R=2K which equals 2R=4K
4(R=K+8) or 4R=4K+32
Subtract first equation from second equation.
2R=32 so R=16
Plug into first equation
16=2K so K=8
Now plug both into second equation to check
4R-4K=4(R-K)=4(8)=32 it works
So Roberto is 16 and Katie is 8
(In 4 years R would be 20 and K would be 12 which has a difference of 8)
OK. These problems are easy if you know the quadratic formula,
and they're impossible if you don't.
Here's the quadratic formula:
When the equation is in the form of Ax² + Bx + C = 0
then x = [ -B plus or minus √(B²-4AC) ] / 2A
I'm sure that formula is in your text or your study notes,
right before these questions. You should cut it out or
copy it, and tape it inside the cover of your notebook.
Then, you'll always have it when you need it, until
you have it memorized and can rattle it off.
The first question says 3x² + 5x + 2 = 0
Is this in the form of Ax² + Bx + C = 0 ?
Yes ! A=3 B=5 C=2
so you can use the quadratic formula to solve it.
x = [ -B plus or minus √(B²-4AC) ] / 2A
= [ -5 plus or minus √(5² - 4·3·2) ] / 2·3
= [ -5 plus or minus √(25 - 24) ] / 6
= [ -5 plus or minus √1 ] / 6
x = -4 / 6 = -2/3
and
x = -6 / 6 = -1 .
_______________________________________
The second question says
4x² + 5x - 1 = 0
Is this in the form of Ax² + Bx + C = 0 ?
Yes it is ! A=4 B=5 C= -1
so you can use the quadratic formula to solve it.
x = [ -B plus or minus √(B²-4AC) ] / 2A
Now, you take it from here.
Length of the aquarium is 35 yd
Step-by-step explanation:
Step 1: Volume of the aquarium = 210 yd³ given by Volume = length × width × height. Width = 3 yd and Height = 2 yd
Length = Volume/Width × Height
= 210/3 × 2 = 210/6
= 35 yd
Answer:
The balance of the account is $1335.6
Step-by-step explanation:
To find the new balance of the account after 212 years, we use simple interest formula to calculate that.
Principal = 450
Rate = 0.35% quarterly = (0.35*4) annually = 1.4% = 1.4 / 100 = 0.014
Reason why the rate was converted from quarterly to annually is because simple interest are calculated annually
T = 212 years
Simple Interest (S.I) = ?
S.I = PRT
S.I = 450 * 0.014 * 212
S.I = $1335.6
The balance of the account after 212 years is $1335.6
Answer:
20/25
Step-by-step explanation:
