High School Math 2011 Algebra 1 Student Companion Grade 8/9
11th Edition
ISBN: 9780133688924
Author: Prentice Hall
Publisher: PEARSON
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Question
Chapter 5.1, Problem 1MP
a.
To determine
To solve: the rate of change in the water height so the number of marbles.
a.
Expert Solution
Answer to Problem 1MP
Rate of change is 0.3 cm in water level per marble addition
Explanation of Solution
Given Information
A table has been given, representing number of marbles & its corresponding height of rise in water level.
We have to find out the respective rate of change in the water height so the number of marbles, water level rises for each marble and also type of relation in terms of function between number of marbles and water height.
Calculation
We can clearly observe that, when there were 3 marbles, water level was at 6.9 cm.
On subsequent addition of 2 more marbles, water level rose by 0.6 cm and so on.
Conclusion
We notice that, it is a case of linear relation function and a discrete rise in level is observed on subsequent addition of marbles.
b.
To determine
To solve: the water level rise for each marble
b.
Expert Solution
Answer to Problem 1MP
0.3 cm.
Explanation of Solution
Given Information
A table has been given, representing number of marbles & its corresponding height of rise in water level.
We have to find out the respective rate of change in the water height so the number of marbles, water level rises for each marble and also type of relation in terms of function between number of marbles and water height.
Calculation From the table we clearly notice that,
(i)Addition of further 2 marbles, defined a change in height of 0.6 cm
(ii)Addition of further 4 marbles, a change of 1.2 cm is observed.
Similarly, for 5 marbles ( 1.5
for 3 marbles ( 0.9
for 6 marbles ( 1.8
So, in each case rise of water level per marble will be
Conclusion Therefore, for each subsequent marble, rise in water level is by 0.3 cm.
c.
To determine
To solve: the type of relation in terms of function between number of marbles and water height.
c.
Expert Solution
Answer to Problem 1MP
Linear relationship
Explanation of Solution
Given Information
A table has been given, representing number of marbles & its corresponding height of rise in water level.
We have to find out the respective rate of change in the water height so the number of marbles, water level rises for each marble and also type of relation in terms of function between number of marbles and water height.
Calculation
Establishing the relationship between number of marbles and water height
where,
y = 6 + 0. 3x
y = height of water (in cm)
x = number of marbles
So, for, x = 0; y = 6 cm which signifies that, initially with no marble, the height of water was 6 cm.
For, x = 3
y = 6 (0.3 × 3)
y = 6 + 0.9 = 6.9 cm
which matches the given table.
Conclusion
Hence, our relation, y = 6 + 0. 3x is verified, and it clearly shows a linear relationship.
Chapter 5 Solutions
High School Math 2011 Algebra 1 Student Companion Grade 8/9
Ch. 5.1 - Prob. 1PCh. 5.1 - Prob. 2PCh. 5.1 - Prob. 3PCh. 5.1 - Prob. 4PCh. 5.1 - Prob. 1LCCh. 5.1 - Prob. 2LCCh. 5.1 - Prob. 3LCCh. 5.1 - Prob. 4LCCh. 5.1 - Prob. 5LCCh. 5.1 - Prob. 6LC
Ch. 5.1 - Prob. 7LCCh. 5.1 - Prob. 8PPECh. 5.1 - Prob. 9PPECh. 5.1 - Prob. 10PPECh. 5.1 - Prob. 11PPECh. 5.1 - Prob. 12PPECh. 5.1 - Prob. 13PPECh. 5.1 - Prob. 14PPECh. 5.1 - Prob. 15PPECh. 5.1 - Prob. 16PPECh. 5.1 - Prob. 17PPECh. 5.1 - Prob. 18PPECh. 5.1 - Prob. 19PPECh. 5.1 - Prob. 20PPECh. 5.1 - Prob. 21PPECh. 5.1 - Prob. 22PPECh. 5.1 - Prob. 23PPECh. 5.1 - Prob. 24PPECh. 5.1 - Prob. 25PPECh. 5.1 - Prob. 26PPECh. 5.1 - Prob. 27PPECh. 5.1 - Prob. 28PPECh. 5.1 - Prob. 29PPECh. 5.1 - Prob. 30PPECh. 5.1 - Prob. 31PPECh. 5.1 - Prob. 32PPECh. 5.1 - Prob. 33PPECh. 5.1 - Prob. 34PPECh. 5.1 - Prob. 35PPECh. 5.1 - Prob. 36PPECh. 5.1 - Prob. 37PPECh. 5.1 - Prob. 38PPECh. 5.1 - Prob. 39PPECh. 5.1 - Prob. 40PPECh. 5.1 - Prob. 41PPECh. 5.1 - Prob. 42PPECh. 5.1 - Prob. 43PPECh. 5.1 - Prob. 44PPECh. 5.1 - Prob. 45PPECh. 5.1 - Prob. 46PPECh. 