use vectors to prove that the line joining the midpoints of two sides of a triangle is parallel to the third side and half its length.
Answers
The line joining the midpoints of two sides of a triangle is parallel to the third side and half its length.
Triangle law of vectors states that for a ΔABC
The sum of vectors of two sides is equal to the third side vector.
Two vectors are said to be Parallel if one vector is scalar multiple of other.
In the given figure
In ΔABC , D is mid point of AB and E is the mid point of AC .
By using triangle law of vectors for ΔADE
AE+AD=ED......(1)
Now using triangle law of vectors addition for ΔABC
CA+AB=CB ....(2)
(as given that E is the mid point of CA , we can write [tex]AE=\frac{1}{2} CA[/tex]
CA=2AE.....(3)
and D is mid point of AB , we can write [tex]AD=\frac{1}{2} AB[/tex]
AB=2AD......(4)
Substituting (3) & (4) in (2) we get
2AE+2AD=CB
2(AE+AD)=CB
SUBSTIUTTING VALUES OF (AE+AD) from (1) we get
2ED=CB
[tex]ED=\frac{1}{2} CB[/tex]
Hence , the line joining the midpoints of two sides of a triangle is half of third side.
Since ED is (1/2) of CB i.e. ED is scalar multiple of CB.
Hence they are parallel.
Therefore , The line joining the midpoints of two sides of a triangle is parallel to the third side and half its length.
Learn more about Vectors here https://brainly.com/question/4193111
#SPJ4
Related Questions
3h = 7 (2/7 - 3/7h) - 10
Answers
Answer:
h = -4/3
Step-by-step explanation:
Worked out on paper
suppose you are conducting a survey regarding illicit drug use among teenagers in the baltimore school district. you obtain a cluster sample of 12 schools within the district and sample all sophomore students in the randomly selected schools. the survey is administered by the teachers.
Answers
Response bias results from the possibility that not all sophomore students provided accurate information about their drug use, which will immediately result in the response bias because of false data.
What is response bias?
Response bias is a catch-all phrase for a variety of inclinations for participants to give misleading or inaccurate answers to queries. These biases are common in studies involving participant self-report, such as structured interviews or surveys. The validity of questionnaires or surveys can be significantly impacted by response biases.
The idea that human subjects do not passively respond to stimuli but rather actively integrate several sources of information to develop a response in a specific scenario is central to the concept that response bias can be induced or caused by a variety of causes. As a result, practically every element of an experimental condition has the ability to sway a respondent.
Explanation:
The remedy is to conduct a survey by licensed social workers since licensed social workers didn't explicitly ask sophomore students about drug use; instead, they interacted with the students as their friends before gathering the data.
To learn more about response bias ,visit:
https://brainly.com/question/2488343
#SPJ4
1j+4>1
Please help me
Answers
Hello,
[tex]1j + 4 > 1[/tex]
[tex]j + 4 - 4 > 1 - 4[/tex]
[tex]j > - 3[/tex]
Adding/Subtracting Inte
Find each sum.
1) (-12)+7
Answers
Answer:
-5
Step-by-step explanation:
(-12)+7 is the same as 7-12 which gives us - 5
Charlotte is visiting Brazil and is looking at souvenirs to purchase. She finds a jersey that costs 137 Brazilian real. If the current exchange rate is 1 dollar:5.43 Brazilian real, how much does the jersey cost in U.S. dollars?
$743.91
$131.57
$25.23
$3.96
Answers
Answer:
$25.23
Step-by-step explanation:
x/3.5 = 20/1.4 get it to be equal
Answers
Answer:
x is 50.
Explanation:
3.5 and 1.4 are both at the bottom of the fraction (denominators), so divide 3.5 by 1.4 to get 2.5.
Then, multiply 20 by 2.5.
This makes sense because 3.5 is greater than 1.4, and the final answer (50) is greater than 20.
