Given: Triangle ABC is right isosceles. X is the
midpoint of AC. AB = BC
Prove: Triangle AXB is isosceles.
Answers
Answer:
Step-by-step explanation:
From the figure attached,
Point X is the midpoint of line AC.
Since coordinates of the midpoint of the segment joining endpoints [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given by,
[tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]
Therefore, coordinates of the point X will be,
= [tex](\frac{0+2a}{2},\frac{2a+0}{2})[/tex]
= (a, a)
From triangle AXB,
Length of AB = 2a
Length of AX = [tex]\sqrt{(a-0)^2+(a-2a)^2}[/tex]
= [tex]a\sqrt{2}[/tex]
Length of BX = [tex]\sqrt{(a-0)^2+(a-0)^2}[/tex]
= [tex]a\sqrt{2}[/tex]
Length of AX = BX = [tex]a\sqrt{2}[/tex]
Therefore, triangle AXB is an isosceles triangle.
Related Questions
NEED HELP ASAP PLEASE.
Answers
Answer:
b.40
Step-by-step explanation:
The area of a square garden is 9ft. How long is each side of the garden
Answers
The length of each side of the square garden is 3ft.
What is a square?A square is a quadrilateral with four equal straight sides and four right angles.
To find the area of a square garden, multiply two equal sides.
The area is the space of a two-dimensional line.
To find the length of each side of a square garden, compute the squared root of the area.
Area of the square garden = 9 ft
Length of each side = √9
= 3 feet
Thus, each side of the garden has 3 ft.
Learn more about the area, length, and width at https://brainly.com/question/25292087
#SPJ1
which of these numbers has the most factors? 6:
17:
25:
36:
Answers
Answer:
36
Step-by-step explanation:
the solution of equation x × 3=0 is
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Answer:
x=0
Step-by-step explanation:
Regroup terms:
3x=0
Divide both sides by 3:
3x divided by 3 = x
0 divided by 3 = 0
x=0
Based on a graph below which sequence of transformation is needed to carry ABCD onto its image A’B’C’D?
Answers
Given:
The vertices of ABCD are A(2,3), B(5,6), C(8,6) and D(8,3).
The vertices of A'B'C'D' are A'(-2,6), B'(-5,3), C'(-8,3) and D'(-8,6).
To find:
The sequence of transformation is needed to carry ABCD onto its image A’B’C’D.
Solution:
The vertices of ABCD are A(2,3), B(5,6), C(8,6) and D(8,3).
If figure ABCD translated by the rule, [tex](x,y)\to (x,y-9)[/tex], then
[tex]A(2,3)\to A_1(2,-6)[/tex]
[tex]B(5,6)\to B_1(5,-3)[/tex]
[tex]C(8,6)\to C_1(8,-3)[/tex]
[tex]D(8,3)\to D_1(8,-6)[/tex]
Then the figure rotated 180 degrees clockwise about the origin. So,
[tex](x,y)\to (-x,-y)[/tex]
[tex]A_1(2,-6)\to A'(-2,6)[/tex]
[tex]B_1(5,-3)\to B'(-5,3)[/tex]
[tex]C_1(8,-3)\to C'(-8,3)[/tex]
[tex]D_1(8,-6)\to D'(-8,6)[/tex]
So, the required sequence of transformation that is needed to carry ABCD onto its image A’B’C’D is " A translation by the rule [tex](x,y)\to (x,y-9)[/tex] and then a 180° clockwise rotation about the origin".
Therefore, the correct option is D.
Find the length of AB if AC = 18 and BC = 7.
Answers
18-7
Answer
AB=11
4.(03.06 MC)
Choose the equation below that represents the line passing through the point (2, -5) with a slope of -3.
