In triangle ABC,
AC = 12/ (sin30) = 12 / (1/2) = 24
DC = 24-x
DB = DC tan 30 = (24-x) tan30 <span>=(24−x)/</span><span>√3
</span>
In triangle ADB using Pythagorean Theorem<span><span>x2</span>+((24−x)/<span>√3</span><span>)2</span>=<span>12^2</span></span><span><span>x2</span>+(24−x<span>)^2</span>/3=<span>12^2</span></span><span>3<span>x2</span>+(24−x<span>)^2</span>=432</span><span>4<span>x2</span>−48x+576=432</span><span>4<span>x2</span>−48x+144=0</span><span><span><span>x2</span>−12x+36=0
x1 = x2 =6
AD = AC - DC = 24- (24-x) = 6</span></span>
Answer:
x = 1
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
Step-by-step explanation:
<u>Step 1: Define Equation</u>
3(4x - 5) - 4x + 1 = -6
<u>Step 2: Solve for </u><em><u>x</u></em>
- Distribute 3: 12x - 15 - 4x + 1 = -6
- Combine like terms: 8x - 14 = -6
- Isolate <em>x</em> term: 8x = 8
- Isolate <em>x</em>: x = 1
<u>Step 3: Check</u>
<em>Plug in x into the original equation to verify it's a solution.</em>
- Substitute in <em>x</em>: 3(4(1) - 5) - 4(1) + 1 = -6
- Multiply: 3(4 - 5) - 4 + 1 = -6
- Subtract: 3(-1) - 4 + 1 = -6
- Multiply: -3 - 4 + 1 = -6
- Subtract: -7 + 1 = -6
- Add: -6 = -6
Here we see that -6 does indeed equal -6.
∴ x = 1 is the solution to the equation.
3c/5-1/2=-31/2 Add 1/2 both sides
+1/2 +1/2
3c/5=-30/2 Then simplify the fraction
(5)3c/5=-15(5) Multiply 5 both sides
3c=75 Finally, divide by 3 both sides
c=25
So the answer to your question is E.
To find the mean of a set, add up all of the data points and divide by the number of data points.
For the first set:
(14+18+21+15+17) ÷ 5 = 85 ÷ 5 = 17
For the second set:
(15+17+22+20+16) ÷ 5 = 90 ÷ 5 = 18
To find the MAD (mean absolute deviation) of a set, find the mean of the distances of each data point from the mean.
For the first set:
(3+1+4+2+0) ÷ 5 = 10 ÷ 5 = 2
For the second set:
(3+1+4+2+2) ÷ 5 = 12 ÷ 5 = 2.4
To find the means-to-MAD ratio of a set, divide its mean by its MAD.
For the first set:
17 ÷ 2 = 8.5
For the second set:
18 ÷ 2.4 = 7.5
