Answer:
x = 9
Step-by-step explanation:
Given
3x -
-
x =
( add
to both sides
3x -
x =
+
=
= 25 ← combine x- terms on left side
x = 25 ( multiply both sides by 9 )
25x = 225 ( divide both sides by 25 )
x = 9
The like terms are 12 and 5, so you have to subtract 5 from both sides.
12 < x + 5
-5. -5
7 < x
We can just switch it around so x is in the left side.
x > 7
9514 1404 393
Answer:
(a) 6² +3² +1² +1² = 47
(b) 5² +4² +2² +1² +1² = 47
(c) 3³ +4² +2² = 47
Step-by-step explanation:
It can work reasonably well to start with the largest square less than the target number, repeating that approach for the remaining differences. When more squares than necessary are asked for, then the first square chosen may need to be the square of a number 1 less than the largest possible.
The approach where a cube is required can work the same way.
(a) floor(√47) = 6; floor(√(47 -6^2)) = 3; floor(√(47 -45)) = 1; floor(√(47-46)) = 1
__
(b) floor(√47 -1) = 5; floor(√(47-25)) = 4; ...
__
(c) floor(∛47) = 3; floor(√(47 -27)) = 4; floor(√(47 -43)) = 2
When the height is 0 that is when it hits the ground
solve
0=-16t²+25x+3
cant factor so use quadratic formula
for
0=ax²+bx+c
![x=\frac{-b+/-\sqrt{b^2-4ac}}{2a}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-b%2B%2F-%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D)
so for
0=-16t²+25t+3
a=-16
b=25
c=3
so
![x=\frac{-25+/-\sqrt{25^2-4(-16)(3)}}{2(-16)}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-25%2B%2F-%5Csqrt%7B25%5E2-4%28-16%29%283%29%7D%7D%7B2%28-16%29%7D)
![x=\frac{-25+/-\frac{625+192}}{-32}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-25%2B%2F-%5Cfrac%7B625%2B192%7D%7D%7B-32%7D)
![x=\frac{-25+/-\frac{817}}{-32}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-25%2B%2F-%5Cfrac%7B817%7D%7D%7B-32%7D)
it has to be a positive time
so it will hit the ground after
![\frac{25+\sqrt{817}}{32}](https://tex.z-dn.net/?f=%5Cfrac%7B25%2B%5Csqrt%7B817%7D%7D%7B32%7D)
seconds