Given the diagram below, if $ P $ is the circumcenter of $\triangle ABC$, $ AD = 8x + 3 $, $ DB = 17x - 15 $, and $ DP = 12 $, find $ PB $. Round answers to the nearest tenth when needed.**Diagram Explanation:**The diagram shows a triangle $ \triangle ABC $ with point $ P $ as its circumcenter. The lines $ AD $, $ DB $, and $ DP $ are indicated as segments within the triangle. The circumcenter $ P $ is equidistant from the vertices of the triangle, making $ PA = PB = PC $. The task is to find the length of $ PB $ given the algebraic expressions for $ AD $ and $ DB $ and the specific length of $ DP $.**Solution Steps:**1. Set $ AD = DB $ because both distances add up to the same line $ AB $.2. Solve for $ x $ using the equations: \[ 8x + 3 = 17x - 15 \]3. Simplify the equation: \[ 8x + 3 = 17x - 15 \implies 18 = 9x \implies x = 2 \]4. Substitute $ x = 2 $ back to find $ AD $: \[ AD = 8(2) + 3 = 19 \]5. Verify $ DB $ with $ x = 2 $: \[ DB = 17(2) - 15 = 19 \]6. Calculate $ PB $: - Since $ P $ is the circumcenter, and given $ DP = 12 $, $ PB = PD = 12 $.So, $ PB = 12 $.

Answered: Image /qna-images/answer/839a5944-51ab-414c-a6d0-9d76d2612a21.jpg

Answered: Given the diagram below, if P is the…

Given the diagram below, if P is the circumcenter of AABC, AD=8x+3, DB=17x- 15, and DP=12, find PB. Round answers to the nearest tenth when needed.

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

See similar textbooks

Related questions

Q: Given P(A) = 0.36, P(A and B) = 0.32, P(A or B) = 0.50, what is P(B)? Answer in decimal form.…

A: From the provided information, P(A) = 0.36, P(A and B) = 0.32, P(A or B) = 0.50

Q: Find the length of the bolded arc. * 8 mm 232

A: As per Bartleby guidelines for more than one question asked only one is to be answered please upload…

Q: Toni’s table is 96 inches in diameter. If she covers her circular table with a table cloth that…

A: The table cloth will be obviously circular in shape. It's radius will be 6 inches more than the…

Q: Find the GCF of the following monomials 1. 10а?, 25а3;B 15а 2. 8b°c*; 24b?c'; 16b°c

A: I am going to solve the given problem by using some simple algebra to get the required result.

Q: The coefficient of determination is symbolized by a. r. b. r2. c. a. d. b.

A: Coefficient of determination: It is the predicted percentage, used to predict the dependent variable…

Q: The coolest circular rug exists and you just have to have it for your room. If the the diameter of…

Q: 62° K N

A: Given the query is to find the measure of angle N.

Q: What is t ? Round to the nearest hundredth decimal place.

A: Statistical hypothesis testing is an important method in inferential statistics. It is used to test…

Q: What is the least possible distance of a water closet in meters to the 7th water closet on the same…

A: A water closest may not be located closer than 15 inches from its center to any side wall ,…

Q: Find the value of 0 3√64.

Q: Given P(B) = 0.47, P(A and B) = 0.29, P(A or B) = 0.55, what is P(A)? Answer in decimal form.…

Q: Find the indicated value. If MP = 5x -34 and PN= 2x - 4, find MP. P.

Q: B. 102 95

A: Central angle = 2× inscribed angle.

Q: Complement of 63º = %3D

A: The complement of 63° is the angle that when added to 63°forms a right angle i.e 90° .

Q: Given w = -175i - 60j, what are the magnitude and direction of -4w? Round the answers to the nearest…

Q: 3 x°dx 4 О 3043 О 260 О 6043 О 1040 О 4

A: Use power rule of integration.

