The proof that MNG ≅ KJG is shown.
Given: angle N and angle J are right angles; NG ≅ JG
Prove: MNG ≅ KJG
What is the missing reason in the proof?
the reflexive property
ASA
AAS
the third angle theorem
Answers
The line [tex]\mathbf{\overline{MK}}[/tex] is a bisector of the line [tex]\mathbf{\overline{JN}}[/tex], and both lines form part of
ΔMNG and ΔKJG.
Correct response:
The missing reason in the proof is; ASAMethod used to prove ΔMNG ≅ ΔKJG, and find the missing reasonA two column proof is presented as follows;
Statement [tex]{}[/tex] Reasons
1. [tex]\overline{NG}[/tex] ≅ [tex]\overline{JG}[/tex] 1. Given (hash marks representing equal length)
2. ∠N and ∠J are right angles 2. Given (symbol for right angle)
3. ∠MGN ≅ ∠KGJ 3. Vertical angle are congruent (theorem)
4. ∠N ≅ ∠J 4. Right angles are (all) congruent
5. ΔMNG ≅ ΔKJG 5. Angle-Side-Angle, ASA, congruency rule
The missing reason in the proof is; ASAAccording to the ASA congruency rule, if two angles and the included
side of one triangle are the same to two angles and the included side of
another triangle, the two triangles are congruent.
∠N, side [tex]\mathbf{\overline{NG}}[/tex]∠MGN in ΔMNG are congruent to ∠J, side [tex]\mathbf{\overline{JG}}[/tex]∠KGJ in ΔKJG
Therefore;
ΔMNG ≅ ΔKJG by ASA congruency ruleLearn more about ASA postulate here:
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Related Questions
A circle has a center of (5,-5) and goes through (6,-2). What is the radius?
Answers
The distance between points O and P, that is |OP|, is the radius of this circle,
We use the distance between 2 points formula:
|OP|=[tex] \sqrt{ (x_2-x_1)^{2} + (y_2-y_1)^{2} }= \sqrt{ (6-5)^{2} + (-2-(-5))^{2} }[/tex]
[tex]= \sqrt{ 1^{2}+ (-2+5)^{2}} = \sqrt{1+9}= \sqrt{10} [/tex] (units)
Answer: [tex]\sqrt{10} [/tex] units
What do the parallel lines shown on segment BD and segment DC represent? _____________________
Answers
the 2 parallel lines mean that the lines are equal
SO since BD = 18, DC is also 18
BD = 18 = DC
Thus, correctly assuming that the point D is the mid point of line segment BC.
(05.01 MC)
The table and the graph each show a different relationship between the same two variables, x and y:
A table with two columns and 5 rows is shown. The column head for the left column is x, and the column head for the right column is y. The row entries in the table are 3,210 and 4,280 and 5,350 and 6,420. On the right of this table is a graph. The x axis values are from 0 to 10 in increments of 2 for each grid line. The y axis values on the graph are from 0 to 550 in increments of 110 for each grid line. A line passing through the ordered pairs 2, 110 and 4, 220 and 6, 330 and 8, 440 is drawn.
How much more would the value of y be in the table than its value on the graph when x = 11?
100
165
395
440
Answers
The value of y in the table is 165 more than the value of y in the graph
The points on the table are represented as:
(3,210) and (4,280)So, the equation of the table is calculated using:
[tex]y = \frac{y_2 -y_1}{x_2 -x_1}(x -x_1) + y_1[/tex]
This gives
[tex]y = \frac{280 - 210}{4 - 3} (x - 3) + 210[/tex]
[tex]y = 70(x - 3) + 210[/tex]
Expand
[tex]y = 70x - 210 + 210[/tex]
[tex]y = 70x [/tex]
When x = 11,
We have:
[tex]y = 70 \times 11[/tex]
[tex]y = 770[/tex]
The points on the graph are represented as:
(2,110) and (4,220)So, the equation of the graph is calculated using:
[tex]y = \frac{y_2 -y_1}{x_2 -x_1}(x -x_1) + y_1[/tex]
This gives
[tex]y = \frac{220 - 110}{4 - 2} (x - 2) + 110[/tex]
[tex]y = 55 (x - 2) + 110[/tex]
Expand
[tex]y = 55x - 110 + 110[/tex]
[tex]y = 55x[/tex]
When x = 11,
We have:
[tex]y = 55 \times 11[/tex]
[tex]y = 605[/tex]
Calculate the difference between the y-values
[tex]y_2 - y_2 =770 - 605[/tex]
[tex]y_2 - y_2 =165[/tex]
Hence, the value of y in the table is 165 more than the value of y in the graph
Read more about linear functions at:
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In the diagram, is the perpendicular bisector of and is also the angle bisector of . If m = x, which quantity is equal to sin ?