We can always check by dividing 50 by 3.5 and 20 by 1.4. See if it is the same number.
help! i need help matching the teachers comments to the right definition asap
Answers
Step-by-step explanation:
Daniela : nice definition
Ori : part is right, but part is not
Kaori : incorrect
Daniela would not even have to say, that the lines are distinct. in any case, yes if you don't change anything about the appearance of the lines, but can move them on top of each other. and they completely blend in with each other, then yes they are parallel.
Ori is wrong about the part that they have to be close together. the second line could be in another galaxy, but if they are in the same plane and never intersect each other, then they are parallel.
Kaori is wrong by understanding that parallel means to opposite of perpendicular. perpendicular just means that the 2 lines are intersecting each other at a right angle (90°). but they can intersect at any other angle. that makes them not perpendicular, but they still intersect each other. so, they are not parallel.
3. A notebook costs $0.15 more than a pen. The total cost of the pen and notebook is
$2.25. How much does the pen cost?
| Total = $2.25
Answers
Answer:1.05
Step-by-step explanation:
total = 2.25
pen = x
notebook = x+0.15
2x+0.15=2.25
2x=2.10
x=1.05
pen = 1.05
Raina runs each lap in 8 minutes. She will run more than 9 laps today. What are the possible numbers of minutes she will run today? Use t for the number of minutes she will run today. Write your answer as an inequality solved for t.
Answers
Considering the definition of an inequality, the number of minutes she will run today will be more than 72 minutes.
Definition of inequalityAn inequality is the existing inequality between two algebraic expressions, connected through the signs:
greater than >.less than <.less than or equal to ≤.greater than or equal to ≥.An inequality contains one or more unknown values called unknowns.
Solving an inequality consists of finding all the values of the unknown for which the inequality relation holds.
Inequality in this caseIn this case, you know that:
Raina runs each lap in 8 minutes. She will run more than 9 laps today.Being "t" the number of minutes Raina will run today, the inequality is
t÷ 8> 9
Solving:
t > 9×8
t > 72 minutes
Finally, the number of minutes she will run today will be more than 72 minutes.
Learn more about inequality:
brainly.com/question/17578702
brainly.com/question/25275758
brainly.com/question/14361489
brainly.com/question/1462764
#SPJ1
Stephen and Paul each purchased a movie ticket at AMC theaters for $11.00 each. Both bought a drink from the concession stand. Stephen used a $5.00 off coupon that he received in the mail. After using the coupon, their total cost before tax was $29.18.
Write an equation that can be used to determine the cost of one drink. Be sure to define your variable.
Answers
The equation that can be used to determine the cost of one drink is 29.18 = 22 + 2x - 5 where the cost of each drink is $6.9
EquationCost of each movie tickets = $11Total of movie tickets = $11 × 2= $22
Coupon = $5Cost of each drink = xTotal cost after coupon = $29.1829.18 = 22 + 2x - 5
29.18 = 17 + 2x
29.18 - 17 = 2x
12.18 = 2x
divide both sides by 2x = 12.18 / 2
x = 6.9
Therefore, the equation that can be used to determine the cost of one drink is 29.18 = 22 + 2x - 5 where the cost of each drink is $6.9
Learn more about equation:
https://brainly.com/question/22688504
#SPJ1
Beekeepers sometimes supplement the diet of honey bees with sugar water to help promote colony growth in the spring and help the bees survive through fall and winter months. The tables show the amount of water and the amount of sugar used in the sping and in the fall. Wite a sentence that compares the ratios if the number of cups of sugar to the number of cups of warer in each table. then determine how you got your answer
Answers
1. For the spring, the sugar-water mixture is in the ratio of 3:2 that is for 2 cups of water, 3 cups of sugar are required. For the fall, for every cup of water, 2 cups of sugar are required, giving a ratio of 2:1.
2. To get the ratio for the mixtures, order the pairs (e.g. (6, 4), (15, 10), and check the proportion of each variable in the other variable, using the least common divisor.
What is a ratio?A ratio is the proportion of each variable in the other.
Ratios are expressed using the ratio sign (:) or in fractions, decimals, or percentages.
