Answer:
Option b and d.
Step-by-step explanation:
Given equation : -5x + 4y > -7
Putting the values of x and y one by one in the options,
a) Putting x as 6 and y as 4.
=> -5(6) + 4(4) > -7
=> -30 + 16 > -7
=> -14 > -7
This doesn't satisfy the inequality, hence this couldn't be the ordered pair.
Similarly,
b) Putting x as 5 and y as 5.
=> -5(5) + 4(5) > -7
=> -25 + 20 > -7
=> -5 > -7
This satisfies the inequality, hence this is the ordered pair.
c) Putting x as 3 and y as 2.
=> -5(3) + 4(2) > -7
=> -15 + 8 > -7
=> -7 > -7
This doesn't satisfy the inequality, hence this couldn't be the ordered pair.
d) Putting x as -2 and y as -4.
=> -5(-2) + 4(-4) > -7
=> 10 - 16 > -7
=> -6 > -7
This satisfies the inequality, hence this is the ordered pair.
<em>Hope</em><em> </em><em>it</em><em> </em><em>helps</em><em> </em><em>:</em><em>)</em>
Answer:
r=20%
Step-by-step explanation:
we know that
The simple interest formula is equal to
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest
t is Number of Time Periods
in this problem we have
substitute in the formula above
solve for r
Answer:
70200
Step-by-step explanation:
8% of 65,000 is 5200
I added 65000 and 5200 and received.
Hopefully this is accurate/true. Not the best at finance.
Answer:
For h= 25, b in the plane spanned by a1 and a2
Step-by-step explanation:
![a1= \left[\begin{array}{c}1\\2\\-1\end{array}\right] \\a2 = \left[\begin{array}{c}-7\\-7\\2\end{array}\right] \\\\b = \left[\begin{array}{c}3\\-22\\h\end{array}\right]](https://tex.z-dn.net/?f=a1%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D1%5C%5C2%5C%5C-1%5Cend%7Barray%7D%5Cright%5D%20%5C%5Ca2%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D-7%5C%5C-7%5C%5C2%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%5C%5Cb%20%20%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D3%5C%5C-22%5C%5Ch%5Cend%7Barray%7D%5Cright%5D)
we have to find value of h for which b in the plane spanned by a1 and a2.
For this the linear systems given by the following augmented matrix must be consistent.
![\left[\begin{array}{cc|c}1&-7&3\\2&-7&-22\\-1&2&h\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Cc%7D1%26-7%263%5C%5C2%26-7%26-22%5C%5C-1%262%26h%5Cend%7Barray%7D%5Cright%5D)
Reduce the augmented matrix into row echelon form:
![R_{2} - 2R_{1} , R_{3} + R_{1}\\\\\left[\begin{array}{cc|c}1&-7&3\\0&7&-28\\-0&-5&h+3\end{array}\right]\\\\7R_{3}+5R_{2}\\\\\left[\begin{array}{cc|c}1&-7&3\\0&7&-28\\-0&0&7h-175\end{array}\right]](https://tex.z-dn.net/?f=R_%7B2%7D%20-%202R_%7B1%7D%20%2C%20R_%7B3%7D%20%2B%20R_%7B1%7D%5C%5C%5C%5C%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Cc%7D1%26-7%263%5C%5C0%267%26-28%5C%5C-0%26-5%26h%2B3%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5C7R_%7B3%7D%2B5R_%7B2%7D%5C%5C%5C%5C%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Cc%7D1%26-7%263%5C%5C0%267%26-28%5C%5C-0%260%267h-175%5Cend%7Barray%7D%5Cright%5D)
For system to be consistent:
