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
label the slope and y intercept
Answers
Slope is 3/2
Subtract.
7/z +3
2/z+3
Simplify your answer as much as possible.
Answers
Answer:
5/z
Step-by-step explanation:
(7/z + 3) - (2/z + 3)
distribute the minus sign
(7/z + 3) - 2/z - 3
simplify
7/z + 3 - 2/z - 3
5/z
Our friend claims that a rectangle with the same perimeter as △QRS will also have the same area. Is your friend correct? Explain. yes; Any rectangle with a perimeter of 12 units will have an area of 6 units. yes; If a rectangle does not have the same perimeter as △QRS, it will not have the same area, so your friend's statement is correct by counterexample. no; A rectangle cannot have a perimeter of 12 units and an area of 6 square units. no; A 1×5 rectangle has a perimeter of 12 units and does not have an area of 6 units, so a counterexample shows that your friend's statement is not correct.
Answers
Answer:
A rectangle cannot have a perimeter of 12 units and an area of 6 square units. no
Step-by-step explanation:
We are given vertices in the attached
To solve this question, we are given vertices, we solve using the formula:
√(x2 - x1)² +(y2 - y1)² when given (x1, y1) and (x2, y2)
We are given Triangle QRS
Where: Q = (-2, 1) , R = (-2, -2), S =(2, -2)
QR : Q = (-2, 1) , R = (-2, -2)
= √(-2 - (-2))² + (-2 - 1)²
= √0² + 3²
= √9
= 3 units
RS : R = (-2, -2), S =(2, -2)
= √(2 -(-2))² + (-2 - (- 2))²
= √4² + (0)2
= √16
= 4 units
QS: Q = (-2, 1), S =(2, -2)
= √(2 -(-2))² + (-2 - 1)²
= √(2 + 2)² + (-3)²
= √4² + 9
= √16 + 9
= √25
= 5 units
The Area of Triangle QRS = 1/2bh
b = base = RS = 4 units
h = height = QR = 3 units
= 1/2 × 4 × 3
= 6 square units
Perimeter of Triangle QRS = QR + RS + QS
=( 3 + 4 + 5)units
= 12 units
Our friend is claiming that a rectangle with the same perimeter as will have the same area as the triangle
The perimeter of a rectangle
= 2L + 2W
12 units = 2L + 2W
12 - 2L = 2W
W = 12 - 2L/2
The Area of a Rectangle = L × W
6 square units = LW
6 = LW
6 = L ×(12 - 2L/2)
6 = 12L - 2L²/2
Cross Multiply
6 × 2 = 12L - 2L²
12 = 12L - 2L²
2L² - 12L + 12
2(L² - 6L + 6)
Therefore, from the calculation above, we can conclude:
A rectangle cannot have a perimeter of 12 units and an area of 6 square units. no.
Answer:
Step-by-step explanation:
Answer:
A rectangle cannot have a perimeter of 12 units and an area of 6 square units. no
Step-by-step explanation:
We are given vertices in the attached
To solve this question, we are given vertices, we solve using the formula:
√(x2 - x1)² +(y2 - y1)² when given (x1, y1) and (x2, y2)
We are given Triangle QRS
Where: Q = (-2, 1) , R = (-2, -2), S =(2, -2)
QR : Q = (-2, 1) , R = (-2, -2)
= √(-2 - (-2))² + (-2 - 1)²
= √0² + 3²
= √9
= 3 units
RS : R = (-2, -2), S =(2, -2)
= √(2 -(-2))² + (-2 - (- 2))²
= √4² + (0)2
= √16
= 4 units
QS: Q = (-2, 1), S =(2, -2)
= √(2 -(-2))² + (-2 - 1)²
= √(2 + 2)² + (-3)²
= √4² + 9
= √16 + 9
= √25
= 5 units
The Area of Triangle QRS = 1/2bh
b = base = RS = 4 units
h = height = QR = 3 units
= 1/2 × 4 × 3
= 6 square units
Perimeter of Triangle QRS = QR + RS + QS
=( 3 + 4 + 5)units
= 12 units
Our friend is claiming that a rectangle with the same perimeter as will have the same area as the triangle
The perimeter of a rectangle
= 2L + 2W
12 units = 2L + 2W
12 - 2L = 2W
W = 12 - 2L/2
The Area of a Rectangle = L × W
6 square units = LW
6 = LW
6 = L ×(12 - 2L/2)
6 = 12L - 2L²/2
Cross Multiply
6 × 2 = 12L - 2L²
12 = 12L - 2L²
2L² - 12L + 12
2(L² - 6L + 6)
Therefore, from the calculation above, we can conclude:
A rectangle cannot have a perimeter of 12 units and an area of 6 square units. no.
A racing car can complete an 700 m long lap in 14 s. What is the speed of the
car?
Answers
Answer:
[tex]\boxed {\tt 50 \ m/s}[/tex]
Step-by-step explanation:
To find the speed, divide the distance by the time. We can use the following formula:
[tex]s=\frac{d}{t}[/tex]
The racing car completed a 700 meter lap in 14 seconds. So, the distance is 700 meters and the time is 14 seconds.
[tex]d= 700 \ m \\t= 14 \ s[/tex]
Substitute the values into the speed formula.
[tex]s=\frac{700 \ m }{14 \ s}[/tex]
Divide.
[tex]s= 50 \ m/s[/tex]
The speed of the racing car is 50 meters per second
Answer:
The answer is 50 m/sStep-by-step explanation:
The speed of an object can be found by using the formula
[tex]v = \frac{d}{t} \\ [/tex]
where
v is the speed
d is the distance
t is the time
From the question
d = 700 m
t = 14 s
We have
[tex]v = \frac{700}{14} \\ [/tex]
We have the final answer as
50 m/sHope this helps you
I will give BRAINLIEST
Answers
Answer:
B
Step-by-step explanation:
Answer:
I think it is B :D
Step-by-step explanation:
What is 0.18 divided by 7.56 plzz help me and the others ones to
Answers
Answer:
0.023
Step-by-step explanation:
Which pairs of angles are always congruent? (select all that apply)
Corresponding Angles
Same Side Exterior Angles
Alternate Exterior Angles
Linear Pair Angles
Vertical Angles
Same Side Interior Angles
Alternate Interior Angles
Answers
Answer:
Corresponding angles
Alternate Exterior Angles
Alternate Interior Angles
I hope this helps I may be wrong I am sorry if i am
Answer:
numbers 1 and 5
Step-by-step explanation:
i toook the test
Find a counterexample for the given conjecture.
The difference of two odd numbers is always an odd number.
Answers
Answer:
The difference of two odd number is always even as seen below.
Step-by-step explanation:
First odd number = x
Second odd number = x + 2
Third odd number = x + 4
Therefore
(x + 4) - (x + 2) = x
Where x is any odd number
Using 1 :
(1 + 4) - (1+2)
5 - 3 = 2
2 is not an odd number
We can say the difference of two odd number is always even
find the cube of 2.9
Answers
[tex] {2.9}^{3} \\ 2.9 \times 2.9 \times 2.9 \\ 8.41 \times 2.9 \\ 24.389[/tex]
Answer:The cube of [tex]2.9[/tex] is [tex]24.389[/tex].
The formula for finding area of a triangle is: A=( 1/2)bh
Solve the equation for height, h.
SOMEBODY PLS HELP ASAP
Answers
Answer:
h=2Ab
Step-by-step explanation:
if you divide b on both sides you get Ab=1/2h
Then you would divide by 1/2 which is the same as multiplying by 2 which gives you the final answer of h=2Ab
Edwin went to the grocery store and bought several pounds of fruits. The fruit cost $2 per pound. He bought 2.5 pounds of apples , 1 3/10 pounds of bananas, and 0.85 pounds of kiwis. If he paid with a $10 bill , how much change will be left?
Answers
Answer:5.5 + 2.6 = 8.1 + 1.7 = 9.8
Step-by-step explanation: Soooo i think 20 cents
4. A triangle has sides of length 7, 10, and s. Write an equation representing the perimeter P of the triangle.
Answers
Answer:dam I got the same thing
Step-by-step explanation:
By the way this Brandon
1500 divided by 3500 would be?
