Which statement justifies that angle XAB is congruent to angle ABC?
A. Corresponding angles of parallel lines cut by a transversal are congruent.
B. Vertical angles are congruent.
C. Same-side interior angles of parallel lines cut by a transversal are supplementary.
D. Alternate interior angles of parallel lines cut by a transversal are congruent.
Given: m || CB
Prove: m∠ABC + m∠BAC + m∠ACB = 180°
Answers
Answer: D. Alternate interior angles of parallel lines cut by a transversal are congruent.
Step-by-step explanation:
In the given picture m is parallel to CB .
Since m is a straight line and the angle of straight line is 180° .
Therefore, m∠XAB+m∠BAC+m∠YAC=180° ........................ (a)
Also, m is parallel to CB and AB is a transversal and because Alternate interior angles of parallel lines cut by a transversal are congruent.
⇒m∠XAB=m∠ABC and m∠YAC=m∠ACB
Put the values of m∠XAB and m∠YAC in equation (a), we get
m∠ABC + m∠BAC + m∠ACB = 180°.
Hence proved.
Statement D Alternate interior angles of parallel lines cut by a transversal are congruent is the most relevant to the congruence of XAB and ABC.
It is proved that m∠ABC + m∠BAC + m∠ACB = 180°.
For angle XAB being congruent to angle ABC, and then prove the equation m∠ABC + m∠BAC + m∠ACB = 180°.
Parallel lines m and CB.
Points X, A, and Y are on line m.
To prove that angle XAB is congruent to angle ABC.
Justification for Congruence:
In this context, use the Alternate Interior Angles Theorem,
which states that when a transversal intersects two parallel lines, the alternate interior angles formed are congruent.
Here's the reasoning:
Line m is parallel to line CB.
The line XY is a transversal line that intersects m and CB.
Therefore, the alternate interior angles formed by this setup are congruent.
This means that angle XAB and angle ABC are congruent.
Now, let's prove the equation m∠ABC + m∠BAC + m∠ACB = 180°.
Angle XAB is congruent to angle ABC (justified by the Alternate Interior Angles Theorem).
Now, let's consider the triangle ABC. By the angle sum property of triangles, the sum of the angles in a triangle is always 180°. Therefore:
m∠ABC + m∠BAC + m∠ACB = 180°
Since angle XAB is congruent to angle ABC, replace angle ABC with angle XAB:
m∠XAB + m∠BAC + m∠ACB = 180°
Now, the equation holds true, and you have successfully proven that m∠ABC + m∠BAC + m∠ACB = 180°.
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Related Questions
A rectangular field has a diagonal of 360 feet. One of the side of the field is 160 feet long. What is the perimeter of the field? Enter your answer, rounded to the nearest hundredth, in the box.
Answers
Using the Pythagorean Theorem,
3rd side^2 = 360^2 -160^2
3rd side^2 = 129,600 - 25,600
3rd side^2 = 104,000
3rd side = 322.49
Perimeter = 2 * (160 + 322.49)
Perimeter = 964.98 feet
Answer:
Perimeter of rectangle rounded to the nearest hundredth is 964.98 feet.
Step-by-step explanation:
Given : A rectangular field has a diagonal of 360 feet. One of the side of the field is 160 feet long.
To find : What is the perimeter of the field? Enter your answer, rounded to the nearest hundredth, in the box.
Formula used : perimeter = 2* length + 2√[tex]d^{2} -l^{2}[/tex].
Solution : We have diagonal of 360 feet and length = 60 feet .
plugging all the values of d and , l in formula .
perimeter = 2* 160 + 2√[tex]360^{2} -160^{2}[/tex].
perimeter = 320 + 2√[129600 -25600].
perimeter = 964.98 feet = nearest hundredth = 964.98 feet.
Therefore, Perimeter of rectangle rounded to the nearest hundredth is 964.98 feet.
which letter has at least one line of symmetry?
D
J
G
P
DOES ANYONE HAVE THE WHOLE QUIZ???? UNIT 4 Compositions of Isometries
Answers
The letter D has a line of symmetry that runs horizontally down the middle. If you were to fold the letter D in half, you would see that the upper and lower half of the letter look the exact same.
If you were asked to find the 87th term in a sequence, which formula would you want to be given?
A) analog form
B) digital form
C) explicit form
D) recursive form,
Answers
Answer:
C) explicit form
Step-by-step explanation:
Since the explicit form is written in terms of the number of the term, it would be the most useful to find the 87th term. To use the recursive form, you would have to know the 86th term.
