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
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:
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)
What is the value of the expression3+3⋅72−9⋅103+3⋅72−9⋅10 ?
-7.763 will be the total to the answer.
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
Please solve with explanation
Answer:
Hope it helps you.......
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
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
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
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)
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
how to order you decimals from least to greatest
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)
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
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]
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
solve please ;3 ( will give brainliest ♡ )
I need answer immediately!!!!!!
Its division and fractions i advise calulater soup
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:
the net force on a
rock with a mass of 20 kg is
19.6 N. What is the accelera-
tion of the rock?
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
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
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:
alguien me ayuda????
What do you need help with?
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!
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
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"
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)
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!
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
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: