Answer:
x -2y = -4
Step-by-step explanation:
The slope of the line between points C and D is ...
m = (y2 -y1)/(x2 -x1)
m = (7 -13)/(5 -2) = -6/3 = -2
The slope of the perpendicular line is the opposite reciprocal of this: -1/(-2) = 1/2. The point-slope equation of the desired line is ...
y -k = m(x -h) . . . . line with slope m through point (h, k)
y -1 = 1/2(x -(-2))
We can rearrange this to standard form.
2y -2 = x +2 . . . . . multiply by 2
-4 = x -2y . . . . . . . subtract 2y+2
x -2y = -4 . . . . . . standard form equation of the desired line
Answer:
x = 6
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
- Multiplication Property of Equality
- Division Property of Equality
- Addition Property of Equality
- Subtract Property of Equality
<u>Algebra I</u>
- Terms/Coefficients/Degrees
- Expand by FOIL (First Outside Inside Last)
- Factoring
- Multiple Roots
<u>Trigonometry</u>
[Right Triangles Only] Pythagorean Theorem: a² + b² = c²
- a is a leg
- b is another leg
- c is the hypotenuse
Step-by-step explanation:
<u>Step 1: Identify</u>
<em>a</em> = x + 3
<em>b</em> = x
<em>c</em> = √117
<u>Step 2: Solve for </u><em><u>x</u></em>
- Substitute [PT]: (x + 3)² + x² = (√117)²
- Expand [FOIL]: x² + 6x + 9 + x² = (√117)²
- Combine like terms: 2x² + 6x + 9 = (√117)²
- Exponents: 2x² + 6x + 9 = 117
- [SPE] Subtract 117 on both sides: 2x² + 6x - 108 = 0
- Factor out GCF: 2(x² + 3x - 54) = 0
- [DPE] Divide 2 on both sides: x² + 3x - 54 = 0
- Factor Quadratic: (x - 6)(x + 9) = 0
- Solve roots/solve <em>x</em>: x = -9, 6
Since we are dealing with positive values, we can disregard the negative root.
∴ x = 6
Answer: QS and QR are the shortest segment of the triangle ΔPQS, and ΔSQR respectively.
Step-by-step explanation:
Since we have given that
ΔPQS, and ΔSQR,
Consider, ΔPQS,
As we know that " the length opposite to the largest angle is the shortest segment."
So, According to the above statement.
Similarly,
Consider, ΔSQR,
Again applying the above statement, we get that,
Hence, QS and QR are the shortest segment of the triangle ΔPQS, and ΔSQR respectively.
Answer:
A
Step-by-step explanation:
y=-3x
Because Y=-3x
