<em>BD</em> = 56
Step-by-step explanation:
Step 1: In rectangle, the diagonals are congruent and bisect each other.
So, <em>AC</em> = <em>BD</em>
⇒<em>AG</em> + <em>GC</em> = <em>BG</em> + <em>GD</em>
⇒<em>AG</em> + <em>AG</em> = <em>GD</em> + <em>GD</em>
⇒ 2<em>AG</em> = 2<em>GD</em>
⇒<em>AG</em> = <em>GD</em>
⇒ –7<em>j </em>+ 7 = 5<em>j</em> + 43
⇒–7<em>j</em> – 5<em>j</em> = 43 – 7
⇒–12<em>j</em> = 36
⇒<em>j</em> = –3
Step 2: <em>BD</em> = 2<em>DG</em>
<em>BD</em> = 2(5<em>j</em> + 43)
= 2(5 (–3) + 43)
= 2(–15 + 43)
= 2 × 28
= 56
Hence, <em>BD</em> = 56.
The problem statement gives rise to two equations.
w = 30 + p . . . . . w is 30 more than p
w = 5 - p . . . . . .. w is p less than 5
Add these two equations to get
2w = 35
w = 35/2 = 17.5
p = 5 - w = -12.5
The unknown number w is 17.5.
The unknown number p is -12.5.
1 ) first offer
total payments
375.76×12×4
=18,036.48
Interest paid
18,036.48−16,000
=2,036.48
Second offer
Total payments
390.61×12×4
=18,749.28
Interest paid
18,749.28−16,000
=2,749.28
Larry will save of taking 6% loan
2,749.28−2,036.48=712.8. .answer
2) credit card 1
Total payments
277.09×12
=3,325.08
Interest paid
3,325.08−3,000
=325.08
Credit card 2
Total payments
152.69×12×2
=3,664.56
Interest paid
3,664.56−3,000
=664.56
Susan will save
664.56−325.08
=339.48...answer
Hope it helps!
Answer:
Width = 2x²
Length = 7x² + 3
Step-by-step explanation:
∵ The area of a rectangle is 
∵ Its width is the greatest common monomial factor of 
and 6x²
- Let us find the greatest common factor of 14 , 6 and 
, x²
∵ The factors of 14 are 1, 2, 7, 14
∵ The factors of 6 are 1, 2, 3, 6
∵ The common factors of 14 and 6 are 1, 2
∵ The greatest one is 2
∴ The greatest common factor of 14 and 6 is 2
- The greatest common factor of monomials is the variable with
the smallest power
∴ The greatest common factor of and x² is x²
∴ The greatest common monomial factor of and 6x² is 2x²
∴ The width of the rectangle is 2x²
To find the length divide the area by the width
∵ The area =
∵ The width = 2x²
∴ The length = ( ) ÷ (2x²)
∵ ÷ 2x² = 7x²
∵ 6x² ÷ 2x² = 3
∴ ( ) ÷ (2x²) = 7x² + 3
∴ The length of the rectangle is 7x² + 3
Associativity means
(A+B)+C=A+(B+C)=A+B+C
Substitute A=9, B=8, C=32 to apply to this problem.
