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
determine if the graph represents a function
Answer:
the asnwer is YES
Step-by-step explanation:
Answer:
Step-by-step explanation:
i think it 3256
In ASL, the position in which certain signs are completed indicates
A-ability to sign
B-age of speaker
C-place of action
D-time of event
Answer:
I am pretty sure it is time of event.
Step-by-step explanation:
Sensei Umeh’s ""Active Hands"" karate program grew from 8 members to 15 last week. What is the percent of change?
Answer:
187.5% increase
Step-by-step explanation:
Percent change formula: [tex]\frac{x_{2}-x_{1}}{x_{1}}[/tex]
Initially, the program had 8 members and ended with 15 so [tex]\frac{15-8}{8}=\frac{7}{8}=0.875=87.5[/tex]
list the coordinate for both pairs.
Answer:
Hi I hope this helps
A = X : -3 Y : -3
B = X : -2 Y : 1
Step-by-step explanation:
please let me know if it's right or wrong
HELP ME PLEASE im begging!!
Answer:
[tex]x = 40[/tex]
Step-by-step explanation:
As the Corresponding angles are equal
[tex]4x - 50 = 2x + 30 \\ 4x - 2x = 50 + 30 \\ 2x = 80 \\ \frac{2x}{2} = \frac{80}{2} \\ x = 40 \degree[/tex]
Hope this helps you.
Let me know if you have any other questions :-)
Answer:
[tex]x = 40 [/tex]
Step-by-step explanation:
that's the answer
plz help my grade went down
Answer:
Slope = -4
Step-by-step explanation:
Perpendicular lines have negative reciprocal slopes, which means that multiplying their slopes result in a product of -1. Given the equation, x - 4y = - 12:
Transform the equation into its slope-intercept form, y = mx + b:
x - 4y = - 12
x - x - 4y = - x - 12
-4y = -x - 12
Divide both sides by -4:
[tex]\frac{-4y}{-4} = \frac{-x - 12}{-4}[/tex]
y = ¼x + 3 ⇒ (This is the slope-intercept form of the given standard equation, x - 4y = - 12).
Since the slope of the given equation is ¼, then it means that its negative reciprocal must be - 4:
(¼) (-4) = -1
Therefore, the slope of the line perpendicular to x - 4y = - 12 is - 4.
There are 80 students in a school. If 40 percent of the students are boys, how many girls are in the school
Answer:
48
Step-by-step explanation:
80x40%=80x.4=32 boys. 80 students-32 boys = 48 girls
If a train travels 420 miles in 24 hours, what is its unit rate of travel?
16 mph
19.5 mph
17.5 mph
15.2 mph
17.5mph
420÷24= 175
Hope this helped you- have a good day bro cya)
Answer:
17.5mph
Step-by-step explanation:
two amounts of money are in the ratio 8:3.if the second amount is $4.05, what is the value of the first amount
Answer:
10.8$
Step-by-step explanation:
(8*4.03)/3 = 10.8
i will give you brainliest if you help
Power: An expression that has a ______________ and an __________________.
Answer:
base number and exponent
Step-by-step explanation:
factor completely x^2-4
Answer:
(x + 2) (x - 2)
Step-by-step explanation:
Given the quadratic expression, x² - 4:
Use the Difference of squares factoring formula:
u² - v² = (u + v)(u - v)
Determine what are possible factors that could have a product of -4:
Since -2 × 2 = -4, these can be used as factors.
Therefore, the factors of the quadratic expression, x² - 4 are:
(x + 2) (x - 2)
help me please.
Rounding questions.
Step-by-step explanation:
a) 6400
b) 4800
c) 32000
hope this answer helps you dear!
