Answer:
D. {1, 12}
Step-by-step explanation:
4X^2-52x+169=121
The equation can be summarized thus:
4X^2-52x+169-121=0
4X^2-52x+48=0
divide the each number of the equation by 4
4X^2/4-52x/4+48/4=0
x^2-13x+12=0
we need to numbers that when we multiply them the result is 12 and -13 when we add together
-1 and -12(-1-12=-13 and -1*-12=12)
x^2-x-12x+12
x(x-1)-12(x-1)
(x-1)(x-12)
x-1=0 or x-12=0
x=1 or x=12
Answer:
Proved
Step-by-step explanation:
Given: EC || AC, DB || AC, ∠A = ∠F
Prove: ΔMDF ∼ ΔNCA
Solution
See diagram attached to the solution to better understand the following workings.
Redrawing ΔMDF or rotating to be facing the same direction.
EC is parallel to AC
DB parallel to AC
Using similar triangle theorem:
If ΔMDF ∼ ΔNCA
Ratio of Corresponding sides would be equal
(adjacent of ΔMDF)/(adjacent of ΔNCA) = (Opposite of ΔMDF)/(opposite of ΔNCA) = (hypotenuse of ΔMDF)/(hypotenuse of ΔNCA)
DF/ CA = MD/NC = FM/AN
∠A = ∠F
∠M = ∠N
∠D = ∠C
Since the ratio of Corresponding sides and angle are equal, ΔMDF is similar to ΔNCA.
ΔMDF ∼ ΔNCA
Check the picture. There are 2 interior common tangents, and 2 exterior common tangents which can be drawn.
Answer: 4
Answer:
They are.
Step-by-step explanation: The postulate is that all the adjacent angles and side lengths are equal between the triangle pairs. Congruency is if all side lengths and angles measure the same amount. In this case, the lines signify that they do.
Answer:
The new mortgage repayment is $10,580.69
Step-by-step explanation:
As at the time Douglas lost his job,he has already made repayments on the mortgage for a period of 7 years,by extending the repayment period by another 7 years,Douglas now have a period of repayment of 30 years now(30-7+7).
The new repayment yearly can be computed using the pmt formula in excel as given below:
=pmt(rate,nper,-pv,fv)
rate is the interest rate on mortgage given as 4.25%
nper is the period of repayment now 30 years
pv is the current of balance of $177,533.62
fv is the total amount repayable on the mortgage and it is not known hence taken as zero
=pmt(4.25%,30,-177533.62,0)=$10,580.69
