Question # 2: Consider line segment AB. If A lies at (9.5, 10.3) and B lies at (7.1, 0.6), what is the midpoint of the segment AB?
Answers
The midpoint of line segment AB lies at (8.3, 5.45).
According to the section formula, a line segment AB with endpoints A(x₁, y₁) and B(x₂, y₂), when divided a point in the ratio m:n, that point will have the coordinates ( {mx₂ + nx₁}/{m + n}, {my₂ + ny₁}/{m + n} ).
The midpoint formula is an extension of the section formula, where the ratio is taken as 1:1, making the coordinates of the required point as ( {x₁ + x₂}/2, {y₁ + y₂}/2 ).
In the question, we are asked for the midpoint of segment AB, if A lies at (9.5, 10.3) and B lies at (7.1, 0.6).
Applying the midpoint formula, we get the midpoint as:
( {9.5 + 7.1}/2, {10.3 + 0.6}/2 )
= ( 16.6/2, 10.9/2 )
= (8.3, 5.45).
Thus, the midpoint of line segment AB lies at (8.3, 5.45).
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Related Questions
Fast plz
The options are
-Is
-Is not
Answers
Answer:
the rate of change is constant
Step-by-step explanation:
The workman’s family car travels 165 miles over 3 hours their cousins family car travels 150 miles over 2 hours if the family reunion is 900 miles away for both families and assuming both families continue at the same rates who will arrive First? What is the speed of each family?
Answers
From the problem, we have two cars.
Workman's family car travels 165 miles over 3 hours. The speed rate will be 165/3 = 55 miles per hour.
Cousin's family car travels 150 miles over 2 hours. The speed rate will be 150/2 = 75 miles per hour.
The fastest car is the the car with the fastest speed rate and that would be cousin's family car which is 75 miles per hour. So they will arrive first.
ANSWER :
Arrived first : cousin's family car
workman's speed : 55 miles per hour
cousin's speed : 75 miles per hour
2/10 x 1/9 = 2/90 = 1/?
Answers
Answer: 2/90 = 1/45
Step-by-step explanation:
Copy center charges $0.08 a page for machine fed copies and $0.20 for hand fed copies.If Logan's bill for 80 copies of his movie script is $13, how many copies of each type were made?
Answers
Answer:
machine fed copies = 25, hand fed copies = 55
Step-by-step explanation:
let machine fed = x, hand fed = y
0.08x+0.2y = 13 (1)
x+y = 80
x= 80-y (2)
sub (2) into (1)
0.08(80-y)+0.2y=13
6.4-0.08y+0.2y=13
0.12y=6.6
y = 55
sub y=55 into eqn 2
x = 80-55 = 25
756 divided by 36
plz need help
Answers
Answer:
21
Step-by-step explanation:
I did the math.
Answer:
756 divided by 36 = 21
1. BOWLING Brooke went bowling with her friends. She bowled 3 games, and
her average score for those games was 121. She had 117 her first game and
108 her second game. Write and solve an equation to find g, the score of
her third game.
pls show your work
Answers
Answer: x = 138
Step-by-step explanation:
\(108+117+x=3 * 121\\3 * 121 = 363\\Rearrange unknown terms to the left side of the equation\\x=(363-108)-117\\\\255-117=138\\x=138\)
Warm-Up
Jug
Use the diagram below to answer the questions.
Intro
K
P
M
Which are shown on the diagram? Check all that apply.
O
OKM
Ojk
OPK
OLJK
COM
Dong
Answers
KM, JK, PK, and MJ are shown on the diagram.
Then the correct options are B, C, D, and F.
Since, Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is m:n ratio, finding the mid-point of the line, etc.
A line segment in mathematics has two different points on it that define its boundaries.
All the line segments will be
JK, JM, KM, MP, PK, and KL
The triangle KPM.
And the angle will be ∠LKJ, ∠PKM. ∠KMP. and ∠MPK.
Then the correct options are B, C, D, and F.
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14b. State the domain of the function below. Use interval notationf(x) = 3Vx + 1 - 5
Answers
Given:
\(f(x)\text{ = 3 }\sqrt{x+1}\text{ - 5}\)To state the domain of this using interval notation, means to find the values which x may assume for the function above.
We have:
Since there is a root, let's exclude any real number that leads to a negative number.
