A, B and C are the vertices of a triangle.
A has coordinates (1,4)
B has coordinates (3, 0)
C has coordinates (-3,-2)
D is the midpoint of AB.
E is the midpoint of AC.
Prove that DE is parallel to BC.
You must show each stage of your working.
PLEASE HELP ASAP THANK YOU
Answers
Answer:
see below
Step-by-step explanation:
To find the coordinates of the midpoints, add the x's and divide by 2 and add the y's and divide by 2.
The coordinates of D, the midpoint of AB, (1+3)/2 will be the x-coordinate and (4+0)/2 will be the y-coordinate.
D (2,2)
You could also see this on a graph, see image.
E, the midpoint of AC has the x-coordinate (1+-3)/2, which is -1 and y-coordinate (4+-2)/2 which is 1.
E is (-1,1)
Then we are able to calculate the slope of DE and BC.
To calculate slope, subtract the y's and put that on top of a fraction and subtract x's and put that on the bottom of a fraction. If the slopes are the same the segment are parallel.
Slope of DE:
(2-1)/(2--1)
= 1/3
Slope of BC:
(0--2)/(3--3)
=2/6
=1/3
The slopes of BC and DE are equal, so the segments are parallel.
(Alternatively, you could show that Triangle ABC and Triangle ADE are similar. Then find the segments parallel because corresponding angles are congruent.)
Related Questions
Please help!!!!!!!!!!!asap
Answers
By solving y = 25 · x² - 100 through the square root method, we conclude that the two roots of the quadratic formula are y₁ = + 2 and y₂ = - 2.
How to obtain the roots of a second order polynomial
Herein we have a polynomials of the form y = a · x² - b. By algebra we find that two roots exists, which are described below according to the square root method:
[tex]y_{1} = +\sqrt{\frac{b}{a} }[/tex], [tex]y_{2} = -\sqrt{\frac{b}{a} }[/tex]
If we know that a = 25 and b = 100, then the two roots of the equation are:
y₁ = + 2, y₂ = - 2
By solving y = 25 · x² - 100 through the square root method, we conclude that the two roots of the quadratic formula are y₁ = + 2 and y₂ = - 2.
To learn more on quadratic equations: https://brainly.com/question/2263981
#SPJ1
Please Help Me Answer These
Answers
Answer:
Question 1 : -2 3/4 × 3 1/5 . Change the fractions to improper fraction and multiply .
= -11/4 × 16/5
= -176/20
= -44/5
= -8 4/5
Question 1 answer : -8 4/5Question 2: -4.6/-2
= -4.6/-2
= 2.3
Question 2 answer : 2.3Question 3: - 7/8 ÷ (-2)(-4)
= 7/6(-4)
= -7/4
Question 3 answer : -7/4Question 4 : -4 27/30
= -147/30
= -4.9
Question 4 answer : cQuestion 5 : -3 13/20
Question 5 answer : -3.65Therefore The answer are -8 1/4 , 2.3 , -7/4 , c , -3.65If the degree of a polynomial function is even and the leading coefficient is negative, then the end behavior of the function is?
Answers
Answer:
Its the last option.
Step-by-step explanation:
The function will rise from the left and descend to the right.
f(x) ---> -∝ as x ---> -∝ and f(x) ---> -∝ as x ---> ∝
HELP !!!
Which of the following best describes the slope of the line below?
• A. Negative
O B. Zero
• C. Positive
D. Undefined
Answers
2x + 5y = 17 6x - 5y = -9
Answers
Answer:
Step-by-step explanation:
Yaqub, Angus and Iris share 18 slices of pizza in the ratio
1:3:2.
How many slices of pizza does Iris have?
Answers
Answer:
6 Slices
Step-by-step explanation:
Total units = 1 + 3 + 2 = 6 Units
6 Units = 18 Slices of Pizza
Iris shared 2 units.
1 Unit = 18/6 = 3 Slices of Pizza
2 Units = 2 * 3 = 6 Slices of Pizza
What is 9 squared?
Why?
Why do we call this "Squared"?
What is 5 cubed?
Why?
Why do we call this "Cubed"?
Answers
Answer:
The squared root of 9 is 3
Why - Half of 9 is 3
Why do we called this squared - It is the positive solution of the equation x2 = 9. The number 9 is a perfect square.
5 Cubed is equal to 125
Why - The number 125 on prime factorization gives 5 × 5 × 5. On combining the prime factors in groups of 3 gives 5
Why do we call this cubed = The cube of a number is that number times itself times itself. 5 cubed, denoted 53, is equal to 5×5×5, or 125.
Examine the nuclear reaction: superscript 1 subscript 1 h plus superscript 1 subscript 0 n right arrow superscript 2 subscript 1 h.. why is this classified as a nuclear reaction rather than a chemical reaction?
