This problem involves finding arc lengths. The formula for arc length
is s = r*theta, where r is the radius and theta the central angle.
In 15 minutes, the minute hand sweeps out 1/4 of a circle, or pi/2 radians. This is the central angle. The arc length (how far the minute hand moves in 15 min) is then
s = (6 inches)(pi/2 rad) = 3pi inches, or about 9.42 inches.
25 minutes is equivalent to a central angle of (25/60)pi rad, or 1.31 radians. What is the associated arc length? Calculate this in the same way as I did for a central angle of pi/2.
Let's solve your equation step-by-step.<span><span><span>16</span><span>(<span>a−4</span>)</span></span>=<span><span>13</span><span>(<span><span>2a</span>+4</span>)</span></span></span>Step 1: Simplify both sides of the equation.<span><span><span>16</span><span>(<span>a−4</span>)</span></span>=<span><span>13</span><span>(<span><span>2a</span>+4</span>)</span></span></span><span><span><span><span>(<span>16</span>)</span><span>(a)</span></span>+<span><span>(<span>16</span>)</span><span>(<span>−4</span>)</span></span></span>=<span><span><span>(<span>13</span>)</span><span>(<span>2a</span>)</span></span>+<span><span>(<span>13</span>)</span><span>(4)</span></span></span></span>(Distribute)<span><span><span><span>16</span>a</span>+<span><span>−2</span>3</span></span>=<span><span><span>23</span>a</span>+<span>43</span></span></span>Step 2: Subtract 2/3a from both sides.<span><span><span><span><span>16</span>a</span>+<span><span>−2</span>3</span></span>−<span><span>23</span>a</span></span>=<span><span><span><span>23</span>a</span>+<span>43</span></span>−<span><span>23</span>a</span></span></span><span><span><span><span><span>−1</span>2</span>a</span>+<span><span>−2</span>3</span></span>=<span>43</span></span>Step 3: Add 2/3 to both sides.<span><span><span><span><span><span>−1</span>2</span>a</span>+<span><span>−2</span>3</span></span>+<span>23</span></span>=<span><span>43</span>+<span>23</span></span></span><span><span><span><span>−1</span>2</span>a</span>=2</span>Step 4: Multiply both sides by 2/(-1).<span><span><span>(<span>2<span>−1</span></span>)</span>*<span>(<span><span><span>−1</span>2</span>a</span>)</span></span>=<span><span>(<span>2<span>−1</span></span>)</span>*<span>(2)</span></span></span><span>a=<span>−4</span></span>
Answer:
u = 12
Step-by-step explanation:
The equation is showing 5(u) = 60
<u>Begin: 5(u)= 60</u>
2. Divide the 5 from both sides to get the u-value alone.
a) 5u/5 = u b) 60/5 = 12
<u>Now: u = 12</u>
Answer:
35 hotdogs
Step-by-step explanation:
You are running a concession stand at a basketball game. You are selling hotdogs and sodas.
Let the number of hot dogs be represented by x
The number of soda be represented by y
You sold a total of 87 hotdogs and sodas combined
x + y = 87
x = 87 - y
Each hotdog cost $1.50 and each soda cost $0.50. At the end of the night you made a total of $78.50.
Hence we have the equation:
$1.50 × x + $0.50 × y = $78.50
1.50x + 0.50y = 78.50
Substitute 87 - y for x
1.50(87 - y) + 0.50y = 78.50
130.5 - 1.50y + 0.50y = 78.50
Collect like terms
- 1.50y + 0.50y = 78.50 - 130.50
-1.00y = -52
y = -52/-1
y = 52 sodas
How many hotdogs did you sell?
Using the equation:
x = 87 - y
x = 87 - 52
x = 35 hotdogs
Hence, you sold 35 hotdogs
To find a he correct points, I counted the units each point was from the line of reflection. The. I took that same number of points and did it to find the new point. D’ is at (5,2) E’ is at (10,2) F’ is at (10,-5) And C’ is at (5,-5)
