Determine the point of intersection of right bisectors in a triangle ∆ABC with vertices A (-3, 5), B (1, 1) and C (−7, −3). Find the distance from the point of intersection to each vertex of the triangle.
Answers
9514 1404 393
Answer:
intersection: (-3 2/3, 1/3)distances to vertices: (10/3)√2Step-by-step explanation:
A) In order to write the equations of the perpendicular bisectors of the segments, we need to know the midpoint and the slope.
The midpoint is the average of the coordinates:
midpoint(A, B) = ((-3, 5) +(1, 1))/2 = (-3+1, 5+1)/2 = (-1, 3)
midpoint(A, C) = ((-3, 5) +(-7, -3))/2 = (-3-7, 5-3)/2 = (-5, 1)
The differences between the coordinates of the points can be helpful:
B-A = (1, 1) -(-3, 5) = (1+3, 1-5) = (4, -4) . . . . . reduces to (∆x, ∆y) = (1, -1)
C-A = (-7, -3) -(-3, 5) = (-7+3, -3-5) = (-4, -8) . . . . . reduces to (∆x, ∆y) = (1, 2)
_____
A line through point (h, k) perpendicular to one with (∆x, ∆y) can be written:
(∆x)(x -h) +(∆y)(y -k) = 0
Then the bisectors of AB and AC will be ...
(x +1) -(y -3) = 0
(x +5) +2(y -1) = 0
Their intersection point can be found by solving this system.
(x +2y +3) -(x - y + 4) = (0) -(0) . . . . . subtract the 1st equation from the 2nd
3y -1 = 0
y = 1/3
x = y -4 = -3 2/3
The point of intersection of the right bisectors is (x, y) = (-3 2/3, 1/3).
__
B) The intersection point is the circumcenter. It will be the same distance from any of the vertices.
That distance can be found using any of the vertices. Using point B, we find the distance to be ...
d = √((-3 2/3 -1)^2 +(1/3 -1)^2) = √((14/3)^2 +(2/3)^2) = √(200/9)
d = (10/3)√2
The distance to each vertex is (10/3)√2 ≈ 4.71.
Related Questions
What is the equation for this line ?
Answers
Answer:
[tex]y = -\frac{1}{3}x + 5[/tex]
Step-by-step explanation:
y = mx + b
Let's start with where the line crosses the y axis. We can see it crosses at 5.
So b = 5.
Let's try another point to figure out m, (3,4).
4 = 3m + 5
3m = -1
m = [tex]-\frac{1}{3}[/tex]
Answer:
y=-1/3+5
Step-by-step explanation:
since the line is going downhill, the slope would be negative (the slope is the number with the x attached). The slope is 3 over and 1 down. You would write it as rise over run, so it would be a -1/3. The line hits the y axis at 5, so the b (y=mx+b is the slope equation) would be 5.
Please solve, need help quick
Answers
Answer:
In my thought it's angle L
Step-by-step explanation:
Hope it's will help you.
Answer:
it's angle l ..................
Jill aunt got her a $50 gift card to her favorite boutique she has already picked out 4 shirts that cost $8.00 each how many pairs of shorts can she buy if shorts cost $10 a pair?
Answers
Answer:
1
Step-by-step explanation:
If she has four $8 shirts, that costs $32, leaving her with $18 dollars, only enough for 1 pair of $10 shorts
Q
H.
The two-column proof below describes the statements and reasons for proving that corresponding angles are congruent:
Step
Statements
Reasons
1
UV || WZ
Given
2
Points S. Q, R, and T all lie on the same line.
Given
3
mZSQT = 180°
Definition of a Straight Angle
Angle Addition Postulate
4
m2SQV + m2VQT = m_SQT
5
Substitution Property of Equality
6
m2VQT + mZZRS = 180°
Same-Side Interior Angles Theorem
Substitution Property of Equality
7
m2SQV+mZVQT = m2VQT + mZZRS
Answers
Answer:
i can't understnd it at all i mean you organized it but what does those mean??
Step-by-step explanation:
Rewrite the function by completing the square
f(x)=x^2-14x+63
Answers
Answer:
f(x) = (x - 7)² - 14
General Formulas and Concepts:
Pre-Algebra
Equality PropertiesAlgebra I
Standard Form: ax² + bx + c = 0Vertex Form: f(x) = a(bx - c)² + dCompleting the Square: (b/2)²Step-by-step explanation:
Step 1: Define
f(x) = x² - 14x + 63
Step 2: Rewrite
Separate: f(x) = (x² - 14x) + 63Complete the Square: f(x) = (x² - 14x + 49) + 63 - 49Simplify: f(x) = (x - 7)² - 14Answer:
-7 and 14 on khan
The table shows the approximate population of Virginia for 5 years. If the trend continues, which could
be a reasonable prediction if the population in 2012?
Answers
Answer:
It is C
Step-by-step explanation:
A scoop of ice cream has a 3-inch diameter. How tall should the ice cream cone of the same diameter be in order to contain all of the ice cream inside the cone?
Answers
Answer:
12 inches
Step-by-step explanation:
Suppose the ice cream scoop has the shape of a sphere of a radius (r) inches.
Thus, the top of the cone will also have a radius (r) inches.
Let consider h to be the height of the cone in inches.
So, the objective is to make the volume of the scoop of the ice cream to be the same as the volume of the cone.
To do that; we need to equate both volumes together and make h the subject of the formula:
The volume of a sphere = 4/3 πr³ and the volume of a cone = 1/3πr²h
4/3 πr³ = 1/3πr²h
Multiply both sides by 3
4πr³ = πr²h
4r = h
h = 4(3)
h = 12 inches
To contain all the ice cream inside the cone, the height of the ice cream cone needs to be 12 inches tall
i need helpppp again
Answers
Answer:
2/7b + 10
Step-by-step explanation:
Use a single digit times a power of 10 to estimate the number 0.00002149
please help :(
Answers
Answer:
2.149 × 10-5
Step-by-step explanation:
The parabola with equation $y=ax^2+bx+c$ is graphed below:
(attached)
The zeros of the quadratic $ax^2 + bx + c$ are at $x=m$ and $x=n$, where $m>n$. What is $m-n$?
Answers
Answer:
[tex]m-n=2[/tex]
Step-by-step explanation:
Instead of using the standard form, we can use the vertex form of a quadratic equation:
[tex]f(x)=a(x-h)^2+k[/tex]
Where a is the leading coefficient, and (h, k) is our vertex.
Our vertex point is at (2, -4). So, let’s substitute 2 for h and -4 for k:
[tex]f(x)=a(x-2)^2-4[/tex]
Now, we need to determine a.
We know that it passes through the point (4, 12). So, when x is 4, y must be 12. In other words:
[tex]12=a((4)-2)^2-4[/tex]
Solve for a. Subtract within the parentheses:
[tex]12=a(2)^2-4[/tex]
Add 4 to both sides:
[tex]16=a(2)^2[/tex]
Square:
[tex]16=4a[/tex]
Solve:
[tex]a=4[/tex]
Thererfore, the value of a is 4.
So, our function is:
[tex]f(x)=4(x-2)^2-4[/tex]
Now, let’s find our roots. Set the equation to 0 and solve for x:
[tex]0=4(x-2)^2-4[/tex]
[tex]4=4(x-2)^2\\1=(x-2)^2\\x-2=\pm1 \\ x=2\pm1 \\ x=3\text{ or } 1[/tex]
So, our roots are 1 and 3.
The greater root is 3 and the lesser root is 1.
Therefore, m-n, where m>n, is 3-1 or 2.
Our final answer is 2.
Answer:
2
Step-by-step explanation:
Source: AOPS
You and your friend went shopping. You bought 2 hats and 3 pairs of gloves for $28.25. Your friend bought 1 hat and 1 pair of gloves for $12.25. How much did one hat cost? How much did one pair of gloves cost? (Answers should reflect the real world scenario by including appropriate units.)
Answers
Answer:
One pair of gloves costs $3.75.
