The midpoint of a line divides the line into equal segments.
See below for the proof of [tex]\mathbf{MN = \frac{1}{2}AC}[/tex]
The given parameters are:
[tex]\mathbf{A = (-5,-4)}[/tex]
[tex]\mathbf{B = (3,-2)}[/tex]
[tex]\mathbf{C = (-1,6)}[/tex]
The coordinates of M (midpoint of AB) are calculated as follows:
[tex]\mathbf{M = \frac{1}{2}(x_1 + x_2, y_1+y_2)}[/tex]
So, we have:
[tex]\mathbf{M = \frac{1}{2}(-5 + 3, -4-2)}[/tex]
[tex]\mathbf{M = \frac{1}{2}(-2, -6)}[/tex]
[tex]\mathbf{M = (-1, -3)}[/tex]
The coordinates of N (midpoint of BC) are calculated as follows:
[tex]\mathbf{N = \frac{1}{2}(x_1 + x_2, y_1+y_2)}[/tex]
So, we have:
[tex]\mathbf{N = \frac{1}{2}(3 - 1, -2 +6)}[/tex]
[tex]\mathbf{N = \frac{1}{2}(2, 4)}[/tex]
[tex]\mathbf{N = (1, 2)}[/tex]
Distance MN is:
[tex]\mathbf{MN = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}}[/tex]
So, we have:
[tex]\mathbf{MN = \sqrt{(-1 - 1)^2 + (-3 - 2)^2}}[/tex]
[tex]\mathbf{MN = \sqrt{29}}[/tex]
Distance AC is calculated as follows:
[tex]\mathbf{AC= \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}}[/tex]
So, we have:
[tex]\mathbf{AC= \sqrt{(-5 - -1)^2 + (-4 - 6)^2}}[/tex]
[tex]\mathbf{AC= \sqrt{116}}[/tex]
Split
[tex]\mathbf{AC= \sqrt{4 \times 29}}[/tex]
Take positive square root of 4
[tex]\mathbf{AC= 2\sqrt{29}}[/tex]
To prove that:
[tex]\mathbf{MN = \frac{1}{2}AC}[/tex]
We have:
[tex]\mathbf{\sqrt{29} = \frac{1}{2} \times 2\sqrt{29}}[/tex]
[tex]\mathbf{\sqrt{29} = \sqrt{29}}[/tex]
The above equation is true.
Hence. [tex]\mathbf{MN = \frac{1}{2}AC}[/tex]
Read more about midpoints and distance at:
https://brainly.com/question/11231122
I need answer immediately!!!!!!
Its division and fractions i advise calulater soup
Which models show the problem 4
6
÷ 2
6
= 2? Check all that apply.
An area model has 4 shaded parts and 2 unshaded parts. 2 circles are each drawn around 2 shaded parts.
A number line going from 0 to 1. An arrow goes from 0.6 to 0.4, and from 0.4 to 0.
A fraction bar. The top bar is labeled 1. 6 bars underneath the bar are labeled one-sixth. 4 of the bars are circled.
An area model has 2 shaded parts and 4 unshaded parts. The 2 shaded parts are circled.
Answer:
the second and last sentences.
Step-by-step explanation:
Its the most reasonable!
Answer:
It is accutally 1st 2nd and 3rd plz trust me
Step-by-step explanation:
it is the corect
Distribute: -(14s+9)-7(s+11)
Answer: -21s-86
Step-by-step explanation:
Distribute the -1 to the 14s+9 (this means multiply-1 and 14s, then multiply -1 and 9) to get -14s-9. Then distribute the -7 to the s+11 (this mean multiply -7 and s, then multiply -7 and 11) to get -7s-77. You will now have the equation -14s-9-7s-77. Simplify this by adding like terms (-14s-7s) and (-9-77) you will get the equation: -21s-86
Distributing -(14s+9)-7(s+11) gives -14s -9 -7s -77; and further simplification results into -21s -86
From the question,
We are to distribute -(14s+9)-7(s+11)
To do this,
We will clear the bracket by distributing the terms outside
That is,
-(14s+9)-7(s+11) becomes
-14s -9 -7s -77
Now, if desired, we can simplify further by collecting like terms
-14s -9 -7s -77
-14s -7s -9 -77
Then, we get
-21s -86
The simplified expression is -21s -86
Hence, distributing -(14s+9)-7(s+11) gives -14s -9 -7s -77; and further simplification results into -21s -86
Learn more here: https://brainly.com/question/11854155
a = 5/3 right angle,find b
Answer: i can't
Step-by-step explanation: what b
there's no picture attached
does b have any value?
