9514 1404 393
Answer:
(d) x = 14√3; y = 14
Step-by-step explanation:
The side length ratios in a 30°-60°-90° triangle are 1 : √3 : 2. That is, the short side (y) is half the length of the hypotenuse (28). Only one answer choice matches ...
y = 28/2 = 14
x = y√3 = 14√3
_____
It is a good idea to remember these ratios. They show up in a lot of problems.
Answer:
C. True; by the Invertible Matrix Theorem if the equation Ax=0 has only the trivial solution, then the matrix is invertible. Thus, A must also be row equivalent to the n x n identity matrix.
Step-by-step explanation:
The Invertible matrix Theorem is a Theorem which gives a list of equivalent conditions for an n X n matrix to have an inverse. For the sake of this question, we would look at only the conditions needed to answer the question.
- There is an n×n matrix C such that CA=
. - There is an n×n matrix D such that AD=.
- The equation Ax=0 has only the trivial solution x=0.
- A is row-equivalent to the n×n identity matrix .
- For each column vector b in
, the equation Ax=b has a unique solution. - The columns of A span .
Therefore the statement:
If there is an n X n matrix D such that AD=I, then there is also an n X n matrix C such that CA = I is true by the conditions for invertibility of matrix:
- The equation Ax=0 has only the trivial solution x=0.
- A is row-equivalent to the n×n identity matrix .
The correct option is C.
The area of the rectangle is
3x4=13
The area of the triangle is 4
The total area will be 13+4=17
Answer:
A = $996.00
Step-by-step explanation:
(I = A - P = $196.00)
Equation:
A = P(1 + rt)
Where:
A = Total Accrued Amount (principal + interest)
P = Principal Amount
I = Interest Amount
r = Rate of Interest per year in decimal; r = R/100
R = Rate of Interest per year as a percent; R = r * 100
t = Time Period involved in months or years
From the base formula, A = P(1 + rt) derived from A = P + I and I = Prt so A = P + I = P + Prt = P(1 + rt)
Calculation:
First, converting R percent to r a decimal
r = R/100 = 7%/100 = 0.07 per year.
Solving our equation:
A = 800(1 + (0.07 × 3.5)) = 996
A = $996.00
The total amount accrued, principal plus interest, from simple interest on a principal of $800.00 at a rate of 7% per year for 3.5 years is $996.00.
