Section 13.1 Answers - Mathematics

2. (y=-x+frac{2}{e-1}(e^{x}-e^{(x-1)}))

3. (y=x^{2}-frac{x^{3}}{3}+cx) with (c) arbitrary

4. (y=-x+2e^{x}+e^{-(x-1)})

5. (y=frac{1}{4}+frac{11}{4}cos 2x+frac{9}{4}sin 2x)

6. (y=(x^{2}+13-8x)e^{x})

7. (y=2e^{2x}+frac{3(5e^{3x}-4e^{4x})}{e^15-16e)}+frac{2e^{4}(4e^{3(x-1)}-3e^{4(x-1)})}{16e-15})

8. (int_{a}^{b}tF(t)dt=0quad y=-xint_{x}^{a}F(t)dt-int_{0}^{x}tF(t)dt+c_{1}x) with (c_{1}) arbitrary


  1. (b-a eq kpi ) ((k=) integer) (y=frac{sin (x-1)}{sin (b-a)}int_{x}^{b} F(t)sin (t-b)dt+frac{sin (x-b)}{sin (b-a)}int_{a}^{x} F(t)sin (t-a)dt)
  2. (int_{a}^{b}F(t)sin (t-a)dt=0quad y=-sin (x-a)int_{x}^{b} F(t)cos (t-a)dt-cos (x-a)int_{a}^{x}F(t)sin (t-a)dt+c_{1}sin (x-a) ext{ with } c_{1} ext{ arbitrary})


  1. (b-a eq (k+1/2)pi : (k= ext{ integer})quad y=-frac{sin (x-a)}{cos (b-a)}int_{x}^{b}F(t)cos (t-b)dt-frac{cos (x-b)}{cos (b-a)}int_{x}^{b}F(t)sin (t-a)dt)
  2. (int_{a}^{b}F(t)sin (t-a)dt=0quad y=-sin (x-a)int_{x}^{b}F(t)cos (t-a)dt-cos (x-a)int_{a}^{x}F(t)sin (t-a)dt+c_{1}sin (x-a) ext{ with }c_{1} ext{ arbitrary})


  1. (b-a eq kpi (k= ext{ integer})quad y=frac{cos (x-a)}{sin (b-a)}int_{x}^{b}F(t)cos (t-b)dt+frac{cos (x-b)}{sin (b-a)}int_{a}^{x}F(t)cos (t-a)dt)
  2. (int_{a}^{b}F(t)cos (t-a)dt =0quad y=cos (x-a)int_{x}^{b}F(t)sin (t-a)dt +sin (x-a)int_{a}^{x}F(t)cos (t-a)dt+c_{1}cos (x-a) ext{ with }c_{1} ext{ arbitrary})

12. (y=frac{sinh (x-a)}{sinh (b-a)}int_{x}^{b}F(t)sinh (t-b)dt+frac{sinh (x-b)}{sinh (b-a)}int_{a}^{x}F(t)sinh (t-a)dt)

13. (y=-frac{sinh (x-a)}{cosh (b-a)}int_{x}^{b}F(t)cosh (t-b)dt-frac{cosh (x-b)}{cosh (b-a)}int_{a}^{x}F(t)sinh (t-a)dt)

14. (y=-frac{cosh (x-a)}{sinh (b-a)}int_{x}^{b}F(t)cosh (t-b)dt-frac{cosh (x-b)}{sinh (b-a)}int_{a}^{x}F(t)cosh (t-a)dt)

15. (y=-frac{1}{2}left(e^{x}int_{x}^{b}e^{-t}F(t)dt+e^{-x}int_{a}^{x}e^{t}F(t)dt ight))

16. If (omega) isn't a positive integer, then (y=frac{1}{omegasinomegapi}left(sinomega xint_{x}^{pi}F(t)sinomega (t-pi )dt+sinomega (x-pi )int_{0}^{x}F(t)sinomega tdt ight).) If (omega =n) (positive integer), then (int_{0}^{pi }F(t)sin ntdt=0) is necessary for existence of a solution. In this case, (y=-frac{1}{n}left(sin nxint_{x}^{pi}F(t)cos ntdt+cos nxint_{0}^{x}F(t)sin ntdt ight)+c_{1}sin nx) with (c_{1})arbitrary.

