Use the figure below.
Select all the lines in the proof of △ABC≅△CDA that have the correct justification.
∠ACB≅∠CAD, Alternate Interior Angles Theorem
△ABC≅△CDA, SAS Triangle Congruence Theorem
∠BAC≅∠DCA, Alternate Interior Angles Theorem
AB || CD and BC || AD, ASA Triangle Congruence Theorem
AC≅AC, Reflexive Property of Congruence
Answers
Answer:
∠ACB≅∠CAD, Alternate Interior Angles Theorem
∠BAC≅∠DCA, Alternate Interior Angles Theorem
AC≅AC, Reflexive Property of Congruence
By A-S-A congruence, the △ABC≅△CDA.
Step-by-step explanation:
Given the figure:
We are given that:
Side BC || AD
Side AB || DC
Let us have a look at a few properties first.
Alternate Interior Angle Theorem: It states that when two parallel lines are cut by a line then the alternate angles which are on the interior side are equal to each other.
Reflexive Property of Congruence: It states that a side or angle is always congruent to itself.
Now, let us consider the triangles:
△ABC and △CDA.
Side BC || AD
Therefore,
∠ACB≅∠CAD, Alternate Interior Angles Theorem
Side AB || DC
Therefore,
∠BAC≅∠DCA, Alternate Interior Angles Theorem
Also, Side AC is common.
AC≅AC, Reflexive Property of Congruence
Therefore, by A-S-A congruence, the △ABC≅△CDA.
Related Questions
whaat is the 2 power tp 4
Answers
2 to the power of 4 = 2 x 2 x 2 x 2 = 16
The answer is 16
Answer: 16
Step-by-step explanation:
2x2x2x2=16
A pound of swiss cheese costs $4.00 at the grocery store. Use the
fact that 16 ounces = 1 pound to help you find the cost of 5/6 pound
of swiss cheese.
Answers
The edge town eagle football team is having a tough season. During one game, they lost a total of 62 yards in 8 plays. What is the average ball movement per play?
Answers
a teacher has created a 100 point test with 22 questions. If each multiple choice question is worth 4 points and each short answer is worth 6 points. How many of each type are on the test?
Answers
Answer:
There are 16 multiple choices and 6 short answers.
Step-by-step explanation:
Let the number of multiple choice questions be x and the number of short answer questions be y.
x + y = 22 (total number of questions)
4x + 6y = 100 (total number of points)
x = 22 - y
4(22 - y) + 6y = 100
88 - 4y + 6y = 100
2y = 100 - 88
y = 6
x + 6 = 22
x = 16
Hence, there are 16 multiple choices and 6 short answers.
Hope this helped!
3,476 divided by 6 with a remainder
Answers
Answer:
look at the pic below!
Step-by-step explanation:
Please help me with this problem
Answers
Answer:
<EFG
Step-by-step explanation:
HELP PLEASE, WILL MARK BRAINLIEST
Find the values of the domain for which the function below is undefined.
y=x^2-16/x+4
A) {4}
B) {-4}
C) {±4}
Answers
The values of the domain for which the function below is undefined is {-4}
Undefined functionThe value of the domain where is a function is undefined is the point where the denominator is zero
Equate the denominator to zero
x + 4 = 0
Subtract 4 from both sides
x + 4 -4 = 0 - 4
x = - 4
Hence the values of the domain for which the function below is undefined is {-4}
Learn more on undefined function here: https://brainly.com/question/12039003
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his week, Michael collected $468 for delivering newspapers. He had 40 repeat customers and 18 new ones. As an incentive, he charged the new subscribers $3 less than the repeat customers. If x represents the amount Michael collects from each repeat customer, which equation models this problem? What is the fee Michael charges each new subscriber?
Answers
Answer:
$6
Step-by-step explanation:
Let x be the amount Michael collects from each repeat customer
Since we are given that he charged the new subscribers $3 less than the repeat customers.
So, amount collects from each new customer = x-3
Since he had 40 repeated customers
So, the amount Michael collects from 40 repeat customer = $40x
Since he has 18 new customers
So, amount Michael collects from 18 new customer =$18(x-3)
We are also given that his week, Michael collected $468 for delivering newspapers.
Answer:
$6
40x+ 18 (x-3) = 468
Paul opened a bakery. The net value of the bakery (in thousands of dollars) ttt months after its creation is modeled by v(t)=2t^2-12t-14v(t)=2t 2 −12t−14v, left parenthesis, t, right parenthesis, equals, 2, t, squared, minus, 12, t, minus, 14 Paul wants to know what his bakery's lowest net value will be. 1) Rewrite the function in a different form (factored or vertex) where the answer appears as a number in the equation.
Answers
Given:
The net value of the bakery (in thousands of dollars) t months after its creation is modeled by
[tex]v(t)=2t^2-12t-14[/tex]
Paul wants to know what his bakery's lowest net value will be.