Here, let's solve for x by setting the radicand to be greater than or equal to zero.
x + 1 ≥ 0
x ≥ 0 -1
x ≥ -1
Therefore, the domain function using notation function will be:
(-1, ∞)
ANSWER:
(-1, ∞)
You insure your home for $125,000. You want to be safe and add coverage on the contents, so you take 55% on the contents. How much coverage will you have on the contents of your home?
Answers
The amount of coverage that you will have on the contents of your home would be = $68,750
How to calculate the amount of coverage for contents of your home?The total amount of money that was insured for the house = $125,000
The percentage of insurance that was left for the contents of the house = 55% of insurance.
That is;
= 55/100 × $125,000
= 6875000/100
= $68,750.
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The director of a community recreation center conducted a six-week study to examine the effects of four types of exercise—strength training, flexibility training, aerobics, and jogging—on maximal oxygen consumption. From the 40
members who participated, the director randomly assigned 10 members to each exercise type. Maximal oxygen consumption was measured for each member at the beginning of the study and again at the end of the six weeks. The director examined the change in maximal oxygen consumption for each member. Which of the following statements is a correct description of a feature of the study?
a. The study has replication because there are four types of exercise.
b. The study has replication because it was conducted over a six-week period.
c. The response variable is the type of exercise with the greatest change in maximal oxygen consumption.
d. The treatments in the study are strength training, flexibility training, aerobics, and jogging.
e. The experimental units are the four different types of exercise.
Answers
Answer: The treatments in the study are strength training, flexibility training, aerobics, and jogging.
Step-by-step explanation:
A correct description of a feature of the study is that the treatments in the study are strength training, flexibility training, aerobics, and jogging.
It should be noted that the study has no replication. Also, the experimental units are the 40 members that participated.
Therefore, the correct option is D.
What are the coordinates of the endpoints of the midsegment for A RST that is parallel TS? Enter your answer by filling in the boxes. (_ , _) and (_ , _)
Answers
Answer:
2,4 3,5
Step-by-step explanation:
Use mental math to solve the proportion. 25 over 40 equals 5 over t
Answers
Answer:
t = 8
Step-by-step explanation:
create the proportion
\(\frac{25}{40} =\frac{5}{t}\)
\(\frac{25}{40}\) simplifies down to \(\frac{5}{8}\)
t = 8
Answer:
8
Step-by-step explanation:
25/40=5/t
0.625=5/t
0.625*t=5
(0.625*t)/0.625=5/0.625
t=8
Factor the following trinomial: x2 + 8x + 15.
Answers
Answer:
(x + 3) (x + 5)
The blue dot is at what value on the number line?
???????
Answers
Answer:
The blue dot is -19
Step-by-step explanation:
Since every 2 ticks are worth 6 (|-10|-|-4|=6), then one tick is worth 3.
We are going backward, so we can count backward.
We have to go down 3 ticks, so -10-3=-13; -13-3=-16; -16-3=-19.
The blue dot is -19
PLEASE MARK AS BRAINLIESTAnswer: The blue dot equals to -19.
Step-by-step explanation:
On the number line, there are the numbers -10 & -4.
-7 would fit in the middle of them. That means the number line goes by minus 3.
Count -10 , -13, -16, then you get on the the blue dot which is -19.
Therefore, -19 is the answer.
PLEASE MARK AS BRAINLIESTFind j.
j
9 ft
10 ft
5 ft
O
N
M
L
K
Write your answer as a whole number or a decimal. Do not round.
j =
feet
Answers
The value of j in the triangle is 8.66 feet
How to determine the value of jThe complete question is added as an attachment
From the question, we have the following parameters that can be used in our computation:
The right triangle
The value of j can be calculated using the following
tan(60) = j/5
So, we have the following representation
j = 5 * tan(60)
Evaluate
j = 5√3
This gives
j = 8.66
Hence, the value is 8.66 feet
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PLEASEE HELP GIVING OUT BRAINLIEST
Answers
Answer:
0 < x + 7 < 5 = [-7,-2)
Step-by-step explanation:
Move all terms not containing x from the center section of the inequality.
7 < x < -2
convert the inequality to interval notation
[-7,-2)
Hope this helps.
Which of the equations below could be the equation of this parabola?
OA y--¹x²
OB. x--²
C. x-²
D. y - x²
10
(0,0)
Vertex
10
Answers
An equation that could be the equation of this parabola include the following: C. x = 1/12(y²).
How to determine the equation of a parabola?In Mathematics, the standard equation of the directrix lines for any parabola that opens to the right is represented by this mathematical expression:
x = a(y - k)² + h.