put a picture and i'll edit my answer
JK has endpoints (-2, 10) and K(10, -14). Point L divides JK into two parts with lengths in a
ratio of 5:1.
What are the two possible locations of L?
(5, 6)
(2, -4)
(8, -10)
(4, -2)
(2, 1)
(0,6)
Answer:
(8, - 10) or (0, 6)Step-by-step explanation:
There are two options as below.
1. JL/JK = 5 : 1
Find the coordinates of L:
x = -2 + 5/6(10 - (-2)) = -2 + 10 = 8y = 10 + 5/6(-14 - 10) = 10 - 20 = - 10The point is L(8, - 10)
2. JL/JK = 1 : 5
Find the coordinates of L:
x = -2 + 1/6(10 - (-2)) = -2 + 2 = 0y = 10 + 1/6(-14 - 10) = 10 - 4 = 6The point is L(0, 6)
work out x when the area is root 4 2^2 and angle C is 45 and ab are (x+2)(2x-3)
Answer:
x = 3.08
Step-by-step explanation:
Area formula:
A = 1/2bhThe height is:
h = (x + 2)sin 45° = (x + 2) ×√2/2Substitute the value for area and set equation:
4√2 = 1/2 × (2x - 3) × √2(x + 2)/2(2x - 3)(x + 2) = 162x² + x - 6 = 162x² + x - 22 = 0D = 1 + 4*2*22 = 177x = (-1 + √177)/4 = 3.08 (rounded)Note the second root ignored as negative
Answer:
x = 3.08 (3 s.f.)
Step-by-step explanation:
Area of a Triangle (using sine)
[tex]\sf Area=\dfrac{1}{2}ac \sin B[/tex]
where:
a and c are adjacent sidesB is the included angleGiven:
Area = 4√2 m²a = (2x - 3) mc = (x + 2) mB = 45°Substitute the given values into the formula:
[tex]\implies 4\sqrt{2}=\dfrac{1}{2}(2x-3)(x+2) \sin 45^{\circ}[/tex]
[tex]\implies 8\sqrt{2}=(2x-3)(x+2) \sin 45^{\circ}[/tex]
[tex]\implies 8\sqrt{2}=(2x-3)(x+2) \left(\dfrac{\sqrt{2}}{2}\right)[/tex]
[tex]\implies 8\sqrt{2}\left(\dfrac{2}{\sqrt{2}}\right)=(2x-3)(x+2)[/tex]
[tex]\implies (2x-3)(x+2) =16[/tex]
[tex]\implies 2x^2+4x-3x-6=16[/tex]
[tex]\implies 2x^2+x-22=0[/tex]
Use the Quadratic Formula to solve for x:
[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]
[tex]\implies a=2, \quad b=1, \quad c=-22[/tex]
[tex]\implies x=\dfrac{-1 \pm \sqrt{1^2-4(2)(-22)} }{2(2)}[/tex]
[tex]\implies x=\dfrac{-1 \pm \sqrt{177}}{4}[/tex]
[tex]\implies x=3.08, -3.58\:\: \sf (3 \:s.f.)[/tex]
As distance is positive:
[tex]\implies x=3.08 \:\:(3 \sf \:s.f.) \:\textsf{only}[/tex]
The average height of a population is unknown. A random sample from the population yields a sample mean of x¯=66.3 inches. Assume the sampling distribution of the mean has a standard deviation of σx¯=0.8 inches. Use the Empirical Rule to construct a 95% confidence interval for the true population mean height.
Answer:
(64.7, 67.9)
Step-by-step explanation:
(66.3-2*08, 66.3+2*0.8)
(66.3-1.6, 66.3+1.6)
(64.7, 67.9)
I need help can someone help?
