Answer:100 10 1
Step-by-step explanation:
Answer:
$0.64/lb
Step-by-step explanation:
For similar triangles, the ratio of the corresponding sides are equal. To determine the common ratio, we take the square root of the ratio of the given areas.
ratio = sqrt (384 / 1057)
ratio = 384/1057
Then, for the volume, we have to cube the ratio calculated above. If we let x be the value of the volume of the smaller solid.
(384/1057)^3 = x/1795
x = 86 yd
Thus, the volume of the smaller figure is 86 yd³.
Answer:
9. a = -7
10. 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>
a + 6a - 14 = 3a + 6a
<u>Step 2: Solve for </u><em><u>a</u></em>
- Combine like terms: 7a - 14 = 9a
- Subtract 7a on both sides: -14 = 2a
- Divide 2 on both sides: -7 = a
- Rewrite: a = -7
<u>Step 3: Check</u>
<em>Plug in a into the original equation to verify it's a solution.</em>
- Substitute in <em>a</em>: -7 + 6(-7) - 14 = 3(-7) + 6(-7)
- Multiply: -7 - 42 - 14 = -21 - 42
- Subtract: -49 - 14 = -63
- Subtract: -63 = -63
Here we see that -63 is equal to -63.
∴ a = -7 is a solution of the equation.
<u>Step 4: Define equation</u>
-12 - 4x = 8x + 4(1 - 7x)
<u>Step 5: Solve for </u><em><u>x</u></em>
- Distribute 4: -12 - 4x = 8x + 4 - 28x
- Combine like terms: -12 - 4x = -20x + 4
- Add 20x on both sides: -12 + 16x = 4
- Add 12 on both sides: 16x = 16
- Divide 16 on both sides: x = 1
<u>Step 6: Check</u>
<em>Plug in x into the original equation to verify it's a solution.</em>
- Substitute in <em>x</em>: -12 - 4(1) = 8(1) + 4(1 - 7(1))
- Multiply: -12 - 4 = 8 + 4(1 - 7)
- Subtract: -16 = 8 + 4(-6)
- Multiply: -16 = 8 - 24
- Subtract: -16 = -16
Here we see that -16 does indeed equal -16.
∴ x = 1 is a solution of the equation.
Answer:
A and C
Step-by-step explanation:
Both angles j and m share one common side and vertex with angle k. Angle n only shares a vertex and not a side with angle k, so it is not adjacent.