Where:
h and k represent the vertex.a represent the leading coefficient.By critically observing the graph which models the equation of this parabola, we can logically deduce that the vertex is at point (0, 0) and as such, we have the following:
h = 0
k = 0
a = positive.
x = a(y - k)² + h.
x = a(y - 0)² + 0.
x = ay²
Therefore, a possible equation is x = 1/12(y²).
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ONLY ANSWER IF YOU KNOW 100% THAT YOUR'E CORRECT
Answers
The value that represents the distance between -10 and 5 on a number line is A) |-15|
How to solve for the valueWe have the value at the negative end to be = -10, while the given value that we have on the positive end is given as 5
To get the value we would have to solve it as
-10-(+5)
= -10 - 5
= -15
Hence we can conclude that the distance between the values is given as |-15|
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All explained on the screenshot!
Identify the center, vertices, co-vertices, foci, length of the major axis, and length of the minor axis of each. Then sketch the graph.
Answers
Center: (3, -2) , Vertices: (3±√(11), -2) , Cο-vertices: (3, -2±(3/2)√(11)) , Foci: (3±√(88), -2),
Length of major axis: 2a = 2√(11),
Length of minor axis: 2b = 2(3/2)√(11) = 3√(11).
How to identify the center, vertices, co-vertices, foci?To identify the center, vertices, co-vertices, foci, length of the major axis, and length of the minor axis, we need to rewrite the equation of the given ellipse in standard form, which is:
\((x-h)^2/a^2 + (y-k)^2/b^2 = 1\)
Where (h,k) represents the center of the ellipse, "a" represents the distance from the center tοa vertex along the major axis, "b" represents the distance from the center to a co-vertex along the minor axis, and "c" represents the distance frοm the center to a focus along the major axis.
Starting with the given equatiοn:
\(-9x^2 +y^2 - 54x + 4y -86 =0\)
We need to complete the square fοr both x and y terms:
\(-9(x^2 - 6x) + (y^2 + 4y) = 86\)
To complete the square fοr the x terms, we need to add and subtract the square of half of the coefficient of x, which is \((6/2)^2 = 9\):
\(-9(x^2 - 6x + 9 - 9) + (y^2 + 4y) = 86\)
\(-9(x - 3)^2 + (y^2 + 4y) = 95\)
To complete the square fοr the y terms, we need to add and subtract the square of half of the coefficient of y, which is \((4/2)^2 = 4:\)
\(-9(x - 3)^2 + (y^2 + 4y + 4 - 4) = 95\)
\(-9(x - 3)^2 + (y + 2)^2 = 99\)
Now, we can rewrite the equatiοn in standard form:
\([(x-3)^2]/(11) + [(y+2)^2]/(99/4) = 1\)
From this form, we can identify the center, vertices, co-vertices, foci, and lengths of the major and minοr axes:
Center: (3, -2)
Vertices: (3±√(11), -2)
Cο-vertices: (3, -2±(3/2)√(11))
Fοci: (3±√(88), -2)
Length οf major axis: 2a = 2√(11)
Length οf minor axis: 2b = 2(3/2)√(11) = 3√(11)
Tο sketch the graph, we can plot the center at (3, -2), draw the major and minor axes, and then sketch the ellipse using the vertices and co-vertices as a guide. The foci should be inside the ellipse along the major axis.
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Johannes needs to buy replacement team uniforms and is looking at different prices he has a budget of 300 he needs 18 pairs of plants and 12 shirts let x represent
Answers
Answer:
12 Shirts would be $275.
18 Pairs of Pants would be about $284 and some change.
Therefore, he would not be able to purchase the amount of shoes AND shirts that he needs for the team uniforms.
Step-by-step explanation:
convert 2.64 to a fraction
please don't just give the answer. can please give some explanation
Answers
Answer:
2 and 16/25
Step-by-step explanation:
first: change 0.64 into a fraction which is 64/100
second: simplify by dividing by four which is:
64/4 = 16
100/4 = 25
so...
2.64 = 2 16/25
HOPE THIS HELPS :)
Answer:
2 and 16/25 OR 66/25
Step-by-step explanation:
As a mixed fraction, 2.64 is 2 and 64/100 because you have 2 whole 100s and a 64/100. Simplify 64/100 to 16/25 (divide both 64 and 100 by 4) and you're left with 2 and 16/25.
In improper form, you have 264/100. Simplify that (divide 264 and 100 by 4) and you're left with 66/25.
