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:
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Related Questions
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
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.
(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.
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:
2.03x13 using standard algorithm
Answers
It came 26 by above calculation.
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
what is the answer to this problem ( 1/5)² (3+2+5²)
Answers
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:
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
NEED ANSWER VERY BAD BAD
Answers
Like terms
9x + 99 = 180
9x = 81
X = 9
Hope this helps!
Brainliest is much appreciated
i really really hope can see this
Answers
Answer:
did u ever figure it out?
Step-by-step explanation:
these two lol, i dont really understand them :D
Answers
me too!!!!!!!!!!!!!!!!!
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
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
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
Help help help help math math
Answers
Answer:
formula:
pie x radius squared
3 x 15^2 = 675 ft^2
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
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
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
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.
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:
PLEASE HELP ME!!!!!!!
Answers
Answer:
x=6
Step-by-step explanation:
hope this helps! :D
have a miraculous day!! <3
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
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.
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.
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
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.
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
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.