Which of the following problem types CANNOT be solved using the law of sines?
**Choose ALL that apply!!!***
A. SAA
B. SSS
C. AAA
D. SAS
E. ASA
**I'm confused :( can you please explain? thank you :)
Answers
(sin A)/a =(sinB)/b = (sinC)/c
To use the above ratios, you need at least one angle and one side and one of either an angle or a side. So SSS and AAA don't work
Answer:
B) SSS C AAA D) SAS
Step-by-step explanation:
The sine rule is used when we are given
a) Two angles and one side (SAA)
b) Two angles and included side (ASA)
Sine rule can not be used in SSS,AAA or SAS.
Among the given options sine rule can not be used in cases B) SSS C AAA D) SAS
A bakery receives an order for 1600 cookies if 12 cookies are packed in each bag how many bags are needed
Answers
You get this by dividing the 1600 by 12 and rounding up.
134 bags are needed to pack all the cookies.
To solve this problem, you need to divide the total number of cookies by the number of cookies that fit in each bag.
Start with the total number of cookies:
1600 cookies.
Each bag can hold 12 cookies:
1 bag= 12 cookies
Divide the total number of cookies by the number of cookies per bag:
1600 ÷ 12.
Using division:
1600 ÷ 12
= 133.33.
Since you can't have a partial bag, you need to round up to the next whole number.
So, you will need 134 bags to pack all the cookies.
A hose dispenses 1,413 cm³ of water every minute into a cone with a radius of 60 cm and a height of 150 cm. How long will it take to fill the cone? Use 3.14 to approximate pi. Enter your answer in the box.
Answers
We are told that the hose spills 1413 cm^3 of water every minute. We are also told the cone has a height of 150 cm and a radius of 60 cm. So far, so good.
First things first, we need to find out how much water can fit in the cone. That means volume. The volume of a cone is
π • r^2 • (h/3)
Let’s go ahead and plug in (remember we use 3.14 for π)
(3.14) • (60)^2 • (150/3)
The volume of the cone is 565,200 cm^3
Wait, I’m lost. What were we supposed to do again? Oh, right. We needed to find how long it would take for the hose to fill in the cone. Well, if we know the hose dispenses 1413 cm^3 per minute, and there is a total of 565,200 cm^3 the cone can take, we can divide the volume of the cone by the amount the hose dispenses per minute to get the number of minutes it’d take to fill it.
565200/1413
400 minutes. Wow, ok. I wouldn’t want to wait that long. That’s like watching 3 movies!
A pile of sand is in the shape of a cone. The diameter of the sand pile is 18 feet and the height is 10 feet.
What is the volume of the sand pile?
Use 3.14 for pi.
Enter your answer as a decimal
Answers
v= 3.14 (9*9 ) * 10
=847.8
The volume of pile of sand having diameter of 18 feet and height of 10 feet is 847.8[tex]feet^{3}[/tex].
What is volume?Volume is basically the amount of something which the container can hold in its capacity or the amount of material with the help of which it is formed.
How to determine volume?It is told that the pile of sand is of cone shaped and it is having diameter 18 feet and height 10 feet. So the volume of sand pile will be
Volume=1/3π[tex]r^{2} h[/tex]
Radius=diameter/2
=18/2
=9 feet
Volume=1/3*3.14*[tex]9^{2}[/tex]*10
=1/3*3.14*81*10
=254.34/3
=847.8 [tex]feet^{3}[/tex]
Hence the volume of the sand pile of diameter 18 feet and height 10 feet is 847.8 [tex]feet^{3}[/tex].
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The figure was created by repeatedly reflecting triangle NMP. What is the perimeter of the figure? 36 in. 42 in. 44 in. 48 in.
Answers
Answer:
Perimeter = 42 inches
Explanation:
The perimeter is the length of the outline of a shape. To find the perimeter of a rectangle or square you have to add the lengths of all the four sides. In case of any diagram or figure, we add all the outer sides of the figure to get perimeter.
Here, outer sides are :
4, 4, 4, 4, 4, 4, 4, 6, 8
Now add all the sides together.
Permeter = 4 + 4 + 4 + 4 + 4 + 4 + 4 + 6 + 8 = 42 inches.
Final answer is 42 inches
Answer:
42 inches
Step-by-step explanation:
1. What is the value of x? Show all of your work.
Answers
AB^2 + 6^2 = square root 117^2
AB^2 + 36 = 117
Now subtract 117 from both sides
AB^2 = 81
AB = square root 81 = 9
[tex] \sqrt{81} = 9[/tex]
Therefore AB is 9 cms.
