The figure below shows parallelograms ABCE, PQRS, and TNLM on a coordinate plane.
• Points S, P, Q, and Rare midpoints of ABCE
• T, N, L, and Mare midpoints of PQRS
Write the equation of line ML. Show your work.
Answers
Answer:
ML = √[¼ (EC)²]
Step-by-step explanation:
ML² = ½(QR)²
QR² = ½(EC)²
so, ML² = ¼ (EC)²
=> ML = √[¼ (EC)²]
The equation of the line ML is given by [tex]ML = \frac{AC}{2\sqrt{2} }[/tex] .
Concept:We will find the length of SE and ER.Then we will find the length of SR by using the Pythagoras theorem in Δ ESR.Then, we will find the length of MR and RL and hence, again using the Pythagoras theorem in Δ MRL and find the length of ML.How to solve the given question?Since, S is the midpoint of AE.[tex]SE = \frac{AE}{2}[/tex]
Similarly, [tex]RE = \frac{CE}{2}[/tex]In Δ SER, ∠E = 90°,
∴ By Pythagoras theorem, SR² = SE² + ER²
∴ [tex]SR^2 = (\frac{AE}{2})^2 + ( \frac{RE}{2})^2 = \frac{AE^2 + CE^2}{4}[/tex] ...... (1)
∴ Similarly, [tex]RQ^2 = \frac{BC^2 + CE^2}{4}[/tex] ............ (2)
Since, M & L are the midpoints of SR and RQ.
[tex]MR = \frac{SR}{2}[/tex] & [tex]RL = \frac{RQ}{2}[/tex]
In Δ LMR, ∠R = 90°,
∴ By Pythagoras theorem, ML² = RM² + RL²
∴ [tex]ML^2 = (\frac{SR}{2})^2 + ( \frac{RQ}{2})^2 = \frac{SR^2 + RQ^2}{4}[/tex]
Substituting value of SR and RQ from 1 and 2.
[tex]ML^2 =\frac{1}{4} [ \frac{AE^2 + CE^2}{4} + \frac{BC^2 + CE^2}{4} ][/tex]
As ABCE is parallelogram, BC = AE
∴ [tex]ML^2 =\frac{1}{4} [ \frac{2AE^2 + 2CE^2}{4} ] = [ \frac{AE^2 + CE^2}{8} ][/tex]
[tex]ML = \frac{AC}{2\sqrt{2} }[/tex]
Thus, the equation of the line ML is given by [tex]ML = \frac{AC}{2\sqrt{2} }[/tex] .
Learn more about parallelogram here:
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Related Questions
12 Here are two equations.
y = 5x - 9 and x + y = 7
a Use this graph to find an
approximate solution of
the equations.
b Use algebra to find exact
solutions of the equations,
Helpppp
Answers
Answer:x=8/3 ; y=13/3
Step-by-step explanation: to find the intersection point or the solution of the graph, you need to equate these equations 1) y=5x-9 2) x+y=7 => y=7-x x equating the equations 5x-9=7-x => 6x=16 => x=8/3 ; y=13/3
Find an area of a circle if the diameter of the circle is 40 cm
Answers
Answer:
1256cm^2
Step-by-step explanation:
The area of a circle is πr^2.
The radius is half of the diameter, so it's 20 cm.
A=3.14*(20cm)^2
A=3.14*400cm^2
A=1256cm^2
PLEASE HELPPP TEST TMR PROBLEM ISW IN PHOTO BELOW
Answers
Answer:
AB = A'B', AD = A'D', CD = C'D', CB = C'B'
Step-by-step explanation:
There is more then one way to give this problem a solution. The point of the question is to explain or provide an argument that will prove that the square ABCD is the same as A'B'C'D.
The way to prove it is by saying that the sides are equal, meaning the answer I provided above, by claiming that side AB is also equal to A'B', and so forth with all four sides.
I REALLY NEED HELP, PLEASE!
EXPLAINING UR ANSWER = BRAINLIEST
A prism with volume 7750 cm³ is dilated by a factor of 1/5.
The volume of the dilated prism is ___ cubic centimeters.
Answers
Answer:
1550m^3
Step-by-step explanation:
Volume of the prism= 7750m^3
Factor of dilated prism= 1/5
7750×1/5= 1550m^3
Two points, a and b, are graphed on the number line below. Maynard says there is not enough information to write an inequality statement comparing a and b. Which statement explains whether or not Maynard is correct? a b -10 0 10 Maynard is correct. There is no way to tell which exact numbers a and b represent, so he cannot write an inequality. Maynard is correct. There is no way to tell if a and b are positive or negative, so he cannot write an inequality Maynard is incorrect. On the number line, a is to the left of b. so a Maynard is incorrect. On the number line, a is to the left of b. So a > b.
Answers
Answer:
c
Step-by-step explanation:
how many edges does a rectangular have
Answers
hope this helps
Use the substitution method to solve the system of equations. Write your answer as an order pair. y=x-2 and y=-2x+7
Answers
i hope this helps
Answer:
The Coordinates are (3, 1)
Step-by-step explanation:
Use the substitution method to solve the system of equations.
Let y = x - 2 be Equation 1
Let y = -2x + 7 be Equation 2
We know that the coordinates are (3, 1) because we graphed the slope intercept equations in part one. Its asking to use the substitution method to prove that the coordinates (3, 1) are viable or satisfies both Equation 1 and 2.
The substitution method is nothing but substituting x and y back into the equation to prove that the coordinates are viable.
For this I'll use equation 1 first,
y = x - 2
1 = 3 - 2
So yes, the coordinates (3, 1) satisfy Equation 1
Lets check equation 2 now,
y = -2x + 7
1 = -2*3 + 7
1 = -6 + 7
This is also another equation where the coordinates (3, 1) satisfy equation 2
So this means that the coordinates (3, 1) are viable for both equations
Hope this helps!
Find a equation of a line that is perpendicular to y=-4x+3 and passes through the point (4,-1).
Answers
Given:
The given equation is:
[tex]y=-4x+3[/tex]
A line is perpendicular to the given line and passes through the point (4,-1).
To find:
The equation of required line.
Solution:
The slope intercept form of a line is:
[tex]y=mx+b[/tex]
Where, m is slope and b is y-intercept.
We have,
[tex]y=-4x+3[/tex]
Here, the slope of the line is -4 and the y-intercept is 3.
Let the slope of required line be m.
We know that the product of slopes of two perpendicular lines is -1. So,
[tex]m\times (-4)=-1[/tex]
[tex]m=\dfrac{-1}{-4}[/tex]
[tex]m=\dfrac{1}{4}[/tex]
The slope of required line is [tex]m=\dfrac{1}{4}[/tex] and it passes through the point (4,-1). So, the equation of the line is:
[tex]y-(-1)=\dfrac{1}{4}(x-4)[/tex]
[tex]y+1=\dfrac{1}{4}(x)-\dfrac{4}{4}[/tex]
[tex]y=\dfrac{1}{4}x-1-1[/tex]
[tex]y=\dfrac{1}{4}x-2[/tex]
Therefore, the equation of the required line is [tex]y=\dfrac{1}{4}x-2[/tex].
does anyone know how to solve this? asap please:((
Answers
Answer:
D)
Step-by-step explanation:
All sides are congruent because all sides are the same.
Hope this helps!
-kiniwih426
In a fruit cocktail, for every 25 ml of orange juice you need 30 ml of apple juice and 45 ml of coconut milk. What proportion of the cocktail is orange juice?
Give your answer as a fraction in its simplest form.
Answers
Answer:
1/4
Step-by-step explanation:
Add the three amounts:
25 ml + 30 ml + 45 ml = 100 ml
These three amounts make 100 ml of fruit cocktail.
The amount of orange juice is 25 ml.
The fraction of orange juice is
(25 ml)/(100 ml) = 25/100 = 1/4
Answer: 1/4
HELLPPPPPPPPPPP PLEASSSEE IM BEGGING " Which linear function has a greatery-intercept than the function depicted in the graph." ***will mark brainliest*
Answers
Answer:
x y
-1 2
0 3
1 1
2 -1
Step-by-step explanation:
Evaluate 9t when t=5.
ITS NOT 95 already tryed that
Answers
Answer:
45
Step-by-step explanation:
9x5=45
Answer:
45
Step-by-step explanation:
9t
substitute 5 for t
9(5)
9(5) is the same as 9 * 5
9 * 5 = 45
so when t = 5 the output is 45
Y-intersect of the liner function
Answers
Answer:
15
Step-by-step explanation:
The y- intercept is the value of y on the y-axis where the line crosses.
The line crosses the y- axis at 15 ← y- intercept
Which solid has a great volume
Answers
2. A Cylinder with the diameter of 8 and height of 8
Let f(x) = 5x2 – 4x and g(x) = 5x + 1.
Find f – g.
Answers
Answer:
[tex]5x^2-9x-1[/tex]
Step-by-step explanation:
f - g
[tex]=5x^2-4x -(5x+1)\\\\=5x^2-4x-5x-1\\\\=5x^2-9x-1[/tex]
5x^2 -9x - 1
Cho alpha+ beta+ gamma = pi. Chứng minh A) sin alpha + sin beta + sin gamma = 4cos alpha/2*cos beta/2*cos gamma /2
Answers
Answer:
It is proved .
Step-by-step explanation:
[tex]\alpha +\beta +\gamma =\pi.....(1)\\\\sin\alpha + sin\beta +sin\gamma=4 cos\frac{\alpha}{2}cos\frac{\beta}{2}cos\frac{\gamma}{2}[/tex]
Take LHS
[tex]=sin\alpha + sin\beta +sin\gamma\\\\=2 sin \frac{\alpha +\beta }{2} cos\frac{\alpha -\beta }{2} + sin\gamma\\\\=2 sin\frac{180-\gamma}{2}cos \frac{\alpha - \beta}{2}+2 sin\frac{\gamma}{2}cos\frac{\gamma}{2}\\\\=2 cos\frac{\gamma}{2}cos \frac{\alpha - \beta}{2}+2 sin\frac{\gamma}{2}cos\frac{\gamma}{2}\\\\=2 cos\frac{\gamma}{2}\left [ cos \frac{\alpha - \beta}{2}+sin\frac{180-\alpha-\beta}{2}\\ \right ]\\\\=2 cos\frac{\gamma}{2}\times 2 cos\frac{\alpha}{2}cos\frac{\beta}{2}\\[/tex]
[tex]=4 cos\frac{\alpha}{2}cos\frac{\beta}{2}cos\frac{\gamma}{2}[/tex]
Hence proved.
What's the probability of randomly selecting an odd number from the numbers 1-10?
Answers
Answer:
There is a 50% chance of getting a odd number.
Step-by-step explanation:
1-10 have 5 old numbers and they are 1, 3, 5, 7, and 9.
5/10 = 0.5 = 50%
5 out of 10
At a pet store, Rhonda paid $55 for 8 dog bowls and 6 bones. Kelly paid $32.50 for 2 dog bowls and 9 bones. Determine the cost of one dog bowl (x) and one bone (y). Write a system of linear equations that models this situation.
Answers
Answer:
8d + 6b = 55
2d + 9b = 32.50
Step-by-step explanation:
let 'd' = # dog bowls
let 'b' + # bones
Rhonda: 8d + 6b = 55
Kelly: 2d + 9b = 32.50
we can multiply Kelly's equation by -4 to eliminate the 'd' terms:
Kelly: -4(2d + 9b) = 32.5(-4)
-8d - 36b = -130
now add the above equation to Rhonda's equation:
-8d - 36b = -130
+ 8d + 6b = 55
-30b = -75
b = 2.50
now we can use either equation and substitute 2.5 for 'b' to find 'd'
2d + 9(2.5) = 32.5
2d + 22.5 = 32.5
2d = 10
d = 5
A pizza shop has 6 kinds of cheese, and 13 different toppings. How many ways are there for a customer to select a pizza with 2 cheeses and 4 toppings?
Answers
Answer:
10725
Step-by-step explanation:
C [tex]\frac{2}{c}[/tex] [tex].[/tex] C [tex]\frac{4}{13}[/tex] = [tex]\frac{6x5}{2}[/tex] ° [tex]\frac{13x12x11x10}{4x3x2x1}[/tex]
= 10725
Determine the horizontal asymptote for the rational function.
Answer choices:
A.) y= 1
B.) y= -5
C.) y= 1
D.) y= -1
Answers
Answer:
[tex]\text{C) } y=1[/tex]
Step-by-step explanation:
A asymptote represents a control for a function where the function will never touch. We see that as the [tex]y[/tex] approaches 1, [tex]x[/tex] approaches infinity, from either direction. However, the function never touches nor crosses the line [tex]y=1[/tex], and never will. Thus, the horizontal asymptote is located at [tex]y=1[/tex].
y=0 is correct answer but is not in the selection.
Step-by-step explanation:
SOLUTION
For these solutions, we will use \displaystyle f\left(x\right)=\frac{p\left(x\right)}{q\left(x\right)}, q\left(x\right)\ne 0f(x)=
q(x)
p(x)
,q(x)≠0.
\displaystyle g\left(x\right)=\frac{6{x}^{3}-10x}{2{x}^{3}+5{x}^{2}}g(x)=
2x
3
+5x
2
6x
3
−10x
: The degree of \displaystyle p=\text{degree of } q=3p=degree of q=3, so we can find the horizontal asymptote by taking the ratio of the leading terms. There is a horizontal asymptote at \displaystyle y=\frac{6}{2}y=
2
6
or \displaystyle y=3y=3.
