Answer:
≈ 77 cm²
Step-by-step explanation:
The area of the shaded portion is calculated as
area of outer sector - area of inner sector
= (πR² - π r²) × ( R is the outer radius, r is the inner radius )
= (π × 14² - π × 7² ) ×
= (196π - 49π ) ÷ 6
= 147π ÷ 6
≈ 77 cm² ( nearest whole number )
Step 1: Simplify both sides of the equation.<span><span><span>3x</span>+<span>2<span>(<span>x−9</span>)</span></span></span>=<span><span><span>8x</span>+x</span>−14</span></span><span><span><span><span>3x</span>+<span><span>(2)</span><span>(x)</span></span></span>+<span><span>(2)</span><span>(<span>−9</span>)</span></span></span>=<span><span><span><span>8x</span>+x</span>+</span>−14</span></span>(Distribute)<span><span><span><span><span>3x</span>+<span>2x</span></span>+</span>−18</span>=<span><span><span><span>8x</span>+x</span>+</span>−14</span></span><span><span><span>(<span><span>3x</span>+<span>2x</span></span>)</span>+<span>(<span>−18</span>)</span></span>=<span><span>(<span><span>8x</span>+x</span>)</span>+<span>(<span>−14</span>)</span></span></span>(Combine Like Terms)<span><span><span>5x</span>+<span>−18</span></span>=<span><span>9x</span>+<span>−14</span></span></span><span><span><span>5x</span>−18</span>=<span><span>9x</span>−14</span></span>Step 2: Subtract 9x from both sides.<span><span><span><span>5x</span>−18</span>−<span>9x</span></span>=<span><span><span>9x</span>−14</span>−<span>9x</span></span></span><span><span><span>−<span>4x</span></span>−18</span>=<span>−14</span></span>Step 3: Add 18 to both sides.<span><span><span><span>−<span>4x</span></span>−18</span>+18</span>=<span><span>−14</span>+18</span></span><span><span>−<span>4x</span></span>=4</span>Step 4: Divide both sides by -4.<span><span><span>−<span>4x</span></span><span>−4</span></span>=<span>4<span>−4</span></span></span><span>x=<span>−1</span></span>
Answer:
y = 3x + 4
Step-by-step explanation:
✔️First, find the slope using any two given pairs form the table, say (2, 10) and (5, 19):
Slope (m) = ∆y/∆x = (19 - 10) / (5 - 2) = 9/3
m = 3
✔️Find y-intercept (b) by substituting (x, y) = (2, 10) and m = 3 into y = mx + b
10 = 3(2) + b
10 = 6 + b
10 - 6 = b
4 = b
b = 4
✔️Write the equation by substituing m = 3 and b = 4 into y = mx + b
y = 3x + 4
The cube root of 81 is 4.32674871092