To find:
The function in a different form (factored or vertex) where the answer appears as a number in the equation.
Solution:
Factor form is used to find the x-intercepts and vertex form is used to find the extreme values (maximum or minimum). So, here we need to find the vertex form.
We have,
[tex]v(t)=2t^2-12t-14[/tex]
[tex]v(t)=2(t^2-6t)-14[/tex]
Adding and subtract square of half of 6 in the parenthesis, we get
[tex]v(t)=2(t^2-6t+3^2-3^2)-14[/tex]
[tex]v(t)=2(t^2-6t+3^2)+2(-9)-14[/tex]
[tex]v(t)=2(t-3)^2-18-14[/tex] [tex][\because (a-b)^2=a^2-2ab+b^2][/tex]
[tex]v(t)=2(t-3)^2-32[/tex]
Vertex form:
[tex]f(x)=a(x-h)^2+k[/tex]
where, (h,k) is vertex.
On comparing this equation with vertex form, we get the of the function is (3,-32).
Therefore, the vertex form is [tex]v(t)=2(t-3)^2-32[/tex] and the function has minimum value at (3,-32). It means, minimum net value of the bakery is -32 after 3 months.
Answer:
v(t) = 2(t - 3)^2 - 32. and -32
Please mark the other one Brainiest.
Hope that this helps!
Solve for the value of k.
Answers
k=13
Step-by-step explanation:
180 =(4k-7) + (3k+6) +90
180= 7k+89
-89 -89
91= 7k
÷7 ÷7
k=13
Please help me, Ive been on this for almost half an hour ;(
which explicit formula describes the sequence −9, −3, 3, 9, 15, …?
Group of answer choices
an = 9n + 6
an = 6n + 15
an = 6n - 15
an = 9n – 6
Answers
Answer:
it's 9n + 6
Step by step :
-9 + 6 = -3
-3 +6 = 3
3 + 6 = 9
9 + 6 = 15
Please help this is urgent!! Will mark brainliest!
Answers
Answer:
C
Step-by-step explanation:
2·π·6·10+2·π·6^2
Answer:
602.88 in^2
Step-by-step explanation:
A=2πrh+2πr^2
A=2(3.14)(6)(10)+2(3.14)(6^2)
A=376.8+226.08
A=602.88
The line plot shows the number of books read by 15 students over the summer. How many students read 3 or fewer books? A. 5 , B. 12, C. 10, or D. 3
Answers
Answer:
5
Step-by-step explanation:
If the plot is like this were the students are the dots and the number of books are the numbers so your answer would be 5 students
1 has 1 dot
2 has 2 dots
3 has 2 dots
4 has 3 dots
5 has 1 dot
6 has 2 dots
7 has 3 dots
8 has 1 dot
The number of students who reads 3 or fewer books is 10 students. Therefore, option C is the correct answer.
Given that, the line plot shows the number of books read by 15 students over the summer.
We need to find out how many students read 3 or fewer books.
What is the line plot?A Line plot can be defined as a graph that displays data as points or checks marks above a number line, showing the frequency of each value. Here, for instance, the line plot shows the number of ribbons of each length.
Now,
The line plot depicted shows, the number of books read by 15 students.
Books read Number of Students
0 0
1 1
2 2
3 2
4 3
5 1
6 2
7 3
8 1
9 0
Number of students who read more than 3 books
= 3 + 1 +2+3+1+0
= 10 students
The number of students who reads 3 or fewer books is 10 students. Therefore, option C is the correct answer.
To learn more about the line plot visit:
https://brainly.com/question/16321364.
#SPJ2
what is the slope of у>- 2х + 3
Answers
Answer:
-2x
Step-by-step explanation:
Graph
y > −2x + 3
Use the slope-intercept form to find the slope and y-intercept.
The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.
y = mx + b
Find the values of m and b using the form y = mx + b. m = −2
b = 3
The slope of the line is the value of m, and the y-intercept is the value of b.
Slope: −2
intercept: (0, 3)
Graph a dashed line, then shade the area above the boundary line since y is greater than
−2x + 3.
y > −2x + 3
What is y=2x-3 in standard form?
Answers
Answer:
2x + y = -3 standard form
Using the distributive law :43x15+43x5
Answers
Answer:
Step-by-step explanation:
43x^15+43x^5= 43x^20
Can y’all help me on this???!!
Answers
she bought it and it was 12 cm tall so that would stay the same while if it grows 3 cm a week then the weak’s could change and so could the variable
please someonw help me with 7(a) please please please please please please please please please please please please please please please please
Answers
Answer: 2+1/x+3
Step-by-step explanation:
Pleaseeee helpp meeee
Solve for x: 8 ≥ 5 - 12x
Answers
Answer:
x ≥ -1/4
Step-by-step explanation:
8 -5 ≥ -12x
3 ≥ -12x
Divide both sides by negative 12 then flip the inequality sign.
x ≥ -1/4
look at my season races in nitro type
couldent get picture but is said
-1,233 / 50 Season Races
Answers
Answer:
-24.66
Step-by-step explanation:
Brainliest??
