Based on the given information and the algebraic and geometric properties presented or proven thus far, choose the congruence theorem that could be used to prove the triangles congruent. If it is not possible to prove the triangles are congruent, choose "not possible".
SSS
SAS
SSA
not possible
Answers
Answer:
The correct option is 2.
Step-by-step explanation:
Given information: DC║AB, DC=AB.
If a transversal line intersect two parallel lines, then the alternative interior angles are equal.
In triangle ABC and CDA,
[tex]AB=DC[/tex] (Given)
[tex]\angle 2=\angle 3[/tex] (Alternative interior angles)
[tex]CA=CA[/tex] (Common side)
Two corresponding sides and their including angle are equal.
By SAS postulate of congruent triangles,
[tex]\triangle ABC\cong \triangle CDA[/tex]
Since both triangles are congruent by SAS postulate, therefore the correct option is 2.
Related Questions
The population of a town is 6500 and is increasing at a rate of 4% per year.at this rate, approximately what will the towns population be in 4 years
Answers
End of 1st year = 1.04 x 6500 = 6760
End of 2nd year = 1.04 x 6760 = 7030
End of 3rd year = 1.04 x 7030 = 7312
End of 4th year = 1.04 x 7312 = 7604
To find the town's population in 4 years with an initial population of 6500 and a 4% annual growth rate, we use the exponential growth formula, resulting in an estimated population of approximately 7609.
The population of a town is 6500 and is increasing at a rate of 4% per year. To calculate the town's population in 4 years, we will use the formula for exponential growth:
P(t) = P0(1 + r)^t
Where:
P(t) is the future population
P0 is the initial population
r is the growth rate (as a decimal)
t is the number of years
Step-by-step calculation:
Convert the growth rate from a percentage to a decimal: r = 4% = 0.04
Use the formula with t = 4 years, P0 = 6500, and r = 0.04:
P(4) = 6500(1 + 0.04)⁴
Calculate P(4) = 6500 * 1.04⁴
Approximate the future population after 4 years.
By performing the calculation, the town's population in 4 years will be approximately 7609.
Let A and B be two events in a sample space S such that
P(A)=.6 P(B)=.5 and P(A intersect B) =.2 Find
A) P(A|B)
B) P(B|A)
Please explain how to do this! Thank you
Answers
A) P(A intersect B) = P(A|B)*P(B)
Replacing the known vallues:
0.2=P(A|B)*0.5
Solving for P(A|B):
0.2/0.5=P(A|B)*0.5/0.5
0.4=P(A|B)
P(A|B)=0.4
B) P(B intersect A) = P(B|A)*P(A)
Replacing the known vallues:
0.2=P(B|A)*0.6
Solving for P(B|A):
0.2/0.6=P(B|A)*0.6/0.6
2/6=P(B|A)
1/3=P(B|A)
P(B|A)=1/3
find the roots of the equation x3-3x^2+x+5
Answers
(x+1)(x^2-4x+5)=0
x+1=0→x+1-1=0-1→x=-1
x^2-4x+5 different to zero
The root of the equation is x=-1
First combined weight of three packages that weigh 5 1/2 pounds 4 7/16 pounds and 3 3/8 pounds
Answers
What is the value of h when the function is converted to vertex form? Note: Vertex form is p(x)=a(x−h)^
2+k . p(x)=x^2−14x+29
Answers
p(x)=a(x-h)^2+k
p(x)=x^2-14x+29
c=(b/2)^2=(-14/2)^2=49
hence:
x^2-14x+49=-29+49
(x-7)^2=20
hence:
p(x)=(x-7)^2-20
thus, h=7
Sarah draws a rectangle with an area of 4,875 square units and a length of 65 units. What is the width of the rectangle? 70 units 75 units 85 units 95 units
Answers
Singing "row, row, row your boat," in a round (each group starting at a different time) would be considered which texture? music appreciation
Answers
Gucci gang, ooh
(That's it right there, Gnealz)
Yuh, Lil Pump, yuh
Gucci gang, ooh
(Ooh, Bi-Big Head on the beat)
Yuh, brr
Solve the following inequality. 2x < 8
Answers
2x / 2 < 8/2
x < 4
hope it helps
The required solution of the given inequality 2x < 8 is x < 4.
