Answer:
The system has no solutions
Step-by-step explanation:
Here, we want to solve the given equation systems
we can simply rewrite the second equation as;
y = 7-8x
So, let’s equate the two y
-8x + 6= 7-8x
As we can see, we have -8x on both sides of the equation and this means that there is no solution to system
This is because no value of x will make it that the addition of 6 to -8x will
be same as that of adding 7
Common denominator
Common multiple
Simplest Form
GCF: Greatest Common Factor
LCM: Least Common Factor
Then Comparing Plain
Answer:
∠4 = 75°
Step-by-step explanation:
Alternate interior angles are equal.
∠6 and ∠4 are alternate interior angles.
∠6 = ∠4 = 75°
Answer:
x = - 3
y = - 2
Step-by-step explanation:
Start with the second equation. Switch
3y = 2x Divide by 3
3y/3 = 2x/3
y = 2x/3
Now go to the first equation. Put the value for y in the first equation.
x - 3(2x/3) = 3 Cancel the 3s on the left.
x - 2x = 3 Combine
-x = 3 Multiply by -1
-1(-x) = 3(-1)
x = - 3
Now go back to the original equation I have called the second equation
2x = 3y
2(-3) = 3y Put in - 3 for x
- 6 = 3y Divide by 3
-6 / 3 = y
y = - 2
Gauss' method for addition relies on the fact that you can 'pair' certain numbers together. Look at the example:
1+2+3+4+5+6+7+8+9+10
We could manually add all these together from left to right but a clever way to think about this is if we add together the ends of the sum (10+1) we get 11. If we then move one in from the ends and add these (2+9) we also get 11. This means that 1+2+...+9+10 is the same as 11+11+...+11+11.
Because each 2 numbers adds to 11 we know the total number of 11's we have to add together is the length of the sum divided by 2. In our case 5 (10 ÷ 2). We need to add 5 lots of 11 to get our answer. This is the same as 11 × 5 which is easily seen to be 55.
(If you add the 10 numbers together on a calculator you'll see 1+2+3+4+5+6+7+8+9+10 = 55) so this method really makes it a lot quicker.
Looking at your sequence, if we pair the ends together we get 401 (400+1) and we multiply this by the length of the sequence divided by 2. In your case, 200 (400 ÷ 2).
So the sum of all the numbers from 1 to 400 must be 401 × 200 = 80,200.
Remember the steps:
1. Pair the ends together and add them
2. Times this number by the length of the sequence halved
Hope this helps.