Answers
Answer:
y=-3x+1
Step-by-step explanation:
Polygons ABCD and A′B′C′D′ are shown on the coordinate grid: A coordinate plane is shown with two polygons represented. Polygon ABCD has vertices A at 2 comma 2, B at 2 comma 4, C at 3 comma 5 and D at 3 comma 1. Polygon A prime B prime C prime D prime has vertices A at negative 1 comma negative 2, B at negative 1 comma negative 4, C at negative 2 comma negative 5, and D at negative 2 comma negative 1. What set of transformations is performed on ABCD to form A′B′C′D′? (4 points) a A translation 1 unit to the left followed by a 180-degree counterclockwise rotation about the origin b A translation 1 unit to the right followed by a 180-degree counterclockwise rotation about the origin c A 90-degree counterclockwise rotation about the origin followed by a translation 1 unit to the right d A 90-degree counterclockwise rotation about the origin followed by a translation 1 unit to the left
Answers
Answer:
Answer is A. I get it right. :3
Answer:
a
Step-by-step explanation:
John is trying to solve for y, but he made a mistake. Where did John mess up? What did he do wrong? Step 1: 2 - 3(y- 1) = 6 Step 2: -1(y- 1) = 6 Step 3: -y+1= 6 Step 4: -y = 5 Step 5: y = -5 Step 2; he combined the 2 and -3 before he distributed O Step 3; he did not distribute the -1 correctly Step 2; he did not combine the 2 & -3 correctly. Step 4; he should have added the 1 to 6, not subtracted it Step 3; he should have added 1 to both sides.
Answers
Answer:
Step 4!!!
Step-by-step explanation:
A computer store pays sales associates $10 per hour
and managers $15 per hour. If the total hours
worked by the sales associates is 100 and the total
hours worked by managers is 50, how much will the
store pay in wages?
Answers
Answer:
They pay a total of $1750.
Step-by-step explanation:
You multiply the hours by the pay per hour SO,
Managers= $15 multiplied by the 50 hours they worked ($15 * 50hrs.) and get "$750"
Associates= $10 multipled by 100 hours ($10 * 100) and get "$1000"
Add the total sums ($750 + $1000) and get a total of $1750
In the next several games, the pitcher threw a total of 384 pitches and used a fastball 240 times. What decimal should Juanita use to update her report? Juanita should use the decimal to update her report. How do you know that the answer is a terminating decimal?
Answers
Answer:
0.625
It has 3 digits (finite) after the decimal point.
Step-by-step explanation:
Given that :
Total number of pitches = 384
Total number of fasfballs = 240
To make an update :
Ratio of the number of fastballs and total number of pitches
240 : 384
240/384
= 0.625
The result is a terminating decimal as it has a known number of digits after the decimal point. In the solution above, 0.625 has 3 digits after the decimal point and it is thus a terminating decimal.
What does this mean exactly?
Answers
Answer: Choice B [tex]y \le 0[/tex]
========================================================
Explanation:
They want to know what are all the possible y values here. The range is the set of all possible outputs of a function.
The largest y value is y = 0 which occurs at the vertex, in this case the highest point. There is no smallest y value as those arrows point downward forever.
So y is between negative infinity and 0, which means we write [tex]-\infty < y \le 0[/tex]
Converting that to interval notation leads to [tex](-\infty, 0][/tex]. Note the square bracket to include the endpoint.
The compound inequality [tex]-\infty < y \le 0[/tex] simplifies to [tex]y \le 0[/tex]
One way to describe this particular relation's range is to say "The set of negative real numbers with 0 included".
Side note: The domain is the set of all possible x inputs. In this case, the domain is the set of all real numbers.
Barnes and noble needs to ship 14 mystery books, 12 science-fiction books, and 8 historical-fiction books. The store can only pack one genre of book in each box, and they must pack the same number of books in each box. What is the greatest number of books Barnes and Noble can pack in each box?
Answers
Answer: 2
Step-by-step explanation:
Given: 14 mystery books, 12 science-fiction books, and 8 historical-fiction books needs to b shipped.
If they want to pack one genre of book in each box such that they pack same number of books in each box.
Then, the greatest number of books Barnes and Noble can pack in each box
= GCD(14,12,8)
Since, 14 = 2 x 7
12 = 2 x 2 x 3
8 = 2 x 2 x 2
GCD(14,12,8)=2
Hence, the greatest number of books Barnes and Noble can pack in each box = 2
Natalie wants to grow it 4 in. Longer than it is now. She knows that hair grows at an average rate of 15 cm/year. How many more months will she wait to have her hair cut? (1 cm ≈ 0.39 in.) Question 1 First, you will need to convert the rate of 15 cm/year to inches per month. Which two conversion factors should you use? Select all correct answers.
Answers
Answer:
8.21 months.
Step-by-step explanation:
The growth rate of hair, R = 15 cm/year
As 1 year = 12 months,
[tex]\Rightarrow R=\frac{15}{12}[/tex] cm/month
As 1 cm ≈ 0.39 in.,
[tex]\Rightarrow R= \frac{15}{12}\times 0.39=0.4875[/tex] inch/month.