Step-by-step explanation:
Using Pythagoras theorem,
Let the ratio of the sides be x
B²=H²-P²
B²= (25x)²-(21x)²
B²=625x²-441x²
B²=184x²
B=13.56x.
hope this helps you.
Answer:
Your answer is [tex]\sqrt{184}[/tex] or 13.5646599663...
Step-by-step explanation:
[tex]A^{2} +B^{2} =C^{2} \\A^{2} +21^{2} = 25^{2} \\A^{2} = 25^{2} - 21^{2} \\A^{2} = 625-441\\A^{2} = 184\\A = \sqrt{184}[/tex]
Hope this helps!
Find an equivalent system of equations for the following system:
2x + 4y = 4
−5x + 5y = 5
A. 2x + 4y = 4
−3x + y = −1
B. 2x + 4y = 4
7x + 5y = −1
C. 2x + 4y = 4
7x − y = 5
D. 2x + 4y = 4
7x − y = −1
Solve for x.
2x/3 +1=3
O x =6
O x =3
O x = 1 1/3
O x = 2 2/3
Answer:
3......................
Answer:
X=3!
Let's solve your equation step-by-step.
Step 1: Simplify both sides of the equation.
Step 2: Subtract 1 from both sides.
Step 3: Multiply both sides by 3/2.
Answer:
x=3
Complete the conjecture based on the pattern you observe in the examples below:
Conjecture: The sum of any two odd numbers is ___
1 + 1 = 2 9 + 11 = 20
1 + 5 = 6 13 + 21 = 34
7 + 9 = 16 101 + 103 = 204
Conjecture: The product of any two numbers is ___
1 . 1 = 1 9 . 11 = 99
1 . 3 = 3 13 . 11 = 143
3 . 7 = 21 101 . 103 = 10,403
Conjecture: The product of a number (x-1) and the number (x+1) is always equal to ___
3 . 5 = 4² - 1 7 . 9 = 8² - 1
4 . 6 = 5² - 1 6 . 8 = 7² - 1
5 . 7 = 6² - 1 8 . 10 = 9² - 1
Step-by-step explanation:
the writing and spacing of the problem description is difficult to understand.
but there is no mystery. look at the examples.
all of them
3×5 = 15 = 16 - 1 = 4² - 1
4×6 = 24 = 25 - 1 = 5² - 1
5×7 = 35 = 36 - 1 = 6² - 1
6×8 = 48 = 49 - 1 = 7² - 1
7×9 = 63 = 64 - 1 = 8² - 1
8×10 = 80 = 81 - 1 = 9² - 1
so, what does this look like ?
(x-1)×(x+1) is always equal to (x² - 1)
What is the value of the expression3+3⋅72−9⋅103+3⋅72−9⋅10 ?
-7.763 will be the total to the answer.
please help I dont understand
Answer:
I dont know The answer sorry
Step-by-step explanation:
Answer: 2
Step-by-step explanation: The average rate of change is calculated as the slope of the line between the two points on the graph. Since at x = 1, y = -3, and at x = 3, y = 1, these are the two points which we calculate the slope from. Using the formula
m = (y2 - y1)/(x2 - x1)
m = (1 - (-3))/(3 - 1)
m = 4/2
m = 2
A book has 5 pages,10 copies of the same books will be made .How many pages will be printed?
Answer:
50
Step-by-step explanation:
5 pages * 10 copies = 50 pages
If the f(x)=2x-1 and g(x)=x^2-1 find what the g(f(a-1)) is
Answer:
GOOD LUCK ON YOUR TEST YOU WILL DO GOOD
Step-by-step explanation:
d/dx (sin^3 x) = d/dx (sinx sinx sinx) = ?
