This is a little long, but it gets you there.
- ΔEBH ≅ ΔEBC . . . . HA theorem
- EH ≅ EC . . . . . . . . . CPCTC
- ∠ECH ≅ ∠EHC . . . base angles of isosceles ΔEHC
- ΔAHE ~ ΔDGB ~ ΔACB . . . . AA similarity
- ∠AEH ≅ ∠ABC . . . corresponding angles of similar triangle
- ∠AEH = ∠ECH + ∠EHC = 2∠ECH . . . external angle is equal to the sum of opposite internal angles (of ΔECH)
- ΔDAC ≅ ΔDAG . . . HA theorem
- DC ≅ DG . . . . . . . . . CPCTC
- ∠DCG ≅ ∠DGC . . . base angles of isosceles ΔDGC
- ∠BDG ≅ ∠BAC . . . .corresponding angles of similar triangles
- ∠BDG = ∠DCG + ∠DGC = 2∠DCG . . . external angle is equal to the sum of opposite internal angles (of ΔDCG)
- ∠BAC + ∠ACB + ∠ABC = 180° . . . . sum of angles of a triangle
- (∠BAC)/2 + (∠ACB)/2 + (∠ABC)/2 = 90° . . . . division property of equality (divide equation of 12 by 2)
- ∠DCG + 45° + ∠ECH = 90° . . . . substitute (∠BAC)/2 = (∠BDG)/2 = ∠DCG (from 10 and 11); substitute (∠ABC)/2 = (∠AEH)/2 = ∠ECH (from 5 and 6)
- This equation represents the sum of angles at point C: ∠DCG + ∠HCG + ∠ECH = 90°, ∴ ∠HCG = 45° . . . . subtraction property of equality, transitive property of equality. (Subtract ∠DCG+∠ECH from both equations (14 and 15).)
To answer this question, start by identifying the total amount of income after 5 years for the first contract.
Since you start with 15,000 and get 1000 more each year, write an expression that represents this relationship.
15000 + 1000(5)
Multiply the parenthesis to begin to simplify your expression.
This leaves you with:
15000 + 5000
Add to find the total salary after five years with the first contract.
This ends up with:
$20,000
For the second contract, you have a diffferent rate of increase. Start by finding what one percent of the initial salary is. To do this, divide 14000 by 100.
14000/100 = 140
Then to find ten percent, multiply that number by 10.
140 x 10 =1400
So, each year you add 1400 dollars to the salary.
Now, using this information, set up an expression to model the salary for contract 2 after 5 years.
This should leave you with:
14000 + 1400(5)
Begin to simplify by multiplying what’s in the parenthesis.
1400 x 5 = 7000
Now rewrite your expression:
14000 + 7000
Add to find the total salary after 5 years with contract 2.
14000 + 7000 = 21000
So the salary with contract 2 is $21,000.
So, since $21000 is $1000 more than just $20000, contract 2 is the better option. I hope this helps! :)
Answer:
Step-by-step explanation:
Length=2*Width
L=2*W
Perimeter=28.8 cm
Perimeter of a rectangle= 2(Length+Width)
The LCD = 6x^2y^3 ( because LCD of 3 and 6 = 6, LCD of x^2 and x = x^2 and LCD of y and y^3 = y^3)
now divide 3x^2y into the LCD then multiply this by 5 to get the first term in the numerator and do similar process to get second term, so we get:-
5(2y^2) - 4(x)
------------------
6x^2y^3
= 2( 5y^2 - 2x)
-----------------
6x^2y^3
= 5y^2 - 2x
-----------
3x^2y^3
Answer:
300.29
Step-by-step explanation:
