The medians of △DEF are DK, EL, and FJ. They meet at a single point M. (In other words, M is the centroid of △DEF.) Suppose EM=12, FJ=60, and MK=11. Find the following lengths.
Given:
In [tex]\Delta DE F,EM=12,FJ=60,MK=11[/tex].
M is the centroid of the triangle DEF.
To find:
The lengths of MJ, DM and EL.
Solution:
We know that the centroid is the intersection points of medians of a triangle and centroid divides each median in 2:1.
M is the centroid of the triangle DEF. It means DK, EL, FJ are medians and M divides these segments in 2:1.
It is given that [tex]FJ=60[/tex].
[tex]MJ=\dfrac{1}{2+1}FJ[/tex]
[tex]MJ=\dfrac{1}{3}(60)[/tex]
[tex]MJ=20[/tex]
Therefore, the length of MJ is 20 units.
Let DM and MK are 2a and a. It is given that, [tex]MK=11[/tex]. Then
[tex]a=11[/tex]
Now,
[tex]DM=2a[/tex]
[tex]DM=2(11)[/tex]
[tex]DM=22[/tex]
So, the length of DM is 22 units.
Let EM and ML are 2a and a. It is given that, [tex]EM=12[/tex]. Then
[tex]2a=12[/tex]
[tex]a=\dfrac{12}{2}[/tex]
[tex]ML=6[/tex]
Now,
[tex]EL=EM+ML[/tex]
[tex]EL=12+6[/tex]
[tex]EL=18[/tex]
So, the length of EL is 18 units.
what is the slope of a line passing through (-3,-7) and (1,4)
solution,
slope(m) = y2-y1/ x2-x1
= 4+7/1+3
=11/4
I hope this is correct, the formula can be wrong so pls double check if u have formula.
1+1=?
im testing out this thing cause I'm new
Answer:
the answer is 2 lol
Step-by-step explanation:
thanks for points
Find the missing measurement round answer to nearest tenth
Answer:
hope this helps you out five is a little harder to read sorry
Angelo rode his bike around the trail that was 1/4 of a mile long. He rode his bike around the trail 8 times. Angelo says he rode a total of 8/4 miles. Terresa says he is wrong and that he actually rode 2 miles. Who is correct? Use your words to explain how you know?
Answer:
They both are correct
Step-by-step explanation:
It is given that :
The length of the trail is = 1/4 of a mile
Angelo rode his bike around the trail = 8 times
So Angelo said that he rode his bike around the trail for = 8/4 miles
Terresa says Angelo actually rode his bike = 2 miles
They both are correct as 8/4 mile is equal to 2 miles in the simplified form.
So both of them are correct.
Damian invested $8,400 in an account paying an interest rate of 2% compounded
daily. Brayden invested $8,400 in an account paying an interest rate of 2%
compounded annually. After 8 years, how much more money would Damian have in
his account than Brayden, to the nearest dollar?
Answer:
$332
Step-by-step explanation:
please helppppppppppp
Answer:
RQ = 5 cm
ST = 8 cm
The triangle and the trapezoid share a 15 inch base and height of 10 inches.
The area of the trapezoid is less than twice the area of the triangle. Find the value of x. Explain your reasoning.
Can the area of the trapezoid be exactly twice the area of the triangle? Explain your reasoning.
Answer:
15 ; yes
Step-by-step explanation:
Base = 15 inches
Height = 10 inches
Area of triangle = 1/2* base * height
Area of triangle = 0.5 * 15 * 10
Area of triangle = 75 in²
Area of trapezium < 2(75)
Area of trapezium, A
A = 1/2*(x+b)h
x = top base ; b = bottom base ; h = 10
1/2*(x + 15)10 < 150
5x + 75 < 150
5x < 150 - 75
5x < 75
x < 15
Hence, Area of trapezoid :
A = 1/2 * (15 + 15)10
A = 1/2 * (30)10
A = 1/2 * 300
A = 150
Hence, Area of trapezium can be twice the area of triangle.
2(75) = 150
What are vertical angles called?
Answer:
They are called vertical angles but are also known as "Vertically Opposite Angles"
Step-by-step explanation:
can i get brainliest im 1 away from ranking up
Answer:
"Vertical" refers to the vertex
Vertical angles are pair angles formed when two lines intersect. Vertical angles are sometimes referred to as vertically opposite angles because the angles are opposite to each other.
