Name:
Chapter 5 Section 1
More Practice Finding the Coordinates of the point of Concurrency
1. The vertices of AABC are A(1,6), B(5,4), C(5,-2). Find the coordinates of the circumcenter.
a) Graph and label the triangle
b) Find the midpoint of each side of the triangle
Midpoint AB = 5, 1)
Midpointbc =
し32)
Midpointac = [1, 2]
c) Find the slope of each side of the triangle
MAB =
MBC =
MAC =
d) Find the slope of each perpendicular bisector
IMAB =
IMBc =
IMAC =
e) Use the midpoint and the perpendicular slope to accurately draw each perpendicu
bisector on the triangle.
Answers
Answer:
see the attachments for the graph, and a spreadsheet with midpoints and slopes
Step-by-step explanation:
We are given the coordinates of the vertices of a triangle, and asked to find the parameters of the perpendicular bisectors of the sides of the triangle. The perpendicular bisectors are to be plotted on the graph.
Given:Coordinates A(1, 6), B(5, 4), C(5, -2)
__
Find:a) Graph and label the triangle
b) Find the midpoint of each side of the triangle
c) Find the slope of each side of the triangle
d) Find the slope of each perpendicular bisector
e) Use the midpoint and the perpendicular slope to accurately draw each perpendicular bisector on the triangle
__
Solution:a)See the attached graph for shaded triangle ABC.
__
b)The midpoint (M) of a segment AB will be ...
M = (A+B)/2
For example, the midpoint of segment AB is ...
D = ((1, 6) +(5, 4))/2 = (1+5, 6+4)/2 = (6, 10)/2 = (3, 5)
This repetitive arithmetic is carried out in the spreadsheet shown in the second attachment. The midpoints are ...
D(3, 5) is midpoint of AB
E(5, 1) is midpoint of BC
F(3, 2) is midpoint of CA
__
c)The slope of a segment is found using the slope formula (or by counting grid squares). That formula is ...
m = (y2 -y1)/(x2 -x1)
For segment AB, this is ...
mAB = (4 -6)/(5 -1) = -2/4 = -1/2
The other slopes are calculated similarly in the spreadsheet. When the denominator is zero (a vertical line), the slope is "undefined."
mBC = undefined
mCA = -2
__
d)The slope of the perpendicular line is the opposite reciprocal of the slope of the segment.
m⟂AB = -1/(-1/2) = 2
m⟂BC = 0 . . . . . a horizontal line has 0 slope
m⟂CA = -1/-2 = 1/2
__
e)The perpendicular bisectors of each of the sides of the triangle are shown in the first attachment. As the lesson title indicates, their point of concurrency is G(1, 1), the circumcenter of the triangle.
Related Questions
Which of the following is an equation of a curve that intersects at right angles every curve of the family y=(1/x)+k (where k takes all real values)?a. y=-xb. y=-x^2c. y=(-1/3)x^3d. y= (1/3)x^3e. y=lnx
Answers
The equation of the curve that intersects at right angles to every curve of the family y=(1/x)+k is y=lnx
y=-x+k is the equation of a curve that meets at right angles every curve in the family y=(1/x)+k (where k can take any real value). This is known as the 'orthogonal curve' of the y=(1/x)+k family. It is calculated by obtaining the reciprocal of the original equation and then removing k from the y-axis.
A straight line with a negative slope is given by the equation y=-x+k. Every point on the line has an x-value that is the inverse of its y-value. At the point where x=1/k and y=k, the equation will always meet the curve of the family y=(1/x)+k at a right angle. This point is the same for all values of k and is known as the 'origin' of the function.
For more such questions on Equations, click on:
https://brainly.com/question/2254632
#SPJ4
fyyyyyyyyyyyyyyyyyyyyyyyy
Answers
Answer:
Standard Form:
80.92
Expanded Form:
80 + 0 + 0.9 + 0.02 = 80.92
Standard Form:
67.03
Expanded Form:
60 + 07 + 0.0 + 0.03 = 67.03
Hope its correct :)
Answer:
what they said
Step-by-step explanation:
M=-6and n=2, the value of the expression
Answers
Answer:
the value of expression is
given below
-6×2
=-12 Ans
What are the two main purposes of all businesses?
-developing communities
-earning revenue
-improving public image
-incurring costs
-maximizing profits
Answers
The two main purposes of all businesses are earning revenue and maximizing profits, the correct option is B and E.
We are given that;
The four options
Now,
Earning revenue means generating income from selling goods or services to customers. Revenue is the lifeblood of a business, as it covers the costs of production, operation, and growth. Without revenue, a business cannot survive or fulfill its other purposes.