17. If (omega eq n+1/2 (n=) integer), then (y=-frac{sinomega x}{omegacosomegapi }int_{x}^{pi}F(t)cosomega (t-pi )dt-frac{cosomega (x-pi )}{omegacosomegapi}in_{0}^{x}F(t)sinomega tdt). If (omega = n+1/2 (n=) integer), then (int_{0}^{pi}F(t)sin (n+1/2)tdt=0) is necessary for existence of a solution. In this case, (y=-frac{sin (n+1/2)x}{n+1/2}int_{x}^{pi}F(t)cos (n+1/2)tdt-frac{cos (n+1/2)x}{n+1/2}int_{0}^{x}F(t)sin (n+1/2)tdt+c_{1}sin (n+1/2)x) with (c_{1}) arbitrary.

18. If (omega eq n+1/2: (n=) integer), then (y=frac{cosomega x}{omegacosomegapi}int_{x}^{pi}F(t)sinomega (t-pi )dt+frac{sinomega (x-pi )}{omegacosomegapi}int_{0}^{x}F(t)cosomega tdt). If (omega = n+1/2 (n=) integer), then (int_{0}^{pi }F(t)cos (n+1/2)tdt=0) is necessary for existence of a solution. In this case, (y=frac{cos (n+1/2)x}{n+1/2}int_{x}^{pi}F(t)sin (n+1/2)tdt+frac{sin (n+1/2)x}{n+1/2}int_{0}^{x}F(t)cos (n+1/2)tdt+c_{1}cos (n+1/2)x) with (c_{1}) arbitrary.

19. If (omega) isn't a positive integer, then (y=frac{1}{omegasinomegapi}left(cosomega xint_{x}^{pi }F(t)cosomega (t-pi )dt+cosomega (x-pi )int_{0}^{x}F(t)cosomega tdt ight)). If (omega = n) (positive integer), then (int_{0}^{pi }F(t)cos ntdt=0) is necessary for existence of a solution. In this case, (y=-frac{1}{n}left(cos nxint_{x}^{pi}F(t)sin ntdt+sin nxint_{0}^{x}F(t)cos ntdt ight) +c_{1}cos nx) with (c_{1}) arbitrary.

20. (y_{1}=B_{1}(z_{2})z_{1}-B_{1}(z_{1})z_{2})


  1. (G(x,t)=left{egin{array}{cl}{frac{(t-a)(x-b)}{b-a}}&{aleq tleq x,}{frac{(x-a)(t-b)}{(b-a)}}&{xleq tleq b}end{array} ight.quad y=frac{1}{b-a}left( (x-a)int_{x}^{b}(t-b)F(t)dt+(x-b)int_{a}^{x}(t-a)F(t)dt ight))
  2. (G(x,t)=left{egin{array}{cl}{a-t}&{aleq tleq x}{a-x}&{xleq tleq b}end{array} ight.quad y=(a-x)int_{x}^{b}F(t)dt+int_{a}^{x}(a-t)F(t)dt)
  3. (G(x,t)=left{egin{array}{cl}{x-b}&{aleq tleq x}{t-b}&{xleq tleq b}end{array} ight.quad y=int_{x}^{b}(t-b)F(t)dt+(x-b)int_{a}^{x}F(t)dt)
  4. (int_{a}^{b}F(t)dt=0) is a necessary condition for existence of a solution. Then (y=int_{x}^{b}tF(t)dt+xint_{a}^{x}F(t)dt+c_{1}) with (c_{1}) arbitrary.

22. (G(x,t)=left{egin{array}{cl}{-frac{(2+t)(3-x)}{5},}&{0leq tleq x,}{-frac{(2+x)(3-t)}{5},}&{xleq tleq 1}end{array} ight.)

  1. (y=frac{x^{2}-x-2}{2})
  2. (y=frac{5x^{2}-7x-14}{30})
  3. (y=frac{5x^{4}-9x-18}{60})

23. (G(x,t)=left{egin{array}{cl}{frac{cos tsin x}{t^{3/2}sqrt{x}},}&{frac{pi }{2}leq tleq x,}{frac{cos xsin t}{t^{3/2}sqrt{x}},}&{xleq tleq pi}end{array} ight.)

  1. (y=frac{1+cos x-sin x}{sqrt{x}})
  2. (y=frac{x+picos x-pi /2sin x}{sqrt{x}})

24. (G(x,t)=left{egin{array}{cl}{frac{(t-1)x(x-2)}{t^{3}},}&{1leq tleq x,}{frac{x(x-1)(t-2)}{t^{3}},}&{xleq tleq 2}end{array} ight.)