Q: 3. 18

Q: Given P(A) = 0.27, P(A and B) = 0.33, P(A or B) = 0.41, what is P(B)? Answer in decimal form.…

A: Formula : P(A or B) = P(A) + P(B) - P(A and B)

Q: 10. In the following diagram find the distance across the river AB if mZA = 80.3 °, %3D mZB = 18.6 o…

A: Sum of all the angles of a triangle is 180 degrees.

Q: Given P(A) = 0.42, P(B) = 0.21, and P(B|A) = 0.27, what is P(A and B)?

A: Given that Given P(A) = 0.42, P(B) = 0.21, and P(B|A) = 0.27, Then P(A and B)

Q: The largest area of the rectangle in the figure below is P, 7

Q: In the diagram below of rectangle AFEB and a semicircle with diameter CD, AB = 5 inches, AB = BC =…

Q: 37° 2x+10 789 99° 98°

A: The sum of the exterior angles of a polygon is 360°.

Q: A helicopter is flying in the air, in-between an aircraft carrier and a navy destroyer, as seen in…

Q: Given P(A) = 0.40, P(B) = 0.25, and P(A and B) = 0.11, what is P(A or B)? Answer in decimal form.…

Concept explainers

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.

Question

Given the diagram below, if $ P $ is the circumcenter of $\triangle ABC$, $ AD = 8x + 3 $, $ DB = 17x - 15 $, and $ DP = 12 $, find $ PB $. Round answers to the nearest tenth when needed.

**Diagram Explanation:**

The diagram shows a triangle $ \triangle ABC $ with point $ P $ as its circumcenter. The lines $ AD $, $ DB $, and $ DP $ are indicated as segments within the triangle. The circumcenter $ P $ is equidistant from the vertices of the triangle, making $ PA = PB = PC $. The task is to find the length of $ PB $ given the algebraic expressions for $ AD $ and $ DB $ and the specific length of $ DP $.

**Solution Steps:**

1. Set $ AD = DB $ because both distances add up to the same line $ AB $.
2. Solve for $ x $ using the equations:
\[
8x + 3 = 17x - 15
\]
3. Simplify the equation:
\[
8x + 3 = 17x - 15 \implies 18 = 9x \implies x = 2
\]
4. Substitute $ x = 2 $ back to find $ AD $:
\[
AD = 8(2) + 3 = 19
\]
5. Verify $ DB $ with $ x = 2 $:
\[
DB = 17(2) - 15 = 19
\]
6. Calculate $ PB $:
- Since $ P $ is the circumcenter, and given $ DP = 12 $, $ PB = PD = 12 $.

So, $ PB = 12 $.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1 : Explanation

VIEW

Step 2 Answer

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Linear Equations$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, geometry and related others by exploring similar questions and additional content below.

Similar questions

If A=0.375 inch, B=0.875 inch, and C 1.062 inches, find D
Prepare a 2 × 2 table from the following information and calculate Yule's Coefficient of Association and interpret the result : N= 1500, (a) = 1117, (B) = 36o, (AB) = 35.
Given P(A) = 0.92, P(B) = 0.91, P(B|A) = 0.41, what is P(A and B)? Answer in decimal form. Round to 3 decimal places as needed.
Given A = <-3.6, -6.2, 6.2> and B = <6, -3.8, -1.8> Determine |A x B|. (Round your answers to 4 decimal places.)
B=56 degrees,C=38 degrees and a=8.9m find b and c
If a 30 degrees - 60 degrees - 90 degrees triangle's shorter leg measures 18 units, what is the approximate measure of the longer leg? ANSWER CHOICES ARE IN THE PHOTO. thanks.
Find the dimensions of the rectangular dog park producing the greatest enclosed area given 260 feet of fencing. The dimensions of each pen will be feet by feet Enter an integer or decimal number [more..]
Given P(B) = 0.38, P(A and B) = 0.26, P(A or B) = 0.45, what is P(A)? Answer in decimal form. Round to 2 decimal places as needed.