Answer:
dang
Step-by-step explanation:
Which is the graph of the function f(x) = Negative StartRoot x EndRoot?
Answers
Answer:
The answer is the third graph or c
Step-by-step explanation:
I just did the test and the other guy is correct to.
Answer:
If you are on edg 2021 then it is the graph with the line going down from 0 to the bottom left square of the graph
Step-by-step explanation:
So it is the first graph.
PLS HELPPPP!!!!! WILL GIVE BRAINLIST!!!!!!!!!!
Answers
Answer: C) y=-2+2
Step-by-step explanation: Rise over run says that the slope is -2 and the line hits the y axis at +2 so the equation would be y = -2 + 2.
A camera has a listed price of $826.95 before tax. If the sales tax rate is 8.75%, find the total cost of the camera with sales tax included.
Round your answer to the nearest cent, as necessary.
Answers
Answer:
899.30
Step-by-step explanation:
10 waffles and 4 pancakes cost $14. Five waffles and eight pancakes cost
$10. How much does a waffle cost? How much does a pancake cost?
Answers
9514 1404 393
Answer:
pancake: $0.50waffle: $1.20Step-by-step explanation:
You can model the bills using w and p for the price of a waffle and pancake, respectively.
10w + 4p = 14
5w +8p = 10
Subtract half the first equation from the second:
(5w +8p) -(1/2)(10w +4p) = (10) -(1/2)(14)
6p = 3 . . . . . . . simplify
p = 0.50 . . . . . divide by 6
10w + 4(0.50) = 14 . . . . substitute into the first equation
10w = 12 . . . . . . . . . . . . subtract 2
w = 1.20 . . . . . . . . . . . . .divide by 10
A waffle costs $1.20; a pancake costs $0.50.
What is the mode of: 9.6, 2, 4.1, 8, 5.9, 2, 3.7, 6, 7.6?
7.6
5.4
5.9
2
Answers
Answer:
The answer is 2.
Step-by-step explanation:
Put the numbers in order, the one that appears most often is the mode.
Answer:
2
Step-by-step explanation:
how to determine proportional relationship?
In your own words PLEASE
Answers
Answer:
to examine the ratio y/x (instead of x/y). If the x and y coordinates form proportional relationships, then there is some non-changing number (a constant) that when multiplied times x will create y. In this example, that number is 3 (y = 3x), and is called the constant of proportionality.
Step-by-step explanation:
Answer:
In a graph the line must pass through the origin and it has to be a straight line,
In an table the y over x has to be the same for each one
Shelly crane us a realtor she is paid a 3 percent commission on every house she sales. Her sales for the month of march were 95,900.00 129,650.00 and 378,420.00 what is shelly commision in march
Answers
Answer: 18119.10
Step-by-step explanation:
Shelly's commision in March will be calculated as:
= (3% × 95,900) + (3% × 129,650) + (3% × 378,420)
= (0.03 × 95900) + (0.03 × 129650) + (0.03 × 378420)
= 2877 + 3889.5 + 11352.6
= 18119.10
Her commission will be 18119.10
Aimee has $10.00 to spend on school supplies. The following shows the price of each item in the school store. No sales tax is charged on these items.
Eraser: $0.89
Folder: $1.29
Notebook: $2.35
Pen: $0.70
For the following problems, determine if Aimee can buy the combination of items with her $10.00. Select Yes or No for each combination of items.
17) 5 folders and 5 pens?
A) Yes
B) No
Save
18) 6 pens and 6 erasers?
A) Yes
B) No
Save
19) 1 pen and 4 notebooks?
A) Yes
B) No
Save
20) 3 folders and 7 erasers?
A) Yes
B) No
Save
21) 4 folders and 2 notebooks?
A) Yes
B) No
Answers
Answer:
17. yes - 9.95
18. yes - 9.45
19. no - 10.01
20. no 10.01
21. yes 9.86
-5x-y=12 solving for y
Answers
Answer:
good luck might be 8
Step-by-step explanation:
Answer:
y = -5x -12
Step-by-step explanation:
-5x - y = 12
=> -(5x + y) = 12
=> 5x + y = -12
=> y = -5x -12
Mr. and Mrs. Suralbo earned a net taxable income of P568,986. Find the income tax due.
Answers
Answer:
$198,000
Step-by-step explanation:
Since Mr. and Mrs. Suralbo are married and filing jointly, they would fall into the tax slab of 35% as their taxable income ranges between $414,701 to $622,050.
Taxable income = $568,986
Tax rate = 35%
Income tax due = $568,000 * 35/100
= $198,000
Thus, the income tax due for Mr. and Mrs. Suralbo would be $198,000.