Let's solve your inequality step-by-step.<span><span><span>|<span>8a+5</span>|</span>−6</span><4</span>Step 1: Add 6 to both sides.<span><span><span><span>|<span>8a+5</span>|</span>−6</span>+6</span><4+6</span><span><span>|<span>8a+5</span>|</span><10</span>Step 2: Solve Absolute Value.<span><span>|<span>8a+5</span>|</span><10</span>We know<span><span>8a+5</span><10</span>and<span><span>8a+5</span>>−10</span><span><span>8a+5</span><10</span>(Condition 1)<span><span><span>8a+5</span>−5</span><10−5</span>(Subtract 5 from both sides)<span>8a<5</span><span><span>8a/8</span><5/8</span>(Divide both sides by 8)<span>a<5/8</span><span><span>8a+5</span>>−10</span>(Condition 2)<span><span><span>8a+5</span>−5</span>><span>−10−5</span></span>(Subtract 5 from both sides)<span>8a>−15</span><span><span>8a/8</span>><span>−15/8</span></span><span>(Divide both sides by 8)
</span><span>a><span><span>−15/</span>8</span></span>Answer:<span><span>a<<span><span><span>5/8</span><span> and </span></span>a</span></span>><span><span>−15/</span><span>8</span></span></span>
Step-by-step explanation:
Since each person will get 1 fork and 1 spoon, we will need 20 forks and 20 spoons.
The lowest multiple of 6 that is above 20 is 24, so we need 4 packages of spoons.
The lowest multiple of 8 that is above 20 is also 24, so we need 3 packages of forks.
Trigonometry can be used to find angles and sides of simple triangles. If an 18-foot ladder touches a building 14 feet up the wall then the angle can be deduced by trigonometry. In this case, the ladder defines the hypotenuse (H) of the triangle and the wall defines the opposite (O) side of the triangle. Therefore we can use the equation theta=sin^-1(O/H) . This yields an angle of 51 degrees.