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]
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Related Questions
Help tell me the numbers in order
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Find the area of the polygon.
Answers
Answer
the area is 26 cm
Step-by-step explanation:
for the first part well call it box C box c is 2 cm by 1 cm the area of that box is 2 because 2 x 1 =2
for box B which is 2 cm by 6 cm because you add the 3 on the bottom to the 3 on the top so box B = 12
for box A it is 3 by 4 so that would be 12
you add the results together 12+12+2=26cm
Identify the horizontal asymptote of f(x) =4x/7
y = 0
y = 2/3
y=1
No horizontal asymptote
Answers
Answer:
y = 1
Step-by-step explanation:
To find the Horizontal Asymptote, you have to look at the degree of the numerator and denominator.
[tex]h(x) = \frac{x^n}{x^m}[/tex]
If n < m, then y = 0If n = m, y = coefficient of [tex]x^n[/tex] divided by the coefficient of [tex]x^m[/tex]If n > m, then there is no Horizontal AsymptotePlease find the area...
Answers
99 680 - 6180 = 93500
answer = 93500
is .816 a terminating decimal or a repeating decimal
Answers
Answer:
Terminating
Step-by-step explanation:
A terminating decimal (0.1) ends and does not continue
A repeating decimal (0.11111...) continues infinitely
Because, it stops and does not continue.
I really need help pls!!!
Answers
Answer:
Option 1
Step-by-step explanation:
To find the slope divide Mass (y) by Volume (x)
1/5 divided by 2/15 as a mixed number
Answers
Answer: 1 1/2
Step-by-step explanation:
Step One: 3 / 2 = 1.5000 = 1
Step Two: 3 - (2 x 1) = 1
Step Three: 1 1/2
Please mark me branliest
Hope this helps
help for brainly pls i think is b bot i dont think im correct im giving brainlist
Answers
Answer:
Step-by-step explanation:
answer:
the answer is = 7/3
so the first one
Find the product -1.2(0.04)
Answers
Answer:
-0.048
Step-by-step explanation:
-1.2 * 0.04 = -1.2 * 4 / 100 = -4.8 / 100 = -).048
Find equivalent expressions of 3+2x−9−4x+11+5x−x. Choose three expressions.
Answers
The expression that is equivalent to the expression, 3 + 2x − 9 − 4x + 11 + 5x − x, is: 2x + 5.
What are Equivalent Expressions?Expressions that have the same value are said to be equivalent expressions.
Evaluate 3+2x−9−4x+11+5x−x:
3 + 2x − 9 − 4x + 11 + 5x − x
Add like terms together
2x - 4x + 5x - x + 3 - 9 + 11
2x + 5
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Answer:
Step-by-step explanation:
The expression that is equivalent to the expression, 3 + 2x − 9 − 4x + 11 + 5x − x, is: 2x + 5.
Brainliest reward need brief working out
Answers
Answer:
1. 125 cm³; 88.8 cm³; 1650 cm³; 0.11 m³
2. about 1.47 kg
3. can't tell what the volume of 1 jar is
Step-by-step explanation:
The relationship between volume, mass, and density is ...
mass = volume × density
Solving for volume, we find ...
volume = mass ÷ density
__
(a) 50 g/(0.4 g/cm³) = 125 cm³
(b) 770 g/(8.67 g/cm³) ≈ 88.8 cm³ . . . (rounded to 3 significant figures)
(c) 4000 g/(2.42 g/cm³) ≈ 1650 cm³ . . . (rounded to 3 significant figures)
(d) 80 kg/(720 kg/m³) ≈ 0.11 m³ . . . (rounded to 2 significant figures)
_____
The volume of the cylinder is ...
V = πr²h
V = π(4 cm)²(15 cm) = 240π cm³ ≈ 754.0 cm³
Using the above relation, we find the mass to be ...
mass = (754.0 cm³)(1.95 g/cm³) ≈ 1470 g = 1.47 kg
_____
We cannot tell if the volume of each jar is 360 liters, or if that is the total volume of all 6 jars. Either way, we suspect a units problem, as the jars would have to be extremely large and unusually thin relative to what we usually think of as a jar for jam (0.77 m diameter; 0.2 mm thick). The density of the jam would be roughly 10 times the density of air, if that is the volume of all 6 jars. The problem would be more sensible if the units of volume were mm³, and the given volume is that of one jar.
The mass of jam in one jar is (5400/6 -200) = 700 g. Divide that by what you think the volume of one jar is in cm³ to find the density in g/cm³. (For comparison, the density of air is about 0.0012 g/cm³.)
_____
Additional comment
We have rounded the answers to 2 or 3 significant figures. In most cases, this is more than would be justified by the number of significant figures in the given measurements. For purposes of ongoing calculations, it is useful to keep intermediate results to at least 1 more significant figure than required for the answer.
Where is point E located?
(2,0)
(2,2)
(0,2)
(0,0)
Answers
Answer:
Send me a picture of the graph and I gottchu =)
Step-by-step explanation:
Answer:
I need a picture of the graph to answer that
How to write a line segment
Answers
Answer:
In geometry, you will write a line segment using the letters for each of the end points and a line over the top of the letters.
What is the answer to -3x + 7y = -16 and -3x + 7y = -16
Answers
Answer:
-16-7y/3
Step-by-step explanation:
-3x+7y=-16
Subtract 7y from both sides
-3x=-16-7y
Divide both sides by -3
x=-16-7y/3
Calculate the value of x
Answers
Answer:
x=15
Step-by-step explanation:
360-330=30
30/2=15
x=15
hope that helps
please mark as brainliest if correct
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30 POINTS!
