The answer goes up by 12 each time
Its False. addition and subtraction, Multiplication and division are inverse operations.
Solution: The missing reason in Step 8 is substitution of
.
Explanation:
The given steps are used to prove the formula for law of cosines.
From step 5 it is noticed that our equation is
..... (1)
From step 7 it is noticed that the value of
is
.
So by substituting
for
in equation (1) we get the equation of step 8, i.e.,

Hence, the missing reason in Step 8 is substitution of
.
Simplify <span /><span><span><span><span><span><span><span><span><span>4</span><span /></span><span><span>8</span><span /></span><span><span /><span /></span></span></span></span><span /></span></span><span /></span><span>48</span></span> to <span /><span><span><span><span><span><span><span><span><span>1</span><span /></span><span><span>2</span><span /></span><span><span /><span /></span></span></span></span><span /></span></span><span /></span><span>12</span></span>
<span /><span><span><span><span><span><span><span><span><span><span>s</span><span>−</span><span>1</span></span><span /></span><span><span>4</span><span /></span><span><span /><span /></span></span></span><span>=</span><span><span><span><span>1</span><span /></span><span><span>2</span><span /></span><span><span /><span /></span></span></span></span><span /></span></span><span /></span><span>s−14=12</span></span>
2<span> </span>Multiply both sides by <span /><span><span><span><span><span><span>4</span></span><span /></span></span><span /></span><span>4</span></span>
<span /><span><span><span><span><span><span>s</span><span>−</span><span>1</span><span>=</span><span><span><span><span>1</span><span /></span><span><span>2</span><span /></span><span><span /><span /></span></span></span><span>×</span><span>4</span></span><span /></span></span><span /></span><span>s−1=12×4</span></span>
<span> </span>Simplify <span /><span><span><span><span><span><span><span><span><span>1</span><span /></span><span><span>2</span><span /></span><span><span /><span /></span></span></span><span>×</span><span>4</span></span><span /></span></span><span /></span><span>12×4</span></span> to <span /><span><span><span><span><span><span><span><span><span>4</span><span /></span><span><span>2</span><span /></span><span><span /><span /></span></span></span></span><span /></span></span><span /></span><span>42</span></span>
<span /><span><span><span><span><span><span>s</span><span>−</span><span>1</span><span>=</span><span><span><span><span>4</span><span /></span><span><span>2</span><span /></span><span><span /><span /></span></span></span></span><span /></span></span><span /></span><span>s−1=42</span></span>
Simplify <span /><span><span><span><span><span><span><span><span><span>4</span><span /></span><span><span>2</span><span /></span><span><span /><span /></span></span></span></span><span /></span></span><span /></span><span>42</span></span> to <span /><span><span><span><span><span><span>2</span></span><span /></span></span><span /></span><span>2</span></span>
<span /><span><span><span><span><span><span>s</span><span>−</span><span>1</span><span>=</span><span>2</span></span><span /></span></span><span /></span><span>s−1=2</span></span>
Add <span /><span><span><span><span><span><span>1</span></span><span /></span></span><span /></span><span>1</span></span> to both sides
<span /><span><span><span><span><span><span>s</span><span>=</span><span>2</span><span>+</span><span>1</span></span><span /></span></span><span /></span><span>s=2+1</span></span>
Simplify <span /><span><span><span><span><span><span>2</span><span>+</span><span>1</span></span><span /></span></span><span /></span><span>2+1</span></span> to <span /><span><span><span><span><span><span>3</span></span><span /></span></span><span /></span><span>3</span></span>
<span /><span><span><span><span><span><span>s</span><span>=</span><span>3</span></span><span /></span></span><span /></span><span>s=3
</span></span>
There are a couple ways to do this, but basically you need to convert the units.
<span>7 yards x 3 ft/yard = 21 feet </span>
<span>4 yards x 3 ft/yard = 12 feet </span>
<span>So the area (in sq. ft) will be: </span>
<span>21 x 12 </span>
<span>= 252 sq. ft. </span>
<span>Alternatively, you can figure the area in square *yards* and then multiply by 9 sq. ft per sq. yard. </span>
<span>7 yards x 4 yards x 9 sq. ft/sq. yard </span>
<span>= 252 sq. ft.
hope this helps :)</span>