The coordinates of the midpoint of the segment HK are (7, 6).
The midpoint coordinates of a line segment can be found using the midpoint formula:
Midpoint =[tex]\((\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})\)[/tex]
Given the endpoints of the segment as H(8,2) and K(6,10), let's plug these values into the formula:
Midpoint =[tex]\((\frac{8 + 6}{2}, \frac{2 + 10}{2})\)[/tex]
Midpoint =[tex]\((\frac{14}{2}, \frac{12}{2})\)[/tex]
Midpoint =[tex]\((7, 6)\)[/tex]
The coordinates of the midpoint of the segment HK are (7, 6).
To calculate the midpoint of a line segment, you can follow these steps:
1. Identify the coordinates of the endpoints of the segment. Let's call them[tex]\( (x_1, y_1) \) and \( (x_2, y_2) \).[/tex]
2. Use the midpoint formula:[tex]\( \text{Midpoint} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \).[/tex]
3. Substitute the coordinates into the formula and calculate.
In this case, the endpoints are H(8,2) and K(6,10). Plug these values into the midpoint formula:
Midpoint = [tex]\( \left( \frac{8 + 6}{2}, \frac{2 + 10}{2} \right) \).[/tex]
Simplify the equation:
Midpoint =[tex]\( \left( \frac{14}{2}, \frac{12}{2} \right) \).[/tex]
Finally, calculate the values:
Midpoint =[tex]\( (7, 6) \).[/tex]
So, the coordinates of the midpoint of the segment HK are (7, 6).
complete question
Find the coordinates of the midpoint of the segment whose endpoints are H(8,2) and K(6,10).
Which pair of triangles are congruent by ASA ?
The pair of triangles that are congruent by ASA is [tex]\boxed{\bf option (d)}[/tex].
Further explanation:
Triangles are congruent when all the corresponding sides and interior angles are equal.
There are four theorems by which we say that the triangles are congruent.
1. Side-Side-Side(SSS)
If all the three sides of a triangle are equal to the corresponding sides of the other triangle, then the two triangles are congruent by SSS theorem.
2. Angle-Side-Angle(ASA)
If any two angles and the included side between the angles of one triangle are equal to the corresponding two angles and the included side between the angles of the second triangle then the two triangles are congruent by ASA theorem.
3. Side-Angle-Side(SAS)
If any two sides and angle between the sides of one triangle are equal to the corresponding two sides and angle between the sides of the second triangle then the two triangles are congruent by SAS theorem.
4. Hypotenuse Leg (HL)
If the hypotenuse and side of a right angled triangle is equal to the hypotenuse and a side of the other right angled triangle then the triangles are congruent by HL theorem.
Option (a)
The first figure shows one side is included between the two angles but the second figure shows two angles and one side as shown in below attachment.
Both the figures don’t have a single property from the above mentioned properties.
Therefore, option (a) is incorrect.
Option (b)
The first figure shows one angle between the two sides and the second figure also shows one angle between the two sides as shown in below attachment.
Both have the same property.
Therefore, the triangles are congruent by SAS rule not by ASA.
Thus, option (b) is incorrect.
Option (c)
The first figure shows one angle between the two sides and the second figure also shows one angle between the two sides as shown in below attachment.
Both have the same property.
Therefore, the triangles are congruent by SAS rule not by ASA rule.
Thus, option (c) is incorrect.
Option (d)
The first figure shows two angles and one side is included between them and the second figure shows two angles and one side is included between them as shown in below attachment.
Both have the same property.
Therefore, the triangles are congruent by ASA rule.
Thus, option (d) is correct.
Hence, the [tex]\boxed{\bf option (d)}[/tex] is correct as the triangles are congruent by ASA rule.
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Answer details:
Grade: Middle school
Subject: Mathematics
Chapter: Angles and Triangles
Keywords: Triangles, angles, sides, congruent triangles, similar triangles, SAS theorem, ASA theorem, SSS theorem, HL theorem, geometry, translation, rotation, reflection, mirror image.
The pair of triangles that are congruent by the Angle-Side-Angle Congruent Theorem (ASA) are the pairs that have two corresponding angles and an included side that are congruent to each other which is: Option D.
Recall:
The Angle-Side-Angle Congruent Theorem (ASA) states that two triangles are considered congruent if they have two corresponding angles that are congruent and an included side that are congruent to each other.
The included side is the side that is lie between the two congruent angles in each of the triangles.
Thus, form the pairs of angles given, the pair in option d has two corresponding angles and an included side that are congruent to each other in each triangle.
Therefore, the pair of triangles that are congruent by the Angle-Side-Angle Congruent Theorem (ASA) are the pairs that have two corresponding angles and an included side that are congruent to each other which is: Option D.