HOW DO YOU FIGURE OUT THE SLOPE OF A LINE ON A GRAPH?!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
There are different ways to find the slope of a line on a graph
Step-by-step explanation:
One way to find the slope of a line is by putting your line into the equation y=mx+b
In case you don't know m= the slope and b= the y-intercept
If you want to put your equation into y=mx+b; you will need to do rise/run
This means you count how much your line goes up on the y-axis so you rise however many and then you go to the right or left and count until you get to the point that is in line with the y and x axis'.
Also you can use the equation Y2-Y1/X2-X1
You will do that by finding 2 points from the line and take the numbers and make it into Y2-Y1/X2-X1
For Example if you had,
(4,3)(6,8) you would do
8-3/6-4= 5/2 so your m, or your slope would be 5/2
I hope this helps!
The drop that riders experience on Dr. Doom's Free Fall can be modeled by the quadratic function, h(t)9.8t2 5t 39 where h is height in meters and t is time in seconds. From what height are the riders dropped? What is the height of the riders after 1.5 seconds?
Answers
The correct answer is 53.55 meters.
To solve this problem, we need to analyze the given quadratic function h(t) = [tex]9.8t^2 - 5t + 39[/tex], where h is the height in meters and t is the time in seconds.
The given quadratic function: [tex]h(t) = 9.8t^2 - 5t + 39[/tex]
Part 1: From what height are the riders dropped?
[tex]h(0) = 9.8(0)^2 - 5(0) + 39[/tex]
[tex]h(0) = 39[/tex]
The riders are dropped from a height of 39 meters.
Part 2: What is the height of the riders after 1.5 seconds?
[tex]h(1.5) = 9.8(1.5)^2 - 5(1.5) + 39[/tex]
[tex]h(1.5) = 9.8(2.25) - 7.5 + 39[/tex]
[tex]h(1.5) = 22.05 - 7.5 + 39[/tex]
[tex]h(1.5) = 53.55[/tex]
The height of the riders after 1.5 seconds is 53.55 meters.
Jeanette purchased a concert ticket on a web site.The original price of the ticket was $75.She used a coupon code to receive a 20% discount.This website applied a 10% service fee to the discounted price.Jeanette ticket was less than the original price by what percent?
Answers
Find discounted price.
Discounted $= original $ - (original $ * % discount)
Discounted $= $75 - ($75 * 20%)
Discounted $= 75 - 15
Discounted $= $60
STEP 2:
Find discounted $ plus service fee.
Price plus fee= discounted $ + (discounted $ * service fee %)
Price plus fee= $60 + ($60 * 10%)
Price plus fee= 60 + 6
Price plus fee= $66
STEP 3:
Find % change.
% change formula= (new # - original #) ÷ original # x 100
% change= (66-75)÷ 75 x 100
% change= -9 ÷ 75 x 100
% change= -0.12 x 100
% change= -12%
***the negative indicates a decrease
ANSWER: Her ticket was less than the original by 12%.
Hope this helps! :)
Suzie drew the line of best fit on the scatter plot shown.
What is the approximate equation of this line of best fit in slope-intercept form?
y = 6 over 5x + 3
y = 3x + 6 over 5
y = 5 over 6x + 3
y = 3x + 5 over 6
Answers
Slope intercept form is defined as:
y = mx +b
In this form for lines, m is the slope, and b is the y intercept. Hence, slope intercept. That means that in order to write it in this form, we need to know both the slope and y intercept. We'll start with the former.
Slope is defined as ride over run, or up over right (you know it's negative when it goes left). In order to calculate this, we can take two points that lie directly on a coordinate and put them into a fraction as rise/run.
We have;
(0,3) and (5,9)
As we can see, the difference between the two points is that (5,9) is 5 more to the right, and is 6 higher. We get 6/5. We can even see that in the coordinates, because they're written as (x, y). Additionally, you can use the slope given two points formula:
y2-y1/x2-x1 =
9-3/5-0 = 6/5
Notice how we get the same thing, because in both methods you're finding the difference between the two coordinates based off of rise/run. That's why it's y2 minus y1.
Now that we have our slope, we need the y intercept. The y intercept is simply where the line crosses the y axis. As we can see, it crosses at (0,3) - so the intercept is 3. Now we can create our equation
Slope = 6/5
Y intercept = 3
y = mx + b --> y = 6/5x + 3
Your answer is A, the first option.
Hope this helps!
WILL GIVE BRAINLIEST ANSWER
PLEASE HELP WITH 9 & 10
Answers
then for 10 i did 49 divided by 7 which is 7 times larger so then you do 28/7 to get 4 so that is your answer for 10 4.
