Answer:
the solution of the system is:
x = 1 and y = 2.
Step-by-step explanation:
I suppose that we want to solve the equation:
-6*x + 6*y = 6
6*x + 3*y = 12
To solve this, we first need to isolate one of the variables in one of the equations.
Let's isolate y in the first equation:
6*y = 6 + 6*x
y = (6 + 6*x)/6
y = 6/6 + (6*x)/6
y = 1 + x
Now we can replace this in the other equation:
6*x + 3*(1 + x) = 12
6*x + 3 + 3*x = 12
9*x + 3 = 12
9*x = 12 - 3 = 9
x = 9/9 = 1
Now that we know that x = 1, we can replace this in the equation "y = 1 + x" to find the value of y.
y = 1 + (1) = 2
Then the solution of the system is:
x = 1 and y = 2.
-3 / 4 + p = 1/2
LCD 4 and 2 = 4
Multiply by LCD = 4
p. (4)- 3/4 .( 4 ) = 1/2.(4)
4 p - 3 = 2
Add 3 to both sides:
4 p - 3 + 3 = 2 + 3
4 p = 5
Divide both sides by 4 :
4p / 4 = 5 /4
p = 5/4
Height of the kite is = 36 inches.
Width of the kite is = 30 inches
One of the ways to find the area is to draw a vertical line to break the kite into two equal triangles. Mark the base as 36 inches and height as 15 inches .
Now we will use the formula
to find the area of each triangle. Then we will add both the areas to find the area of the kite.
Area of 1 triangle =
= 270 square inches
Area of the 2nd triangle is also = 270 square inches
Hence, area of the kite = 270+270 = 540 square inches
<u>Solution</u><u>:</u>
![\sqrt{4x + 13} = x + 2](https://tex.z-dn.net/?f=%20%5Csqrt%7B4x%20%2B%2013%7D%20%20%3D%20x%20%2B%202)
![= > ( \sqrt{4x + 13} ) ^{2} = (x + 2) ^{2}](https://tex.z-dn.net/?f=%20%3D%20%20%3E%20%28%20%5Csqrt%7B4x%20%2B%2013%7D%20%29%20%5E%7B2%7D%20%20%3D%20%28x%20%2B%202%29%20%5E%7B2%7D%20)
- Now, square root and square gets cancel out in the LHS. And in the RHS, apply the identity: (a + b)² = a² + 2ab + b².
![= > 4x + 13 = {(x)}^{2} + 2 \times x \times 2 + (2) ^{2} \\ = > 4x + 13 = {x}^{2} + 4x + 4](https://tex.z-dn.net/?f=%20%3D%20%20%3E%204x%20%2B%2013%20%3D%20%20%7B%28x%29%7D%5E%7B2%7D%20%20%2B%202%20%5Ctimes%20x%20%5Ctimes%202%20%2B%20%282%29%20%5E%7B2%7D%20%5C%5C%20%20%3D%20%20%3E%204x%20%2B%2013%20%3D%20%20%7Bx%7D%5E%7B2%7D%20%20%20%2B%204x%20%2B%204)
- Now, transpose 4x and 4 to LHS.
![= > 4x - 4x + 13 - 4 = {x}^{2} \\](https://tex.z-dn.net/?f=%20%3D%20%20%3E%204x%20-%204x%20%2B%2013%20-%204%20%3D%20%20%7Bx%7D%5E%7B2%7D%20%20%5C%5C%20)
- Now, do the addition and subtraction.
![= > {x}^{2} = 9 \\ = > x = \sqrt{9} \\ = > x = ±3](https://tex.z-dn.net/?f=%20%3D%20%20%3E%20%20%7Bx%7D%5E%7B2%7D%20%20%3D%209%20%5C%5C%20%20%3D%20%20%3E%20%20x%20%3D%20%20%5Csqrt%7B9%7D%20%20%5C%5C%20%20%3D%20%20%3E%20x%20%3D%20%C2%B13)
<u>Answer</u><u>:</u>
<u>x </u><u>=</u><u> </u><u>±</u><u> </u><u>3</u>
Hope you could understand.
If you have any query, feel free to ask.
Find the percentage of ratio to weight.
180/72 = 2.5
So 2.5 Earth Pounds = 1 Mars Pound
16*2.5 = 40 Pounds the rock weighs on earth.