Maximizing profits means increasing the difference between revenue and costs. Profits are the reward for creating value for customers and stakeholders. Profits can be reinvested in the business to improve quality, efficiency, innovation, and competitiveness. Profits can also be distributed to shareholders, employees, or society as dividends, wages, or donations.
Therefore, by unitary method the answer will be earning revenue and maximizing profits.
Learn more about the unitary method, please visit the link given below;
https://brainly.com/question/23423168
#SPJ1
ur smart if u can answer this ez question and extra points
Answers
please for a test
\( \sqrt{?} \)
![please for a test[tex] \sqrt{?} [/tex]](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/ZlMMD8v9GyrLQEKb67seJgorDKfnfN7O.jpeg)
Answers
Answer:
im going to your mother im your teacher
(6+2)-15divided5*2. How can I add all this up
Answers
Answer
2
Step-by-step explanation:
6+2=8 15/5*2=6 8-6=2
Please can someone who knows the right answer help me? From a group of 5 boys and 3 girls, a boy and a girl will be selected to attend a conference. In how many ways can the select be made?
Answers
The selection can be made in 15 different ways, taking into account the distinct combinations of a boy and a girl from the given group of 5 boys and 3 girls.
To determine the number of ways a boy and a girl can be selected from a group of 5 boys and 3 girls to attend a conference, we can use the concept of combinations.
The number of ways to choose one boy from 5 boys is 5C1, which is equal to 5. Similarly, the number of ways to choose one girl from 3 girls is 3C1, which is equal to 3.
To select one boy and one girl, we need to multiply the number of ways to choose a boy and a girl together. Using the multiplication principle, we multiply the number of choices for each category: 5C1 * 3C1 = 5 * 3 = 15.
Therefore, there are 15 ways to select a boy and a girl from the given group to attend the conference.
Each combination represents a unique pair consisting of one boy and one girl. For example, if the boys are labeled as B1, B2, B3, B4, and B5, and the girls are labeled as G1, G2, and G3, the possible pairs could be (B1, G1), (B1, G2), (B1, G3), (B2, G1), (B2, G2), and so on, up to (B5, G3).
For more such question on selection. visit :
https://brainly.com/question/251701
#SPJ8
Parallel lines r and s are cut by two transversals, parallel lines t and u. Lines r and s are crossed by lines t and u to form 16 angles. Clockwise from top left, at the intersection of r and t, the angles are 1, 2, 3, 4; at the intersection of s and t, 5, 6, 7, 8; at the intersection of u and s, 9, 10, 11, 12; at the intersection of u and r, 13, 14, 15, 16. Which angles are alternate interior angles with angle 3? Angle5 and Angle13 Angle7 and Angle15 Angle6 and Angle16 Angle8 and Angle14 Mark this an
Answers
Answer:
5 and 13
Step-by-step explanation:
I got it right on edge
Answer:
5 and 13, got in right in edge 2020
Step-by-step explanation:
7. Serena bought a scarf for $16.99 and was charged 7.5% tax on her purchase. Which of the
following was the amount of sales tax that Serena had to pay?
(1) $1.19
(3) $1.36
(2) $1.27
(4) $1.51
Answers
Answer:
$1.27
Step-by-step explanation:
We know
The tax is 7.5%
7.5% = 0.075
Which of the following was the sales tax Serena had to pay?
We take
16.99 times 0.075 = $1.27
So, the answer is $1.27
Find what percent 768 is of 3,200.
Answers
Answer:
3200 of 768 is 416.67%
Step-by-step explanation:
There's your answer hope this helps.
X% ————— 768
X= 24%
What is -2.93(b + 12) = -11.72
What is b
(Solve two-step linear equations)
Answers
Step 1: Divide both sides by -2.93
b+12=4
Step 2: Move constant and change symbol
b=4-12
Step 3: Calculate Equation
b=-8
6 3/8 - 1 5/8 =
What is the answere?
I'll give brainest if right
Answers
Solve each system by substitution. Tell whether the system has one solution ,infinitely many solutions,or no solution
Answers
22) In order to make use of the Substitution Method, we need to rewrite one of those equations
7x+2y=-13
-3x-8y=23
22.1) So let's rewrite the first equation:
\(\begin{gathered} 7x+2y=-13 \\ 7x=-13-2y \\ x=\frac{-13-2y}{7} \end{gathered}\)Now, we can plug this into the II equation.
