Use the graph of △ABC with midsegments DE, EF and DF. Show that EF is parallel to AC and that EF=1/2 AC
Answers
According to the midsegment theorem, the midsegments are parallel to
and half the length of the opposite side.
The completed statement are as follows;
Because the slopes of [tex]\overline{EF}[/tex] and [tex]\overline{AC}[/tex] are both -4, [tex]\overline{EF}[/tex] ║ [tex]\overline{AC}[/tex]EF = [tex]\underline{\sqrt{17}}[/tex] and AC = [tex]\underline{2 \cdot \sqrt{17} }[/tex]Because [tex]\underline{\sqrt{17} }[/tex] = [tex]\underline{\frac{1}{2} \cdot 2 \cdot \sqrt{17} }[/tex], [tex]EF = \frac{1}{2} \cdot AC[/tex]Reasons:
From the given graph of ΔABC, we have;
Coordinates of the points A, B, and C are; A(-5, 2), B(1, -2), and C(-3, -6)
The coordinates of the point D and E on [tex]\mathbf{\overline{DE}}[/tex] are; D(-4, -2), and E(-2, 0)
The coordinates of the point F is; F(-1, -4)
[tex]Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]\displaystyle Slope \ of \ line \ \overline{AC} = \mathbf{\frac{(-6) - 2}{-3 - (-5)} = \frac{-8}{2}} = -4[/tex]
[tex]\displaystyle Slope \ of \ line \ \overline{EF} = \frac{0 - (-4)}{-2 - (-1)} = \frac{4}{-1} = -4[/tex]
[tex]Length \ of \ segment,\ l = \sqrt{\left (x_{2}-x_{1} \right )^{2}+\left (y_{2}-y_{1} \right )^{2}}[/tex]Length of EF = √((-1 - (-2))² + (-4 - 0)²) = √(17)
Length of AC = √((-3 - (-5))² + (-6 - 2)²) = √(4 × 17) = 2·√(17)
Therefore, we have;
Because the slope of [tex]\mathbf{\overline {EF}}[/tex] and [tex]\mathbf{\overline {AC}}[/tex] are both , -4, [tex]\overline {EF}[/tex] ║ [tex]\overline {AC}[/tex]. EF = [tex]\underline{\sqrt{17}}[/tex], and AC
= [tex]\underline{\frac{1}{2} \cdot 2 \cdot \sqrt{17}}[/tex],. Because [tex]\underline{\sqrt{17}}[/tex] = [tex]\underline{\frac{1}{2} \cdot 2 \cdot \sqrt{17}}[/tex], [tex]EF =\mathbf{ \frac{1}{2} AC}[/tex]
Learn more about midsegment theorem of a triangle here:
https://brainly.com/question/7423948
Related Questions
what is the answer to this problem ( 1/5)² (3+2+5²)
Answers
Identify the center and radius of the circle (x – 5)^2 + (y+1)^2 = 4.
²
O A. Center: (5,-1), r= 4
O B. Center: (-5,1), r = 4
C. Center: (5, -1), r= 2
O D. Center: (-5,1),r= 2
Answers
Answer:
The answer is C.
Step-by-step explanation:
The equation of a circle, centre (a, b), radius r is given by (x - a)² + (y - b)² = r².
Yao bought 3 feet of blue ribbon and
24 inches of red ribbon. The ribbon costs
$2.00 per foot. What is the total cost of
the ribbon?
Answers
Answer:
It would've costed $8 to buy these ribbons.
Step-by-step explanation:
Given:
3 feet of blue ribbon = 36 inches of blue ribbons2 feet of red ribbon = 24 inches of red ribbons\1 foot of ribbon = $2(3 + 2) x 2 = Total cost
=> (5) x 2
= $10
Therefore, it would've costed $10 to buy these ribbons.
Hoped this helped.
Question 47 of 55
Expression A: 3(x + 1)
Expression B: 3x+3
Which statement does not show that these expressions are equivalent?
A. Both expressions involve addition
B. The expressions name the same number regardless of the value
of x
C. 3(x+ 1) can be rewritten as 3x+ 3 using the distributive property.
D. Substituting any value of x makes the expressions equivalent.
SUBMIT
Answers
Answer:
D
Step-by-step explanation:
Substituting any value of x does not make the expressions equivalent. Replacing x for any two different values would equate to different unequal values.
2.03x13 using standard algorithm
Answers
It came 26 by above calculation.
