Answer:
x = -20
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
Step-by-step explanation:
<u>Step 1: Define</u>
2x - 12 = -52
<u>Step 2: Solve for </u><em><u>x</u></em>
- Add 12 on both sides: 2x = -40
- Divide 2 on both sides: x = -20
<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>: 2(-20) - 12 = -52
- Multiply: -40 - 12 = -52
- Subtract: -52 = -52
Here we see that -52 does indeed equal -52.
∴ x = -20 is the solution to the equation.
Answer:
(∠C) ≅ (∠B)
∴ tan(∠B) = tan(∠C) and
Slope AB = Slope BC
Step-by-step explanation:
Part A:
To explain why the slope from point from A to B is the same with the slope from B to C with similar triangles we have;
The angle between segment AB and the vertical is the same as the angle between segment BC and the vertical - (corresponding angles)
The angle between segment AB and the horizontal is the same as the angle between segment BC and the horizontal - (corresponding angles)
The length of a segment opposite to the angle between segment AB and the horizontal is the as the length of a segment opposite to the angle between segment BC and the horizontal
Therefore, the triangle formed by A, B and the point of intersection of the vertical line from A with the horizontal line from B is congruent to the triangle formed by B, C and the point of intersection of the vertical line from B with the horizontal line from C
Which gives the angle with the horizontal at C (∠C) is congruent to the angle with horizontal B (∠B)
The slope AB = tan(∠B)
Slope BC = tan(∠C)
(∠C) ≅ (∠B)
Therefore, tan(∠B) = tan(∠C) and slope AB = Slope BC.
Answer:
Step-by-step explanation:
The length and the width are based on the height.
height: h
length: 5h + 2
width: 3h - 2
If the sum of those is 126, then:
h + 5h + 2 + 3h - 2 = 126 and
9h = 126 so
h = 14
length is 5(14) + 2 which is 72
width is 3(14) - 2 which is 40
The volume is found by multiplying the length times the width times the height:
14 * 72 * 40 = 40,320 inches cubed
9514 1404 393
Answer:
x = 3.6
Step-by-step explanation:
The angle bisector divides the segments proportionally. This means they satisfy ...
bottom segment / side segment = x/6 = (6-x)/4
Multiplying by 12 gives ...
2x = 3(6 -x)
2x = 18 -3x . . . . . eliminate parentheses
5x = 18 . . . . . . . . add 3x
x = 3.6 . . . . . . . . . divide by 5
_____
<em>Alternate solution</em>
I like to try to work these mentally. The total of side lengths is 10, so the total base length (6) is 6/10 = 0.6 times that. Then x will be 0.6 times the left side length: 0.6·6 = 3.6 = x.
Answer:
1.56
Step-by-step explanation:
156 divided by 100