So if you solve for n
4n^2+3=7n
make into trinomial
subtract 7n from both sides
4n^2-7n+3=0
if we can factor this, then we can asume that the factors are equal to zero becase if
xy=0 then assume x and/or y=0 so
to factor an equation in ax^2+bx+c where a is greater than 1 then
b=t+z
a times c=t times z
to factor 4n^2-7n+3 you do
4 times 3=12
what 2 numbers multiply to get 12 and add to get -7
the numbers are -3 and -4 so
split up the -7
4n^2-4n-3n+3
group
(4n^2-4n)+(-3n+3)
undistribute
(4n)(n-1)+(-3)(n-1)
reverse distributive property
ab+ac=a(b+c)
(4n-3)(n-1)=0
set each to zero
4n-3=0
add 3 to both sides
4n=3
divide both sides by 4
n=3/4
n-1=0
add 1 to both sides
n=1
n=3/4 or 1
Answer:
The answer is 7.4 × 10³ ( or 0.74 × 10⁴).
Step-by-step explanation:
The steps are :
(1.5 × 10⁴) - (7.6 × 10³)
= (15 × 10³) - (7.6 × 10³)
= (15 - 7.6) × 10³
= 7.4 × 10³
Let the two numbers be x and y, with y being larger than x.
Then y=3x+1.
Also, 8x-2y= 10.
The first equation has already been solved for y. Substitute 3x+1 for y in the second equation:
8x-2(3x+1)=10, or 8x - 6x - 2 = 10, or 2x = 12 and x = 6.
If x = 6, then by the first equation y must be 3(6)+1, or 19.
The numbers are 6 and 19.
3/4 of the rest of the tank needs to be filled
