The first step is to identify the order in which the equation must be solved, by following PEMDAS (you might know it as BEDMAS):
Parenthesis (or Brackets)
Exponents
Multiplication and Division
Addition and Subtraction
My advice would be to add parenthesis, following these rules, if you are not very good at finding them immediately by sight.
So:
![4 - 5 / 2 * (\frac{1}{10x}) = 1\\\\4 - [(5/2)*(\frac{1}{10x})]=1\\\\4-(2.5*\frac{1}{10x})=1\\\\4-\frac{2.5}{10x}-1=0\\3-\frac{x}{4}=0\\\frac{x}{4}=3\\x=3*4\\x=12](https://tex.z-dn.net/?f=4%20-%205%20%2F%202%20%2A%20%28%5Cfrac%7B1%7D%7B10x%7D%29%20%20%3D%201%5C%5C%5C%5C4%20-%20%5B%285%2F2%29%2A%28%5Cfrac%7B1%7D%7B10x%7D%29%5D%3D1%5C%5C%5C%5C4-%282.5%2A%5Cfrac%7B1%7D%7B10x%7D%29%3D1%5C%5C%5C%5C4-%5Cfrac%7B2.5%7D%7B10x%7D-1%3D0%5C%5C3-%5Cfrac%7Bx%7D%7B4%7D%3D0%5C%5C%5Cfrac%7Bx%7D%7B4%7D%3D3%5C%5Cx%3D3%2A4%5C%5Cx%3D12)
We check our answer:
![x=12\\4 - [(5 / 2) * (1/10)*(x)] = 1\\4 - [(5 / 2) * (\frac{1}{10}) * (12))] = 1\\4 - [2.5 * (\frac{1}{10})*12] = 1\\4 - [(\frac{2.5}{10})*12] = 1\\4 - [(\frac{1}{4})*12] = 1\\4 - 3 = 1\\1=1](https://tex.z-dn.net/?f=x%3D12%5C%5C4%20-%20%5B%285%20%2F%202%29%20%2A%20%281%2F10%29%2A%28x%29%5D%20%3D%201%5C%5C4%20-%20%5B%285%20%2F%202%29%20%2A%20%28%5Cfrac%7B1%7D%7B10%7D%29%20%2A%20%2812%29%29%5D%20%3D%201%5C%5C4%20-%20%5B2.5%20%2A%20%28%5Cfrac%7B1%7D%7B10%7D%29%2A12%5D%20%3D%201%5C%5C4%20-%20%5B%28%5Cfrac%7B2.5%7D%7B10%7D%29%2A12%5D%20%3D%201%5C%5C4%20-%20%5B%28%5Cfrac%7B1%7D%7B4%7D%29%2A12%5D%20%3D%201%5C%5C4%20-%203%20%3D%201%5C%5C1%3D1)
We are right!
So, 
.
We are given the following equation and want to find which value of x will make it true:
Subtract 3 from both sides
Divide both sides by -6
Thus, the value that will make 3-6x=21 is x=-3. Let me know if you need any clarifications, thanks!
~ Padoru
Answer:
13) Angle A is 30°
14) Angle A is 45°
15) Angle A is 40°
16) Angle A is 40.5°
Step-by-step explanation:
By the angle sum theorem for the interior angles of a triangle, we have;
13) 130° + 2·x + 3·x = 180°
∴ 2·x + 3·x = 180° - 130° = 50°
2·x + 3·x = 5·x = 50°
x = 50°/5 = 10°
∠A = 3·x = 3 × 10° = 30°
∠A = 30°
14) 3·x + 9 + 4·x + 9 + 78° = 180°
7·x + 18 + 78° = 180°
7·x = 180° - (18 + 78)° = 180° - 96° = 84°
x = 84°/7 = 12°
∠A = 3·x + 9 = 3 × 12° + 9 = 45°
∠A = 45°
15) 90° + x + 51 + x + 61 = 180°
∴ x + 51 + x + 61 = 180° - 90° = 90°
2·x + 112 = 90°
2·x = (90 - 112)° = -22°
x = -22°/2 = -11°
x = -11°
∠A = x + 51 = -11° + 51 = 40°
∠A = 40°
16) x + 79 + x + 49 + 70° = 180°
x + x = (180 - 70 - 79 - 48)° = -17°
2·x = -17°
x = -17°/2 = -8.5°
x = -8.5°
∠A = x + 49 = (-8.5 + 49)° = 40.5°
∠A = 40.5°.
9514 1404 393
Answer:
$2.50
Step-by-step explanation:
The question asks for the total cost of a notebook and pen together. We don't need to find their individual costs in order to answer the question.
Sometimes we get bored solving systems of equations in the usual ways. For this question, let's try this.
The first equation has one more notebook than pens. The second equation has 4 more notebooks than pens. If we subtract 4 times the first equation from the second, we should have equal numbers of notebooks and pens.
(8n +4p) -4(3n +2p) = (16.00) -4(6.50)
-4n -4p = -10.00 . . . . . . . . . . . simplify
n + p = -10.00/-4 = 2.50 . . . . divide by the coefficient of (n+p)
The total cost for one notebook and one pen is $2.50.
__
<em>Additional comment</em>
The first equation has 1 more notebook than 2 (n+p) combinations, telling us that a notebook costs $6.50 -2(2.50) = $1.50. Then the pen is $2.50 -1.50 = $1.00.
One could solve for the costs of a notebook (n) and a pen (p) individually, then add them together to answer the question. We judge that to be more work.