9:8
10:4
Luisa sells stuffed animals.she sells a stuffed elephant for $34.90, and the sale tax is 6% of the sale price.about how much is the sales tax on the elephant
Answers
1. You have that Luisa sells a stuffed elephant for $34.90 and the sale tax is 6% of the sale price.
2. Then, you only have to multiply $34.90 by the sale tax, as below:
6/100=0.06
Sales tax on the elephant=$34.90x0.06
Sales tax on the elephant=$2.094
About how much is the sales tax on the elephant?
The answer is: $2.094
what is the image of n for a 144° counterclockwise rotation about the center of the regular pentagon
A. A
B. E
C. P
D. T
Answers
144 is two fifths of 360 so for a pentagon, it would cause the point to shift two places
Answer:
The correct option is C. The image of N for a 144° counterclockwise rotation about the center is P.
Step-by-step explanation:
The number of vertices of a regular pentagon is 5.
The central angle between two consecutive vertices is
[tex]\frac{360}{5}=72[/tex]
It means the central angle between two consecutive vertices is 72 degrees.
We have to find the image of N for a 144° counterclockwise rotation about the center.
If pentagon rotates 72 degree counterclockwise rotation about the center, then the image of N is E.
If pentagon rotates (72+72) degree counterclockwise rotation about the center, then the image of N is P.
The image of N for a 144° counterclockwise rotation about the center is P.
Therefore the correct option is C.
The rectangular room is given by the trinomial x^2+4x-12. What are the possible dimensions of the rectangle? Use factoring. (1 point) (x-6) and (x-2) (x+6) and (x+2) (x-6) and (x+2) (x+6) and (x-2) 17. What is the factored form of the following expression? X^2+2xy-48y^2 (1 point) a. (x+6y)(x-8y) b. (x-6y)(x-8y) c. (x+6y)(x+8y) d. (x-6y)(x+8y) 18. The area of a rectangular art studio is given by the trinomial 24x^2-4x-8. What are the possible dimensions of the studio? Use factoring. a. (3x-2) and (8x-4) b. (3x-2) and (8x+4) (3x-2) and (8x-4) (3x+2) and (8x-4)
Answers
a]
x²+4x-12
=x²+6x-2x-12
=x(x+6)-2(x+6)
=(x-2)(x+6)
thus the dimensions are (x-2) units (x+6) units
b]
x²+2xy-48y²
factorizing the above is:
x²+8xy-6xy-48y²
=x(x+8y)-6y(x+8y)
=(x+8y)(x-6y)
c]
24x²-4x-8
factoring the above we get:
=4(6x²-x-2)
=4(6x²+3x-4x-2)
=4(3x(x+2)-2(x+2))
=4(3x-2)(x+2)
=(12x-8)(4x+8)
Which of the following are necessary when proving that the opposite sides of a parallelogram are congruent? Check all that apply.
A. Corresponding parts of similar triangles are similar.
B. Alternate interior angles are supplementary.
C. Alternate interior angles are congruent.
D. Corresponding parts of congruent triangles are congruent.,
Answers
The opposite sides of a parallelogram can be proved congruent by joining the diagonal of the parallelogram and proving the two triangles congruent by ASA .In any parallelogram opposite sides are parallel.We prove the triangles to be congruent by taking the property of parallel lines that Alternate interior angles are congruent.
When the triangles are proved congruent the opposite sides of parallelogram can be proved equal by using the property Corresponding parts of congruent triangles are congruent.,
The options which hold true to prove opposite sides of a parallelogram are congruent are options C and D.
C. Alternate interior angles are congruent.
D. Corresponding parts of congruent triangles are congruent.,
Which rational number is one-half of the way between 2 and 6.5: 2.25, 4.25, 4.5, or 4.75? And please explain.,
Answers
1. Add up the 2 numbers
2. Divide the number by 2
Midpoint of 2 and 6.5:
1) 2 + 6.5 = 8.5
2) 8.5 ÷ 2 = 4.25
Ans: The midpoint of 2 and 6.5 is 4.25
You roll an fair number cube. The six possible outcomes when rolling are one, two, three, four, five, six. What are the favorable outcomes when rolling an odd number?
1, 3, 5
2, 4, 6
1, 2, 3, 4, 5, 6
1, 2, 3
Answers
The answer is choice A) 1, 3, 5
A builder has 7200kg of sand.