Solve to find X. 1/5(x - 2) = 1/10 (x + 6)
Answer:
x = 10
Step-by-step explanation:
First, distribute:
[tex]\frac{1}{5} x - \frac{2}{5} =\frac{1}{10} x+\frac{6}{10}[/tex]
Next, subtract [tex]\frac{1}{5}x[/tex] from both sides:
[tex]-\frac{2}{5} = \frac{1}{10} x -\frac{1}{5} x+\frac{6}{10}[/tex]
(multiply [tex]\frac{1}{5}x[/tex] by 2 to get common denominator, [tex]\frac{2}{10} x[/tex] )
[tex]-\frac{2}{5} =-\frac{1}{10}x +\frac{6}{10}[/tex]
Next, subtract [tex]\frac{6}{10}[/tex] from both sides:
[tex]-\frac{2}{5} -\frac{6}{10} =-\frac{1}{10} x[/tex]
(multiply [tex]\frac{2}{5}[/tex] by 2 to get common denominator, [tex]\frac{4}{10}[/tex] )
[tex]-\frac{10}{10} =-\frac{1}{10} x[/tex] ⇒ [tex]-1=-\frac{1}{10} x[/tex]
Next, multiply both sides by 10:
[tex]-10=-x[/tex]
FInally, divide both sides by -1:
x = 10
Answer:
Step-by-step explanation:
1/5(x-2) =1/10(x+6)
1/5x-2 = 1/10x+0.6
1/5x+1/10x= 0.6-2
0.2x+0.1x= -1.4
0.3x= -1.4
x= -4.67
x= -4.7
x= -5
(9)
2 in
5 in
Perimeter:
Area:
Step-by-step explanation:
The area = 2 × 5 = 10
The perimeter = 2(2 + 5) = 14
please give me a brainliest answer
Given the function h(x) = x2 – 7x + 6, determine the average rate of change of
the function over the interval 3 x < 7.
Step-by-step explanation:
the average rate of change between two input values is the total change of the function values (output values) divided by the change in the input values.
so,
(h(7) - (h(3)) / (7 - 3)
h(7) = 7² - 7×7 + 6 = 49 - 49 + 6 = 6
h(3) = 3² - 7×3 + 6 = 9 - 21 + 6 = -6
7 - 3 = 4
(6 - -6)/4 = 12/4 = 3
the average change rate in that interval is 3 (or fully 3/1).
Which equation models the area of the geometric figure, below. Select all that apply:
Answer:
20x+50......
and 10(2x+5)
please solve this question...
Answer:
Refer to the attachment
Find m Give explanation please
Answer: The measurement of ∠EFG is equal to 70°.
Step-by-step explanation:
Two interior angles who are always opposite to an exterior angle sums to that exterior angle. So we would start as the following:
(6x - 10) + 38 = 7x + 18
In order to find m∠EFG, we must first isolate x. In order to do that, we first add like terms together on both sides.
(6x - 10) + 38 = 7x + 18
6x + 28 = 7x + 18
We then substract 18 on both sides.
6x + 10 = 7x
We finally substract 6x from both sides in order to have the value of x.
x = 10
Now that we know the value of x, we substitute it in our the equation in order to find m∠EFG.
m∠EFG = 6x + 10
m∠EFG = 6(10) + 10
m∠EFG = 60 + 10
m∠EFG = 70
Answer:
50°
Step-by-step explanation:
( 7x + 18 )° = ( 6x - 10 )° + 38°
7x + 18 = 6x - 10 + 38
7x - 6x = 28 - 18
x = 10
m∠EFG = 6(10) - 10
m∠EFG = 50°
Jolene is creating a model of a pyramid. The model created will need to be scaled up from the blueprint. triangle ACB, point D is on segment AC between points A and C, point E is on segment BC between points B and C If segments DE and AB are parallel, which of the following expressions will help Jolene determine the length of segment AC? AC equals CB times CD all over CE AC = AB AC equals CB times AC all over CE AC = BC
Answer:
AC equals CB times CD all over CE
The lengths of the sides of the scaled drawing can be determined from the
relation between similar triangles.
The expression that will help Jolene determine the length segment AC is the option;
[tex]\displaystyle \underline{CD= \frac{CB\cdot CD}{CE}}[/tex]Reasons:
The given parameters are;
The figure Jolene is trying to create = A scaled up blue print
Given that in ΔACB and ΔABC, we have;
DE and AB are parallel
Therefore;
∠CED ≅ ∠CBA by corresponding angles
∠CDE ≅ ∠CAB by corresponding angles
∠C ≅ ∠C by reflexive properties
ΔCDE ~ ΔACB by Angle-Angle similarity postulate
Therefore, by similar triangles, and triangle proportionality, we have;
[tex]\displaystyle \frac{AC}{CD} = \mathbf{\frac{CB}{CE}}[/tex]
Therefore;
[tex]\displaystyle CD= \mathbf{ \frac{CB\cdot CD}{CE}}[/tex]
Therefore, if segments DE and AB are parallel, the expression that will help Jolene determine the length segment AC is; [tex]\displaystyle CD= \frac{CB\cdot CD}{CE}[/tex]
Learn more about similar triangles here:
https://brainly.com/question/14445094
Order each set of numbers from least to greatest.