Answers
The given reaction is considered as nuclear reaction instead of chemical reaction as the change is coming in the nucleus.
A nuclear reaction is one in which the number of protons or neutrons changes as a result of collisions between two nuclei or an atom and a subatomic particle.
In the given reaction also which is superscript 1 subscript 1 h plus superscript 1 subscript 0 n right arrow superscript 2 subscript 1 h.
A neutron is added to the nucleus of a hydrogen atom here. As a result, it is a nuclear reaction.
A chemical reaction involves the acquisition or loss of electrons, which leads in the synthesis of a new molecule while leaving the nucleus of an atom unchanged.
Thus, we can give a conclusion that because a change in a nucleus happened, the described event is categorised as a nuclear reaction rather than a chemical reaction.
Learn more about Nuclear Reactions here:
https://brainly.com/question/984564
#SPJ10
Choose any set of Pythagorean triplets of your choice and illustrate them using graph sheet.
Example given below:
Answers
The required Pythagorean triplets are hypotenuse, perpendicular and base is 13, 12 and 5 respectively.
In a right angled triangle, its side, such as hypotenuse, perpendicular and base is Pythagorean triplets.
We have
Hypohypotenuse = 13
perpendicular = 12
base = 5
Which satisfies the condition of the Pythagorean theorem.
[tex]a^2+b^2=c^2\\12^2+5^2=c^2\\169=c^2[/tex]
and c = 13
Thus, the required value of Pythagorean triplets satisfies the Pythagorean theorem.
Learn more about Pythagorean triplets here:
https://brainly.com/question/22160915
#SPJ1
Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options.
2.3p – 10.1 = 6.4p – 4
2.3p – 10.1 = 6.49p – 4
230p – 1010 = 650p – 400 – p
23p – 101 = 65p – 40 – p
2.3p – 14.1 = 6.4p – 4
Answers
Answer:
2.3p – 10.1 = 6.49p – 4 [tex]\huge \checkmark[/tex]
230p – 1010 = 650p – 400 – p [tex]\huge \checkmark[/tex]
Step-by-step explanation:
……………………………………………
2.3p – 10.1 = 6.5p – 4 – 0.01p
⇔ 2.3p – 10.1 = (6.5p – 0.01p) – 4
⇔ 2.3p – 10.1 = (6.5 – 0.01)p – 4
⇔ 2.3p – 10.1 = (6.49)p – 4
⇔ 2.3p – 10.1 = 6.49p – 4
_______________________
_______________________
2.3p – 10.1 = 6.5p – 4 – 0.01p
⇔ 100 × (2.3p – 10.1) = 100 × (6.5p – 4 – 0.01p) multiply both sides by 100
⇔ 100 × (2.3p – 10.1) = 100 × (6.5p – 4 – 0.01p)
⇔ 230p – 1010 = 650p – 400 – p
……………………………………………………
Match the verbal expression (term) with its algebraic expression (definition).
Match Term Definition
d
Some number increased by two A) a ÷ 2
c
A variable decreased by two B) y2
e
Product of an unknown value and two C) x − 2
2
Quotient of some number and two D) b + 2
b
An unknown value squared E) 2z
Answers
The matching of definitions and terms are done below.
Some number increased by two ⇒ b + 2A variable decreased by two ⇒ x – 2Product of an unknown value and two ⇒ 2zQuotient of some number and two ⇒ a ÷ 2An unknown value squared ⇒ y²What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
Match the verbal expression (term) with its algebraic expression (definition).
Some number increased by two ⇒ b + 2
A variable decreased by two ⇒ x – 2
Product of an unknown value and two ⇒ 2z
Quotient of some number and two ⇒ a ÷ 2
An unknown value squared ⇒ y²
More about the Algebra link is given below.
https://brainly.com/question/953809
#SPJ1
Which graph represents the function of f(x) = 4x^2-16/2x-4 ?
Answers
See the graph in the image.
y = (4x² - 16)/(2x - 4)y = [4(x-2)(x+2)]/[2(x-2)]y = 2(x+2), with a domain of all real numbers other than 2A function is a relationship between inputs where each input is related to exactly one output.
The graph of f(x) = (4x² - 16) / (2x - 4) is given below.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
Function:
f(x) = (4x² - 16) / (2x - 4)
This can be written as,
f(x) = (2x)² - 4² / (2x - 4) [ a² - b² = (a + b)(a - b) ]
f(x) = (2x - 4)(2x + 4) / (2x - 4)
f(x) = 2x + 4
Now,
We will find the coordinates from the function f(x) = 2x + 4
x = 0, f(x) = 4
(0, 4)
x = 1, f(x) = 6
(1, 6)
x = 3, f(x) = 10
(3, 10)
And so on.....
