Consider the segment AB with A positioned at (6,2). The midpoint of AB, M is located at (5, -3). What are the coordinates of point B? * O (7,7) O (4,-8) O (5.5, -0.5) O (4,5)
Answers
Answer:
I didn't "do the math" yet at all, but draw it out on an X,Y axis... Thinking about it logically... If point A is in the upper right quadrant of the axis, because both X and Y coordinates are positive numbers, so you go right on the horizontal axis and up on the vertical axis... Then the midpoint is in the lower right quadrant of the due to the X coordinate being a positive, thus you go right on the horizontal axis, but the Y coordinate is a negative, so you go down vertically... So point B cannot be above both the midpoint or point A, ruling out (7,7) and (4,5) as both Y coordinates of those answers (7 or 5) are higher than point A's Y coordinate of 2... B would have to be below point A because the midpoint is below point A with a Y coordinate of -3... So this leaves either option (5,-0.5) or option (4,-8)... However.... While (5,-0.5) has a lower Y coordinate than point A with -0.5, its Y coordinate is above the Y coordinate of the midpoint as well, since -0.5 is above -3... So this doesn't jive as point B cannot be between point A and the midpoint to point B... This logically leaves (4,-8) left to be the answer... And if you drew on an X,Y axis the coordinates (6,2) as well as (5,-3) and (4,-8), then connect the dots, you'd find (5,-3) sits about half ways between (6,2) and (4,-8)...
So (4,-8) is probably the answer...
The best way to come to this conclusion mathematically is finding the slope (rise over run) of point A and the midpoint between point A and point B, then continuing the slope down, etc... But this particular question with the multiple choice answers ruled all but 1 answer out...
To find the slope you take rise over run, which is the Y of the 2nd coordinate minus the Y of the 1st coordinate, divided by (or over) the X of the 2nd coordinate minus the X of the 1st coordinate....
IE: ( Y2 - Y1 ) / ( X2 - X1 ) = Rise / Run
So.... The 2nd coordinate's Y value is -3, and the 1st coordinate's Y value is 2... Subtract 2 from -3, and you get -5...
Then the 2nd coordinate's X value is 5, and the first coordinate's X value is 6... Subtract 6 from 5, and you get -1...
Divide -5 over -1, which equals the same as 5 over 1... The rise is 5, the run is 1, the slope is 5 steps vertically for every 1 step horizontally...
Or visually... ( -3 - 2 ) / ( 5 - 6 ) which is -5 / -1... Since both sides are negative, that's the same as 5 / 1... which is 5 vertical steps (rise) for every 1 horizontal step (run), or a slope of 5...
So add the slope rise of 5 to the Y coordinate of the midpoint, -3, and you get 2, which is the Y coordinate of point A... And add slope run of 1 to the midpoint X coordinate, 5, and you get 6, the X coordinate of point A... Now subtract the slope rise of 5 from the midpoint, -3, and you get -8... So that tells you that point B has to have a Y coordinate of -8.... And now subtract the slope run of 1 from the midpoint X coordinate, 5, and you get 4... The X coordinate of point B... Giving you a point B coordinate of (4,-8)...
Related Questions
The price of an item is reduced by $1.39. The new sale price is $92.44. What is the original price
Answers
Answer:
92.44 + 1.39 = $93.83
Step-by-step explanation:
Since it was reduced by a certain amount, simply, add it back!
whats 4000 x48. i'm to lazy to use a countulater
Answers
Answer: 192,000
Step-by-step explanation:
Which relationship is always true for the angles x, y, and z of triangle MNP?
Answers
Answer:
Step-by-step explanation:
In every triangle, all the measures of the angles combined is 180 degrees.
So x + y + z = 180 degrees
Answer:
180 dg
Step-by-step explanation:
Cheryl has $56 and wants to buy as many notebooks as she can to donate to her school. If each notebook costs $1.60,
which inequality shows n, the maximum number of notebooks she can buy with her money?
1.672 56
O 1.6n s56
56931.6
O 56n2 1.6
Answers
Answer:
1.6n [tex]\leq[/tex] 56
Step-by-step explanation:
1.6n [tex]\leq[/tex] 56
This states,
'$1.60 per notebook, but use up to 56 dollars.'
I
The sum of a number and 9.4
Answers
Given
N = number
9.4
Since it says sum, that means we have to add
N + 9.4
The sum of x and 9.4 will be x + 9.4.
What is the arithmetic operator?Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,
Summation = addition of two or more numbers or variable
For example = 2 + 8 + 9
Subtraction = Minus of any two or more numbers with each other called subtraction.