  1. (y=x(x-1)(x-2))
  2. (y=x(x-1)(x-2)(x+3))

25. (G(x,t)=left{egin{array}{cl}{-frac{1}{22}left(3+frac{1}{t^{2}} ight)left(x+frac{4}{x} ight),}&{1leq xleq 2,}{-frac{1}{22}left(3x+frac{1}{x} ight)left(1+frac{4}{t^{2}} ight),}&{xleq tleq 2}end{array} ight.)

  1. (y=frac{x^{2}-11x+4}{11x})
  2. (y=frac{11x^{3}-45x^{2}-4}{33x})
  3. (y=frac{11x^{4}-139x^{2}-28}{88x})

26. (alpha ( ho +delta )-eta ho eq 0quad G(x,t)=left{egin{array}{cl}{frac{(eta -alpha t)( ho +delta - ho x)}{alpha ( ho +delta )-eta ho },}&{0leq tleq x,}{frac{(eta -alpha x)( ho +delta - ho t)}{alpha ( ho +delta )-eta ho },}&{xleq tleq 1}end{array} ight.)

27. (alphadelta -eta ho eq 0quad G(x,t)=left{egin{array}{cl}{frac{(etacos t-alphasin t)(deltacos x- hosin x)}{alphadelta -eta ho },}&{0leq tleq x,}{frac{(etacos x-alphasin x)(deltacos t- hosin x)}{alphadelta -eta ho }}&{xleq tleqpi }end{array} ight.)

28. (alpha ho +etadelta eq 0quad G(x,t)=left{egin{array}{cl}{frac{(etacos t-alphasin t)( hocos x+deltasin x)}{alpha ho +etadelta },}&{xleq tleqpi }{frac{(etacos x-alphasin x)( hocos t+deltasin t)}{alpha ho +etadelta }}&{0leq tleq x}end{array} ight.)

29. (alphadelta -eta ho eq 0quad G(x,t)=left{egin{array}{cl}{frac{e^{(x-t)}(etacos t-(alpha +eta )sin t)(deltacos x-( ho +delta )sin x) }{alphadelta -eta ho }}&{0leq tleq x,}{frac{e^{x-t}(etacos x-(alpha +eta )sin x)(deltacos t-( ho +delta )sin t)}{alphadelta -eta ho }}&{xleq tleqpi}end{array} ight.)

30. (etadelta +(alpha +eta ) eq 0quad G(x,t)=left{egin{array}{cl}{frac{e^{x-t}(etacos t-(alpha +eta )sin t)(( ho +delta )cos x+deltasin x)}{etadelta + (alpha +eta )( ho +delta )},}&{0leq tleq x,}{frac{e^{x-t}(etacos x-(alpha +eta )sin x)(( ho +delta )cos t+deltasin t)}{etadelta +(alpha +eta )( ho +delta )},}&{xleq tleq pi /2}end{array} ight.)

31. (( ho +delta )(alpha -eta )e^{(b-a)}-( ho -delta )(alpha +eta )e^{(a-b)} eq 0quad G(x,t)=left{egin{array}{cl}{frac{((alpha -eta )e^{(t-a)}-(alpha +eta )e^{-(t-a)}(( ho -delta )e^{(x-b)}-( ho +delta )e^{-(x-b)} )}{2left[ ( ho +delta )(alpha -eta )e^{(b-a)}-( ho -delta )(alpha +eta )e^{(a-b)} ight] },}&{0leq tleq x,}{frac{((alpha -eta )e^{(x-a)}-(alpha +eta )e^{-(x-a)})(( ho -delta )e^{(t-b)}-( ho +delta )e^{-(t-b)} )}{2left[ ( ho +delta )(alpha -eta )e^{(b-a)} -( ho -delta )(alpha +eta )e^{(a-b)} ight] },}&{xleq tleqpi}end{array} ight.)

Section 13.1 Answers - Mathematics

Lesson 13: Geometry Unit Test
Essential Math 7 B Unit 1: Geometry

plz all answers i need it im not lying my grandpa has cancer stage 4 terminal i need them so i can go up to maryland and say goodbye please

maybe you can work some of the problems on the trip.
Say, didn't your uncle die last month, too?

21. The rectangle has 4 sides, but not all sides are equal, there are 4 right angle, and 4 points. The square has 4 sides, all sides are equal, 4 right angles. The rhombus has 4 sides, all sides are equal, 4 angles, not always right, and 4 points. The trapezoid has 4 sides, not all sides are equal, 4 angles and 4 points.

