Answer:
x = 11.2
Step-by-step explanation:
-5x - 12y = -8
5x + 2y = 48
you can combine all like terms from both equations together:
0x-10y=40
simplified:
-10y=40
y=-4
now you plug in the value of y into either equation:
5x+2(-4)=48
simplify
5x-8=48
add 8
5x=56
divide by 5
x=56/5=11.2
Answer:
15 cm²
Step-by-step explanation:
To find the volume of a prism you multiply the area of the end face (pentagon in this example) by the length (9 cm). Here you would reverse that and divide the volume by the length to find the area. 135/9 is 15 so the area of the pentagon is 15 cm².
<u>In equation form would be:</u>
V=A×L [V=volume A=area L=length]
So if you do inverse operations you would divide the volume by the length to get the area.
V/L=A
Answer:
D
Step-by-step explanation:
The geometric sequence formula is:
An=a*r^(n-1)
An= nth term of the sequence
a= first term of the sequence. In this case, the amount Monica had in the first month
r= common ratio. In this case, is the interest rate, which is constant in all months.
n= number of periods
Following this equation, option A and B are not correct because "a" the first term of the sequence is $225.
It is not option C because Monica will have her first $225 plus interest not only the interest she gained, then the common ratio should be a number greater than 1.
It is option D and let´s proved it:
A6= 225*(1.04)^(6-1)
A6=225* (1.21665)
A6=$273.746
A6=$273.75
All real numbers above -4
This problem is basically asking you to find a perpendicular vector to Gandalf's initial path. The direction if this vector will be set no matter when he turns so we can start by calculating that.
Vectors are perpendicular if their dot product is 0, so we need <x,y> such that 5x + 2j = 0. The obvious choice will be <-2,5>, as that clearly satisfies our conditions (this is of course identical to <2, -5>).
So now we have reduced this problem to finding where the line that goes through (1,6) with a slope of -2.5 intersects our original line, which we can easily see is y = 0.4x + 3.
The equation for the new line can be seen to be y = -2.5x + 8.5.
Setting these equal,
0.4x + 3 = -2.5x + 8.5
2.9x = 5.5
x = 5.5/2.9 = 1.896, plugging back in yields y = 3.7586
This approach sort of reduces the problem to just a planar geometry exercise, which may or may not be desirable, but it surely yields the correct result.