Help help math math
Answers
Answer:
C=31.41592654
Step-by-step explanation:
C=2πr
r=5
C=2π(5)
Therefore C= 10π or C=31.41592654
Answer:
C = 31.4
Step-by-step explanation:
one kilogram of cheese costs £9.48
chris buys 650 g of this cheese
work out how much chris pays
Answers
Answer: $6.16
Step-by-step explanation:
100g = $0.948
50g = $0.475
$0.948*6 = $5.688
$5.688 + $0.475 = $6.163
Rounded = $6.16
9/4 divided 5/8
I don’t know help me
Answers
Answer:
9/4 divided 5/8 = 3.6 (Ans)
Answer
9/4 ÷ 5/8 = 3.6
i hope it will help you
NEED ANSWER VERY BAD BAD
Answers
Like terms
9x + 99 = 180
9x = 81
X = 9
Hope this helps!
Brainliest is much appreciated
Two-Variable Statistics:Question 2
You obtain a correlation value of r = -0.744 when you
analyze the relationship between the time it takes
someone to swim a mile and her heart rate at the end of
the swim. Choose the word completes this interpretation
of the correlation value: The correlation between the time
it takes to swim and heart rate is ___ and ___
Answers
order from greatest to least 55% of 180 30% of 260 12% of 700
Answers
Answer: 55% of 180, 12% of 700, and 30% of 260.
Step-by-step explanation:
55% of 180 = 99…
30% of 260 = 78…
and 12% 700 = 84…
Answer:
55% of 180 > 12% of 700 > 30% of 260
Step-by-step explanation:
55% of 180 = 99
30% of 260 = 78
12% of 700 = 84
Any polygon with two pairs of parallel opposite sides is a parallelogram
Answers
Answer:
It is false that any polygon with two pairs of parallel opposite sides is a parallelogram. Let's understand the answer in detail. Explanation: ... There can be other polygons that have more than 4 sides but have only two pairs of parallel sides, which can't be called a parallelogram.
Step-by-step explanation:false.
WILL GIVE BRAINLIEST
Answers
Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
[tex]m[/tex] - slope
[tex]b[/tex] - y-intercept
[tex]11)\ m=-1,\ b=2\\\\y=-x+2\\\\12)\ m=-\dfrac{3}{2},\ b=3\\\\y=-\dfrac{3}{2}x+3\\\\13)\ m=3,\ y=-2\\\\y=3x-2\\\\14)\ y=\dfrac{3}{4},\ b=1\\\\y=\dfrac{3}{4}x+1\\\\15)\ m=\dfrac{1}{2},\ b=1\\\\y=\dfrac{1}{2}x+1\\\\16)\ m=-\dfrac{2}{5},\ b=0\\\\y=-\dfrac{2}{5}x\\\\17)\ m=-7,\ b=2\\\\y=-7x+2\\\\18)\ m=\dfrac{4}{3},\ b=-4\\\\y=\dfrac{4}{3}x-4[/tex]
19) and 20) you have in other your question.
PLEASE HELP ME!!!!!!!
Answers
Answer:
x=6
Step-by-step explanation:
hope this helps! :D
have a miraculous day!! <3
A zookeeper is monitoring the population of gazelles. The herd needs to have exactly three times more males than females to thrive. The zoo only has room for a maximum of 12 female gazelles. Let x represent the number of female gazelles and y represent the number of male gazelles. Write the constraints that represent the possible number of male and female gazelles that can live in a thriving population at the zoo. X > 0 and y > 0 0 < x ≤ 12 and 0 < y ≤ 36 0 < x ≤ 12 and y > 36 x > 0 and y < 23.
Answers
Option C is correct.
Given to us:
female gazelles[tex](x)[/tex] can be maximum of 12 only. therefore,
Condition 1 is [tex]12\geq x>0[/tex].
while,
male gazelles[tex](y)[/tex] should be exactly 3 times more than females to thrive. therefore,
Condition 2 is [tex]36\geq y>0[/tex].
There is only one option among all the options available which is satisfying both the conditions. therefore, option C is the correct option.
To know more visit:
https://brainly.com/question/2141743
Answer:
c is the answer
Step-by-step explanation:
it took the test and got it correct
The function f(x) is graphed below. Determine whether the degree of the function is
even or odd and whether the function itself is even or odd.
Answers
Answer:
even
Step-by-step explanation:
27/70 in simplest form
Answers
Answer:
27/70
Step-by-step explanation:
27/70 is the simplest form anyway
but it's 0.385 if we calculate
these two lol, i dont really understand them :D
Answers
me too!!!!!!!!!!!!!!!!!
(PLS HELP <3)
The proportional relationship between the number of songs Stella downloads,
s, and the total cost in dollars and cents, c, can be represented by the equation
c=1.17s. How much does it cost to download a single song?
Answers
Answer:
1.17 dollars!
Step-by-step explanation:
We are given the equation c=1.17s
To break it down, it means that the cost in dollars=1.17 times amount of songs.