5.1 - Prob. 47PPECh. 5.1 - Prob. 48PPECh. 5.1 - Prob. 49PPECh. 5.1 - Prob. 50PPECh. 5.1 - Prob. 51PPECh. 5.1 - Prob. 52PPECh. 5.1 - Prob. 53PPECh. 5.1 - Prob. 54PPECh. 5.1 - 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- 5. Consider the following vectors 0.1 3.2 -0-0-0 = 5.4 6.0 = z= 3 0.1 For each of exercises a-e, either compute the desired quantity by hand with work shown or explain why the desired quantity is not defined. (a) 10x (b) 10-27 (c) J+Z (d) (x, y) (e) (x, z)arrow_forwardConsider the graph/network plotted below. 1 6 5 3 Explicitly give (i.e., write down all of the entries) the adjacency matrix A of the graph.arrow_forward. Given the function f: XY (with X and Y as above) defined as f(2) = 2, f(4) = 1, ƒ(6)=3, ƒ(8) = 2, answer the following questions. Justify your answers. (a) [4 points] Is f injective? (b) [4 points] Is f surjective? (c) [2 points] Is f bijective?arrow_forward
- 1. Let 15 -14 A = -10 9 13-12 -8 7 11 15 -14 13 -12 -6 and B = -10 9 -8 7 -6 5 -4 3 -2 E 5 -4 3 -2 1 Explicitly give the values of A2,3, A1,5, and B1,4- Is A a 5 x 3 matrix? Explain your answer. Are A and B (mathematically) equal? Explain your answer.arrow_forwardGiven the following set X = {2, 4, 6, 8} and Y = {1, 2, 3}, explicitly give (e.g., write down the sets with numerical entries) of the outputs of the following requested set operations: (a) [2 points] XUY (Union) (b) [2 points] XY (Intersection) (c) [3 points] X\Y (Difference) (d) [3 points] XAY (Symmetric Difference)arrow_forwardFor what values of k will the equation (k + 1)x² + 6kx + 2k² - x = 0 have: a) one root equal zero b) one root the reciprocal of the other c) roots numerically equal but of opposite signarrow_forward
- 1) Find The inverse The domain of m(x) = tion and of the function The inverse function 3- √x-aarrow_forwardGraph the following function. Please also graph the asymptote. Thank you.arrow_forwardFile Edit View History Bookmarks Profiles Tab Window Window Help Things Quadratics! Part 1 X SM◄))) 61% Fri 25 student.desmos.com/activitybuilder/instance/67b739e7356cae7898fd0dbd/student/67b8f115811d42186c239e23#screenid=41a95 ngs Quadratics! Part 1: Parabolas Mitchell 30 30 foo feet 20- 20 10 0 -10 FEB 21 3 10 10 80 FS F3 X Intercepts #2 20 20 Approximately how tall is the shooter? > Which intercept did you use to solve the above problem? x-intercept y-intercept 30 feet Explain your thinking. 1 √E Submit 00000 acBook stv 399 ? DOD 000 F4 % 5 W E R F5 A F6 F7 F9 & * 7 8 9 0 Y U C 014arrow_forward
- The table below shows the acreage, number of visitors, and total revenue of state parks and recreational areas in Massachusetts, New York, and Vermont in 2010. State Acreage (in thousands) Visitors (in thousands) Revenue (in thousands) Massachusetts 350 35,271 $12,644 New York 1,354 56,322 $85,558 Vermont 69 758 $10,969 Select the three true statements based on the data in the table. A. Vermont had the highest revenue per acre of state parks and recreational areas. B. Vermont had approximately 11 visitors per acre of state parks and recreational areas. C. New York had the highest number of visitors per acre of state parks and recreational areas. D. Massachusetts had approximately 36 visitors per acre of state parks and recreational areas. E. New York had revenue of approximately $63.19 per acre of state parks and recreational areas. F. Massachusetts had revenue of approximately $0.03 per acre of state parks and recreational areas.arrow_forwarda) show that the empty set and sigletonset are convex set. 6) show that every sub space of linear space X is convex but the convers heed not be true. c) let Mand N be two convex set of a linear Space X and KEF Show that MUN is conevex and (ii) M-N is convex or hot A and is MSN or NSM show that MUN convex or not, 385arrow_forwardI write with prove one-to-one linear Sanction but not onto Lexample.) b) write with Prove on to linear function but not oh-to-on (example). c) write with prove example x=y St Xandy two linear space over Sielad F.arrow_forward
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