For example = 4 - 8
Division = divide any two numbers or variable called division.
For example 4/8
Multiplication = to multiply any two or more numbers or variables called multiplication.
For example 5 × 7.
Let's say that number is x
Saying sum x with 9.4 means we need to add x and 9.4
So,
⇒ x + 9.4
Hence "The sum of x and 9.4 will be x + 9.4".
To learn more about the arithmetic operators,
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Can anyone help me with this? I've been stuck on this question for some time-
Answers
Answer:
Angle E is 43 degrees.
Step-by-step explanation:
So we know that AB is parallel to CD.
We also know that Angle CHF is 119 degrees and that Angle B is 18 degrees.
First, let's find Angle DHF. It is the supplementary angle to Angle CHF. Thus, they must total 180:
[tex]\angle DHF+\angle CHF=180[/tex]
We already know that Angle CFH is 119. Substitute:
[tex]\angle DHF+119=180[/tex]
Subtract 119 from both sides:
[tex]\angle DHF=61[/tex]
Therefore, Angle DHF is 61 degrees.
Since Angle DHF is 61 degrees, then angle BGH must also be 61 degrees. This is because they are corresponding angles, and corresponding angles have the same measure.
Also, Angle BGE is the supplementary angle to Angle BGH. In other words:
[tex]\angle BGE+\angle BGH=180[/tex]
Find Angle BGE. Substitute 61 for BGH:
[tex]\angle BGE+61=180[/tex]
Subtract 61:
[tex]\angle BGE=119[/tex]
So, angle BGE is 119 degrees.
Recall that a triangle's interior angles sum to 180. This means that Angle B plus Angle BGE plus Angle E must equal 180. Thus:
[tex]\angle B+\angle BGE+\angle E=180[/tex]
Substitute 18 for B and 119 for BGE. Thus:
[tex]18+119+\angle E=180[/tex]
Add:
[tex]137+\angle E=180[/tex]
Subtract:"
[tex]\angle E=43\textdegree[/tex]
And we're done!
Remarks:
I just realized that you can just use the fact that alternate exterior angles have the same measures to figure out that BGE is equivalent to CHF. Regardless, we will arrive at the same answer :)
The Johnson family is going to build a new home. They need to have working drawings of their house plans created by a design firm. They will choose between Rock the House Digital Designs and Elegant Home Architects. Rock the House Digital Designs charges $500.00 for the initial consultation with the Johnson family, plus $50.00 for every additional hour of work for the house plans. Elegant Home Architects charge $75.00 per hour for the house plans. Let ℎ represent the number of hours for which the Johnson family hires the design firm. Which of the following statements are true? Select all that apply.The Johnson family is going to build a new home. They need to have working drawings of their house plans created by a design firm. They will choose between Rock the House Digital Designs and Elegant Home Architects. Rock the House Digital Designs charges $500.00 for the initial consultation with the Johnson family, plus $50.00 for every additional hour of work for the house plans. Elegant Home Architects charge $75.00 per hour for the house plans. Let ℎ represent the number of hours for which the Johnson family hires the design firm. Which of the following statements are true? Select all that apply. -The expression 50ℎ represents the total charge for Rock the House Digital Designs. -The expression 75ℎ represents the total charge for Elegance Home Architects. -The cost for using Rock the House Digital Designs for an initial consultation only is $550. -If the Johnson family hires the design firm for 15 hours, then Elegance Home Architects will be cheaper. -If the Johnson family hires the design firm for 40 hours, then Rock the House Digital Designs will be cheaper.
Answers
Answer:
The expression 75ℎ represents the total charge for Elegance Home Architects.
If the Johnson family hires the design firm for 15 hours, then Elegance Home Architects will be cheaper.
If the Johnson family hires the design firm for 40 hours, then Rock the House Digital Designs will be cheaper.
Step-by-step explanation:
Given the following :
Rock the house digital designs :
Initial consultation charge = $500
Additional hour of work for house plan = $50 /hr
Elegant Home Architect:
Charge = $75 / hr
h = number of hours fro which Johnson's family hires the design firm
Total amount charged by Elegant home Architect = 75 × h = 75h
Total amount charged by Rock the house digital design = (500 + 50h)
If h = 15 hours :
Total amount charged by Elegant home Architect = 75 × 15 = $1,125
Total amount charged by Rock the house digital design = (500 + 50(15)) = 500 + 750 = $1,250
Hence, Elegant home Architect is cheaper.
If h = 40 hours :
Total amount charged by Elegant home Architect = 75 × 40 = $3,000
Total amount charged by Rock the house digital design = (500 + 50(40)) = 500 + 2000 = $2,500
Hence, Rock the house digital design is cheaper.
A skier is trying to decide whether or not to buy season ski pass. Daily pass cost $77.. A seasons pass cost $400.. this year would have to rent skis with either pass for $30 per day. How many days with the skier have to go skiing in order to make the season pass less expensive than the daily pass
Answers
Answer:
4 days
Step-by-step explanation:
77+30=107
400/107=3.73
The sum of 4 consecutive odd integers is equal to zero. Write an equation to model the sentence.
Answers
Answer: X + (X + 2) + (X + 4) + (X + 6) = 0
Step-by-step explanation:
We were already given the sum of four consecutive integers. Consecutive means coming after another. Let's first define our first consecutive odd number as X. Since it says consecutive odd integers, there is a difference of 2 between two odd numbers. We keep on adding 2 to the value of X, since they asked for four consecutive odd integers, so we get the 4 values of X, (X+2), (X+4), and (X+6). Once we put this in an equation, we get X + (X + 2) + (X + 4) + (X + 6) = 0.
The equation that models the sentence is : x + (x + 2) + (x + 4) + + (x + 6) = 0.
An odd number is a number that cannot be divided into half without any remainders. Examples of odd numbers are 1,3, 7, 11.
For example when 11 is divided in half, its value is 5.5
Consecutive odd numbers are odd numbers that follow each other. Examples are 1, 3, 5.
Consecutive odd numbers increase by 2
In order to model the sentence, let x represent the first odd number
Second odd number = x + 2
Third odd number = x + 4
Fourth odd number = x + 6
The equation is: x + (x + 2) + (x + 4) + + (x + 6) = 0
To learn more about odd numbers, please check: https://brainly.com/question/20432427?referrer=searchResults
A band marches in the African American Day Parade in New York City. The band marches 800 meters every 15 minutes. At this rate, how many kilometers does the band march in 1 hour?
Answers
reasoning:
there are 1000 meters in a kilometer. If they march 800 meters in 15 minutes, in 60 minutes they will march 3200 meters (800x4) . You then divide 3200 by 1000 to get 3.2 kilometers
The band will march 3.2 kilometers at the same rate.
What are the ratio and proportion?The ratio is the division of the two numbers.
For example, a/b, where a will be the numerator and b will be the denominator.
Proportion is the relation of a variable with another. It could be direct or inverse.
Given that,
800 meters for every 15 minutes
800 meters ⇔ 15 minutes
Multiply 4 by both sides
3200 meters ⇔ 60 minutes
Now,
60 minutes = 1 hour
And,
Since 1000 meter = 1 kilometer ⇒ 3200 meter = 3.2 kilometer.
So,
1 hour ⇔ 3.2-kilometer.
Hence "The band will march 3.2 kilometers at the same rate".
For more information about ratio and proportion,
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is number 6 integers, irrational, or real number, or whole number
Answers
Answer:
Hey there!
6 is an integer, whole number, and real number.
Let me know if this helps :)
A bag contains 4 red marbles, 5 blue marbles, 6 yellow marbles, and 7 green marbles; Jonathan randomly grabs one marble, puts it back then draws a second marble. What is the probability that the first marble was red, and the second marble was green?
Answers
p ( first marble red ) = 4/22
p ( second marble green ) = 7/22
Since total number of marbles r 22, then the denominator is 22 also. When Jonathan puts back the red marble aft the first round, this means with replacement so there's no change in denominator for the second round.
helpppp plssssss :(
Answers
what is the product of a number and 20 is 75
Answers
Answer:
20(x)=75
Step-by-step explanation:
x= unknown number
product= multiplication equation
same side exterior angles if m<1=4x+15 and m<8=3x+11, solve for the value of x
Answers
Answer:
x = 22
Step-by-step explanation:
same- side exterior angles are supplementary, thus
4x + 15 + 3x + 11 = 180, that is
7x + 26 = 180 ( subtract 26 from both sides )
7x = 154 ( divide both sides by 7 )
x = 22
need help I really need help WILL MARK BRANLEST
Answers
By definition, the absolute value of a constant is the distance from that number to zero, regardless of it's negative or positive coefficient.
The distance from -38 to 0 is 38, meaning that the absolute value is 38.
Hope this helps.
頑張って!