Answers
( also if you can put brainliest that would help a lot it’s ok if not tho )
Answer:
0.42857142857
Step-by-step explanation:
correct me if im wrong
PLZ HELP its a test re rake i really need to get it right or im gonna fail
Answers
Answer:
D
Step-by-step explanation:
if it was written in scientific notation, it would be 5*10^1
There shouldn't be decimals or part of numbers(6.0 is okay because 6.0 =6) in scientific notation
For a given recipe, 6 cups of flour are mixed with 12 cups of sugar. How many cups of sugar should be used if 16 cups of flour are used?
Answers
Answer:
32 cups
Step-by-step explanation:
hope this helps plz mark brainliest
7/8 divided by (-13/7)
Answers
To make 5 dinner rolls, 1 third cup of flour is used.
How much flour is needed to make one dinner roll? someone helpp
Answers
Answer:
1/3 ÷ 5 = 1/3 x 1/5 (the reciprocal of 5) or 1/15 cup to make a single dinner roll
Step-by-step explanation:
Lula Krobo is paid a commission of 7% commission on all sales over $15,000 in a month and a monthly salary of $2,300. Her last month’s sales were $29,700. What were Lula’s total earnings for the month?
Answers
Answer: $33,029.00
Step-by-step explanation: 29700 + 1029 + 2300
sales = $29,700
commission = $1,029
salary = $2,300
Plz mark brainliest:)
Find the rate of change in the graph
Answers
Answer:
4/3
hope this helped :)
HELP HAVING BAD DAY
Jackie's dad drives her to a friend's house at the speed 30 mph. The friend's mom drives her back using the same route at the speed 25 mph. If the way back takes 6 minutes longer how far away is the friend's house?
Answers
===========================================
Work Shown:
t = time it takes to go from Jackie's house to her friends house
distance = rate*time
d = 30*t
This represents the distance they travel if they go 30 mph
Then when going back home, they take 6 minutes longer
6 minutes = 6/60 = 0.1 hours
So they take 0.1 hours longer meaning the t updates to t+0.1
d = r*t
d = 25*(t+0.1)
d = 25t+2.5
This represents the trip back home.
Since the distance d doesn't change, we can equate the two right hand sides and solve for t
30t = 25t+2.5
30t-25t = 2.5
5t = 2.5
t = 2.5/5
t = 0.5 hours = 30 minutes
d = 30t = 30*0.5 = 15 miles
Explication:
I had the same question and this was right
Kelvin purchased two Madden 21 games for $125.00. How much did each game
cost?
Answers
Answer: 125.00$
Step-by-step explanation:
the answers in the question
Answer: $62.50
Step-by-step explanation:
125/2=62.50
Given point Q (2,5), which of the following points is NOT 5 units away from point Q?
A(-2,2)
B(5, 1)
C (3,2)
D(-1, 1)
Answers
Answer;
C ; (3,2)
Explanations;
Mathematically, the equation of the distance between two points can be given as;
D^2 = (y2-y1)^2 + (x2-x1)^2
The distance we are dealing with is 25
Mathematically, the square of 3 and the square of 4 added together gives 25
So the coordinates that will be our answer will be such coordinates that will not give 3 and 4 for either of x or y axes
Looking at it;
Let’s work with the first option;
D^2 = (5-2)^2 + (2-(-2))^2
D^2 =3^2 + 4^2
We can see that this works
Second option;
D^2 = (5-1)^2 + (2-5)^2
D^2 = 4^2 + (-3)^2
Since (-3)^2 is same as 3^2, this option works too
Third option
D^2 = (5-2)^2 + (2-3)^2
D^2 = (3)^2 + (-1)^2
We can see that the sum here won’t give 25 , so this is our answer
A family bought a total of 16 adult and child tickets to a magic show. Adult tickets are $10.50 each and child tickets are $7.50 each. The family paid a total of $141. How many of adult tickets, a, and child tickets, c, did they buy?
Answers
9514 1404 393
Answer:
7 adult tickets9 child ticketsStep-by-step explanation:
Using the variables defined in the problem statement, we can write the equations ...
a + c = 16 . . . . . . . . . . . . number of tickets bought
10.50a +7.50c = 141 . . . cost of tickets bought
Substituting for c in the second equation, we get ...
10.50a +7.50(16 -a) = 141
3.00a +120 = 141 . . . . . . . . simplify
3a = 21 . . . . . . . . . . . subtract 120
a = 7 . . . . . . . . divide by 3
16 -a = c = 9 . . . . . . . find the number of child tickets
They bought 7 adult tickets and 9 child tickets.