Step-by-step explanation:
Systems of equations
x=hats y=gloves
2x+3y=28.25
x+y=12.25
2(12.25-y)+3y=28.25
24.5+y=28.25
y=3.75
Find the value of x. *
Please help
Answers
Answer:
x = 78
Step-by-step explanation:
(x-8) + 20 = 90
x - 8 = 90 - 20
x - 8 = 70
x = 70 + 8
x = 78
Check:
(78-8) + 20 = 90
70 + 20 = 90
But all this-the mysterious, far-reaching hair-line trail, the absence of sun from the sky, the tremendous cold, and the strangeness and weirdness of it all-made no impression on the man.
What can you infer about the man from the excerpt above?
Answers
Answer:huh
Step-by-step explanation:
Explanation
If the man is completely unaffected by the bad weather that means he is very focused or serious about something.
Find the exact length of the third side.
10
6
PLEASE HELP GUH
Answers
Answer:
8
Step-by-step explanation:
I'm using this equation: a^2+b^2=c^2
x^2+6^2=10^2
x^2+36+100
x^2= 64
x=sqrt64
x=8
Find the component form of the vector that represents the velocity of an airplane at the instant its wheels leave the ground, if the plane is going 75 miles per hour and the body of the plane makes an9° angle with the horizontal.
Answers
Answer:
The component form of the vector that represents the velocity of the airplane is [tex](74.1 i , \ 11.73j)\ mph[/tex]
Step-by-step explanation:
Given;
velocity of the airplane, v = 75 mph
direction of the plane, θ = 9°
The vertical component of the velocity is given by;
[tex]V_y = vsin\theta\\\\V_y = (75)(sin \ 9^0)\\\\V_y = 11.73 \ mph[/tex]
The horizontal component of the velocity is given by;
[tex]V_x = vcos \theta\\\\V_x = (75)(cos9^0)\\\\V_x = 74.1 \ mph[/tex]
Therefore, the component form of the vector that represents the velocity of the airplane is given as;
[tex](V_x , \ V_y) = (74.1 , \ 11.73)\ mph[/tex]
Find the rate of change of y with respect to the x of the line that passes through points (-28,8) and (-42,15)
Answers
Answer:
-1/2
Step-by-step explanation:
8-15 = -7
-28 - -42 = 14
-7/14 = -1/2
Help me pleade help me
Answers
For a relation to be a function every x-value must be associated with one y-value. C has the x-value of 1 have two separate y-values. The others do not have an x-value that repeats.
Kevin is opening up a bookstore, where he sells both new and old books. He charges $10.75 for a new book, and $3.50 for an old book. What was Kevin's revenue last month if he sold 18 new books and 21 old books?
Answers
The revenue last month Kevin, if he sold 18 new books and 21 old books, will be $ 267.
What is the linear system?A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
Kevin is opening up a bookstore, where he sells both new and old books.
He charges $10.75 for a new book and $3.50 for an old book.
Then the revenue last month Kevin, if he sold 18 new books and 21 old books, will be
Then the total revenue will be
Total revenue = 10.75 x 18 + 3.50 x 21
Total revenue = 193.5 + 73.5
Total revenue = $ 267
More about the linear system link is given below.
https://brainly.com/question/20379472
#SPJ1
The graph of a function f is shown below.
Find f(-2).
Answers
Answer:
-4
Step-by-step explanation:
The value of the function evaluated at [tex]x = -2[/tex] is -4.
The horizontal axis represents the set of the domain of the function, whereas the vertical axis is for the set of the range of the function. In this exercise, we need to need to find the value on the vertical axis that corresponds with a given value of the horizontal axis ([tex]x = -2[/tex]).
By direct inspection, we conclude that [tex]f(-2) = -4[/tex].
We kindly invite you to see this problem related to functions: https://brainly.com/question/12431044
What is the domain of the following function? Show work
f(x)=(2x-1)/((2x^2)-9x+10)
Answers
Step-by-step explanation:
f ( X) = ( 2X - I ) / 2X ^ 2 - 9X + 10
= 2X-1 ) /( 2X- 5 ) ( x - 2 )
set of zeros of denominator are :
2X- 5 . = 0
X= 5/2
or
X-2=0
X=2
set of zeros of denominator = { 5/2 ,2 }
domain = R - { 5/2,2 }
Explain why the exponents cannot be added in the product 12^3 x 11^3?? I need a simple answer that won’t be confusing pls.