OOFER can you put correct answers

I suggest you use

Omg can someone just put the right answers

Oofer, if your test has 19 questions. and the one the other guy answered had 22, he might not be wrong since the tests are different ooo

anybody else ahead in this class

I dont know but when im done ill give the answers
bc im like that -

And sorry if you get it wronggg

thank you none if your bizz -

pls bruh give us the answers.

those answers never did come back and everyone got F's hooraay

CONGRATULATIONS. we are all screwed.

cuz I have 17 questions 2 of them are essays. T_T

Mine has 20 questions, I do connexus for Pennsylvania if that helps

IM FINE im in ur boat, 20 questions 2 essay questions :/ buttttttt after im done i WILL post the answers for geometry A unit 3 lesson 6 reasoning and proof unit test u can thank me in advance for the answers :)))))))))

oops i meant 17 questions and 2 essay questions LOL

U3 L6 Reasoning and Proof unit test
11 essay question
12 essay question
13 essay question
14 essay question
15 essay question
16 essay question
17 essay question

I know for a fact 1 is wrong. an if-then statement is a conditional. Proof:

Search: conditional definition math

Result: Definition: A conditional statement, symbolized by p q, is an if-then statement in which p is a hypothesis and q is a conclusion. The logical connector in a conditional statement is denoted by the symbol . The conditional is defined to be true unless a true hypothesis leads to a false conclusion.

Search: counterexample definition math

Result: Counterexample. An example which disproves a proposition. For example, the prime number 2 is a counterexample to the statement "All prime numbers are odd."

I also have 17 questions for mine but I don't know all the answers but here's what I know is correct:

11. Angle 4 equals 34 degrees since angle 2 and 4 are opposite angles and opposite angles are congruent.

12. [a] substitution
[b] definition of supplementary angles
[c] subtraction property of equality

14. [a] segment addition postulate
[b] substitution
[c] simplification
[d] subtraction property of equality
[e] division property of equality

15. If a shape is a square, then it is a quadrilateral

17. 11x-12+8x+2=180
11*10-12= 98

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Lesson 13: Geometry Unit Test
Essential Math 7 B
Unit 1: Geometry

General Formatting Guidelines

This chapter provides detailed guidelines for using the citation and formatting conventions developed by the American Psychological Association, or APA. Writers in disciplines as diverse as astrophysics, biology, psychology, and education follow APA style. The major components of a paper written in APA style are listed in the following box.

These are the major components of an APA-style paper:

Body, which includes the following:

  • Headings and, if necessary, subheadings to organize the content
  • In-text citations of research sources

All these components must be saved in one document, not as separate documents.


The method is applicable for numerically solving the equation f(x) = 0 for the real variable x, where f is a continuous function defined on an interval [a, b] and where f(a) and f(b) have opposite signs. In this case a and b are said to bracket a root since, by the intermediate value theorem, the continuous function f must have at least one root in the interval (a, b).

At each step the method divides the interval in two by computing the midpoint c = (a+b) / 2 of the interval and the value of the function f(c) at that point. Unless c is itself a root (which is very unlikely, but possible) there are now only two possibilities: either f(a) and f(c) have opposite signs and bracket a root, or f(c) and f(b) have opposite signs and bracket a root. [5] The method selects the subinterval that is guaranteed to be a bracket as the new interval to be used in the next step. In this way an interval that contains a zero of f is reduced in width by 50% at each step. The process is continued until the interval is sufficiently small.

Explicitly, if f(a) and f(c) have opposite signs, then the method sets c as the new value for b, and if f(b) and f(c) have opposite signs then the method sets c as the new a. (If f(c)=0 then c may be taken as the solution and the process stops.) In both cases, the new f(a) and f(b) have opposite signs, so the method is applicable to this smaller interval. [6]

Iteration tasks Edit

The input for the method is a continuous function f, an interval [a, b], and the function values f(a) and f(b). The function values are of opposite sign (there is at least one zero crossing within the interval). Each iteration performs these steps:

  1. Calculate c, the midpoint of the interval, c = a + b / 2 .
  2. Calculate the function value at the midpoint, f(c).
  3. If convergence is satisfactory (that is, c - a is sufficiently small, or |f(c)| is sufficiently small), return c and stop iterating.
  4. Examine the sign of f(c) and replace either (a, f(a)) or (b, f(b)) with (c, f(c)) so that there is a zero crossing within the new interval.