Ethan saves $1.25 on Monday and $4.25 on Friday each week. How long would it take him to save enough for a $99 pair of AirPods?
Answers
Answer:
18 weeks
Step-by-step explanation:
Ethan earns $5.50 per week (5.5w) in an attempt to reach $99 (99)
5.5w=99
divide both sides by 5.5 and you get:
w=18
Therefore, Ethan must work 18 weeks in order to save enough for a $99 pair of AirPods
The store cell 3 new comic book for 10.50 and two vintage comic book for 7.80. What is the price for a new comic book at the store
Answers
The price of a new comic book at the store is 3.50
Calculating the price of a new comic bookFrom the question, we are to determine the price of a new comic book at the store.
Let the price of a new comic book be x
From the given information,
"The store sell 3 new comic book for 10.50"
and
The store sells two vintage comic book for 7.80
If the store sells 3 new comic book for 10.50
Then,
The store will sell 1 new comic book for x
3 × x = 1 × 10.50
3x = 10.50
Divide both sides by 3
3x/3 = 10.50/3
x = 3.50
Hence, the price is 3.50
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Look at the system of equations graphed below.
What is the solution to the system?
A. X=4, y=-2
68
B. X=4, y=1
5
4
C.x=1, y=-2
3
D D. x=2, y=-1
2
.
2.
4 5 6
-6-5-4 -3 -2 -1 0 1
-1
-3
-4
-5
Answers
Answer: The correct answer to the equation is B.
Hope this helps :)
Not my handwriting sorry if it's sloppy.
Can someone divide this using long division please :)
(4x^3– 2x^2 – 3) divide by (2x^2 - 1)
Answers
Answer:
The quotient is 2x+1. The remainder is 2x-2
Step-by-step explanation:
- 1 13 and its opposite on a number line.
Answers
Answer:
-113 and 113
Step-by-step explanation:
I'm not sure exactly what you mean by -1 13, so I'll assume you mean -113.
It's opposite would be 113.
If what you mean is -1 1/3 then it would be -4/3
Hope I helped
A friend lends you $400, which you agree to repay with 6% interest. How much will you have to repay?
Answers
Answer:
The worth of the bond will be $5000 in 6 month
Step-by-step explanation:
Answer:
$5000 in 6 months
Step-by-step explanation:
What is 10 times as much as $10? Do not forget to use $.
Answers
Answer:
$100
Step-by-step explanation:
There, I didn’t forget the dollar sign.
For the following vectors, (a) find the dot product v•w ; (b) find the angle between v and w , (c) state whether the vectors are parallel, octagonal, or neither. V=-3i-4j, w=6i+8j
A- v•w
B-the angle between v and w is theta ^•?
C- the vectors v and w are?
Answers
B) The angle between vectors v and w can be found using the formula: cos(theta) = (v • w) / (||v|| ||w||), where ||v|| and ||w|| are the magnitudes of vectors v and w respectively.
First, we need to find ||v|| and ||w||:
||v|| = sqrt((-3)^2 + (-4)^2) = 5
||w|| = sqrt((6)^2 + (8)^2) = 10
Now, we can substitute in the values to get:
cos(theta) = (-50) / (5 * 10) = -1
theta = arccos(-1) = pi radians or 180 degrees.
Therefore, the angle between vectors v and w is 180 degrees.
C) Two vectors are parallel if their directions are the same, which can be determined by comparing their unit vectors.
The unit vector of v is:
v_hat = v / ||v|| = (-3/5)i + (-4/5)j
The unit vector of w is:
w_hat = w / ||w|| = (6/10)i + (8/10)j = (3/5)i + (4/5)j
We can see that the unit vectors are in opposite directions, which means that the vectors are anti-parallel or opposite. Therefore, the vectors v and w are neither parallel nor orthogonal.
A section of the grocery store displays water bottles. The bottles come in packages of 6 or 8. Let x represent the number of 6-bottle packages, and let y represent the number of 8-bottle packages. The total number of packages displayed is 270, and the total number of bottles are 1860. To find the values of x and y, which of the following systems of equations would you use? Show your work
Answers
The total number of packages is x + y
So you get x + y = 270
The total number of bottles is 6 x the number of 6 bottle packages + 8 x the number of 8 bottle packages, so you get
6x + 8y = 1860.
Then you solve:
X + y = 270
x6
6x + 6y = 1620
6x + 8y = 1860
Take them away
2y = 240 so y= 140
Then solve for x
X+ y = 270
X + 140 = 270
X = 130