Find the gravitational force between Earth (5.97 x 1024 kg) and the Sun (1.99 x 1030 kg) knowing they are 1.48 x 1011 m apart.
Answers
Answer:
The correct answare would be 3.54 x 10^22 N
What does R represent?
A. a line segment
B. a point
C. a line
D. a rat
Answers
Answer:
B
Step-by-step explanation:
) Are 9:6 and 18: 12 equivalent?
Answers
Answer:
Yes
Step-by-step explanation:
9 18
_ = _
6 12
9*2=18
6*2=12
2=2 TRUE
do you use multiplication at all when solving for x
Answers
Marco is five years less then twice hi sister Leah's age. Their mother is 14 years older than Marco and Leah's combined ages. If their mother is 48 years old, how old is Marco?
Answers
Answer:
Marco is 21
Step-by-step explanation:
Let the sister's age = x
Marco's age = 2*x - 5
x + 2x - 5 + 14 = 48 Combine the left side of the equation.
3x + 9 = 48 Subtract 9 from both sides
3x = 48 - 9
3x = 39 Divide by 3
x = 39/3
x = 13
So the sister is 13
Marco = 2x - 5 = 2*13 - 5
Marco = 21
If f(x) = x2 + 3x and g(x) = x + 2, find (f ∘ g)(x) and (g ∘ f)(x).
Answers
Answer:
(f ∘ g)(x) = x²+7x+10
(g ∘ f)(x) = x²+3x+2
Step-by-step explanation:
(f ∘ g)(x) = f(g(x)) = f(x+2) = (x+2)² + 3(x+2) = x² + 4x + 4 + 3x + 6 = x² + 7x + 10
(g ∘ f)(x) = g(f(x)) = g(x²+3x) = (x²+3x) + 2 = x² + 3x + 2
Make sure to review composite functions
Help ASAPPPPP PLZZZZZZ
Answers
If x is not equal to zero, what is the value of [tex]\frac{4(3x)^2}{(2x)^2}[/tex]
Answers
Answer:
[tex]\displaystyle \frac{4(3x)^2}{(2x)^2} = 9 ,\ x \neq 0[/tex]
General Formulas and Concepts:
Pre-Algebra
Evaluations
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Distributive Property
Terms/Coefficients
Step-by-step explanation:
Step 1: Define
Identify.
[tex]\displaystyle \frac{4(3x)^2}{(2x)^2}[/tex]
Step 2: Simplify:
Rewrite [Exponential Distributive Property]: [tex]\displaystyle \frac{4(3x)^2}{(2x)^2} = \frac{4(3^2x^2)}{2^2x^2}[/tex][Order of Operations] Evaluate exponents: [tex]\displaystyle \frac{4(3x)^2}{(2x)^2} = \frac{4(9x^2)}{4x^2}[/tex][Order of Operations] Multiply: [tex]\displaystyle \frac{4(3x)^2}{(2x)^2} = \frac{36x^2}{4x^2}[/tex]Simplify: [tex]\displaystyle \frac{4(3x)^2}{(2x)^2} = \frac{36}{4} ,\ x \neq 0[/tex][Order of Operations] Divide: [tex]\displaystyle \frac{4(3x)^2}{(2x)^2} = 9 ,\ x \neq 0[/tex][tex]\\ \sf\longmapsto \dfrac{4(3x)^2}{(2x)^2}[/tex]
[tex]\\ \sf\longmapsto\dfrac{ 4(9x^2)}{4x^2}[/tex]
[tex]\\ \sf\longmapsto \dfrac{36x^2}{4x^2}[/tex]
Take x^2 common and cancel.[tex]\\ \sf\longmapsto \dfrac{x^2}{x^2}\left(\dfrac{36}{4}\right)[/tex]
[tex]\\ \sf\longmapsto \dfrac{36}{4}[/tex]
[tex]\\ \sf\longmapsto 9[/tex]
Write an inequality that represents the graph.
Answers
espaneool
Step-by-step explanation:
Ayo. Bestie. Had enough yet?
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Answer:
the answer is e
Step-by-step explanation:
Here’s another one for you people
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Please help worth 20 points
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Answer:
Try going on D.e.s.m.o.s.c.o.m it worked for me when I had something like this
Step-by-step explanation:
GURL POWER
solve one step equation
x/-2 = -3
Answers
Answer:
x=6
Step-by-step explanation:
x/-2=-3
*-2 *-2
x=6
-hope it helps
Jayden purchases a television when his local electronics store had a sale. The television was 40% off its original price of $672. What was the sale price that jayden paid?
Answers
Answer:
The sale price he paid for the TV was $403.20
Step-by-step explanation:
You multiply the original price by .4 (40%). Then, you subtract that number from $672 to find the price Jayden paid! :)
out of 300 students at rsm summer camp 180 are boys what fraction of all students are boys
Answers
Answer:
3/5
Step-by-step explanation:
so first of all...
out of
300
students,
180
are boys.
180/300
which, simply by 60
3/5
so.. 3/5 of the people at rsm (whatever that is) summer camp are boys! Explanation isn't good, but you didn't really ask for it so i think you're ok... I guess. Now i just need an answer to my problem...
In rsm summer camp, fraction of boys is 3/5.
What is a fraction?A fraction is a numeral that represents a rational number.
Let a and b be two numbers, then their fraction can be represented as a/b.
Given that,
Total number of students at rsm summer camp = 300.
Total number of boys at rsm summer camp = 180.
To find the fraction of boys to all students.
Fraction of boys = number of boys / total number of students
= 180 / 300
= 18 / 30
= 3 / 5
The required fraction of boys is 3/5.
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