\displaystyle h\left(x\right)=\frac{{x}^{2}-4x+1}{x+2}h(x)=
x+2
x
2
−4x+1
: The degree of \displaystyle p=2p=2 and degree of \displaystyle q=1q=1. Since \displaystyle p>qp>q by 1, there is a slant asymptote found at \displaystyle \frac{{x}^{2}-4x+1}{x+2}
x+2
x
2
−4x+1
.
Synthetic division of the polynomial x^2-4x+1 by x+2 in which it only contains the coefficients of each polynomial.
The quotient is \displaystyle x - 6x−6 and the remainder is 13. There is a slant asymptote at \displaystyle y=x - 6y=x−6.
\displaystyle k\left(x\right)=\frac{{x}^{2}+4x}{{x}^{3}-8}k(x)=
x
3
−8
x
2
+4x
: The degree of \displaystyle p=2\text{ }<p=2 < degree of \displaystyle q=3q=3, so there is a horizontal asymptote y = 0.
What is the value of b in the equation below?
9^-6 . 9^-2= a^b
A. -10, B. -6, C. 9, D. 16
Answers
Answer:
-10
Step-by-step explanation:
please help me! what’s the answer?
1) Two points
2) One point
3) One equation
Answers
Answer:
I think 2 points
Step-by-step explanation:
I may be wrong bc I suck at algebra. literally who is gonna use algebra ever?
Answer: two points hope it helps
in the equation 50=2y-5y^2 what is the value of c
Answers
Answer:
No solution because there is no c variable
Step-by-step explanation:
Answer:
50
Step-by-step explanation:
What is the value of s in the equation 3r=10+5s , when r=10 ?
4
8
100
200
Answers
Answer:
4
Step-by-step explanation:
when r = 10
3r = 10 + 5s
3(10) = 10 + 5s
30 = 10 + 5s
30 - 10 = 10 + 5s -10
20 = 5s
20/5 = 5s/5
4 = s
A window cleaning service charges under $75 to clean all of the windows of a house. Write an inequality to represent the amount charged.
Answers
Answer:
C < $75.
Step-by-step explanation:
Let C be the charge of a window cleaning service, that cleans all the windows of the house.
Since it charges less than $75. this means
C < $75.
So, this is the required inequality equation.
PLEASE HELP ME PLS PLS!
i need help please i’m confused
Answers
Area as a product: (x^2 + 3x) • (2x + 1)
(I hope I’m correct)
Which statements are true? Select all that apply.
A. The amplitude of y = 2 sin(12x) is 12.
B. The period of y = 2 sin(12x) is π.
C. The amplitude of y = 2 sin(12x) is π2.
D. The period of y = 2 sin(12x) is 4π.
E. The period of y = 2 sin(12x) is 12.
F. The amplitude of y = 2 sin(12x) is 2.
Answers
If the supplement of an angle is 4 times of its compliment, find the angle.
PLSSSSSSSSSSS HELP ASAP
Answers
Answer:
The angle is 60°
Step-by-step explanation:
A supplement angle is the angle whose sum is equal to 180°.
The supplement angle = 180° - x
A complement angle is the angle whose sum is equal to 90°.
The complement angle = 90° - x
Given,
supplement angle = 4 × complement angle
(180° - x) = 4 × (90° - x)
180° - x = 360° - 4x
4x - x = 360° - 180°
3x = 180°
x = 60°
The supplement angle = 180° - x
⇒ 180° - 60°
⇒ 120°
The complement angle = 90° - x
⇒ 90° - 60°
⇒ 30°
Answer:
The angle is 60 degrees.
Step-by-step explanation:
Let the angle be x.
Then its supplement = 180-x.
Its complement = 90-x, so we have the equation:
180 - x = 4(90 - x)
180 - x = 360 - 4x
-x + 4x = 360 - 180
3x = 180
x= 60 degrees.
How do you solve for x in this using trignometric ratios
Answers
Answer:
[tex]x= 23.775.[/tex]
Step-by-step explanation:
[tex]\text{We have} \\\cos(18\textdegree) = \frac{x}{25} \\\Rightarrow x= 25\cos(18\textdegree)\\\Rightarrow x= 25 \times 0.951\\\Rightarrow x= 23.775.[/tex]
Help me find B asap!
Answers
Answer:
11)
complimentary angle
b = 90 - 65
b = 25º
12)
supplementary angle
b = 180 - 117
b = 63º
13)
360º in a circle
b = 360 - 244 -23
b = 93º
14)
vertical angle
b = 46º