5/7x+1/7=3
multiple both sides by 7
7•5/7x+7•1/7=7•3
reduce the numbers with 7
5x+7•1/7=7•3
5x+1=7•3
5x+1=21
move the constant to the right side of the equation and change its sign
5x+1=21
-1 -1
5x=21-1
subject the numbers
5x=20
divide both sides of the equation by 5
5x=20
÷5 ÷5
x=4
Answer:
We will take option B.
Step-by-step explanation:
Option A) |4 − 1| = 3 units
Option B) |4 − (−1)| = 5 units
Option C) |−4 + (−1)| = 5 units
Option D) |−4 − (−1)| = 3 units.
Now, from the number line and from the points given on the number line it is clear that the distance from one point to another is 5 units.
So. option B or Option C can be the right one.
Now, the right side point is on +4 point and the left side point is on -1 point.
So, the distance between those points will be calculated as 4 - (- 1) = 5.
Therefore, we will take option B. (Answer)
Answer:
2
Step-by-step explanation:
Add 7 to both sides.
7x=7+7
2 Simplify 7+7 to 14.
7x=14
3 Divide both sides by 7.
x= 14 divided by 7
x=2
S = total sales
$45,000 is his goal
$13,000 is his base salary
Luca gets 4% commission on his sales. 1.04s = total sales + 4% commission on sales
base salary + (total sales + 4% commission) = 45,000
AKA
13,000 + 1.04s = 45,000 --> Subtract 13,000 from both sides
1.04s = 32,000 --> Divide both sides by 1.04 to find the total sales
<u>s = $30769.24 (2.d.p.)</u>
<h2>
Hello!</h2>
The answer is:
- The first operation match with the polynomial:
B. ![9x^{2} -2x+2](https://tex.z-dn.net/?f=9x%5E%7B2%7D%20-2x%2B2)
- The second operation match with the polynomial:
A. ![-9x^{2}-2x+7](https://tex.z-dn.net/?f=-9x%5E%7B2%7D-2x%2B7)
- The third operation match with the polynomial:
C. ![9x^{2} +2x-7](https://tex.z-dn.net/?f=9x%5E%7B2%7D%20%2B2x-7)
<h2>Why?</h2>
In order to solve the given operations, we need to group the like terms.
Remember, like terms are terms that share the same variable and the same exponent.
For example:
![x^{2} +2x^{2} +3x^{3} +2=3x^{2} +3x^{3} +2](https://tex.z-dn.net/?f=x%5E%7B2%7D%20%2B2x%5E%7B2%7D%20%2B3x%5E%7B3%7D%20%2B2%3D3x%5E%7B2%7D%20%2B3x%5E%7B3%7D%20%2B2)
We only operate with the variables that shares the same exponent.
Also, we need to remember the distributive property:
![(a+b)(c+d)=ac+ad+bc+bd](https://tex.z-dn.net/?f=%28a%2Bb%29%28c%2Bd%29%3Dac%2Bad%2Bbc%2Bbd)
So, we are given the following polynomials:
![A.9x^{2} -2x+7\\\\B. 9x^{2} -2x+2\\\\C. 9x^{2} +2x-7](https://tex.z-dn.net/?f=A.9x%5E%7B2%7D%20-2x%2B7%5C%5C%5C%5CB.%209x%5E%7B2%7D%20-2x%2B2%5C%5C%5C%5CC.%209x%5E%7B2%7D%20%2B2x-7)
And we need to perform the following operations:
First operation,
![(7x^{2}-5x+3)+(2x^{2} +3x-1)=7x^{2} +2x^{2} -5x+3x+3-1\\\\7x^{2} +2x^{2} -5x+3x+3-1=9x^{2} -2x+2](https://tex.z-dn.net/?f=%287x%5E%7B2%7D-5x%2B3%29%2B%282x%5E%7B2%7D%20%2B3x-1%29%3D7x%5E%7B2%7D%20%2B2x%5E%7B2%7D%20-5x%2B3x%2B3-1%5C%5C%5C%5C7x%5E%7B2%7D%20%2B2x%5E%7B2%7D%20-5x%2B3x%2B3-1%3D9x%5E%7B2%7D%20-2x%2B2)
So, the first operation match with the polynomial:
B. ![9x^{2} -2x+2](https://tex.z-dn.net/?f=9x%5E%7B2%7D%20-2x%2B2)
Second operation,
![(3x^{2}-4x-4)+(-12x^{2}+2x+11)=3x^{2} -12x^{2} -4x+2x-4+11\\\\3x^{2} -12x^{2} -4x+2x-4+11=-9x^{2}-2x+7](https://tex.z-dn.net/?f=%283x%5E%7B2%7D-4x-4%29%2B%28-12x%5E%7B2%7D%2B2x%2B11%29%3D3x%5E%7B2%7D%20-12x%5E%7B2%7D%20-4x%2B2x-4%2B11%5C%5C%5C%5C3x%5E%7B2%7D%20-12x%5E%7B2%7D%20-4x%2B2x-4%2B11%3D-9x%5E%7B2%7D-2x%2B7)
So, the second operation match with the polynomial:
A. ![-9x^{2}-2x+7](https://tex.z-dn.net/?f=-9x%5E%7B2%7D-2x%2B7)
Third operation,
![(4x^{2} -3x-9)+(5x^{2} +5x+2)=4x^{2}+5x^{2} -3x+5x-9+2\\\\4x^{2}+5x^{2} -3x+5x-9+2=9x^{2} +2x-7](https://tex.z-dn.net/?f=%284x%5E%7B2%7D%20-3x-9%29%2B%285x%5E%7B2%7D%20%2B5x%2B2%29%3D4x%5E%7B2%7D%2B5x%5E%7B2%7D%20-3x%2B5x-9%2B2%5C%5C%5C%5C4x%5E%7B2%7D%2B5x%5E%7B2%7D%20-3x%2B5x-9%2B2%3D9x%5E%7B2%7D%20%2B2x-7)
So, the second operation match with the polynomial:
C. ![9x^{2} +2x-7](https://tex.z-dn.net/?f=%3C%2Fstrong%3E9x%5E%7B2%7D%20%2B2x-7%3Cstrong%3E)
Have a nice day!