1: -4,-7, 3, 16,-18
2: -12, 20, 24, -39, -24
3: 9,-57,-64, -32, 0
4: -3,-13, -24,-1,-8
Answer:
1. -18,-7,-4,3,16
2. -39,-24,-12,20,24
3. -64,-57,-32,0,9
4. -24,-14,-8,-3,-1
Step-by-step explanation:
Negative numbers are always least.
Please help me solve this!! I will give brainliest and this is due in 10 minutes
There's a big soccer game next month, and Juan has purchased 3 tickets for himself and his siblings. He spent 53 dollars.
Rosie wants to take her family also, but knows her parents and some cousins will want to attend as well. She knows she will have to purchase 9 tickets. Estimate approximately how much money Rosie will likely have to spend on the tickets. Explain your reasoning below.
Answer:
53 divided by 3 would be $17.66
so 17.66 times 9 would be $158.94
Answer:
158.4 dollars
Step-by-step explanation:
so first of all the three tickets were 53 dollars so we divide the dollars and the no of tickets like this 53÷3 = 17.6 dollars
so since each ticket is 17.6 dollars now we know that Rosie wants to purchase 9 tickets so we will multiply the no of tickets by dollars per ticket like this
9×17.6= 158.4 dollars
and 158.4 is your answer
PLEASE HELPPPPPPPPPPPP!
Answer:
10
Step-by-step explanation:
[tex]2^{2} +10^{2} =c^{2}[/tex]
4+100=[tex]c^{2}[/tex]
c=[tex]\sqrt{104}[/tex]
c=10.198
Round to nearest thousandth
c=10
Hope this helps :)
Comment if you need more help :) :)
Solve the math problem
Answer:iqual like 12
Step-by-step explanation:xD i think :/
Please do help.Thanks :)
Jasmine surveyed the people at a local playground. She found that 33 out of 55 people brought water bottles. On Wednesday, Jasmine returns to the park and finds that 1212 people brought water bottles. About how many people do you expect were at the park on Wednesday? Enter the number of people at the park on Wednesday.
Answer:
2,020 people were at the park.
Step-by-step explanation:
33/55 = 1212/x
(1212 * 55)/33 = 2,020
What is the slope of this line?
Answer:
Slope = 2
Step-by-step explanation:
(x₁ , y₁) = ( 1 , 1) & (x₂,y₂) = (-1,-3)
[tex]Slope=\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\=\dfrac{-3-1}{-1-1}\\\\=\dfrac{-4}{-2}\\\\=2[/tex]
Find the EQUATION of the line through (-10,-12) and (-15,3). Use the form y=mx+b.
t (x) = 5x^2- 3x+4, what is the value t (-3)?
Work out the value of 3.14
157/5....................
Solve the inequality- 5/2(3x+4)<6-3x. Show your work.
Answer:
x < -8/21
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
[tex](\frac{5}{2} * 3x) + (\frac{5}{2} * 4) < -3x + 6[/tex] [tex]\frac{15}{2}x + 10 < -3x + 6[/tex]Step 2: Add 3x to both sides.
[tex]\frac{15}{2}x + 10 + 3x < -3x + 6 + 3x[/tex] [tex]\frac{21}{2}x + 10 < 6[/tex]Step 3: Subtract 10 from both sides.
[tex]\frac{21}{2}x + 10 - 10 < 6 - 10[/tex] [tex]\frac{21}{2}x < -4[/tex]Step 4: Multiply both sides by 2/21.
[tex]\frac{21}{2}x * \frac{2}{21} < -4 * \frac{2}{21}[/tex] [tex]x < -\frac{8}{21}[/tex]Therefore, the answer is x < -8/21.
