Answer:
original is 4 & 6.
for 54 sq inch= 6 & 9 and for 96 sq inch=8 & 12
Step-by-step explanation:
Given: The length is 1.5 times the width.
so the length is, l = 1.5w
----(a)
lw = 24 =1.5w(w)
lw = 54=
1.5w(w)
lw = 96
=1.5w(w)
Further simplifying it,
1.5
=24
1.5
=54
1.5
=96
so,
=
=16
=
36
=
64
taking the square root, we get:
w = 4
w = 6
w = 8
By putting the above values in eq (a), we can find their corresponding lengths:
l = 1.5(4) = 6
l = 1.5(6) = 9
l = 1.5(8) = 12
So a few lengths could be:
(l, w)
(6,4)
(9,6)
(12,8)
Answer:
2x - 7y + 17
Step-by-step explanation:
Subtracting the 2 expressions
2x - 4y + 6 - (3y - 11) ← distribute parenthesis by - 1 )
= 2x - 4y + 6 - 3y + 11 ← collect like terms
= 2x - 7y + 17
Answer:
He will have to pay $1,650 in interest at the end of 3 years.
Step-by-step explanation:
This is a simple interest problem.
The simple interest formula is given by:
![E = P*I*t](https://tex.z-dn.net/?f=E%20%3D%20P%2AI%2At)
In which E is the amount of interest earned, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time.
After t years, the total amount of money is:
![T = E + P](https://tex.z-dn.net/?f=T%20%3D%20E%20%2B%20P)
Anvi borrowed $5,000 from a bank at a flat interest rate of 11% per year for a 3-year period.
This means that ![P = 5000, I = 0.11, t = 3](https://tex.z-dn.net/?f=P%20%3D%205000%2C%20I%20%3D%200.11%2C%20t%20%3D%203)
How much interest does she have to pay the bank at the end of 3 years?
![E = P*I*t = 5000*0.11*3 = 1650](https://tex.z-dn.net/?f=E%20%3D%20P%2AI%2At%20%3D%205000%2A0.11%2A3%20%3D%201650)
He will have to pay $1,650 in interest at the end of 3 years.
<span>40 units^2
The figure has the vertexes (2,7), (3,3), (3,-3), (-5,-5), (-6,-1), and (2,1). If you draw a line from (2,1) to (3,-3) you'll divide the figure into the rectangle and parallelogram. The total area will be the sum of the area of the parallelogram and the rectangle. The area of the parallelogram will be base times height, where the height is the distance between the line (2,7) to (2,1) and line (3,3) to (3,-3) which is 1 and the base is the length of the line (2,7) to (2,1) which is 6. So the parallelogram has an area of 6.
The length and width of the rectangle can be calculated from the Pythagorean theorem, so:
L = sqrt((2- -6)^2 + (1- -1)^2) = sqrt(8^2 + 2^2) = sqrt(64+4) = sqrt(68) = 2*sqrt(17)
W = sqrt((-6 - -5)^2 + (-1 - -5)^2) = sqrt(-1^2 + 4^2) = sqrt(1 + 16) = sqrt(17)
So the area of the rectangle is 2*sqrt(17)*sqrt(17) = 2*17 = 34.
And the total area is 34 + 6 = 40.</span>
The axis of symmetry is x=-1