Answers
The quantity equal to sin ∠DPB is sin(x/2), corresponding to option B.
In the given diagram, overline PN serves as the perpendicular bisector of overline AB, implying that point N lies on the midpoint of segment AB.
Additionally, overline PN functions as the angle bisector of ∠CPD. Since ∠CPD measures x degrees, by the angle bisector theorem, ∠DPN and ∠DPB each measure x/2 degrees.
Now, to determine sin ∠DPB, we consider the right triangle DPN. By definition, sin θ = opposite/hypotenuse.
In this triangle, the opposite side to ∠DPB is overline DN, and the hypotenuse is overline DP.
Therefore, sin ∠DPB = DN/DP.
Since ∠DPN = x/2, applying trigonometric ratios in right triangle DPN, sin(x/2) = DN/DP.
Hence, the quantity equal to sin ∠DPB is sin(x/2), corresponding to option B.
The probable question may be:
In the diagram, overline PN is the perpendicular bisector of overline AB and is also the angle bisector of ∠ CPD If m∠ CPD=x , which quantity is equal to sin ∠ DPB ?
A. sin π /2
B. sin x/2
C. cos x/2
D. cos π /3
There are 20 wild pigs on an island and the number of pigs doubled each year for the past 5 years. The independent variable is
Answers
The independent variable is time.
Answer:
The independent variable is time.
Step-by-step explanation:
Given,
The original number of pigs on the island = 20,
Also, the number of pigs doubled each year,
After 1 year the pigs = 20(2),
After 2 years = 20(2)²,
After 3 years = 20(2)³,
......................., so on...
Similarly, the number of pigs after t years would be,
[tex]y=20.2^t[/tex]
⇒ The value of y depends upon t,
⇒ The number of pigs depends upon the time ( in years ),
Since, the variable in which the other variable depends is called independent variable,
Hence, the independent variable must be time.
The function $f : \mathbb{r} \rightarrow \mathbb{r}$ satisfies $f(x) f(y) - f(xy) = x + y$ for all $x$, $y \in \mathbb{r}$. find $f(x)$.
Answers
Find two geometric means between 10 and 1250.
Answers
a 1 = 10, a 4 = 1250
a 4 = a 1 * q^3
1250 = 10 * q^3
q^3 = 1250 : 10
q^3 = 125
q = 5
a 2 = 10 * 5 = 50
a 3 = 10 * 5² = 10 * 25 = 250
Answer: The two geometric means are: 50 and 250, since 10, 50, 250 , 1250 forms a geometric sequence.
How many feet of chain fence are necessary to enclose a dog pen that is square and has an area of 64 square feet?
Answers
x^2=64
(length)(width)=64
length=width
(x)(x)=64
x=8
Now we know all the sides of the square which is 8ft.
However, we're not done.
The question is asking for the amount of chain fence that is needed in order to enclose the square dog pen.
The question is asking us to find the perimeter.
Since we know what the sides of this square are, we can either add all the sides or just multiply one of the sides by four.
8 x 4= 32ft
Answer: 32ft
Doing this, we get that 32 feet are needed.
Square:
The area of a square of side s is:
[tex]A = s^2[/tex]
And the perimeter is:
[tex]P = 4s[/tex]
Area of 64 square feet
This means that:
[tex]s^2 = 64[/tex]
[tex]s = \sqrt{64}[/tex]
[tex]s = 8[/tex]
The side of the square is of 8 feet.
Perimeter:
Side of 8 feet, so:
[tex]P = 4s = 4(8) = 32[/tex]
32 feet of chain fence are needed.
A similar question is given at https://brainly.com/question/12256084
Marie is taking a test that contains a section of 10 true-false questions. How many of the possible groups of answers to these questions have at least 5 correct answers of true? Hint: Assign the variable x in the binomial expansion to be the number of true answers and y to be the number of false answers.
Answers
To solve this problem, we use the combination equation to find for the possible groups of answer to the questions. Since we are looking for at least 5 correct answers out of 10 questions, therefore we find for 10 ≥ r ≥ 5. We use the formula for combination:
nCr = n! / r! (n – r)!