When implementing the method on a computer, there can be problems with finite precision, so there are often additional convergence tests or limits to the number of iterations. Although f is continuous, finite precision may preclude a function value ever being zero. For example, consider f(x) = x − π there will never be a finite representation of x that gives zero. Additionally, the difference between a and b is limited by the floating point precision i.e., as the difference between a and b decreases, at some point the midpoint of [a, b] will be numerically identical to (within floating point precision of) either a or b..

Algorithm Edit

The method may be written in pseudocode as follows: [7]

Suppose that the bisection method is used to find a root of the polynomial

Because the function is continuous, there must be a root within the interval [1, 2].

In the first iteration, the end points of the interval which brackets the root are a 1 = 1 =1> and b 1 = 2 =2> , so the midpoint is

After 13 iterations, it becomes apparent that there is a convergence to about 1.521: a root for the polynomial.

This formula can be used to determine, in advance, an upper bound on the number of iterations that the bisection method needs to converge to a root to within a certain tolerance. The number n of iterations needed to achieve a required tolerance ε (that is, an error guaranteed to be at most ε), is bounded by

However, despite the bisection method being optimal with respect to worst case performance under absolute error criteria it is sub-optimal with respect to average performance under standard assumptions [11] [12] as well as asymptotic performance. [13] Popular alternatives to the bisection method, such as the secant method, Ridders' method or Brent's method (amongst others), typically perform better since they trade-off worst case performance to achieve higher orders of convergence to the root. And, a strict improvement to the bisection method can be achieved with a higher order of convergence without trading-off worst case performance with the ITP Method. [13] [14]

Operation Activities

Debbie has a collection of mathematics activities for the students in her middle level classroom. She keeps these activities in the "math center". What follows is some of her activities centered around operations with integers and fractions.

Two by Two

  1. At the math center find 2 or 3 calendar pages.
  2. Choose a 2 by 2 square of dates.
  3. Find the sum of the number on one diagonal and then find the sum on the other diagonal.
  4. What have you discovered?
  5. Now choose another 2 by 2 square section and test for similar relationships.
  6. Can you find a 2 by 2 square where this relationship does not exist.
  7. Repeat the experiment with 3 by 3 squares and 4 by 4 squares. Results.

One, Two, Three, Four

Use any combination of addition, subtraction, multiplication, divsion and parethesis symbols to make the sentences true.


Possible Answers:

1. (1 + 2 - 3) x 4 = 0
2. 1 x 2 + 3 - 4 = 1
3. 1 + 2 + 3 - 4 = 2
4. -[(1 + 2) / 3] + 4 = 3
5. (1+2) / 3 x 4 = 4
6. (1 + 2) x 3 - 4 = 5
7. 1/2 x 3 x 4 = 6
8. 1 + 2 + 3 + 4 = 10
9. (1 + 2) x 3 + 4 = 13
10. 1 x 2 + 3 x 4 = 14
11. 1 x (2 + 3) x 4 = 20
12. 1 + [(2 + 3) x 4] = 21
13. 1 x 2 x 3 x 4 = 24

A Jack of All Trades

  1. From the math center take out a deck of cards.
  2. If a Jack =11, a Queen =12, a King=13 and all other cards equal the value printed on them, what is the total of a deck of cards?
  3. What are all the clubs worth?
  4. What is the total value of all the face cards?

Tinker Totals

Place the numbers 1, 2, 3, 4, 5, 7, 12 in the first hexagon on circles at the top so that the sum of any 3 circles that form the side of a triangle will total 22.

Place the numbers 1, 2, 3, 4, 7, 8, 9, 10, 13, 14, 15, 16 in the second hexagon of circles at the right so that the sum of any three circles that form the sides of a triangle will total 23.

Answer Key

Congratulations: You Just Inherited 500.00 Dollars

You may buy things from a catalog with the money and you must be able to use what you buy.
You must spent exactly $500.00 dollars-no more-no less!! not even a penny over.

You have 30 minutes to complete your task. If you fail. Sorry the money goes back to the giver.

T.V. Math

  • Watch TV for any half hour segment.
  • Time the various commercials and station breaks. What is the total time of all this?
  • How much time does the program take?
  • What is the time of a commercial? Are they all the same length? Why or Why not?

Name Math

  1. Add your names. Find the answer.
  2. Write something about yourself with the correct number of letters.
  3. Now try something else. Try a subtraction problem.

Magic Hexagon

This puzzle was created by 19 year old Clifford Adams in 1910. The puzzle is to write the first 19 positive integers in the nineteen blank cells so that any straight line will add to 38. It is a very difficult puzzle so some numbers have been furnished for you. Try your luck!


Money Magic

  1. How much is the whole alphabet worth?
  2. What is the value of your name?
  3. What is the value of December?
  4. Find a word worth 75 cents.
  5. Find a word worth less than 29 cents.
  6. How many words can you find worth exactly one dollar?
  7. Find someone whose name is worth ten cents more than yours.
  8. If you have five dollars how many words could you write with it?
  9. What is the value of your teacher's name? . Your principal's?
  10. What is the difference between your first name and your last name?
  11. What is the most expensive word you can write with 15 letters or less?
  1. Write the year you were born on the top of the page.
  2. Now operate with the numbers anyway you can to see how many numbers you can get.

Fractional Friends

  1. Give a fraction to tell what part of the class are girls
  2. Give a fraction to tell what part of the class are boys.
  3. Give a fraction to tell what part of the class wear glasses.
  4. Give a fraction to tell what part of the set of girls wear glasses.
  5. Give a fraction to tell what part of the set of children are girls wearing glasses.
  6. Give a fraction to tell what part of the set of boys is wearing blue jeans.


  1. Go to the math center and take out an egg carton and the marbles. Put one marble in the egg carton. What fraction is filled?
  2. Continue on in this way until the whole egg carton is filled. Write down all the fractions you made.
  3. Write equivalent fractions in simplest form for the ones that can be broken down.


  1. Make a checker board on a sheet of paper so you have 6 squares on each side.
  2. Put 4 markers on the paper. What fraction have you created?
  3. Fill 1/6 of the squares. How many have you covered?
  4. Fill 1/9 of the squares. How many have you covered?
  5. Use the board to complete these:

2. 4/36=1/9
3. One sixth of 36 is 6 so there would be 6 squares covered
4. One ninth of 36 is 4 so there would be 4 squares covered
5 a) From 4 above one ninth of 36 is 4 and 4+4 = 8 so 1/9+1/9=8/36=2/9
b) One twelth of 36 is 3 so 1/12+1/12=6/36=1/6
c) 1/12+1/6=(3+6)/36=1/4
d) One ninth of 36 is 4 so two ninths of 36 is 8. Thus two ninths of 36 plus
one sixth of 36 is (8+6)/36=14/36=7/18.

Domino Daze

  1. Choose a partner.
  2. At the math center find the set of dominoes.
  3. Lay all the dominoes face down in front of you.
  4. Each domino represents a fraction. The smaller number in each case represents the numerator, so there are no fractions greater then 1.
  5. Each player takes a turn and turns over two dominoes.
  6. Each player must add the two fractions together. (Use paper if needed).
  7. The first player to finish is the winner of the round.

Fraction Fun

  1. Go to the math center and take out an egg carton and the marbles.
  2. Use the egg carton and marbles to compute the following. (Work in partners if you wish and see who can get the answer the quickest. )

Boil, Bake or Fry a Fraction

Crisp Cookies

Sift flour, b. soda and salt. Cream together lard and sugars. Beat in eggs, hot water and vanilla. Blend in dry ingredients, nuts, choc. chips and rolled oats. Using a teaspoon, drop on greased cooke sheet. Bake at 350 degrees for 8-10 minutes. Makes 7 1/2 dozen

Solution for half a batch of cookies:
3/4 c. flour
1/2 tsp.b soda
1/2 tsp salt
1/2 c. lard
3/8 c. brown sugar
1 egg
3/8 c. white sugar
1/2 tbsp. hot water
1/2 tsp. vanilla
1/2 chopped nuts
3 oz.. choc. chips
1c. rolled oats

Fracturing Fraction

  1. 3/10 of figure (a) is shaded. Another way of writing that is 0.3 and we read it as "zero decimal three".
  2. 0.3 means the same as 3/10.
  3. Write the fraction and decimal that names the shaded part of each shape.

Pentagon Power

  1. Cut out a large paper pentagon.
  2. Fold the pentagon to show ten equal parts.
  3. Colour one of the equal parts red.
  4. What fraction of the pentagon is coloured red?
    • Write this fraction on the red part.
  5. Colour two of the equal parts green.
  6. What fraction of the pentagon is coloured green?
    • Write this fraction on the green part.

