} [/tex]
Mr. Ellington has a total of 32 students in his class , The ratio of girls to boys is 3:5, how many girls are in Mr . Ellington's class ?
Answers
Add the ratio: 3 + 5 = 8
Divide total students by that:
32/8 = 4
The ratio for girls is 3, multiply the 4 by 3:
4 x 3 = 12
There are 12 girls
Answer:
12
Step-by-step explanation:
If the ratio of girls to boys is 3:5, that means that for every 8 total students, 3 would be girls and 5 would be boys. Therefore 3/8 of the students are girls and 5/8 are boys. If 3/8 are girls, then:
[tex]\frac{3}{8}[/tex] of 32
= [tex]\frac{3}{8} * 32[/tex]
[tex]=\frac{3 * 32}{8} \\= \frac{96}{8} \\= 12[/tex]
There are 12 girls.
Match the answers……………..
Answers
9 in 8956 = 900
9 in 95675 = 90000
9 = 9 in 124569
9 in 68795 = 90
90000 = 9 in 2549652.........
hope it helps...
20) solve:
[tex] {8}^{2} + 2 = [/tex]
21) solve:
[tex]4(2x + 5y = [/tex]
22) simplify the expression
[tex]4( {2}^{2} + 30) - 4 = [/tex]
Answers
Ques21. 8x+20y
Ques22. 132
A person walks away from a pulley pulling a rope slung over it. The rope is being held at a height 10 feet below the pulley. Suppose that the weight at the opposite end of the rope is rising at 4 feet per second. At what rate is the person walking when s/he is 20 feet from being directly under the pulley
Answers
The image of this question is missing and so i have attached it.
Answer:
dd/dt = 4.47 ft/s
Step-by-step explanation:
From the image attached, let's denote the following;
d = horizontal distance beneath pulley
h = height of pulley
l = diagonal from the pulley to the head of the person
v = velocity of rope rising
Using pythagoras theorem;
l² = d² + h²
Differentiating with respect to time and considering h = c^(te) gives;
2l(dl/dt) = 2d(dd/dt)
We are given;
d = 20 ft
h = 10 ft
v = 4 ft/s
We know that velocity in this case is change in diagonal distance with time. Thus;
v = dl/dt = 4 ft/s
From earlier, we saw that;
2l(dl/dt) = 2d(dd/dt)
Thus, reducing it gives
(dl/dt)(l/d) = dd/dt
Now, l² = d² + h²
l = √(d² + h²)
Also, v = dl/dt = 4
Thus;
4(√(d² + h²))/d = dd/dt
4(√(20² + 10²))/20 = dd/dt
dd/dt = 4.47 ft/s
see attached photo, please help asap!!!
Answers
Answer:
3.398
Step-by-step explanation:
log(10) 2500 = log(10) (5^2*10^2) = log(10) 5^2 + log(10) 10^2 = 2*log(10) 5 + 2=3.398
Item 1 Which fraction is equivalent to 3.47? 3_23/50 3_47/100 3_12/25 I don't know.
Answers
Answer: 3 and 47/100
Step-by-step explanation:
I need help plz help
Answers
We know
[tex]\boxed{\sf cos\Theta=\dfrac{b}{h}}[/tex]
[tex]\\ \sf\longmapsto cos22=\dfrac{x}{47}[/tex]
[tex]\\ \sf\longmapsto 0.9=\dfrac{x}{47}[/tex]
[tex]\\ \sf\longmapsto x=47(0.9)[/tex]
[tex]\\ \sf\longmapsto x=42.3[/tex]
PLEASE ELP ME ITS URGENT!!! 25 POINTS!!!!!
Write 2.4 × 1012 in standard notation.
Answers
Answer:
2,400,000,000,000
Step-by-step explanation:
2.4 x 10^12 means that the decimal point is moved 12 places to the right (hence the power of 12)
So by moving the decimal point 12 times you get this: 2,400,000,000,000
The reason why there are only 11 zeroes is because the 4 was a decimal place to the right of 2, thus losing a zero.
Solve the equation sin(x° − 20°) = cos(42°) for x, where 0 < x < 90. A. 22 B. 28 C. 62 D. 68
Answers
[tex] \sin(x - 20°) = \cos(42°) [/tex]
[tex] \sin(x - 20°) = \sin(90° - 42°) [/tex]
[tex] \sin(x - 20°) = \sin 48°[/tex]
[tex]x - 20° = 48°[/tex]
[tex]x = 48° + 20°[/tex]
[tex]x = 68°[/tex]
______________________________■ HOPE IT HELPS YOU DEAR!!!______________________________Answer:68
Step-by-step explanation:
pls help i will give brainliest for answer and explanation.
Answers
Answer:
36
Step-by-step explanation:
girls:boys=2:3
2units=24
1unit=24÷2=12
boys have 3 units
3units=12 x 3 =36
There are 36 boys
Check if -2 is the solution of equation 2 – x = 4x + 3
Answers
Answer:
7x the answer i think
Step-by-step explanation:
Answer:
[tex]\boxed {\boxed {\sf -2 \ is \ not \ a \ solution}}[/tex]
Step-by-step explanation:
We are asked to check is -2 is the solution of the following equation.
[tex]2-x= 4x+3[/tex]
We must substitute -2 in for x and solve both sides of the equation. If the two sides are equal, then -2 is the solution.
[tex]2- (-2) = 4(-2)+3[/tex]
Solve both sides of the equation according to PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.
Let's start with the left side.
[tex]2+2= 4(-2)+3 \\[/tex]
[tex]4= 4(-2)+3[/tex]
Now solve the right side. Remember to multiply first.
[tex]4= -8+3[/tex]
[tex]4= -5[/tex]
[tex]4\neq -5[/tex]
4 is not equal to -5, so -2 is not the solution for this equation.
A plank 6m long leans against a vertical wall so that the foot of the plank is 4m away from the wall. A lizard climbs 2m up the plank. Calculate the horizontal distance between the lizard and the wall.
Answers
Answer: [tex]\dfrac{8}{3}\ m[/tex]
Step-by-step explanation:
Given
Length of the plank is [tex]6\ m[/tex]
Foot of the flank is [tex]4\ m[/tex] away from the wall
Lizard climbs 2 m up the wall
from the figure, the two triangles are similar
[tex]\therefore \dfrac{2}{6}=\dfrac{x}{4}\\\\\Rightarrow x=4\times \dfrac{2}{6}\\\\\Rightarrow x=\dfrac{4}{3}\ m[/tex]
So, the distance from the wall is
[tex]\Rightarrow 4-x\\\\\Rightarrow 4-\dfrac{4}{3}\\\\\Rightarrow \dfrac{8}{3}\ m[/tex]
