Step-by-step explanation:
x = number of true/false questions
y = number of multiple choice questions
x + y = 40
2x + 3y = 144
from the first equation we get
x = -y + 40
this identity we can then use in the second equation
2(-y + 40) + 3y = 144
-2y + 80 + 3y = 144
y + 80 = 144
y = 64
and
x + 64 = 40
x = -24
that does not make any sense.
something is wrong with the problem description.
just think about it :
40 questions - if all of them would be multiple choice tests (creating the max. possible points for 40 questions), we could have only 40×3 = 120 points.
but the description says 144 points.
for 144 points we need at least 48 (144/3) questions.
that does not fit.
the described system does not have any natural number solution. therefore we are getting such crazy numbers as result, when we try.
Circumference: C=2pir
C stands for circumference. pi is 3.14... and r is the radius.
of course, you can always do, C=pid. where d is diameter because the radius is half the diameter
Area: A=pir^2
A stands for the Area, pi stands for 3.14... r stands for radius, and the little ^2 is the equation squared. The way to solve that is square the radius and then multiply what you got from squaring the radius by pi.
DO NOT replace radius with the diameter when trying to find the Area
To find the volume of a square-based pyramid, use the formula V = A(h/3), where V is the volume and A is the area of the base.
Given:
The base is a rectangle of dimension 7 cm×6 cm.
The length of each diagonal side = 10 cm
To find the height of MT.
Formula
By Pythagoras theorem we get,
where, h be the hypotenuse
b be the base and
l be the height.
Now, in this diagram,
The perpendicular distance of M from BC = 3 cm
Slant height = 10 cm
Taking, b = 3 and h = 10 we get,
or, 
or, 
or, 
Hence,
The height of MT is 9.5 cm.
Answer/Step-by-step explanation:
[1] x+9+1+3x
Add the numbers
x + 10 +3x
Combine like terms
4x+10
Common factor
2(2x+5)
<u>Solution = </u><u>2(2x+5)</u>
<u>.............................................................................................................................................</u>
[2] 5a+6c+2a+3c
Combine like terms
7a+6c+3c
Combine like terms
7a+9c
<u>Solution</u><u> = 7a + 9c</u>
<u>...............................................................................................................................................</u>
[3] 5n+6m+3n
Combine like terms
8n + 6m
Rearrange terms
6m + 8n
<u>Solution </u><u>= 6m+8n</u>
<u>.............................................................................................................................................</u>
[RevyBreeze]