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Write an expression describing all the angles that are coterminal with 141°.
For carlees birthday her mother is baking cupcakes for her 12 friends at daycare. the recipe calls for
[tex]3\frac{1}{3} [/tex]
cups of flour. this recipe makes
[tex]2 \frac{1}{2} dozen \: cupcakes[/tex]
carlees mother only has 1 cup of flour. is there enough flour for each of her friends to get a cupcake
If you shift the quadratic parent function, f(x) = x2, right 12 units, what is the equation of the new function?
A. g(x) = (x – 12)2
B. g(x) = (x + 12)2
C. g(x) = x2 – 12
D. g(x) = x2
Answer:
A. [tex]f(x) = (x-12)^2[/tex]
Step-by-step explanation:
The parent function [tex]f(x) = x^2[/tex] can be shifted 12 units to the right by moving its vertex 12 units to the right. The parent function has a vertex at (0,0) since [tex]f(0) = 0^2=0[/tex]. It will shift to (12,0) so [tex]f(12) =(12-a)^2=0[/tex]. The only value of a which will make it 0 is 12. So the equation is [tex]f(x) = (x-12)^2[/tex]
Find the total area of the solid figure with the length, 3 width 5, and height 6
You deposit $1,000 in a savings account that earns 0.5% each month. Assuming you do not deposit or withdraw any money from the account, how much will you have in the account after 3 years?
How do you find a literal equation for d=rt,
solve for t.
Answer: [tex]\frac{d}{r} = t[/tex]
Step-by-step explanation: To solve for t in the equation d = rt, all we have to do is get t by itself on the right side of the equation.
Since t is being multiplied by r, we simply divide both sides of the equation by r. On the right, the r's cancel and we are left with r.
On the left side of the equation we have [tex]\frac{d}{r}[/tex].
Therefore, our answer is [tex]\frac{d}{r} = t[/tex].
The sum of two numbers is 90. if twice the smaller number is subtracted from the larger number, the result is 12. find the two numbers.
Line AB contains points A (3, −2) and B (1, 8). The slope of line AB is −5 negative 1 over 5 1 over 5 5
Answer: -5
Step-by-step explanation:
The slope of a line passing through (a,b) and (c,d) is given by :-
[tex]\text{Slope}=\dfrac{d-b}{c-a}[/tex]
Then the slope of the line AB contains points A (3, −2) and B (1, 8) will be :-
[tex]\text{Slope}=\dfrac{8-(-2)}{1-(3)}\\\\\Rightarrow\text{Slope}=\dfrac{10}{-2}-5[/tex]
Hence, the slope of the line AB contains points A (3, −2) and B (1, 8) = -5
Simplify. 4^3 x 4^4/ 4^9
A. 4^16
B. 4^2
C. 1/4^2
D 1/4
How many numbers between 100000 and 999999?
Answer:
there's actually 900000
Step-by-step explanation:
lets do the same thing for a smaller number to show where the previous solution went wrong if you take the interval between 255 and 0 (this is the size of one part of an ipv4 we know there is 256 bits because you have the digits 1 to 255 which makes up 255 bits and then if you ad the 0 (lower limit of the interval) you get 256-- the same principle applies here if you just do 999999-100000 you are not counting the lower limit and you are counting the upper limit which is wrong because between may be ambiguous so that it can mean including or excluding the upper and lower limit but it cannot exclude one and include the other thus making the answer 900000 including its limits and 899998 excluding them
Can someone clearly explain and workout Q19? Much appreciated
A package delivery company has determined that they can meet their schedules if they have 4 drivers for every 30 square miles of area they cover. If they want to offer service to a county of 75 square miles, how many drivers must they have?
A. 9 drivers
B. 10 drivers
C. 15 drivers
D. 12 drivers
Please explain your answer! : )
Answer:10 hahhahaahaahahaahahahhhahahaahahahhahahahahhahahahahahahahahahahahahahahhahahahahahhaahhaahahahhahahaahhahaaaaahahahahahahahahahahahahahahahaahahahahahaahahhaahahahaaaahahhahaahahaahahahahaaaahhahhahhahahahahhahahahahahhahahahahhahahahahahahhahhahahahahahahahhaahhaahhahahahahahhaahaahahahahahahahaaahhahahahahahahahahhahahahahahahahahahahahahahaha
HELP PLEASE!! I'LL GIVE 5 STARS, SAY THANKS, AND MARK AS BRAINLIEST ANSWER FOR CORRECT ANSWERS!!!
Solve the linear-quadratic system algebraically.
y = x^2 + 2x + 9
y − 9 = x
im pretty sure somone answered this but
Rosemary left a 15% tip for a meal that cost $39.