\(\begin{gathered} -3(\frac{-13-2y}{7})-8y=-23 \\ \frac{39}{7}+\frac{6y}{7}-8y=-23 \\ \frac{6y}{7}-8y=-23-\frac{39}{7} \\ -\frac{50}{7}y=-\frac{200}{7} \\ 7\times-\frac{50}{7}y=-\frac{200}{7}\times7 \\ -50y=-200 \\ \frac{-50y}{-50}=\frac{-200}{-50} \\ y=4 \end{gathered}\)With this step, we could find the quantity of y. Let's plug into any equation, usually the simplest one (for convenience)
22.2)
\(\begin{gathered} 7x+2y=-13 \\ 7x+2(4)=-13 \\ 7x+8=-13 \\ 7x+8-8=-13-8 \\ 7x=-21 \\ \frac{7x}{7}=\frac{-21}{7} \\ x=-3 \end{gathered}\)And then the answer is x=-3, y=4
HELP? can anyone help? I’ll give Brainly the answer is not 3,240... thank you!
Answers
9514 1404 393
Answer:
$3144
Step-by-step explanation:
The tax due on $60,000 is ...
$60,000 × 5.4% - $96 = $3144 . . . tax due
_____
The detailed calculation is described at https://brainly.com/question/23711444. The only difference is the value used in the highest bracket, $60,000 instead of $50,000. This adds $540 to the tax that would be due for $50,000.
Question 9 of 60
Which symbol correctly compares the fractions below? 3/7 ? 4/14
O A. =
B. >
O C. <
OD. None of these are correct.
SUBMIT
Answers
Find all solutions of the equation 2\cos 3x =1 in the interval [0,\pi).
x1=
x2=
x3=
Answers
Answer:
x1= pi/9
x2=5pi/9
x3=7pi/9
Step-by-step explanation:
An isosceles triangle has angle measures (x^2+4) and (22x+12). Find all possible values for x rounded to the nearest hundreth.
Answers
Step-by-step explanation:
As Isosceles triangel has for sure 2 equal angles
and the sum of angles in any triangle is 180
so you have only thes 2 conditions either :
2(x^2+4)+22x+12=180 or 2(22x+12)+(x^2+4)=180
2x^2+8 +22x+12-180=0 or 44x+24+x^2 +4 - 180=0
2x^2+22x-160=0. or x^2+44x-152=0
x1=5 x2=-16. or x3=3.22 x4=-47.22
Churchill is selling tickets to a choral performance. They sell senior citizen
tickets and student tickets. On the day of the performance they sold 20
tickets. The school took in $125 by selling senior citizen tickets for $3 each and student tickets for $8 each. What is the number of senior citizen
tickets and student tickets that were sold?
Answers
Join QuestionCove!! We have helpers willing to help!!
help please
What is the measure of
∠
�
∠xstart color #11accd, angle, x, end color #11accd?
Angles are not necessarily drawn to scale.
∠
�
=
∠x=start color #11accd, angle, x, end color #11accd, equals
∘
∘
Answers
Answer:
∠ x = 58°
Step-by-step explanation:
the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
∠ BAD is an exterior angle of the triangle , then
x + 56° = 114° ( subtract 56° from both sides )
x = 58°
The box whisker plots below (sometimes called boxplots) summarize the noon temperatures for each city. Use the box-and-whisker plots to answer the questions.
(a) Which city had more noon temperatures above 76 °F?
(b) Which city had noon temperatures with a larger interquartile range (IQR)?
(c) Which city had a larger median noon temperature?
(d) Which city had the highest noon temperature?
Answers
From the box-and-whisker plot, we have that:
a) City B had more noon temperatures above 76ºF.
b) City A had the largest IQR.
c) City B had the larger median temperature.
d) City A had the highest noon temperature.
What is shown by the box-and-whisker plots?For City A, the measures are given as follows:
Minimum temperature: 65ºF.First quartile: 67 ºF.Median: 70 ºF.Third quartile: 75 ºF.Highest temperature: 85ºF.Hence the interquartile range of temperatures is of:
75 - 67 = 8ºF.
For City B, the measures are given as follows:
Minimum temperature: 59ºF.First quartile: 73 ºF.Median: 78 ºF.Third quartile: 80 ºF.Highest temperature: 82ºF.Hence the interquartile range of temperatures is of:
80 - 73 = 7ºF.
More can be learned about box-and-whisker plots at https://brainly.com/question/3473797
#SPJ1
can you find the slope
Answers
The slope of the points in this table is equal to -3.
