Find the closest whole number estimate for 3.8 and 6.1
The estimate for both numbers are, 4 and 6.
3.8 is rounded up to the nearest whole number, while 6.1 is rounded down to 6because the 1 after the decimal is an insignificant number (its less than 5)
If you mean 12x by “1and2x”. it’s 9x - 5y = 0.
If it’s 1x and 2x it’s y= 2/5x^2 -3/5x, x
Looking at the first system of equations,
16x - 10y = 10
-8x - 6y = 6
If we multiply both sides of the second equation by 2, the coefficient of x is exactly the negative of the coefficient of x in the first equation.
-8x - 6y = 6
⇒ 2 (-8x - 6y) = 2 (6)
⇒ -16x - 12y = 12
By combining this new equation with the first one, we can eliminate x and solve for y :
(16x - 10y) + (-16x - 12y) = 10 + 12
⇒ -22y = 22
⇒ y = -1
Then we just solve for x by replacing y in either equation.
16x - 10y = 10
⇒ 16x - 10 (-1) = 10
⇒ 16x + 10 = 10
⇒ 16x = 0
⇒ x = 0
The main idea behind elimination is combining the given equations in just the right amount so that one of the variables disappears. The "right amount" involves using the LCM of the coefficients of a given variable. In this example, the x-coefficients had LCM(8, 16) = 16, so we only had to scale one of the equations (the one with -8x) to cancel all the x terms.
If we wanted to eliminate y first instead, we first note that LCM(6, 10) = 30. To get 30 as a coefficient on y, in the first equation we would have multiplied by 3:
16x - 10y = 10
⇒ 3 (16x - 10y) = 3 (10)
⇒ 48x - 30y = 30
And in the second equation, we would have multiplied by -5 (negative so that upon combining the equations, we end up with -30y + 30y = 0):
-8x - 6y = 6
⇒ -5 (-8x - 6y) = -5 (6)
⇒ 40x + 30y = -30
Now combining the two scaled equations gives
(48x - 30y) + (40x + 30y) = 30 + (-30)
⇒ 88x = 0
⇒ x = 0
We then solve for y :
16x - 10y = 10
⇒ -10y = 10
⇒ y = -1
so we end up with the same solution as before.
Answer: 1 minute 33 seconds
Step-by-step explanation:
Theo is practicing for a 5 km race which he usually runs for a normal time of 25 minutes and 19 seconds
but yesterday, he ran for only 23 minutes and 43 seconds.
From the above information,
Normal time = 25 minutes and 19 seconds.
Yesterday's time= 23 minutes and 43 seconds
To know how much faster Theo ran, we find the difference between the normal time and yesterday's time which is.
25 minutes 19 seconds - 23 minutes 43 seconds
25 minutes 19 seconds
- 23 minutes 43 seconds
= 1 minute 36 seconds.
He ran 1 minute 33 seconds faster.