Data and Calculations:Spring Sugar-Water Mixture
Cups of Sugar Cups of Water
6 4
15 10
18 12
27 18
The ratio of the spring sugar-water mixture is 3:2. For instance, 27:18 can be reduced to 3:2 by divisor 9.
Fall Sugar-Water Mixture
Cups of Sugar Cups of Water
4 2
10 5
14 7
30 15
The ratio of the fall sugar-water mixture is 2:1.
Learn more about ratios at https://brainly.com/question/2914376
#SPJ1
ZRQT is a straight angle. What are mZRQS and mZTQS?
mZRQS = 109°
mZTQS=
R
(10x+9)°(7x+1)°
i
Answers
The unknown angles on the straight line are as follows:
m∠RQS = 109° m∠TQS = 71°How to find angles?∠RQT is a straight angle.
Therefore,
∠RQT = 180 degrees(angle on a straight line)
Therefore, let's find m∠RQS and m∠TQS
∠RQT = m∠RQS + m∠TQS
where,
m∠RQS = 10x + 9
m∠TQS = 7x + 1
Therefore,
∠RQT = 10x + 9 + 7x + 1
∠RQT = 17x + 10
180 - 10 = 17x
170 = 17x
divide both sides by 17
x = 170 / 17
x = 10
Therefore,
m∠RQS = 10(10) + 9 = 109°
m∠TQS = 7(10) + 1 = 71°
learn more on angles here: https://brainly.com/question/17702384
#SPJ1
Can someone help me please?
Answers
Answer:
B) y = 0.6xStep-by-step explanation:
Proportional relationship equation:
y = kx, where k- coefficient of proportionality.Use given values in table to find the value of k:
9 = 15k ⇒ k = 9/15 = 0.67.2 = 12k ⇒ k = 7.2/12 = 0.61.5 = 2.5k ⇒ k = 1.5/2.5 = 0.6So the equation is:
y = 0.6xa pack of 6 hair clips costs $14.82. what is the unit price HELP
Answers
Answer:
2.47
Step-by-step explanation:
Perform long division.
[tex]Borrow\:8\:and\:2.\:You\:will\:see\: :)\\6 \cdot 2 = 12\\= 14 - 12 \\= 2\\Drop\:8\\= 28\\6 \cdot 4 = 24\\= 28 - 24\\= 4\\Drop\:2\\= 42\\6 \cdot 7 = 42\\= 42 - 42\\= 0\\\\= \boxed{2.47}[/tex]
➲ Hope it helps.
Use what you know about the properties of operations to rewrite the expression.
3(5-2)=
Answers
Answer:
Step-by-step explanation:
3 * (5 - 2) =
15 - 6 =
9
or
3 * (5 - 2) =
3 * 3 =
9
An agriculturist takes 50 samples of soil and measures the levels of two nutrients, nitrogen
and phosphorus. In 46% of the samples the nitrogen levels are low and in 28% of the samples
the phosphorus levels are low. In 10% of the samples both the nitrogen and the phosphorus
levels are low. What percentage of the samples have nitrogen levels or phosphorus levels
that are low?
Answers
In linear equations, 64% of samples have nitrogen levels and phosphorus levels that are low.
What is linear equations?
A linear equation with one variable is one that contains just one variable. It has the formula Ax + B = 0, with A and B being any two real numbers and x being an ambiguous variable with only one possible value. One such linear equation in one variable is 9x + 78 = 18.P(low nitrogen) = 46% = 0.46
P(low phosphorus) = 28% = 0.28
P(low nitrogen and low phosphorus) = 10% = 0.10
P(low nitrogen or low phosphorus) = P(low nitrogen) + P(low phosphorus) - P(low nitrogen and low phosphorus)
= 0.46 + 0.28 - 0.10
= 0.64 = 64%
Hence , 64% of samples have nitrogen levels and phosphorus levels that are low.