What is inequality?The relation between two expressions that are not equal, employing a sign such as ≠ ‘not equal to’, > ‘greater than’, or < ‘less than’.
Given:
The given inequality is
2x < 8
According to given question we have
Write inequality
2x < 8
Divide both sides by 2 we get,
x < 4
Therefore, the required solution of the given inequality 2x < 8 is x < 4.
Learn more details about inequality here:
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Sarah is shopping for groceries at the local supermarket. She paid for her groceries using a $100 bill recently issued by the US government. What type of money did Sarah use for this transaction? commodity money fiat money digital money representative money
Answers
If ΔABC≅ΔMNO, then what corresponding angle is congruent to angle N? (Enter your answer using the angle letter only.)
Answers
Hope it helps
Answer: [tex]\angle{B}[/tex]
Step-by-step explanation:
We know that if two triangles are congruent , then their corresponding sides and angles are congruent (by CPCTC).
[CPCTC is the acronym use for the property of congruent triangles that says that corresponding parts of two congruent triangles are congruent]
Given : ΔABC ≅ ΔMNO
Then , [tex]\angle{A}[/tex] corresponds [tex]\angle{M}[/tex] [First letter]
[tex]\angle{B}[/tex] corresponds [tex]\angle{N}[/tex] [Middle letter]
[tex]\angle{C[/tex] corresponds [tex]\angle{O}[/tex] [last letter]
Then , by CPCTC, we have
[tex]\angle{B}\cong\angle{N}[/tex]
Hence, angle B is the corresponding angle which is congruent to angle N.
Let f(x)=x2−3x−4 .
What is the average rate of change from x = 7 to x = 10?
Enter your answer in the box.
Answers
[tex] \frac{change \: in \: y}{change \: in \: x} [/tex]
f(7) is
[tex] {7}^{2} - 3(7) - 4[/tex]
[tex]49 - 21 - 4[/tex]
when x is 7, y=24
f(10) is
[tex] {10}^{2} - 3(10) - 4[/tex]
[tex]100 - 30 - 4[/tex]
when x is 10, y=66
the difference in the y values is 42 when the x values change by 3
[tex] \frac{66 - 24}{10 - 7} = \frac{42}{3} = 14[/tex]
the average rate of change is 14
there are four brands of smartphones that are most popular in the united states . the number of people in the united states that have each brand is given.
brand A; 4.48x104;
brand b : 3.84 x107; brand c : 6.4x10^6; brand d: 1.50 x107
what is the order of these brands from most to least popular?
Answers
For this case we must write the numbers from highest to lowest.
We observe that the numbers are written in exponential notation.
Therefore, by rewriting we have:
Brand A:
[tex] 4.48 * 10 ^ 4 = 44,800
[/tex]
Brand B:
[tex] 3.84 * 10 ^ 7 = 38,400,000
[/tex]
Brand C:
[tex] 6.4 * 10 ^ 6 = 6,400,000
[/tex]
Brand D:
[tex] 1.50 * 10 ^ 7 = 15,000,000
[/tex]
Ordering from highest to lowest we have:
[tex] 3.84 * 10 ^ 7 = 38,400,000
1.50 * 10 ^ 7 = 15,000,000
6.4 * 10 ^ 6 = 6,400,000
4.48 * 10 ^ 4 = 44,800
[/tex]
Answer:
The order of these brands from most to least popular is:
Brand B
Brand D
Brand C
Brand A
Write a real word problem that involves classifying a quadrilateral
Answers
Maybe this helps or at least take ideas from this for me it wasn’t good but at least its something
Alice needs to classify her garden quadrilateral to determine if it is suitable for a specific species of flowers. She finds the sides equal in length and consecutive angles supplementary, which leads her to conclude the garden plot is a rhombus, meeting the criteria for her flowers.