_____
If you examine the solution, you see that the number of adult tickets (the higher priced item) is the quotient of the difference between the actual expenditure (141) and the amount that would have been spent on all child tickets (16×7.50=120), and the difference in ticket prices (10.50-7.50=3.00). Knowing this, you can often work problems of this kind in your head.
1) Gracie has a piece of wood that is 5 feet long to use for two projects. She uses 2 feet of the wood on her first project. Which statement describes how a number line can be used to find the length of wood Gracie has remaining for her second project? * Start at 5 and then move left 2 Start at 5 and then move right 2 Start at 2 and then move left 5 Start at 2 and then move right 5
Answers
Answer:
Start at 5 and then move left 2
Step-by-step explanation:
Given:
Length of a piece of wood with Gracie = 5 feets
Length of a piece of wood used on the first project = 2 feets
To find: statement that describes how a number line can be used to find the length of wood Gracie has remaining for her second project
Solution:
The statement that describes how a number line can be used to find the length of wood Gracie has remaining for her second project is
Start at 5 and then move left 2
In this way [tex]5-2=3[/tex]
That is Gracie has now 3 feets of wood available that can be used for her second project.
Using the concept of a number line, the number of wood grace has left would be Start at 5 and then move left 2
Using the concept of a number line :
Positive values are to the right of 0 ; hence, the initial amount of wood grace has is +5 Using two feets from the initial length, then we would Subtract 2 from the the initial value ;To perform subtraction on a number line, we count to the left ;Therefore, the correct statement is Start at 5 and then move left 2
Learn more : https://brainly.com/question/18109354
Evaluate x/y when x=9/4 and y=3/5
Answers
Answer:
[tex]\displaystyle x/y=\frac{15}{4}[/tex]
Step-by-step explanation:
Division of fractions
To calculate the division of fractions a/b and c/d, it's usually easier to multiply a/b by the reciprocal of the denominator, that is:
[tex]\displaystyle \frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a}{b}\cdot \frac{d}{c}[/tex]
We will evaluate x/y when x=9/4 and y=3/5:
[tex]\displaystyle \frac{\frac{9}{4}}{\frac{3}{5}}=\frac{9}{4}\cdot \frac{5}{3}[/tex]
[tex]\displaystyle=\frac{45}{12}[/tex]
Simplifying:
[tex]\displaystyle \boxed{x/y=\frac{15}{4}}[/tex]
Write the equation in slope-intercept form of a line that is parallel to y= -8x - 2 and goes through the point (-1, 11)
Answers
Answer:
y=-8x+3
Step-by-step explanation:
Slope-intercept form means
[tex]y=mx+c[/tex]
To write the equation in this form we need two things firstly m which is the slope and secondly c which is the y-intercept.
Since the line is parallel to [tex]y=-8x-2[/tex] as given in the equation and as we know that parallel lines have the same slope. So our new desired line that we need has a slope of -8 which is m. Now all we need is the y-intercept. For that we take the coordinate [tex](0,y)[/tex] because y-intercept means the line intersects the y-axis and if the line intersects the y-axis that specific point lies on the y-axis which is [tex](0,y)[/tex] so we put all the values in our desired equation and the coordinate that is also given to us [tex](-1,11)[/tex] because the line goes through this point it must lie on the line and hence we can use this point as well so now,
[tex]y=mx+c\\y=-8x+c\\11=-8(-1)+c\\11=8+c\\3=c[/tex]
so, the equation becomes,
[tex]y=-8x+3[/tex]
Pls help please!!!
Answers
i am gonna have to go with B
Find the missing measure for Angle E.
m ∠ E =
Answers
Step-by-step explanation:
40°+63°+e=180°
103°+e=180°
e=180°-103°
e=73°
I need the measurements ASAP!! Pls help me
Answers
Answer:
Step-by-step explanation:
A=53
B=53
C=74
D=122
okay so i worked from D up so you would do 180-58 to get 122
then for C you would do 4858 to get 106 then do 180-106 to get 74
then for A and B you would do 106 divided by 2 bc they ae the same size
5 divided by 5/6.please help
Answers
Answer:
5 divided by 5/6=6