Learn more about linear equations
brainly.com/question/10638383
#SPJ9
The second term of an A.P is 2 and the sixth term is - 14. What is he first term and the 9th term?
Answers
denote by u¹ the first term
hence u⁹ is the 9th term
[tex]u_{n} = u_{1} + (n - 1)d[/tex]
[tex]u_{2} = 2 \: \: \: \: \: \: u_{6} = - 14 \\ u_{1} + (2 - 1)d = 2 \\ u_{1} + (6 - 1)d = - 14[/tex]
[tex]u_{1} + d = 2 \\ u_{1} + 5d = - 14 \\ \\ \: \: \: (u_{1},d)=(6,-4)[/tex]
[tex]u_{9} = u_{1} + (9 - 1)d \\ u_{9} = u_{1} + 8d \\ u_{9} = 6+ (8)( - 4) \: \\ u_{9} = - 26[/tex]
Answer: a₁=6 a₉=-26
Step-by-step explanation:
a₂=2 a₆=-14 a₁=? a₉=?
a₂=a₁+(2-1)d
a₆=a₁+(6-1)d
a₁+d=2 (1)
a₁+5d=-14 (2)
Subtract equation (1) from equation (2):
4d=-16
Divide both parts of the equation by 4:
d=-4
Hence,
a₁+(-4)=2
a₁-4+4=2+4
a₁=6
a₉=a₁+(9-1)d
a₉=6+8(-4)
a₉=6+(-32)
a₉=6-32
a₉=-26
Find the total number of different permutations of the set {a, b, c, d, e, f, g}.
Answers
The total number of different permutations of the set is 5040
How to determine the total number of different permutations of the set?The set of elements is given as
Set = {a, b, c, d, e, f, g}.
The cardinality of the above set is
n = 7
So, the total number of different permutations of the set is
Permutation = n!
This gives
Permutation = 7!
Expand
Permutation = 7 * 6 * 5 * 4 * 3 * 2 * 1
Evaluate
Permutation = 5040
Hence, the total number of different permutations of the set is 5040
Read more about permutations at
https://brainly.com/question/12468032
#SPJ1
Write the equation that can be used to find the number of sales Luke made this week. Represent the number of sales as x and don't use any $ symbols.
luke works at a store and earns a fixed amount of $191 plus $16.55 per sale. Noah works at a different store and earns a fixed amount of $573 plus $49.65 per sale. They both made the same number of sales, but Luke earned
1/3 as much money as Noah this week.
Answers
An equation that can can be used to find the number of sales Luke made this week is; 191 + 16.55x = ¹/₃(573 + 49.65x)
How to Solve Equation Word Problems?
We are told to represent the number of sales as x.
Now, Luke works at a store and earns a fixed amount of $191 plus $16.55 per sale. This is represented as; 191 + 16.55x
Noah works at a different store and earns a fixed amount of $573 plus $49.65 per sale. This is represented as; 573 + 49.65x
We are told that they both made the same number of sales but Luke earned a third of what Noah earned. Thus;
191 + 16.55x = ¹/₃(573 + 49.65x)
An equation that can can be used to find the number of sales Luke made this week is;
191 + 16.55x = ¹/₃(573 + 49.65x)
Read more about Equation Word Problems at; https://brainly.com/question/21405634
#SPJ1
what is
-8 - (-6) - 0
Answers
Answer: -2
Step-by-step explanation:
Answer:
-2
Step-by-step explanation:
the - (-6) becomes a + 6
-8 + 6 - 0 = -2
HELP ASPPP WILL GET BRAINLEST
Answers
Answer:
The answer to your question is v= 1/3 bh
multiply by : 3
3v = bh
divided by b : h = 3v/b
Step-by-step explanation:Did this help?so its the second
2√5 is this rational or irrational?
Answers
Answer:
irrational number
Step-by-step explanation:
cause it just is
stan bts,txt,enhypen,ateez, and straykids
4⁄6 + 2⁄4 + 3⁄5 = [tex]\frac{x}{y}[/tex]
Answers
Answer:
53/30
Step-by-step explanation:
Just got to derive the lowest common multiple of the denominator and make it same for all fraction. Don't forget to multiply the numerator just the same.