Alice designs a garden plot in the shape of a quadrilateral. She knows that for a certain species of flower to grow optimally, her garden must have a specific shape: it needs to be a parallelogram with equal sides but not necessarily equal angles. In order to classify the quadrilateral of her garden, she begins by measuring the sides and finds that they are all of equal length. Then she measures the angles and finds that consecutive angles are supplementary, which means their measures add up to 180 degrees.
To determine if the quadrilateral meets the criteria for the species of flowers, she must classify her garden plot based on her measurements. Is Alice's garden a rectangle, a square, a rhombus, or a parallelogram with unequal angles?
Since the sides of the quadrilateral are all equal and the consecutive angles are supplementary, Alice can conclude that her garden plot is a rhombus, which is a type of parallelogram with all sides equal in length and opposite angles equal. Thus, it fulfills the requirements for her special species of flowers.
Anslee is designing a doll house shaped like a rectangular prism. The doll house is 8 feet long, 2 feet wide and 3 feet high. What is the surface area of the doll house?
Answers
L=8 ft
W=2 ft
H=3 ft
[surface area of the doll house]=2*[W*H]+2*[L*H]+2*[W*L]
[surface area of the doll house]=2*[2*3]+2*[8*3]+2*[2*8]
[surface area of the doll house]=2*[6]+2*[24]+2*[16]
[surface area of the doll house]=12+48+32--------> 92 ft²
the answer is 92 ft²
[100 POINTS]
Question 1)
The graph for the equation y = 2x - 2 is shown below.
If another equation is graphed so that the system has one solution, which equation could that be?
A) y = 2(x+1)
B) y = 2(x-1)
C) y = 2(x-2)
D) y = -2(x+1)
Question 2)
Solve the inequality and then graph its solution.
1/5(x-2) > -1
a) x > -7
b) x < -3
c) x > -3
d) x > 3
Answers
D
The answer is D because every other option has the same slope (2), and even if the intercepts are different, the lines would only be parallel, whereas in D, the slope is -2, which has one solution.
Question 2)
C
You would multiply everything by 5 to get rid of the fraction. Then, you can simplify and get the answer.
The first question is D, because when graphed, intercepts with the slope of 3, the only with the solution.
The second question is C, because u can multiple the LHS and RHS to get x-2 is greater than -5. Add 5 to get x is greater than -3
urgent help needed!
write y = (-5/8)x + 3 in standard form using integers.
a. 5x + 8y = -24
b. 5x + 8y = 24
c. 5x - 8y = 24
d. -5x + 8y = 24
Answers
To write this in standard form, you need to eliminate the fraction in the coefficient of variable x. You can do this by multiplying 8 to the two sides of the equation:
8(y) = 8[(-5/8)x + 3]
8y = -5x + 24
Transpose the variable x to the other side:
5x + 8y = 24
The complement of an angle is 8 times as large as the angle. find the measure of the complement
Answers
Answer:
80⁰
Step-by-step explanation:
Angle = x
Complement = 90 - x
Given:
8x = 90 - x
9x = 90
x = 10⁰
Complement = 90 - 10 = 80⁰
The complement of an angle is 8 times as large as the angle. The measure of other angle is 80⁰.
What are complementary angles?The complement of an angle is the sum of angles which is equal to 90 degrees.
Let one Angle = x
Complement = 90 - x
The complement of an angle is 8 times as large as the angle.
so,
8x = 90 - x
9x = 90
x = 10⁰
Complement = 90 - 10
= 80⁰
Learn more about angles;
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How to find side of triangle if two sides and one angle is known?
Answers
If the given angle is opposite one of the given sides, the Law of Sines can be used.
Law of Cosines:
.. c^2 = a^2 +b^2 -2ab*cos(C) . . . . . for any permutation of sides a, b, c, and opposite angle C
Law of Sines:
.. a/sin(A) = b/sin(B) = c/sin(C)
Hint: Omars equation doesn't work!