Where,
n = total number of questions = 10
r = questions with correct answers
For 10 ≥ r ≥ 5:
10C5 = 10! / 5! (10 – 5)! = 252
10C6 = 10! / 6! (10 – 6)! = 210
10C7 = 10! / 7! (10 – 7)! = 120
10C8 = 10! / 8! (10 – 8)! = 45
10C9 = 10! / 9! (10 – 9)! = 10
10C10 = 10! / 10! (10 – 10)! = 1
Summing up all combinations will give the total possibilities:
Total possibilities = 252 + 210 + 120 + 45 + 10 + 1 = 638
Answer: 638
Create a set of numbers where:
the mode is equal to 10
the median is equal to 12
the average is 12
Answers
Given:
mode = 10
median = 12
average = 12
The possible set would be:
(10,10,12,13,15)
Is the value of [tex] \sqrt{42} [/tex] a rational or irrational number? Is it's value between 3 and 5, 5 and 7, or 7 and 9?
Answers
now, all those three factors are all irrationals. thus their product is also irrational.
[tex]\bf \sqrt{42}\approx 6.48 \qquad\qquad \boxed{5}------6--6.48---\boxed{7}[/tex]
Given a group of 8 women and 11 men, how many different ways are there of choosing one man and one woman for a committee?
Answers
Final answer:
There are 88 different ways of choosing one man and one woman for a committee.
Explanation:
In order to find the number of different ways of choosing one man and one woman for a committee, we can use the concept of combinations. The number of ways of choosing one item from a group of n items is denoted by n C 1, which is equal to n. So, the number of ways of choosing one man from a group of 11 men is 11, and the number of ways of choosing one woman from a group of 8 women is 8. To find the total number of ways, we multiply these two numbers:
Total number of ways = 11 * 8 = 88
Therefore, there are 88 different ways of choosing one man and one woman for a committee.
What causes water molecules to stick together in liquid water?
A. Water vapor
B. Carbon dioxide
C. Sun's gravity
D. Hydrogen bonds
Answers
HELP If f(x)=15x+3, then f^-1(x)=?
Answers
PM me
The inverse of the function f(x) = 15x + 3 is found by swapping x and f(x) in the equation and solving for f^-1(x), which leads to f^-1(x) = (x - 3) / 15.
Explanation:To find the inverse of the function f(x) = 15x + 3, it is necessary to first swap x and f(x) in the function equation. This results in x = 15f^-1(x) + 3. Secondly, solving for f^-1(x) means isolating this on one side of the equation. That results in f^-1(x) = (x - 3) / 15.
So, the inverse function of f(x) = 15x + 3 is f^-1(x) = (x - 3) / 15.
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Which polynomial is a perfect square trinomial? (1 point) 49x2 − 28x + 16 4a2 − 20a + 25 25b2 − 20b − 16 16x2 − 24x − 9?
Answers
4a² − 20a + 25 =
(2a)² - 2*2a*5 + 5² =
(2a - 5)²
4 workers get paid 160,000 for working for five days, how much will 5 workers get paid for working for a day
Answers
Hence,
1 worker gets paid = [tex] \frac{160,000}{4} = 40,000[/tex] for 5 days.
From here we can find out how much 1 worker is paid for 1 day by dividing by 5;
1 worker gets paid = [tex] \frac{40,000}{5} = 8,000[/tex] for 1 day.
Therefore,
5 workers get paid = [tex]8,000 * 5 = 40, 000[/tex] for 1 day.
Andrew makes $6 an hour plus $9 an hour for every hour of overtime. Overtime hours are any hours more than 40 hours for the week. Part A: Create an equation that shows the amount of wages earned, W, for working x hours in a week when there is no overtime. (3 points) Part B: Create an equation that shows the amount of wages earned, S, for working y hours of overtime. Hint: Remember to include in the equation the amount earned from working 40 hours. (3 points) Part C: Andrew earned $330 in 1 week. How many hours (regular plus overtime) did he work? Show your work. (4 points)
Answers
For Part A, all you need to do is write out an equation for how many dollars Andrew would make for x hours during regular hours (not overtime). Since he makes 6 dollars per hour, this will be 6x.
W = 6x
For Part B, create a similar equation for overtime hours. Overtime hours only apply after Andrew has worked 40 hours, so plug that into your first equation and add that to the second equation.
W = 6x
W = 6(40)
W = 240
S = 240 + 9y
For Part C, consider what we now know. If Andrew earns any money over 240 dollars (which is how much he earns after 40 hours), we know he worked overtime. So, we can just plug 330 into the second equation for S and solve for the number of additional hours he worked, y.
330 = 240 + 9y
– 240 – 240
90 = 9y
9 9
10 = y
Now, we can add up the initial 40 hours plus the additional 10 hours, which is 50 hours total.
Hope this helped you out! :-)
The manager of a baseball team has 15 players to choose from for his nine person batting order. How many different ways can he arrange the players in the lineup. A.5005. B.362880. C.3603600. D.1816214400
Answers
= 15! / (15-9)!
