First of all, let's divide 572÷4.
572÷4=143
In order to find the first digit of the quotient, divide 5 and 4 first, since that is where 5 > 4.
5÷4=1.25
The 1 is in the hundreds place
Given problem is
![\frac{2}{3}w-\frac{1}{4}=\frac{2}{3}\left(w-\frac{1}{4}\right)](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B3%7Dw-%5Cfrac%7B1%7D%7B4%7D%3D%5Cfrac%7B2%7D%7B3%7D%5Cleft%28w-%5Cfrac%7B1%7D%7B4%7D%5Cright%29)
Here unknown variable is w so we will solve this equation for w.
Common denominator for given denominators 3 and 4 is 12 so we can multiply both sides by 12 so that we can cancel out all the fractions
![\frac{2}{3}w\cdot12-\frac{1}{4}\cdot12=\frac{2}{3}\cdot12\left(w-\frac{1}{4}\right)](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B3%7Dw%5Ccdot12-%5Cfrac%7B1%7D%7B4%7D%5Ccdot12%3D%5Cfrac%7B2%7D%7B3%7D%5Ccdot12%5Cleft%28w-%5Cfrac%7B1%7D%7B4%7D%5Cright%29)
![\frac{24}{3}w-\frac{12}{4}=\frac{24}{3}\left(w-\frac{1}{4}\right)](https://tex.z-dn.net/?f=%5Cfrac%7B24%7D%7B3%7Dw-%5Cfrac%7B12%7D%7B4%7D%3D%5Cfrac%7B24%7D%7B3%7D%5Cleft%28w-%5Cfrac%7B1%7D%7B4%7D%5Cright%29)
![8w-3=8\left(w-\frac{1}{4}\right)](https://tex.z-dn.net/?f=8w-3%3D8%5Cleft%28w-%5Cfrac%7B1%7D%7B4%7D%5Cright%29)
![8w-3=8w-\frac{8}{4}](https://tex.z-dn.net/?f=8w-3%3D8w-%5Cfrac%7B8%7D%7B4%7D)
![8w-3=8w-2](https://tex.z-dn.net/?f=8w-3%3D8w-2)
![8w-8w=3-2](https://tex.z-dn.net/?f=8w-8w%3D3-2)
![0=1](https://tex.z-dn.net/?f=0%3D1)
We know that 0=1 is not possible
Hence there is no solution for w.
Answer:
![y=\frac{1}{6}x+6](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B1%7D%7B6%7Dx%2B6)
Step-by-step explanation:
Let
and ![(x_2,y_2)\rightarrow(6,7)](https://tex.z-dn.net/?f=%28x_2%2Cy_2%29%5Crightarrow%286%2C7%29)
<u>Determine slope</u>
<u />![m=\frac{y_2-y_1}{x_2-x_1}\\ \\m=\frac{7-5}{6-(-6)}\\ \\m=\frac{2}{6+6}\\ \\m=\frac{2}{12}\\ \\m=\frac{1}{6}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D%5C%5C%20%5C%5Cm%3D%5Cfrac%7B7-5%7D%7B6-%28-6%29%7D%5C%5C%20%5C%5Cm%3D%5Cfrac%7B2%7D%7B6%2B6%7D%5C%5C%20%5C%5Cm%3D%5Cfrac%7B2%7D%7B12%7D%5C%5C%20%5C%5Cm%3D%5Cfrac%7B1%7D%7B6%7D)
<u>Use either ordered pair to find the y-intercept</u>
<u />![y=mx+b\\\\7=\frac{1}{6}(6)+b\\\\7=1+b\\\\6=b](https://tex.z-dn.net/?f=y%3Dmx%2Bb%5C%5C%5C%5C7%3D%5Cfrac%7B1%7D%7B6%7D%286%29%2Bb%5C%5C%5C%5C7%3D1%2Bb%5C%5C%5C%5C6%3Db)
<u>Final equation</u>
<u />![y=\frac{1}{6}x+6](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B1%7D%7B6%7Dx%2B6)
Answer:
x ≈ 9.4
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
<u>Trigonometry</u>
- [Right Triangles Only] Pythagorean Theorem: a² + b² = c²
Step-by-step explanation:
<u>Step 1: Define</u>
We are given a right triangle. We can use PT to find the missing length.
<u>Step 2: Identify Variables</u>
Leg <em>a</em> = 9
Leg <em>b</em> = <em>x</em>
Hypotenuse <em>c</em> = 13
<u>Step 3: Solve for </u><em><u>x</u></em>
- Substitute [PT]: 9² + x² = 13²
- Isolate <em>x</em> term: x² = 13² - 9²
- Exponents: x² = 169 - 81
- Subtract: x² = 88
- Isolate <em>x</em>: x = 2√22
- Evaluate: x = 9.38083
- Round: x ≈ 9.4
Answer:
the answer is 900
Step-by-step explanation:
the 900 will not be necessary