Identify his error and correct it by showing the steps Omar should have taken and determine the correct value of x.
Answers
He should have added the two expressions to get 180
(10x-1) + (59) = 180
10x+(-1+59) = 180
10x+58 = 180
10x+58-58 = 180-58
10x = 122
10x/10 = 122/10
x = 12.2
Math help!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
6,032
6,407
6,704
6,023; 6,032; 6,407; and 6,704.
From this list, the most accurate answer choice is the first one, A.
I hope this helps!
The graph shows the path of a rider on a ride at an amusement park.
What does the x-coordinate of the vertex represent?
The rider’s minimum height above the ground is 25 ft.
The rider travels a total distance of 25 ft.
The difference between the rider’s maximum and minimum’s height above the ground is 25 ft.
The rider is closest to the ground when he is 25 ft from the left side of the ride.
https://static.k12.com/nextgen_media/assets/8090397-NG_AL1_O_07_U12_Quiz_08.png
Answers
Answer:
D. The rider is closest to the ground when he is 25 ft from the left side of the ride.
Step-by-step explanation:
The vertex of x-coordinate represents the distance from the from the origin of the pendulum, which is the closest to the ground when he is 25 ft away from 0.
Hope this will helpful.
Thank you.
Find the area of the triangle. Round the answer to the nearest tenth.
A.
68.4 square units
B.
75.3 square units
C.
84.5 square units
D.
136.7 square units
Answers
Answer:
Option A. 68.4 square units.
Step-by-step explanation:
Since sides ED = EF = 13 units
So the given triangle is an isosceles triangle and in an isosceles triangle EFD, perpendicular drawn from E to DF, will be perpendicular bisector of DF.
Moreover, to this perpendicular bisector to DF will be the height of the triangle.
Now Area of a triangle of [tex]\frac{1}{2}[/tex] × base × height.
Sin 63 = [tex]\frac{Height}{Hypotenuse}[/tex] = [tex]\frac{h}{13}[/tex]
h = 13 sin 63 = 13 ( 0.891) = 11.583 units
Cos 63 = [tex]\frac{Base}{Hypotenuse}[/tex] = [tex]\frac{Base}{13}[/tex]
Base = 13 cos 63 = 13 × (0.454)
= 5.90 units
Since DF = 2 × base = 2 × 5.90
= 11.80 units
Now area of EDF = [tex]\frac{1}{2}[/tex] × 11.80 × 11.583
= 68.86 ≈ 68.40 square units.
Option A. 68.4 square units.
Which of the following is the solution to the equation 25^(z + 2) = 125?
Answers
Answer:
z = -0.5
Step-by-step explanation:
Using exponent rule:
[tex]x^a = x^b[/tex] then a = b
Given the equation:
[tex]25^{z+2} = 125[/tex]
We can write 25 and 125 as:
[tex]25 = 5 \cdot 5 = 5^2[/tex]
[tex]125 = 5 \cdot 5 \cdot 5 = 5^3[/tex]
then;
[tex]5^{2(z+2)}= 5^3[/tex]
Apply the rule:
[tex]2(z+2) = 3[/tex]
using distributive property [tex]a \cdot (b+c) = a\cdot b+ a\cdot c[/tex]
[tex]2z+4 = 3[/tex]
Subtract 4 from both sides we have;
[tex]2z = -1[/tex]
Divide both sides by 2 we have;
z = -0.5
Therefore, the solution for the given equation is, z = -0.5
Mia’s work to find the slope of a trend line through the points (3, 10) and (35, 91) is shown below.
Mia’s Work
Step 1: 3-35/10-91
Step 2: -32/-81
Step 3: 32/81
What was the first error that Mia made?
A: Mia simplified incorrectly and made the slope positive.
B: Mia subtracted in the wrong order.
C: Mia switched the numerator and the denominator.
D: Mia used subtraction instead of addition.