Step-by-step explanation:
The angles opposite each other when two lines cross. They are always equal. In this example a° and b° are vertical angles. "Vertical" refers to the vertex (where they cross), NOT up/down. They are also called vertically opposite angles.
I'M SO SORRY IF WRONG FORGIVE ME the internet gave me this3/8 + 2 1/2
pls help!!! make sure to show work. thanks :)
Answer:
2 7/8
Step-by-step explanation:
Let's convert to common denominator
3/8 = 3/8
2 1/2 = 2 4/8
3/8 + 2 4/8 = 2 7/8
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
The following table of values represents a...
A) Linear Function
B) Quadratic Function
C) Exponential Function
D) Rational Function
Answer:
C: Exponential function
Step-by-step explanation:
This is an exponential function. While the terms decrease steadily, they do not decrease by subtraction of any common difference. Definitely not a linear function (y = mx + b) or a quadratic (ax^2 + bx + c) either.
Consider the net of a prism below. Describe the prism that the net models.
Answer:
See Explanation
Step-by-step explanation:
The question is incomplete, as the net of the prism is not shown.
However, I will give a general explanation on how to determine the net of the three popular prisms.
(1) Rectangular prism.
It is made up of 6 rectangles
(2) Triangular prism
It consists of 3 rectangles and 2 triangles
(3) Square prism
It is made up of 6 squares
See attachment for the net of each prism
help please!
integrate the following:
[tex] \displaystyle \int \frac{ \cos(2x) - \cos(2a) }{ \cos(x) - \cos( \alpha ) } dx[/tex]
Answer:
[tex] \displaystyle 2 \sin(x) + 2x \cos( \alpha ) + \rm C[/tex]
Step-by-step explanation:
we would like to integrate the following integration:
[tex] \displaystyle \int \frac{ \cos(2x) - \cos(2 \alpha ) }{ \cos(x) - \cos( \alpha ) } dx[/tex]
notice that you can simplify the integrand
recall that,
[tex] \displaystyle \cos(2 \theta) = 2 \cos(\theta) ^{2} - 1[/tex]
thus substitute:
[tex]\displaystyle \int \frac{ 2\cos^{2} (x)- 1 - \{2\cos ^{2} (\alpha ) - 1 \} }{ \cos(x) - \cos( \alpha ) } dx[/tex]
remove parentheses:
[tex]\displaystyle \int \frac{ 2\cos^{2} (x)- 1 - 2\cos ^{2} (\alpha ) + 1}{ \cos(x) - \cos( \alpha ) } dx[/tex]
[tex]\displaystyle \int \frac{ 2\cos^{2} (x) - 2\cos ^{2} (\alpha ) }{ \cos(x) - \cos( \alpha ) } dx[/tex]
factor out 2:
[tex]\displaystyle \int \frac{ 2(\cos^{2} (x) - \cos ^{2} (\alpha )) }{ \cos(x) - \cos( \alpha ) } dx[/tex]
we can use algebraic identity i.e
a²-b²=(a+b)(a-b) to factor the denominator
[tex]\displaystyle \int \frac{ 2(\cos^{} (x) + \cos ^{} (\alpha ))( \cos(x) - \cos( \alpha ) ) }{ \cos(x) - \cos( \alpha ) } dx[/tex]
reduce fraction:
[tex]\displaystyle \int \frac{ 2(\cos^{} (x) + \cos ^{} (\alpha ))( \cancel{\cos(x) - \cos( \alpha ) ) }}{ \cancel{\cos(x) - \cos( \alpha ) }} dx[/tex]
[tex] \displaystyle \int 2( \cos(x) + \cos( \alpha ) )dx[/tex]
distribute:
[tex] \displaystyle \int 2 \cos(x) + 2\cos( \alpha ) dx[/tex]
use sum integration formula:
[tex] \rm \displaystyle \int 2 \cos(x) dx+ \int2\cos( \alpha ) dx[/tex]
recall integration rules:
[tex] \displaystyle 2 \sin(x) + 2x \cos( \alpha ) [/tex]
and we of course have to add constant of integration
[tex] \displaystyle 2 \sin(x) + 2x \cos( \alpha ) + \rm C[/tex]
What is the equation?