1. cos x sin^2x
2. 1+2 sin^2x cos x
3. 3 sin^2x cos x
4. 2 sinx cos x+sin^2x cos x
5. 2 cos x sin^2x+ sin x cos x
Step-by-step explanation:
1)2*(Cos(x)^2*Sin(x))-Sin(x)^3
2)4*(Cos(x)^2*Sin(x))-2*Sin(x)^3
3)6*(Cos(x)^2*Sin(x))-3*Sin(x)^3
4)2*Cos(x)^2+2*(Cos(x)^2*Sin(x))-2*Sin(x)^2-Sin(x)^3
5)Cos(x)^2+4*(Cos(x)^2*Sin(x))-Sin(x)^2-2*Sin(x)^3
Please help me solve this
Answer:
-2
Step-by-step explanation:
y+z-2y
First substitue y and z for 4 and 2.
4+2-2(4)
Then using PEMDAS, multiply.
4+2-8
Then solve normally.
-2
alguien me ayuda????
What do you need help with?
how to order you decimals from least to greatest
the net force on a
rock with a mass of 20 kg is
19.6 N. What is the accelera-
tion of the rock?
Line segment RS has endpoints R (-2, 4) and S (-4, -1).
Line segment R''S'' has endpoints R'' (3, -3) and S'' (5, 2).
Name the transformation that maps line segment RS to line segment R''S''.
Answer:
rotation 180° (ccw) over point (0.5 , 0.5)
Step-by-step explanation:
R (-2, 4) , S (-4, -1) -> R'' (3, -3) , S'' (5, 2)
check: rotation over (0.5,0.5) 180°
x'' = - (x - x₀) + x₀ .. x: original x coordinate, x₀ : center of rotation
y" = - (y - y₀) + y₀
for R" : x" = - (-2 - 0.5) + 0.5 = 3
y" = -(4 - 0.5) + 0.5 = -3
You can verify the coordinates of S" by the above formula.
** (0.5,0.5) is the intersect of RR" and SS"
Calculate the sum of each expression. Arrange the expressions in the order of their value from largest to smallest
Big bag don't mean everything wavy
I got 99 problems like Jay Z
Caught a felony judge tried to slave me
Lost my grandmother R.I.P Mavy
I got money and move shady
The set of ordered pairs below represents a relation that is a function.
Which point, when added to the set, would form a relation that is not a function?
A
(0,6)(0,6)(0,6)
B
(4,2)(4,2)(4,2)
C
(−6,8)(-6,8)(−6,8)
D
(−8,10)(-8,10)(−8,10)
Answer:
I'm confused by the points:
Why three points for each (A, B, C, and D)?: A: (0,6)(0,6)(0,6), etc.
Points A and B [(0,6) and (4,2)] are consistant with a straight line of the form y=-x+6.
Points C and D [(-6,8),(-8,10)]are on the line y=-x+2.
A and B aren't related to C and D.
Step-by-step explanation:
solve 4(2x-5)=5x+4 pls
Answer:
x=8
Step-by-step explanation:
4(2x-5)=5x+4
Distribute
8x -20 = 5x+4
Subtract 5x from each side
8x -20 -5x = 5x+4-5x
3x-20 = 4
Add 20 to each side
3x-20+20 = 4+20
3x = 24
Divide by 3
3x/3 =24/3
x=8
What is the formula for distance?
Answer:
Hope my answer helps you mark me brianliest plz
Step-by-step explanation:
d =√(x2-x1)+(y2-y1)
what is the equation for the line that is parallel to the y-axis and passes through the point (2, -5)?
Answer:
X = 2
Step-by-step explanation:
solve please ;3 ( will give brainliest ♡ )
ABCD is a rectangle and AC and BD are its diagonals. If AC = 10 cm, then BD is?
A. 10 cm
B. 5 cm
C. 15 cm
Or D. 20 cm
Lemme know, take ur timeee
Answer:
A. 10 cm
Step-by-step explanation:
In a right angled triangle, a² + b² = c² where c is the diagonal or hypotenuse. If you split a rectangle diagonally into two right angle triangles, the a and b of both triangles would be the same length. Therefore, the c or diagonals would also be the same length - 10 cm.
Hope this helps!
consider the following simplified algebraic expression 10x²y+6x²-7y²-6 which could be the original expression
Answer:
You technically can't do anything with it since it the algebraic expression doesn't factor.
Step-by-step explanation:
Please solve with explanation
Answer:
Hope it helps you.......