Colour one half of the pentagon blue and, on the blue part, write the decimal fraction for the portion of the pentagon that is coloured blue.

13 U.S. Code § 221 - Refusal or neglect to answer questions false answers

Based on title 13, U.S.C., 1952 ed., §§ 122, 209, and section 1442 of title 42, U.S.C., 1952 ed., The Public Health and Welfare (June 18, 1929, ch. 28, § 9, 46 Stat. 23 June 19, 1948, ch. 502, § 2, 62 Stat. 479 July 15, 1949, ch. 338, title VI, § 607, 63 Stat. 441).

Section consolidates the first paragraph of section 209 of title 13, U.S.C., 1952 ed., which section related to the decennial censuses of population, agriculture, etc. (see subchapter II of chapter 5 of this revised title), with that part of section 122 of such title which made such section 209 applicable to the quinquennial censuses of manufactures, the mineral industries, and other businesses (see subchapter I of chapter 5 of this revised title) and applicable to the surveys provided for by section 121(b) of such title (see subchapter IV of chapter 5 of this revised title), and that part of subsection (b) of section 1442 of title 42, U.S.C., 1952 ed., which made such section 209 applicable to the decennial censuses of housing (see subchapter II of chapter 5 of this revised title). For remainder of sections 122 and 209 of title 13, U.S.C., 1952 ed., and of section 1442 of title 42, U.S.C., 1952 ed. (which section has been transferred in its entirety to this revised title), see Distribution Table.

The language of section 209 of title 13, U.S.C., 1952 ed., providing that it should “be the duty” of all persons over eighteen years of age, to answer correctly, to the best of their knowledge, when requested, etc., was omitted as unnecessary and redundant. The provisions, as herein revised, define offenses and prescribe penalties for committing them, and are deemed sufficient for the purpose of enforcement. However, some of the language used in the omitted provisions was necessarily included in the description of the offense.

The designation of the first offense, herein described, as a “misdemeanor”, was omitted as covered by section 1 of title 18, U.S.C., 1952 ed., Crimes and Criminal Procedure, classifying crimes and words “upon conviction thereof” were omitted as surplusage.

References to the Secretary (of Commerce) and to any “authorized officer or employee of the Department of Commerce or bureau or agency thereof”, etc., were substituted for references to the Director of the Census and to any “supervisor, enumerator, or special agent, or other employee of the Census Office”, to conform with 1950 Reorganization Plan No. 5, §§ 1, 2, eff. May 24, 1950 , 15 F.R. 3174, 64 Stat. 1263. See revision note to section 4 of this title.

Changes were made in phraseology.

1976—Subsec. (a). Pub. L. 94–521, § 13(1), struck out provision authorizing imprisonment for not more than sixty days for refusing or willfully neglecting to answer questions under this section.

Subsec. (b). Pub. L. 94–521, § 13(2), struck out provision authorizing imprisonment for not more than one year for willfully giving a false answer to a question under this section.

1957—Subsec. (a). Pub. L. 85–207 substituted “I, II, IV, and V” for “I, II, and IV”.

Amendment by Pub. L. 94–521 effective Oct. 17, 1976 , see section 17 of Pub. L. 94–521, set out as a note under section 1 of this title.

ML Aggarwal Class 10 Solutions for ICSE Maths

Get Latest Edition of ML Aggarwal Class 10 Solutions for ICSE Maths PDF Download 2020-2021 on It provides step by step solutions for ML Aggarwal Maths for Class 10 ICSE Solutions Pdf Download. You can download the Understanding ICSE Mathematics Class 10 ML Aggarwal Solved Solutions with Free PDF download option, which contains chapter-wise solutions. APC Maths Class 10 ICSE Solutions all questions are solved and explained by expert Mathematics teachers as per ICSE board guidelines.