The graph is given below,
Thus,
The graph of f(x) = (4x² - 16) / (2x - 4) is given below.
Learn more about functions here:
https://brainly.com/question/28533782
#SPJ2
If 1=3 2=3 3=5 4=4 5=4 then 6=?
Answers
The value of the 6 is 3.
If you write 1 in word then you will write one and if you count the letter it will give you 3
Similarly, if you write the numbers 2,3,4,5 in word and count the number you will get 3,5,4,4 respectively.
What are the counting letters?counting Letters provides a perfect way to introduce number words to beginning readers, as well as discuss the concepts of letters and words.
So, if you write 6 in words you will write six and on counting the letter you will get 3.
Hence, 6 = 3 ans.
Therefore the value of the 6 is 3.
To learn more about counting visit:
https://brainly.com/question/623156
#SPJ1
Which ordered pair would form a proportional relationship with the point graphed below?
On a coordinate plane, a line goes through points (0, 0), (10, 40) and (negative 10, negative 40).
(40, 10)
(–5, –10)
(5, 20)
(–10, –20)
Answers
Answer:
(5,20)
Step-by-step explanation:
divide both sides of (10, 40) by the same number 2 and you will get (5,20). The points should all lie on the same straight line to form a proportional relationship.
Answer: 5,20
Step-by-step explanation:
Do this for me pls its mdths
Answers
Answer:
A = -1
B = -3
C = -7
Step-by-step explanation:
See attached image.
Your family is driving to Disney which is 1000 miles away The first day your family drives 600 miles in 10 hours and the second day they drive the remaining distance in 8 hours . What is the average speed of travel for the second day?
Answers
Answer:
50 miles per hour
Step-by-step explanation:
Step 1: We subtract 600 from 1000. That gives us 400 miles for the second day.
Step 2: Now we divide that by 8, giving us 50 miles per hour. We have our answer!
I hope this helped!! PLEASE MARK AS BRAINLIEST!! :)What is the solution to the following equation?
3(x-4)-5-x-3
A. x = 12
B. x=3
C. x=8
D. x = 7
Answers
Answer:
D. x = 7
Step-by-step explanation:
NOTE : there should be an equal sign somewhere in the given expression.
suppose the equation is the following:
3(x-4)-5 = x-3
………………………………………………………
3(x - 4) - 5 = x - 3
⇔ 3x - 12 - 5 = x - 3
⇔ 3x - 17 = x - 3
⇔ 3x - 17 + 17= x - 3 + 17
⇔ 3x = x + 14
⇔ 2x = 14
⇔ x = 14/2
⇔ x = 7
Match each inequality to the number line that represents its solution:
Answers
Step-by-step explanation:
I have solve all the questions and your work is to match with that option
Please Help
What does the missing angle in the triangle measure?
Answers
Answer:
x = 60
Step-by-step explanation:
The sum of the angles of a triangle is 180
95+25 +x = 180
120 +x = 180
Subtract 120 from each side
120+x-120 = 180-120
x = 60
A middle school took all of its 6th grade students on a field trip to see a play. The
students filled 341 seats, which was 55% of the total number of seats in the theater.
How many total seats were in the theater?
Answers
341/0.55 = 620
A boat leaves a dock and goes 240 miles in a direction of 290 degrees. It then turns and goes 50 miles in a direction on 30 degrees. How far is the boat from the dock and in what direction?
Answers
By Pythagorean theorem and trigonometric functions, the magnitude and direction of the boat are approximately 284.403 miles and 295.043° with respect to the east.
What is the direction and magnitude of the resulting displacement with respect to the origin
In this problem we assume that the first angle is measured with respect to the east side and that the second angle is counterclockwise and measured with respect to the direction of the first vector. First, we need to determine the resulting vector by using trigonometric and vectorial formulas:
(x, y) = (240 · cos 290°, 240 · sin 290°) + (50 · cos 320°, 50 · sin 320°)
(x, y) = (120.387, - 257.666) [mi]
The magnitude is found by Pythagorean theorem:
[tex]r = \sqrt{(120.387\,mi)^{2}+(-257.666\,mi)^{2}}[/tex]
r ≈ 284.403 mi
The direction of the boat is obtained by inverse trigonometric functions:
θ = tan⁻¹ (- 257.666/120.387)
θ ≈ 295.043°
By Pythagorean theorem and trigonometric functions, the magnitude and direction of the boat are approximately 284.403 miles and 295.043° with respect to the east.
To learn more on vectors: https://brainly.com/question/13322477
#SPJ1
simplify (–2 – c )(–1)
Answers
The simplified expression of (-2 - c)(-1) is 2 + c
How to simplify the expression?We have:
(-2 - c)(-1)
Express as product
(-2 - c) * (-1)
Evaluate the product
2 + c
Hence, the simplified expression of (-2 - c)(-1) is 2 + c
Read more about expressions at:
https://brainly.com/question/723406
#SPJ1
If a_1=9a
1
=9 and a_n=-3a_{n-1}a
n
=−3a
n−1
then find the value of a_5a
5
.