= 1816214400
Answer: D. 1816214400
Step-by-step explanation:
When we select r things from n things in order we apply permutations and the number of ways to select r things = [tex]^nP_r=\dfrac{n!}{(n-r)!}[/tex]
Given : Total player = 15
Required number of players for Batting order = 9
Then the number of different ways to select 9 person batting order so that he arrange the players in the lineup would be [tex]^{15}P_9=\dfrac{15!}{(15-9)!}[/tex]
[tex]=\dfrac{15\times14\times13\times12\times11\times10\times9\times8\times7\times6!}{6!}[/tex]
[tex]=1816214400[/tex]
∴ The number of different ways can he arrange the players in the lineup = 1816214400
Hence, the correct answer is D. 1816214400
Write an algebraic expression for 4 more than p
Answers
Find the inverse
f(x) = [tex] \frac{x}{x + 2} [/tex]
Answers
For each equation below find y if x=2
Answers
B - would be 2 to the second - 1 = 3
Double-checking my answer.. Given 3^2x = 9^6, what value of x satisfies this equation? (Use Laws of Exponents).
Thanks:)
Answers
Solve for X:
3^2x = 9^6
Simplify
9x=9^6
9x=531441
Divide both sides by 9.
(9x)/9=(531441)/9
x=59049
Hope this helps!
-Benjamin
The area of a parallelogram is modeled by the formula, A = lw. Solve the equation for w.
A. w=Al
B. w=I/A
C. w=A/I
D. w=2AI
Answers
First, let's look at our problem.
"A = L * W, solve for W."
This is basic algebra, but I will teach you how to tackle this problem, so you can do it on your own.
So, we have the following equation:
A = L * W
To solve for W, we need to get it alone on one side of the equation. Currently, it is not alone, but rather is being multiplied by L.
To isolate W, we need to perform the opposite order of operations on both sides of the equation.
A = L * W
Divide both sides by L to isolate and solve for W.
W = [tex] \frac{A}{L} [/tex] is our solution.
The following equation matches the answer choice "C".
Your answer is "C."
I hope this helps!
Answer:
.C
Step-by-step explanation:
Please, would somebody help me solve this math problem? I have no idea how to solve it.
Answers
Plug in the values
(2x+2)(2x)/2
(4x^2+4x)/2
2x^2+2x
Final answer: B
What is the midpoint of (4,8) and (3,12)
Answers
A choir has 3 spots open for altos, and 8 altos are interested in them. In how many ways can the open spots be filled?
Answers
n!/(k!(n-k)!), n=number of elements to choose from, k=number of choices made
In this case:
8!/(3!(8-3)!)
56
So there are 56 unique threesomes possible with 8 members.
There are total 56 ways to fill the open spot .
What is combination?
A combination is a way for determining the number of possible arrangements in a collection of items where the order of selection does not matter.
Formula for combination[tex]C(n, r) =\frac{n!}{(n - r)!r!}[/tex]
where,
n is the number of items in set.
r is the number of items selected from the set.
According to the question we have,
Number of altos, n = 8
Number of open spots, r = 3
Therefore, the number of ways to fill open spots = C(8, r)
Number of ways = [tex]\frac{8!}{3!(8-3)!}[/tex]
Number of ways = [tex]\frac{8!}{5!3!}[/tex][tex]= \frac{(8)(7)(6)(5!)}{5!3!}[/tex] = [tex]\frac{(8)(7)(6)}{(3)(2)} =8(7) = 56[/tex]
Hence, there are total 56 ways to fill the open spot .
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Solve for x..
a) x= 8
B) x= 22.5
C) x= 32.4
D) x= 40.5
Answers
so
x = 15*18 / 12
x = 270/12
x = 40.5
answer
D . x = 40.5
x/18 = 27/12 <=== cross multiply it
12x = 27×18
x = 486/12
x = 40.5
What 12 multiplied by 3
Answers
Please solve for c :3
3c - 2 = 5(c+2)
Answers
First of all, solve 5(c+2) by applying the distributive property.
I mean, 5*c and 5*2
So rewrite:
3c - 2 = 5c + 10
Now, you have to solve for c and then move all the Cs to the left of equal and change them sign, same to all known terms but move them to the right instead!
3c - 5c = 10 + 2
-2c = 12
The c can't be negative so divide both terms for -1
2c = -12
divide both terms for 2
2c/2 = -12/2
c = -6
An amusement park charges $9.00 for admission $4.00 per ride. Write an equation that gives the cost in dollars as a function of number of rides
Answers
T = total cost
X= number of rides
T=4.00x+9.00