Answer:
38
Step-by-step explanation:
The absolute value of a number may be thought of as its distance from zero along real number line. which means - 38 is 38 times away from 0
Pls help work due in 10 min What is 0.000005 in scientific notation
Answers
Answer:
5 × 10 ^ -6
to get the answer move the decimal in 0.000005 to 5 which 6 place forward
which can also be written as 5 × 10 ^ -6
hope it helps
5×10- 6
Step-by-step explanation:
because we are converting decimal into scientific notation
Write 20.65 in expanded notation
Answers
Answer:
2 * 10 + 6 * .1 + 5 * .01
Step-by-step explanation:
The Wilson family had a family portrait framed for their living room. The frame measures 45 inches long and 37 inches wide. Which is a reasonable value for how much wall space the portrait will cover?
A. 12 ft
B. 12 ft2
C. 14 ft
D. 14 ft2
Answers
Answer:
12ft²Step-by-step explanation:
The frame is rectangular in nature, to determine a reasonable value for how much wall space the portrait will cover, we will take the area of the frame.
Given
Length of the frame = 45in
Width of the frame = 37in
Required
Area of the frame
Area of the rectangular frame = Length * Breadth
Area of the rectangular frame = 45in * 37in
Given 1feet = 12in
45in = 45/12 ft= 3.75ft
37 in = 37/12 ft = 3.083 ft
Area of the frame = 3.75ft * 3.083 ft
Area of the frame = 11.56ft²
Area of the frame ≈ 12ft²
Nick went on a bike ride to the store 5 miles away. If it took Nick of an hour to get there and ſof an
hour to get back, what was his average rate of speed (miles per hour) for the entire trip?
(Hint: To find the average, divide the total distance by the total duration.)
Answers
nick avg speed = s = 10/(1/5 + 2/5)
s = 10/(3/5)
s = (10*5)/3
s = 50/3
s = 16.6666666
---
answer:
s = 16.67 mph
Answer:
11.1
Step-by-step explanation:
Name the types of angles shown.
Check all that apply.
A. Complementary angles
B. Straight angle
C. Right angle
D. Supplementary angle
Answers
Answer:
supplementary and straight
Step-by-step explanation:
1. angle D and angle B add up to make a 180 degree angle so they are supplementary.
2. A and C each equal 180 degrees (straight angle= 180 degrees)
D. supplementary angles, C. right angle ,B. straight angle
(19) Larry can run a mile in 9 minutes. At the same pace, can he run 26 miles in 3
hours?
Answers
A train travels at a constant rate. If the train travels 496 miles in
8 hours, how many miles does the train travel in 1 hour?
Answers
Answer:
It is 62 miles.
Step-by-step explanation:
Hope this helps! :)
Answer:
62miles in one hour
Step-by-step explanation:
First, you have to identify your miles and you hour.
496 miles in 8 hours.
This automatically implies division because we want to know how far the train goes in 1 hour
Divide 496 by 8
Answer is 62 miles in one hour.
PLEASE HELP I DONT HAVE LONG
Answers
Answer:
The answer is A. 2
Step-by-step explanation:
The data values 8 - 10 is 2 because there are only 9 and 10.
Hope it helps :)
7. Solve the equation r cubed = 216.
Answers
Answer:
6
Explaination:
r^3=216
r= cuberoot(216)
r= cuberoot(6x6x6)
r=6
216//
cubed root 6*6*6 = 216
It takes 2 cups of sugar to bake 10 cookies. How many cups of sugar will it take to bake 30 cookies
Answers
A true conditional statement is below.
"If two angles form a linear pair, then the
two angles are supplementary."
Which of the following statements is false?
I.
If two angles are supplementary,
then they are a linear pair.
II.
If two angles are not a linear pair,
then they are not supplementary.
III. If two angles are not
supplementary, then they are not a
linear pair
A. I and III only
B. II and III only
C. I and II only
D. I, II, and III
Answers
Answer:
I and II only
Step-by-step explanation:
Can you guys help me? Plz
Answers
Answer:
x = 0 hopefully this helps
square root of 50
Rational
Irrational
Rational , integer, whole number
Integer
Whole nmber
Rational , integer
None of the above
Answers
Answer:
7.05 simplified rational
Answer:
irrational number
Step-by-step explanation:
Which of the following pairs of fractions consists of 5/8 and 17/24 rewritten with a common denominator? A. 1524 and 1724 B. 2036 and 1736 C. 2536 and 3436 D. 2024 and 1724
Answers
Answer:
[tex] \frac{5}{8} \frac{17}{24} [/tex]
[tex] \frac{15}{24} \frac{17}{24} [/tex]
The answer is A
Answer:
A
Step-by-step explanation: