Answer:
k = -9.
Step-by-step explanation:
As the triangle is right-angled at Q, by Pythagoras:
PR^2 = PQ^2 + RQ^2
So, substituting the given data and using the distance formula between 2 points:
(7 - 1)^2 + (k - 4)^2 = (-4-4)^2 + (-3-1)^2 + (7 - (-3))^2 + (k - (-4))^2
36 + (k - 4)^2 = 64 + 16 + 100 + ( k + 4)^2
(k - 4)^2 - (k + 4)^2 = 180 - 36
k^2 - 8k + 16 - (k^2 + 8k + 16) = 144
-16k = 144
k = -9.
Answer:
d. 20+10+5+2.5+...
Step-by-step explanation:
No geometric series with a common ratio of magnitude greater than 1 will have a finite sum. Nor will any arithmetic series.
Those descriptions exclude answer choices a, b, c. Choice d is a geometric series with a common ratio of 1/2, so will have a finite sum. (It is 40.)
1/4(2x - 14) = 4....multiply both sides by 4
2x - 14 = 4 * 4
2x - 14 = 16
2x = 16 + 14
2x = 30
x = 30/2
x = 15 <==
Answer:
(8, -8)
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
- Subtraction Property of Equality
<u>Algebra I</u>
- Terms/Coefficients
- Coordinates (x, y)
- Solving systems of equations using substitution/elimination
Step-by-step explanation:
<u>Step 1: Define Systems</u>
y = x - 16
5y = 2x - 56
<u>Step 2: Solve for </u><em><u>x</u></em>
- Substitute in <em>y</em>: 5(x - 16) = 2x - 56
- Distribute 5: 5x - 80 = 2x - 56
- [Subtraction Property of Equality] Subtract 2x on both sides: 3x - 80 = -56
- [Addition Property of Equality] Add 80 on both sides: 3x = 24
- [Division Property of Equality] Divide 3 on both sides: x = 8
<u>Step 3: Solve for </u><em><u>y</u></em>
- Define original equation: y = x - 16
- Substitute in <em>x</em>: y = 8 - 16
- Subtract: y = -8