Answers
m = (y2-y1) / (x2-x1)
Where we have two ordered pairs:
P1 = (x1, y1)
P2 = (x2, y2)
We observe then that according to the formula, the error of mine was to invert the numerator with the denominator.
Answer:
C: Mia switched the numerator and the denominator.
Answer:
Answer:
C: Mia switched the numerator and the denominator.
Step-by-step explanation:
just took the test
16. Which of the following are the measures of a right isosceles triangle?
a. 36°, 60°, 90°
b. 40°, 40°, 90°
c. 60°, 60°, 60°
d. 45°, 90°, 45°
17. Of the following triangles, which one is impossible to construct?
a. acute scalene
b. acute equilateral
c. obtuse scalene
d. obtuse equilateral
Answers
The angles of right isosceles triangle are such that there is the right angle, 90 degrees, and there are two identical angles that add up to 90.
17.
It is impossible to have an obtuse equilateral because and obtuse triangle has an angle that is more than 90 but less than 190. The equilateral triangle has all the angles equaling the same; 60 degrees. 60 degrees isn't obtuse so it is impossible to have an obtuse equilateral triangle.
Hope this helps :)
Solve for w.
1/7 = -3/2w -4/5 Simplify your answer as much as possible.
Answers
add 4/5 to both sides
1/7 + 4/5= -3/2w
change to common denominator; 5 & 7 go into 35
(1*5)/35 + (4*7)/34= -3/2w
5/35 + 28/35= -3/2w
33/35= -3/2w
divide by -3/2 on both sides; multiply by the reciprocal of -3/2
33/35 * -2/3= w
-66/105= w
simplify by 3
-22/35= w
CHECK:
1/7 = -3/2w - 4/5
1/7= -3/2(-22/35) - 4/5
1/7= 66/70 - 4/5
1/7= 66/70 - 56/70
1/7= 10/70
1/7= 1/7
ANSWER: w= -22/35
Hope this helps! :)
Answer:
7 on k-12
Step-by-step explanation:
7(w+1)7w+77w+77w+7−7w7217=======5(2w−3)+110w−15+110w−1410w−14−7w3w−143wwDistribute on each side.Simplify the right side.Subtract 7w from each side.Combine like terms.Add 14 to each side.Divide each side by 3.
Answer for number 5?
Answers
P = 2L + 2W
Where,
L: side
W: width
On the other hand we have that the ratio is:
L / W = 5/3
Clearing L we have:
L = (5/3) * (W)
Substituting in the expression of the perimeter:
P = 2 ((5/3) * (W)) + 2W
Rewriting:
P = (16/3) W
The perimeter is 192:
192 = (16/3) W
We cleared W:
W = (3/16) * (192)
W = 36
Finally we substitute W in the expression for L:
L = (5/3) * (W)
L = (5/3) * (36)
L = 60
Answer:
The width and length are:
W = 36 yards
L = 60 yards
What is the quotient of
13
÷
8
? Leave your answer as a mixed number
Answers
In Washington, D.C., Constitution Ave. meets Pennsylvania Ave. at a 25° angle. What is the measure of the complementary angle to the angle formed by these two avenues?
Answers
The problem indicates that Constitution Avenue meets Pennsylvania Avenue at a 25° angle. Then, the complementary angle is:
Complementary angle=90°-25°
Complementary angle=65°
What is the measure of the complementary angle to the angle formed by these two avenues?
The answer is: The measure of the complementary angle to the angle formed by these two avenues is 65°.
What is the first step to be done when solving this equation: 3(x-2+3) + 5 = 25
Answers
3(x - 2 + 3) + 5 = 25
Ok, so the first step is to distribute the parentheses:
3(x - 2 + 3) = 3x - 6 + 9 <<< answer
Next step:
plug it in the equation
3x - 6 + 9 + 5 = 25
Simplify,
3x + 8 = 25
Then,
subtract 8 from both sides
3x = 25 - 8
so, 3x = 17
Divide both sides by 3
x = 17/3