Answer:
76
Step-by-step explanation: and explain
Answer:
Step-by-step explanation:
hello : here is an solution
I need help please ASAP
Answer:
length of C'B' is 4 units
length of CB is 8 units
the larger hexagon is twice as large as the smaller; scale is 2:1
Step-by-step explanation:
Translate algebra expressions take away 2 from 8 times f
Answer:
Algebraic Expression:
[tex]8f - 2[/tex]
Answer:
(8f)-2
Step-by-step explanation:
8 times f is multiplication, take two away is subtraction.
Find c.
Round to the nearest tenth:
8 cm
82
55°
b
c = [? ]cm
Law of Sines:
sin A
sin C
sin B
b
Please help asap
Answer:
9.7cm
Step-by-step explanation
According to the sine rule;
a/sinA = c/sinC
8/sin55 = c/sin82
Cross multiply
csin55 = 8sin82
c(0.8192) = 8(0.9903)
c = 8(0.9903)/0.8192
c = 7.9221/0.8192
c = 9.67
Hence the value of c to the nearest tenth is 9.7cm
which can be computed
Answer:
ba is the correct answer
Answer:
CA
Step-by-step explanation:
sana makatulong po ❤❤
The East Side Bulldogs and the West Side Bears are playing a football game. A fan is keeping score using T for a touchdown, worth 7 points, and F for a field goal, worth 3 points. East 5ide Bulldogs quarter 3rd quarter West Side gears
?: How can you represent the score of each team using expressions?
Answer:
touchdown babay
Step-by-step explanation:
score touchdowns
so this is the first question/ discussion i have to do.
Answer:
arrange 3+4=5
Step-by-step explanation:
because 3 square = 9 and 4 square =16 and their sum is 25 and the square of 5 is 25 . both are same .
Hence proved
pls help i need it asap
Answer: y = 4x - 4
Step-by-step explanation:
The line goes through -4 on the y axis meaning its y intercept is -4
and the line goes up by 4 ( that being the slope )
9multiply root 3 by 3 root 5
Answer:
[tex] \frac{9 \sqrt{3} }{3 \sqrt{5} } \\ = \frac{3 \sqrt{3} }{ \sqrt{5} } [/tex]
Hope it helps!
evaluate 4^3+3x5-8Captionless Image
Answer:
71
Step-by-step explanation:
64+3×5-8
64+15-8
79-8
71
Answer:
71
Step-by-step explanation:
4^3 = 64 + 15 = 79 - 8 = 71
Give me my brainllest
Answer:
2x + 2x + x - 8 = 4 (x + 2)
x = 16
Step-by-step explanation:
Because that's a square, the perimeter would be 4s where s is the measure of the side:
2x + 2x + x - 8 = 4 (x + 2)
To solve, refer below:
2x + 2x + x - 8 = 4x + 8
5x - 8 = 4x + 8
5x = 4x + 8 + 8
x = 16
1. How many terms are in the expression
4a + a² + 6a²?
A 3
B 4
C 5
D 7
Answer: A.3
Step-by-step explanation:
Can someone please help me on this math question
2. What property is used to say that the
expression 5x + 7 - 2x is equivalent to
the expression 5x - 2x + 7?
Answer:
The commutative property.
Scarlett's math teacher finds that there's roughly a linear relationship between the
amount of time students spend on their homework and their weekly quiz scores. This
relationship can be represented by the equation y = 60 + 8x, where y represents
the expected quiz score and x represents hours spent on homework that week. What
is the meaning of the x-value when y = 89?
Answer:
.
Step-by-step explanation:
Plz help with this math
Answer:
[tex]\frac{n^4p+n^2}{p^3} \\[/tex]
Step-by-step explanation:
We are given the equation [tex]\frac{n^4}{p^2} + \frac{n^2}{p^3}[/tex]
To solve we need to first find the LCM of the denominators, which would be [tex]p^3[/tex].
[tex]\frac{n^4p}{p^3} + \frac{n^2}{p^3}[/tex]
Now combine the fractions to get the final answer :
[tex]\frac{n^4p+n^2}{p^3} \\[/tex]
please show work
Max has a collection of 99 dimes and pennies worth $4.41. How many pennies does he have?
Answer:
61 pennies
Step-by-step explanation:
d + p = 99
0.1d + 0.01p = 4.41
d = 99 - p
0.1(99 - p) + 0.01p = 4.41
9.9 - 0.1p + 0.01p = 4.41
-0.09p = -5.49
p = 61
Answer: 61 pennies