APC Understanding ICSE Mathematics Class 10 ML Aggarwal Solutions 2019 Edition for 2020 Examinations

ICSE Class 10 Maths Solutions ML Aggarwal Chapter 1 Value Added Tax

Understanding Mathematics Class 10 Chapter 2 Banking

ML Aggarwal Class 10 ICSE Solutions Solutions Chapter 3 Shares and Dividends

ICSE 10th Maths Solutions Chapter 4 Linear Inequations

ICSE Class 10 Maths Solution Chapter 5 Quadratic Equations in One Variable

Maths ICSE Class 10 Solutions Chapter 6 Factorization

Class 10 ML Aggarwal SolutionsChapter 7 Ratio and Proportion

Class 10 ICSE Maths Solutions Chapter 8 Matrices

ML Aggarwal Class 10 Maths Solutions Chapter 9 Arithmetic and Geometric Progressions

ML Aggarwal Class 10 Solution Chapter 10 Reflection

ICSE Solutions For Class 10 Maths Chapter 11 Section Formula

Class 10 ICSE Maths Solution Chapter 12 Equation of a Straight Line

ML Aggarwal Solutions For Class 10 Chapter 13 Similarity

ML Aggarwal Class 10 ICSE Chapter 14 Locus

ML Aggarwal Class 10 Solutions Chapter 15 Circles

ICSE Mathematics Class 10 Solutions Chapter 16 Constructions

M L Aggarwal Class 10 Solutions Chapter 17 Mensuration

Class 10 ICSE ML Aggarwal Solutions Trigonometric Identities

Maths Solutions Class 10 ICSE ML Aggarwal Chapter 19 Trigonometric Tables

Functions of Small Groups

Why do we join groups? Even with the challenges of group membership that we have all faced, we still seek out and desire to be a part of numerous groups. In some cases, we join a group because we need a service or access to information. We may also be drawn to a group because we admire the group or its members. Whether we are conscious of it or not, our identities and self-concepts are built on the groups with which we identify. So, to answer the earlier question, we join groups because they function to help us meet instrumental, interpersonal, and identity needs.


In the final step of solving the given equation, the variable 'x' is no more.

And also, the result '20  =  -26' is false. 

So, the given equation has no solution.

Solve the following equation : 

Subtract 4y from each side. 

In the final step of solving the given equation, the variable 'x' is no more.

And also, the result '-3  =  -3' is true. 

Because the result is true, the given equation is true for all real values of x. 

So, the given equation has infinitely has many solutions.

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This unit introduces algebra by examining similar models. You should be able to read a problem and create a table to find an equation that relates two variables. If you are given information about one of the variables, you should be able to use algebra to find the other variable.

Signed Numbers:

Adding or subtracting like signs: Add the two numbers and use the common sign.

Adding or subtracting unlike signs: Subtract the two numbers and use the sign of the larger, (more precisely, the sign of the number whose absolute value is largest.)

Multiplying or dividing like signs: The product or quotient of two numbers with like signs is always positive.

Multiplying or dividing unlike signs: The product or quotient of two numbers with unlike signs is always negative.

Order of operations: Please Excuse My Dear Aunt Sally
1. Inside Parentheses, ().
2. Exponents.
3. Multiplication and Division (left to right)
4. Addition and Subtraction (left to right)

Study Tip: All of these informal rules should be written on note cards.

Introduction to Variables:

Generate a table to find an equation that relates two variables.

Example 6. A car company charges $14.95 plus 35 cents per mile.

Simplifying Algebraic Equations:

Distributive property:

Solving Equations:

1. Simplify both sides of the equation.
2. Write the equation as a variable term equal to a constant.
3. Divide both sides by the coefficient or multiply by the reciprocal.
4. Three possible outcomes to solving an equation.
a. One solution ( a conditional equation )
b. No solution ( a contradiction )
c. Every number is a solution (an identity )

Applications of Linear Equations:

This section summarizes the major skills taught in this chapter.

Example 9. A cell phone company charges $12.50 plus 15 cents per minute after the first six minutes.

a. Create a table to find the equation that relates cost and minutes.

c. If the call costs $23.50, how long were you on the phone?

If the call costs $23.50, then you were on the phone for approximately 79 minutes.

Literal Equations:

A literal equation involves solving an equation for one of two variables.


Write percentages as decimals.

Example 11. An English teacher computes his grades as follows:

Sue has an 87 on the short essays and a 72 on the research paper. If she wants an 80 for the course, what grade does Sue have to get on the final?

Sue has to get a 78.36 in the final exam to get an 80 for the course.

Study Tips:

1. Make sure you have done all of the homework exercises.
2. Practice the review test on the following pages by placing yourself under realistic exam conditions.
3. Find a quiet place and use a timer to simulate the test period.
4. Write your answers in your homework notebook. Make copies of the exam so you may then re-take it for extra practice.
5. Check your answers.
6. There is an additional exam available on the Beginning Algebra web page.
7. DO NOT wait until the night before the exam to study.