Answer:
<u>The solution of this system of equation is ( 3, - 8)</u>
Step-by-step explanation:
1. Let's solve the system of equations:
First equation:
x + 2y = - 13
x = - 13 - 2y
Second equation:
12x + 5y = -4
12 * (- 13 - 2y) + 5y = - 4 (Replacing x with - 13 - 2y)
-156 -24y + 5y = - 4
-24y + 5y = - 4 + 156 (Like terms)
-19y = 152
y = - 152/19
<u>y = -8</u> (Dividing by 19)
Solving x
x + 2y = -13
x + 2 (- 8 ) = - 13
x - 16 = - 13
x = - 13 + 16
<u>x = 3</u>
2. Proving that x = 3 and y = - 8 are correct:
12x + 5y = -4
12 * 3 + 5 * -8 = -4
36 - 40 = - 4
- 4 = - 4
<u>We proved that x = 3 and y = - 8 are correct</u>
1.1x+1.2x-5.4=-10x
Move all terms to the left:
1.1x+1.2x-5.4-(-10x)=0
Add all the numbers together, and all the variables
2.3x-(-10x)-5.4=0
Get rid of parentheses
2.3x+10x-5.4=0
Add all the numbers together, and all the variables
12.3x-5.4=0
Move all terms containing x to the left, all other terms to the right
12.3x=5.4
x=5.4/12.3
x=3.8571428571429/8.7857142857143
Hope it helps!
Answer:
(5,-2)
Step-by-step explanation:
Midpoint formula
If we have coordinates (x₁,y₁) and (x₂,y₂), then the midpoint of these coordinates is determined by (x₁ + x₂)/2, (y₁ + y₂)/2. This forms a new coordinate you can call (x₃,y₃). The midpoint calculator will solve this instantaneously if you input the coordinates. Follow the steps above if calculating by hand.
For small numbers, it's easy to calculate the midpoint by hand, but with larger and decimal values, the calculator is the simplest and most convenient way to calculate the midpoint.
Answer:
k = 0.02278
Step-by-step explanation:
Given that:
The population P = 1674.7e^kt
where;
t represents the year,
if year 2000 represents t = 0
Then, the year 2007 represents = 7; &
year 2006 represents = 6
In 2006, population recorded in the city was about 1,920 thousand
Therefore;
Taking the logarithm of both sides, we get:
7.560080465= 7.423389324 + 6k
7.560080465 - 7.423389324 = 6k
0.136691141 = 6k
k = 0.136691141/6
k ≅ 0.02278
<span>3/28 exactly, or approximately 10.7%
Since we're drawing without replacement, let's first calculate the probability that the 1st marble is white. There are 3 white marbles out of a total of 8 marbles. So the probability of the 1st marble being white is 3/8.
Now assuming that the first marble picked is white, the probability of the second marble is 2 out of the 7 remaining marbles. So it's probability is 2/7.
This means that the probability of both marbles being white is 3/8 * 2/7 = 6/56 = 3/28, or approximately 10.7%</span>