A) write 7200 in grams
B) Give our answer in standard form,
Answers
Find the area of the regular pentagon if the apothem is 4.9 m and a side is 7.1 m. round to the nearest whole number. 62 m2 34 m2 87 m2 17 m2
Answers
[Area of the regular pentagon]=5*[side length * apothem] / 2
side length=7.1 m
apothem=4.9 m
then
Area=5*[7.1 * 4.9] / 2-----------> 86.975 m²----------> 87 m²
the answer is 87 m²
Please help asap!!! 13 points!
Answers
-3(0) +9y = 18 = 9y = 18 = 18 ÷ 9 = 2 = y intercept
-3x + 9(0) = 18 = -3x = 18 = 18 ÷ -3 = -6 = x intercept
the answer would be D
The area of a rectangular classroom is given by the trinomial 10x^2 + 3x - 4
What are the possible dimensions of the classroom? Use Factoring.
A.(5x - 4) and (2x + 1)
B.(5x - 4) and (2x - 1)
C.(5x + 4) and (2x - 1)
D.(5x + 4) and (2x + 1)
Answers
To solve this, you can factor the polynomial by grouping. There are numerous ways to do this.
If you are given a multiple choice question like this, you can use the FOIL method to test the answers until you get the correct one.
Choice C with the FOIL method.
(5x + 4)(2x - 1)
10x^2 - 5x + 8x - 4
10x^2 +3x - 4
It is correct!
EASY MEDAL !!!!!
Given the trinomial, what is the value of the coefficient 'B' in the factored form?
2x2 - 12xy - 32y2 = 2(x - 8y)(x + By)
B= ____________
Numerical Answers Expected!,
Answers
2x² - 12xy - 32y²
As a first step, we want to regroup 2:
= 2(x² - 6xy - 16y²)
Now, we want to re-write the term -6xy in order to be able to perform a partial factoring. In this case, we can write:
-6xy = -8xy + 2xy
Therefore, the polynomial becomes:
= 2(x² - 8xy + 2xy - 16y²)
Now we factorize x within the first two terms and 2y within the last two:
= 2[x(x - 8y) + 2y(x - 8y)]
We can now regroup the common term:
=2(x - 8y)(x + 2y)
Your answer is hence B = 2
12-packs of skwunch apple juice cost $3.00 after a 40% discount.Which equation would allow you to find the original price of the 12-packs?
Answers
Hope this help and plz give me points thank u :)
Answer:
The Iready Answer:
0.6x = 3
The graph shown is the graph of which function?
Answers
Answer:
The function of the graph is y = f(x) = x².
Step-by-step explanation:
From the graph we have
At x = 0, y = 0
Therefore f(x) = ax + c where c = 0
At x = 1 y = 1
At x = 4 y = 2
At x = 9 y = 3
At x = 16 y = 4
Therefore the graph is of the form, y= f(x) = x²
That is the graph can be plotted with a slope given by dy/dx = 2x an an intercept of c = 0.
Values of the graph are as follows
x y
1 1
2 √2
3 √3
4 2
5 √5
6 √6
7 √7
8 2√2
9 3.
How can transposable elements promote functional genetic diversity in a population?
Insertion into a regulatory sequence may alter the strength of transcription.
Insertion into an intro may provide an alternative splice site, producing a protein with a new exon.
Insertion into an mRNA strand may change the amino acid sequence produced.,
Answers
Suppose the velocities of golf swings for amateur golfers are normally distributed with a mean of 95 mph and a standard deviation of 3.9 mph.
What is the difference in velocities between a golfer whose z-score is 0 and another golfer whose z-score is −1?
1.95 mph
2.9 mph
3.9 mph
7.8 mph
Answers
the z-score is given by:
z=(x-μ)/σ
the score for golfer with z-score of 0 will be:
μ- mean
σ- standard deviation
0=(x-95)/3.9
the value of x will be
0=x-95
x=95
the score for the golfer with z-score of -1 is:
-1=(x-95)/3.9
-3.9=x-95
x=-3.9+95
x=91.1
the difference in the score of the golfers will be:
95-91.1
=3.9
the answer is C] 3.9 mph
which law would you use to simplify the expression (x^4)^9?
Answers
Hope this helps, byeee :)
The law that will be used to simplify the expression is the law of exponents.
What are Exponents?Exponents are the powers of the base numbers.
The law of exponents will be used to simplify the expression (x⁴)⁹
According to the law of exponents,
(aⁿ )ˣ = [tex]\rm a^{xn}[/tex]
So,
(x⁴)⁹ = x³⁶
Therefore, the law that will be used to simplify the expression is the law of exponents.
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