$\bf (\stackrel{a}{-20},\stackrel{b}{-21})\impliedby \textit{let's find the \underline{hypotenuse}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2+b^2} \qquad \begin{cases} c=hypotenuse\\ a=\stackrel{adjacent}{-20}\\ b=\stackrel{opposite}{-21}\\ \end{cases} \\\\\\ c=\sqrt{(-20)^2+(-21)^2}\implies c=\sqrt{841}\implies c=29 \\\\[-0.35em] ~\dotfill\\\\ ~\hfill cos(\theta )=\cfrac{\stackrel{adjacent}{-20}}{\stackrel{hypotenuse}{29}}~\hfill$

5 0

3 years ago

6. A certain $400 investment is increasing 10%

Mars2501 [29]

Answer:

0.10

Step-by-step explanation:

0.10 = 10/100 or 10%

Multiply 400*0.10 to get 10% of 400.

6 0

2 years ago

Jess has 60 ounces of an alloy that is 40% gold. How many ounces of pure gold must be added to this alloy to create a new alloy

tia_tia [17]

Answer:

84 ounces of pure gold

Step-by-step explanation:

Jess has 60 ounces of an alloy that is 40% gold. How many ounces of pure gold must be added to this alloy to create a new alloy that is 75% gold?

Pure gold = 100% gold

Let the number of ounces of pure gold = x

Hence, we have the equation

40% × 60 ounces + 100%× x ounces = 75%(60 + x)ounces

= 0.4 × 60 + 1x = 0.75(60 + x)

= 24 + x = 45 + 0.75x

Collect like terms

x - 0.75x = 45 - 24

0.25x = 21

x = 21/0.25

x = 84 ounces

Therefore, we need 84 ounces of pure gold

6 0

3 years ago