As she wants to grow it 4 inches longer than it now, So, the time required for 4 inches growth = 4/0.4875=8.21 months.
Hence, she needs to wait for 8.21 months.
Maggie needs to spend at least six hours each week practicing the piano. She has already practiced three and one fourth hours this week. She wants to split the remaining practice time evenly between the last two days of the week. Write an inequality to determine the minimum number of hours she needs to practice on each of the two days.
WILL GIVE BRAINIEST IF RIGHT :)
A three and one fourth + 2x ≤ 6
B three and one fourth + 2x ≥ 6
C three and one fourthx + 2 ≤ 6
D three and one fourthx + 2 ≥ 6
Answers
Answer:
option 2 is correct-three and one fourth + 2x ≥ 6.
someone help with this ASAP I HAVE FEW MINS !!!
Answers
Answer:
Symmetric
Step-by-step explanation:
The sum of triple a number d and 5
(it’s translating expressions)
Answers
Answer:
3d+5
Step-by-step explanation:
Pls I really need help with this
Answers
B is the answer.............
Find the slope of the line
(1,-5),(-4,0)
Answers
Y^2-Y^1/X^2-X^1
0-(-5)/-4-1
5/-5
-1
Answer:
-1
Step-by-step explanation:
slope = ΔY / ΔX = 5/(-5)=-1
0 -x + y = 1
9x – 7y = 1
Answers
Answer:
X = 4 and Y = 5
Step-by-step explanation:
Which of the following is an example of the atmosphere interacting with the biosphere?
Answers
I’d say option 4
However, one may think option 3 might be possible as well. But that it is not interacting, it’s affecting.
So I’d stick with option 4.
Good luck!
Professor Burger orders flowers to be delivered to his mother. The flowers cost $59.95, not including tax. A bouquet of flowers is shown. Its price tag reads fifty-nine dollars and ninety-five cents. If there is a 6% sales tax, what is the total cost of the flowers to the nearest cent? Enter the correct answer in the box.
Answers
Answer:$60.30
Step-by-step explanation:
Add together 59.95 and 3.597. This gives you 63.547.
The directions say to round to the nearest cent, so round up to $63.55.
Hope this helps!
Two integers have a difference of 18 and a sum of 2. What is the product of the two integers?
Answers
Answer:
the product of the two integers is -80
Answer:
-80
Explanation:
it was on a mathcounts competition
400.34 + 678.397
210
Answers
Answer:
1078.73721
Step-by-step explanation:
PLEASE PLEASE HELP 5 MINUTES HELPP HELPP WILL MARK BRAINLIEST!!!!!
Answers
Answer:
Step-by-step explanation:
I & III look good
Line AB is 14 inches long. What is the approximate area of the circle?
615.44 inches
21.98 inches
153.86 inches
43.96 inches
Answers
Answer:
The third one is closest
Step-by-step explanation:
half of the diameter=the radius 14/2 = 7 and the formula for the area of a circle is r^2π so 49 × π is 153.93804
PLEASE HELP ME WITH THIS
Answers
Answer:
Hello!!! Princess Sakura here ^^
Step-by-step explanation: (sorry you'll have to graph them on your own)
Number 2:
So if x was this y would be...
x=-3 y=4 (-3,4)
x=0 y=2 (0,2)
x=3 y=0 (3,0)
The solution would be (3,0).
Number 3:
So before we begin we'd have to solve for y by subtracting 1 from both sides to get... [tex]y=3x-1[/tex]
Now we should choose -1, 0, and 1 so now...
x=-1 y=-4 (-3,4)
x=0 y=-1 (0,2)
x=1 y=2 (3,0)
The solution would be (1,2).
Which expression is equivalent to 5 (h + 9)?
Answers
Answer:
5(m+9) = 5m+25
Answer:
5(m+9) = 5m+25
Step-by-step explanation:
durrrrrrrrrrrrrrr
Which student rounded properly?
Answers
Answer:
c is the answer
Step-by-step explanation:
Marcia has a monthly income of $3,500. She budgets 8% for her cell phone. What amount does she budget for her cell phone, in dollars and cents?
Answers
Answer:
[tex]280 \: dollars[/tex]
Step-by-step explanation:
[tex]3500 \times .08 = 280[/tex]
Simple as that ^^^ Just find 8% of 3500
280,00$
8% of 3500$ equals to
(8/100)*3500=
280,00$=