What was the amount of the tip?
What are the intercepts of the line 4x+3y=24?
Solve the compound inequality 2x > –10 and 3x < 24
5 > x > –8
5 > x < –8
–5 < x < 8
–5 < x > 8
Answer: Third option is correct.
Step-by-step explanation:
Since we have given that
[tex]2x>-10---------------------------(1)[/tex]
and
[tex]3x<24------------------------------(2)[/tex]
From eq(1), we have
[tex]\dfrac{2x}{2}>\dfrac{-10}{2}\\\\x>-5[/tex]
From eq(2), we have
[tex]3x<24\\\\\dfrac{3x}{3}<\dfrac{24}{3}\\\\x<8[/tex]
So, compound inequality becomes
[tex]-5<x<8[/tex]
Hence, Third option is correct.
every months, a man deposit in his bank account a savings of php 5,000 , in how many years would he have saved php 250,000?
What is the equation of a line that passes through the point (4, 2) and is perpendicular to the line whose equation is y=x/3−1 ?
How many times larger is 2 x 10-6 than 2 x 10-11?
Maddie plays 16 Games of tennis. Her went to loss ratio is 10 to 6. She is expected to play 12 more games during the season. How many do you expect her to win
On a tour of an old gold mine, you find a nugget containing 0.82 ounce of gold. gold is worth $1566.80 per ounce. how much is your nugget worth?
Since the gold is worth $1566.80 per ounce, then the nugget is worth $1284.776.
Worth of gold per ounce = $1566.80 per ounceAmount of gold that the nugget contains = 0.82 ounces of goldThis is a question relating to multiplication. Therefore, in order to know the worth of the nugget, we've to multiply 0.82 by $1566.80. This will be:
= 0.82 × $1566.80
= $1284.776
Therefore, the value of the nuggets is $1284.776.
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please help, I am really bad at algebra
Answer:
a, b, c
Step-by-step explanation:
f(x) = 3(1/4)^x
a. (-2, 48)
f(-2) = 3(1/4)^(-2) = 3(4)^2 = 3 * 16 = 48
(-2, 48) is on the graph.
b. (0, 3)
f(0) = 3(1/4)^(0) = 3(1) = 3
(0, 3) is on the graph.
c. (2, 3/16)
f(2) = 3(1/4)^(2) = 3(1/16) = 3/16
(2, 3/16) is on the graph.
d. (12, 0)
f(12) = 3(1/4)^(12) = 3(0.000000596)
f(12) does not equal zero.
(12, 0) is not correct
Solve - ( c - 3) = 6
A train leaves chicago and travels east at 60 mph. another train at the same depot leaves at the same time and travels west at 72 mph. how long before the two trains are 330 miles apart?
The two trains will be 330 miles apart after 2.5 hours.
Explanation:To find how long it takes for the two trains to be 330 miles apart, we can apply the formula for relative velocity:
Relative velocity = sum of their speeds
The first train is moving east at 60 mph, and the second train is moving west at 72 mph. So their relative velocity is 60 mph + 72 mph = 132 mph.
To find the time it takes for the trains to be 330 miles apart, we can use the formula:
Distance = speed × time
330 miles = 132 mph × time
Solving for time, we have:
Time = 330 miles / 132 mph = 2.5 hours
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Larissa asked 40 students to name their favorite food 10 students said their favorite food was pizza what percent of the students Larissa surveyed said their favorite food was pizza?
10 out of 40 said pizza =
divide 10 by 40 = 0.25
0.25 = 25% said pizza
How many different primes are in the prime factorization of 20! or 20 factorial?
What is the length, in units, of the hypotenuse of a right triangle if each of the two legs is 2 units?
4 units
2 units
Square root of 6 units
Square root of 8 units
Answer:
square root of 8
Step-by-step explanation:
because it is 8 squared
The length of the hypotenuse of a right triangle with legs of 2 units each is the square root of 8 units.
Explanation:In a right triangle, the length of the hypotenuse can be found using the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. If each of the two legs is 2 units, then the length of the hypotenuse can be found as follows:
hypotenuse2 = leg12 + leg22
hypotenuse2 = 22 + 22
hypotenuse2 = 4 + 4
hypotenuse2 = 8
Therefore, the length of the hypotenuse is the square root of 8 units.
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If m∠1 = 68°, what is y?
9
Angela is buying a dress that is on sale for 20% off. If the original price of the dress is $60.00, how much money is Angela saving on the dress?
Angela is Saving $12 on the dress.
What is Percentage?To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.
Given:
Original Price of Dress = $60
Discount = 20% off
So, the Price of Dress after discount
= 60- 20% of 60
= 60- 12
= $48
Hence, Angela saving $12.
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