Lets plug in 1 for s.
1.17*1=1.17!
For one song, it will cost 1.17 dollars !
Step-by-step instructions:
The equation c=1.17s is provided to us.
To put it another way, the cost in dollars equals 1.17 times the number of songs.
Let's substitute 1 for s.
i really really hope can see this
Answers
Answer:
did u ever figure it out?
Step-by-step explanation:
1 point
15.) Vincent pays $202 in advance on his account at the health spa. Each
time he uses the spa, $6 is deducted from the account. Write an equation
that represents the value remaining in his account after x visits to the spa.
Find the value remaining in the account after 18 visits. *
O V = 6 - 202x; $94
O V = 6 - 202x; $1,216
O V = 202 - 6x; $94
O V = 202 - 6x; $1,230
Answers
Answer:
O V=202-6x; $94
Step-by-step explanation:
202 needs to be placed before the 6, eliminating options 1 and 2. It can't be option 4 because thats more than 202, leaving us with option 3. Check you answer by replacing x with 18. O V=202-6(18) ->O V=202-108 -> 202-108=$94.
Find the equation that has a slope of -2 and passes through the point (0,4)
Answers
Answer:
y=-2x+4
Step-by-step explanation:
equation: y-y1=m(x-x1)
x1=0,y1=4,m=-2
y-4=-2(x-0)
y-4=-2x
y=-2x+4
Help help help help math math
Answers
Answer:
formula:
pie x radius squared
3 x 15^2 = 675 ft^2
Answer the questions below to find the total surface area of the can. (55 points, help fast)
Answers
Answer:
Hope this helps
Step-by-step explanation:
first question --> area of circle ---> [tex]\pi r^{2}[/tex] ---> [tex]1.5^{2} \pi[/tex] ---> [tex]2.25\pi[/tex]
second question --> unclear quetion but I assume 4?
third question --> area of cylinder --> [tex]r^{2} \pi h[/tex] --> [tex]2.25\pi h[/tex] --> [tex]2.25\pi 4[/tex] --> [tex]9\pi[/tex]
h --> height
r --> Radius
[tex]\pi[/tex] --> pi
The total surface area of the can is 61.23 square inches
How to calculate the total surface area of a canThe formula for calculating the total surface area of a can is expressed as:
S = 2πr(r+h)
where:
h is the height
r is the radius
Given the following parameters
h = 5in
r = 1.5in
S = 2(3.14)(1.5)(1.5 + 5)
S = 6.28(1.5)(6.5)
S = 61.23 square inches
Hence the total surface area of the can is 61.23 square inches
Learn more on total surface area here: https://brainly.com/question/16997207
A Hospital telephone operator has observed that calls arrive at a rate of 300 calls per hour. What is the probability that there are exactly 5 calls in 10 minutes?
Answers
Answer:
It can be done using poisson distribution.
λ = 30 calls/hr = 1.5 calls/3min
Now P(X=x)=e−λ.λxx!
So P(X=0)=e−1.5
Step-by-step explanation:
Admission to the gymnastics meet was $2.40 for adults and $1.25 for students. If 540
tickets were sold for a total of $934.90, how many tickets of each were sold? (i’ll give brainliest just answer within the next 15 mins pls!!)
Answers
Answer:
hi friends I need help with the following me
PLEASE HELP ASAP!!!!
Answers
Answer:
I think its D? I'm not sure sorry if I get it wrong
ALGEBRA Find x and y so that each quadrilateral is a parallelogram.
(Please do at least 2, but doing all 4 would be greatly appreciated, and i will mark u brainliest.)
Answers
y=19
2x-8=x+16
2x=x+24
x=24
8) y=14
x=3
9) x=44
y=20
10) x=17
y=9
Hey y’all , please give me the correct answer.
Answers
Answer:
-s-6>-7
Step-by-step explanation:
Just ask!
Hope this helps. :)
Answer:
-s-6>-7 (top right)
Step-by-step explanation:
s = -18 > means what is on the left is bigger than what is on the right
top right one = - s - 6 > - 7
top right one = - ( - 18) - 6 > -7
top right one = 18 - 6 > -7
top right one = 12 is bigger than -7
John solved the inequality 3x – 5 ≥ 28 and determined that x could equal 12. Is John correct? Explain why or why not.
Answers
Answer:
John is correct
Step-by-step explanation:
Let's solve the inequality:
[tex]3x-5\geq28[/tex]
[tex]3x\geq33[/tex]
[tex]x\geq11[/tex]
As we can see, the value of x can be either 11 or anything greater than 11. Since 12 is included in that solution set, John is correct.
wait
Step-by-step explanation:
ignore what I just said I was on crack bro