True because the rectangle represents the universe and closed figures.
Consecutive odd integers are 2 apart
they are x and x+2
the product (x times (x+2)) is 1 less than 4 times their sum
x(x+2)=-1+4(x+x+2)


![x^2+2x=8x+7 minus (8x+7) from both sides [tex]x^2-6x-7=0](https://tex.z-dn.net/?f=x%5E2%2B2x%3D8x%2B7%20minus%20%288x%2B7%29%20from%20both%20sides%20%5Btex%5Dx%5E2-6x-7%3D0)
factor
what numbers multliply to get -7 and add to get -6?
-7 and 1
(x-7)(x+1)=0
set equal to 0
x-7=0
x=7
x+1=0
x=-1
so the x can be 7 or -1
the other number (x+2) can be 7 or 1
test each
7 and 9
7(9)=-1+4(7+9)
63=-1+4(16)
63=-1+64
63=63
true
-1 and 1
-1(1)=-1+4(-1+1)
-1=-1+4(0)
-1=-1+0
-1=-1
true
the 2 integers can be 7 and 9 or -1 and 1 (both pairs of numbers work)
Answer:
(2, -1)
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
- Multiplication Property of Equality
- Division Property of Equality
- Addition Property of Equality
- Subtract Property of Equality
<u>Algebra I</u>
- Solving systems of equations using substitution/elimination
Step-by-step explanation:
<u>Step 1: Define Systems</u>
2x + y = 3
-2x + 5y = -9
<u>Step 2: Solve for </u><em><u>y</u></em>
<em>Elimination</em>
- Combine equations: 6y = -6
- Divide 6 on both sides: y = -1
<u>Step 3: Solve for </u><em><u>x</u></em>
- Define equation: 2x + y = 3
- Substitute in <em>y</em>: 2x - 1 = 3
- Isolate <em>y</em> term: 2x = 4
- Isolate <em>y</em>: x = 2
6s^2; where s is the side length
5/8 divided by 4 cones= 5/32 so the answer is 5/32.
Hope this helps :)