Answers
Answer:
The bases aren't the same
Step-by-step explanation:
If the bases are the same, then their exponents are added. In this case, since the exponents are the same, then 12^3*11^3=(12*11)^3=132^3=2299968
Is the equation, y= 12x proportional or non-proportional? Explain why or why not. *
Answers
Answer:
proportional
Step-by-step explanation:
because it has a constant ratio
Answer: Proportional
Step-by-step explanation:
The equation for a proportional relationship is y=kx. This equation: y=12x fits the equation, so it's proportional.
y+c=14........ solve for y
Answers
Answer:
7+7=14
Step-by-step explanation:
there is no times in it it's just addition so there for you just need to find what adds up to 14
Answer:
y=14-c
this question is weird
I will give Brainlyest to the person who is first
After the temperature rose 9', the thermometer read 37°F
What is an equation that can be used to find x, the temperature before the gº increase
Drag the number, symbol, or operation sign to each box to complete the equation or symbol to
Answers
Answer:
37-9=28
Step-by-step explanation:
it was 28 F then rose 9 which is 37 so 37-9 =28
The equation is 37 - 9= x.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
After the temperature rose 9°F, the thermometer read 37°F.
let x be the temperature before the 9º increase.
So, 37 - 9= x
x= 28°F.
Hence, the equation is 37 - 9= x.
Learn more about equation here:
https://brainly.com/question/10413253
#SPJ5
Write an equation for the following data plz :)
Answers
Answer:
y = 4x + 1
Y values increase by 4, X values increase by 1.
M or slope, = 4/1 or 4
Y-intercept is when x = 0
When x = 0 in this case, y = 1.
So,
y = 4x +1
Answer:
y = 4x + 1
Step-by-step explanation:
This is the y = mx + b format, hopefully its useful for you! It's a linear equation because all the values grow at a constant rate.
The y-intercept is 1 and it's rise over run which means that you start at 1 on your y-intercept when graphing and then rise 4 and run 1 to the right because it's a positive slope.
Help please for math
Answers
Answer:
1 5/8 feet/year
Step-by-step explanation:
Height tree grew in 10 years
= 36 3/4-20 1/2
= 16 1/4 feet
Rate tree grew in a year
= 16 1/4÷10
= 1 5/8 feet/year
It’s what they said and I needed some extra points, if this didn’t satisfy you here is a pic of my kitty cat!
The ratio of the angle measure of the acute angle in a right triangle is 1:3
Answers
Answer:
2:6 because 2:6 is equivalent to 1:3
Step-by-step explanation:
1x1=1 and 3x2=6
He width of a rectangular postcard is 4 inches and the diagonal is 7.6 inches long. What is the length of the postcard? Round your answer to the nearest hundredth.
Answers
Answer:
Adjacent = x = length = 6.46 inches
Step-by-step explanation:
Given the width and diagonal of a rectangular postcard,
Find the length using Pythagoras theorem
Hypotenuse ² = opposite ² + adjacent ²
Hypotenuse = 7.6 inches
Opposite = 4 inches
Adjacent = x
Hypotenuse ² = opposite ² + adjacent ²
7.6² = 4² + x²
57.76 = 16 + x²
subtract 16 from both sides
57.76 - 16 = x²
41.76 = x²
Find the square root of both sides
x = √ 41.76
= 6.46
x = 6.46 inches
Adjacent = x = length = 6.46 inches
#30 PLEASE HELP!! DUE SOON :(
Answers
Answer:
Step-by-step explanation:
Use this to help; starting out, this is coordinate plain, NOT TO SCALE.
Use the coordinates to figure out midpoints. If you don't know how to, look up the calculation method for it.
Sorry I couldn't help out more, gotta get back to essay.
A cheesecake recipe says to mix 12 oz of cream cheese with 15 oz of sugar. How many ounces of cream cheese will be needed for 45 oz of sugar?
Answers
Answer:
1.5
Step-by-step explanation:
it is one and one half, in other words.
Answer:
36 oz of cream cheese
sugar: 45 divided by 15 equals 3
12 times 3 equals 36