Answer: 53/30
Step-by-step explanation:
[tex]\displaystyle\\\frac{4}{6}+\frac{2}{4} +\frac{3}{5} =\\\\\frac{2*2}{2*3} +\frac{2}{2*2}+\frac{3}{5}=\\\\\frac{2}{3} +\frac{1}{2} +\frac{3}{5}=\\\\\frac{2*10+1*15+3*6}{3*2*5} =\\\\\frac{20+15+18}{30} =\\\\\frac{53}{30}[/tex]
Solve equation.
r/4 = -8
Answers
To solve the equation, multiply both sides by 4. The solution is r = -32.
A linear equation is an equation of which the highest degree of its variables is 1.
Steps to solve linear equations:
Simplify the expressions. If there are parentheses, remove them by multiplying the corresponding terms.Combine the same terms.Isolate the variable on one side by using subtraction or addition.Use division or multiplication to find the value of the variable.Recall that if we subtract or add the same number to both sides of an equation, it does not change the equality.The given problem:
Solve r/4 = -8
Notice that the variable, r, is already isolated on left side.
Multiply both sides by 4:
r/4 . 4 = -8 . 4
r = -32 (solved)
Learn more about linear equation here:
https://brainly.com/question/723406
#SPJ4
Geometry please help me I'll give brainliest <3
Question 24
Answers
Answer:
∠ TVW = 65°
Step-by-step explanation:
∠ UVW = ∠ TVW + ∠ UVT ( substitute values )
21x + 6 = 8x + 9 + 88
21x + 6 = 8x + 97 ( subtract 8x from both sides )
13x + 6 = 97 ( subtract 6 from both sides )
13x = 91 ( divide both sides by 13 )
x = 7
Then
∠ TVW = 8x + 9 = 8(7) + 9 = 56 + 9 = 65°
The manufacturer of an energy drink spends $1.20 to make each drink and sells them for $2. The manufacturer
also has fixed costs each month of $8,000.
a. Find the cost function C when "x" energy drinks are manufactured. C(x) =
Write your answer in slope-intercept form.
b. Find the revenue function R when "x" drinks are sold. R(x) =
Write your answer in slope-intercept form.
c. Graph both your Revenue and Cost functions on the graph below that shows the break-even point.
Answers
Answer:
Find the revenue function R when x energy drinks are sold.
Step-by-step explanation:
Manny saves 2/20 of each paycheck for a new motorcycle and 3/20 of each paycheck for retirement. Manny earns $2918 per paycheck.
How much does Manny save per paycheck?
Enter your answer in the box.
Answers
Manny would save $729.50 per paycheck
What are dollar savings on new motorcycle and retirement?
The amount of savings on new motorcycle and retirement can be determined by multiplying the fractions by the earnings per paycheck
savings for new motorcycle=$2918*2/20
savings for new motorcycle=$291.80
savings on retirement=$2918*3/20
savings on retirement=$437.70
total savings=$291.80+$437.70
total savings=$729.50
Find out more about savings on:https://brainly.com/question/24597238
#SPJ1
The sum of the first ten positive even integers.
Answers
Answer:
14
Step-by-step explanation:
the fist 20 characters equal 14
Answer:
110
Step-by-step explanation:
integers are basically whole numbers
first 10 even integers would be 2,4,6,8,10,12,14,16,18,20
if you add all those numbers, it would be 110
Please help me.
20 points
If you put “I don’t know” or something like that just to get the points I will not hesitate to report.
Answers
Answer: B. 3x+6<6 or -2x+9>3
C. 3x-5<10 and -2x+9>3
FIRST ANSWER GETS BRAINLIEST
Answers
Answer:
about 55,000 pounds
Step-by-step explanation:
1,575(3.125) + 5,020(9.9) = 54,619.875
To the nearest thousand, 54,619.875 rounds to 55,000.