Answers
A geometric series is the collection of an unlimited number of terms with a fixed ratio between them. The value of a₅ is -729.
What is geometrical series?A geometric series is the collection of an unlimited number of terms with a fixed ratio between them.
Given the value of a₁=9 and the value of [tex]a_n=-3a_{(n-1)}[/tex]. Therefore, the value of a₅ can be written as,
a₂ = -3(a₁) = -3(9) = -27
a₃ = -3(a₂) = -3(-27) = 81
a₄ = -3(a₃) = -3(81) = -243
a₅ = -3(a₄) = -3(-243) = -729
Hence, the value of a₅ is -729.
Learn more about Geometrical Series:
https://brainly.com/question/4617980
#SPJ1
A,B and C are points in the cartesian plane. the coordinates of A are (3,-2),BA=(4,-3)and AC=(4,9). Calculate
i. the coordinates of B and C
Answers
Then B is at (3 - 4, -2 + 3) = (-1, 1)
and C is at (3 + 4, -2 + 9) = (7, 7)
which statement is true about fiction
Answers
Answer:
The function is even because of symmetry over x axis
Mr. McMillan and Ms. Burke are teaching their classes how to write in cursive. Mr. McMillan has already taught his class 8 letters. The students in Ms. Burke's class, who started the unit later, currently know how to write 12 letters. Mr. McMillan plans to teach his class 4 new letters per week, and Ms. Burke intends to cover 3 new letters per week. Eventually, the students in both classes will know how to write the same number of letters. How long will that take? How many letters will the students know?
Answers
The number of weeks by which the students in both classes will know how to write the same number of letters will be 4 weeks.
What is the linear system?A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
Mr. McMillan and Ms. Burke are teaching their classes how to write in cursive.
Mr. McMillan has already taught his class 8 letters.
The students in Ms. Burke's class, who started the unit later, currently know how to write 12 letters.
Mr. McMillan plans to teach his class 4 new letters per week.
Ms. Burke intends to cover 3 new letters per week.
Eventually, the students in both classes will know how to write the same number of letters.
Then the number of weeks by which the students in both classes will know how to write the same number of letters will be
Let x be the number of the weeks and y be the total number of the letters.
Then the equation will be
y = 4x + 8 …1
y = 3x + 12 …2
Then by solving the equations 1 and 2, we have
x = 4 and y = 24
More about the linear system link is given below.
https://brainly.com/question/20379472
#SPJ1
simplify (6 to the power of 5)power 2
Answers
Answer:
60466176
Step-by-step explanation:
(x - 4)/(x + 6) - (x - 6)/(x + 4)
Answers
Answer:
[tex]\frac{20}{(x+4)(x+6)}[/tex]
Step-by-step explanation:
assuming you require the expression simplified
[tex]\frac{x-4}{x+6}[/tex] - [tex]\frac{x-6}{x+4}[/tex]
multiply the numerator/denominator of the first fraction by (x + 4)
multiply the numerator/denominator of the second fraction by (x + 6)
= [tex]\frac{(x-4)(x+4)}{(x+4)(x+6)}[/tex] - [tex]\frac{(x-6)(x+6)}{(x+4)(x+6)}[/tex] ← expand and simplify numerators leaving the common denominator
= [tex]\frac{x^2-16-(x^2-36)}{(x+4)(x+6)}[/tex]
= [tex]\frac{x^2-16-x^2+36}{(x+4)(x+6)}[/tex]
= [tex]\frac{20}{(x+4)(x+6)}[/tex]
please help i dont know how to do this
Answers
Horizontal lines n and m are intersected by lines q and p. At the intersection of lines q and n, the uppercase right angle is angle 4. At the intersection of lines q and m, the uppercase left angle is angle 1. At the intersection of lines p and n, the bottom left angle is angle 3. At the intersection of lines p and m, the uppercase left angle is angle 2.
If angle 1 is 110°, what would the other angle measures have to be in order for m || n and
q || p?
Angle 2 = °
Angle 3 = °
Angle 4 = °
Answers
The values of the angles based on the information will be:
Angle 2 = 110°Angle 3 = 70°Angle 4 = 70°How to calculate the angles?From the information given, angle 1 is 110° and the horizontal lines n and m are intersected by lines q and p.
In this case, it should be noted that opposite angles are equal. Hence, angle 2 is also 110°.
Angle 3 will be:
= 180° - 110° = 70° (angle on a straight line).
Angle 4 will also be 70° as opposite angle to angle 3.
Learn more about angles on:
brainly.com/question/25716982
#SPJ1