How to calculate the slope based on the table?In Mathematics and Geometry, the slope of any straight line can be determined by using this mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Based on the information provided in the table, we can logically deduce the following data points on the line:
Points on x-axis = (0, 1).Points on y-axis = (7, 4).By substituting the given points into the slope formula, we have the following;
Slope, m = (4 - 7)/(1 - 0)
Slope, m = -3/1
Slope, m = -3.
Read more on slope here: brainly.com/question/3493733
#SPJ1
Use algebraic methods to find as many intersection points of the following curves as possible. Use graphical methods to identify the remaining intersection points. R = 6 sin theta and r = 6 cos theta the intersection point(s) is/are_______
(Type an ordered pair. Type exact answer for each coordinate, using phi as needed. Type the coordinate for theta in radians between 0 and phi. Use a comma to separate answers as needed)
Answers
The intersection points are (6, 6) and (-6, -6).
What is Intersection points?
The point at which two lines or curves intersect is referred to as the point of intersection. The point at which two curves intersect is crucial because it is the point at which the two curves take on the same value.
The given curves are the polar equations of two circles with radii 6. To find their intersection points, we can set the two equations equal to each other and solve for Ф.
6 sin(Ф) = 6 cos(Ф)
Dividing both sides by 6 and rearranging terms, we get:
tan(Ф) = 1
This equation has infinitely many solutions, but we are only interested in those that lie in the interval [0, π/2].
Ф = π/4 satisfies this condition and corresponds to the point (6, 6) in Cartesian coordinates.
Since the two curves are circles, they are symmetrical about the origin. Therefore, we can deduce that the other intersection point is (-6, -6).
Therefore, the intersection points are (6, 6) and (-6, -6).
To know more about Intersection points visit,
https://brainly.com/question/29248863
#SPJ4
pls help me so i can keep my kitten
Answers
Answer:
118
Step-by-step explanation:
15x - 2
Substitute the value given, in this case, it's x = 8.
15(8) - 2
Multiply 15 and 8.
120 - 2
Subtract 2 from 120.
118
When x=8
15x-2
=15*8-2
=120-2
=118
ANSWER: 118
Hope it helps u!
What is 1/9 as a decimal rounde to 2decimal places.
Answers
Answer:
3/11 = 0.27 is the answer of this question
Salinas Corporation has net income of $15 million per year on net sales of $90 million per year. It currently has no long-term debt but is considering a debt issue of $20 million. The interest rate on the debt would be 7%. Salinas Corp. currently faces an effective tax rate of 40%. What would be the annual interest tax shield to Salinas Corp. if it goes through with the debt issuance?
Answers
Answer:
The annual interest tax shield to Salinas Corp would be of $560,000
Step-by-step explanation:
In order to calculate the annual interest tax shield to Salinas Corp if it goes through with the debt issuance we would have to calculate the following formula:
Annual Interest tax shield = Interest * tax
Interest = debt *rate of interest
Interest=$20 million * 0.07
Interest= $ 1.40 million
tax= 40%
Therefore, Annual Interest tax shield =$1.40 million * 0.40
Annual Interest tax shield = $560,000
The annual interest tax shield to Salinas Corp would be of $560,000
The formula for the volume of a cone with a base of radius r is . Find the radius to the nearest hundredth centimeter if the volume is 60 cm^3. Branliest to first correct answer
Answers
Answer:
not ennough information to answer the question
Step-by-step explanation:
What is the greatest acceptable length for a package that has a square base measuring 12 in. by 12 in.
Answers
For the credit card account, assume one month between billing dates (with the appropriate number of days) and interest of 1.5% per month on the average daily balance. Find (a) the average daily balance,
(b) the monthly finance charge, and (c) the account balance for the next billing.
Previous Balance: $783.53
July 6
Billing Date
Payment
July 18
July 28 Lunch
August 5 Concert tickets
$300
$32.57
$85.87
(a) The average daily balance is $
(Round to the nearest cent as needed.)
(b) The finance charge is $
(Round to the nearest cent as needed.)
(c) The account balance for the next billing is $
(Round to the nearest cent as needed.)
Answers
Answer:
a) The average daily balance is $739.43.
b) The finance charge is $11.09.
c) The account balance for the next billing is $646.51.
Step-by-step explanation:
Jimmy's lunch box in the shape of a half cylinder on a rectangular box.
Find the total volume of metal needed to manufacture it
Answers
Answer:10cm 5cm 7 Jim's lunch box is in the shape of a half cylinder on a rectangular box. To the nearest whole unit, what is a The total volume it contains? b The total area of the sheet metal in 10 in needed to manufacture it? This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts
Step-by-step explanation: