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zaharov [31]
3 years ago
9

Find the tangents of the acute angles in the right triangle

Mathematics
1 answer:
crimeas [40]3 years ago
8 0

f=50

d=40

Hope this helps

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Detmermine the best method to solve the following equation, then solve the equation. (3x-5)^2=-125
liq [111]

For the given equation;

(3x-5)^2=-125

We shall begin by expanding the parenthesis on the left side, after which we would combine all terms on and move all of them to the left side, which shall yield a quadratic equation. Then we shall solve.

Let us begin by expanding the parenthesis;

\begin{gathered} (3x-5)^2\Rightarrow(3x-5)(3x-5) \\ (3x-5)(3x-5)=9x^2-15x-15x+25 \\ (3x-5)^2=9x^2-30x+25 \end{gathered}

Now that we have expanded the left side of the equation, we would have;

\begin{gathered} 9x^2-30x+25=-125 \\ \text{Add 125 to both sides and we'll have;} \\ 9x^2-30x+25+125=-125+125 \\ 9x^2-30x+150=0 \end{gathered}

We shall now solve the resulting quadratic equation using the quadratic formula as follows;

\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ \text{Where;} \\ a=9,b=-30,c=150 \\ x=\frac{-(-30)\pm\sqrt[]{(-30)^2-4(9)(150)}}{2(9)} \\ x=\frac{30\pm\sqrt[]{900-5400}}{18} \\ x=\frac{30\pm\sqrt[]{-4500}}{18} \\ x=\frac{30\pm\sqrt[]{-900\times5}}{18} \\ x=\frac{30\pm\sqrt[]{-900}\times\sqrt[]{5}}{18} \\ x=\frac{30\pm30i\sqrt[]{5}}{18} \\ \text{Therefore;} \\ x=\frac{30+30i\sqrt[]{5}}{18},x=\frac{30-30i\sqrt[]{5}}{18} \\ \text{Divide all through by 6, and we'll have;} \\ x=\frac{5+5i\sqrt[]{5}}{3},x=\frac{5-5i\sqrt[]{5}}{3} \end{gathered}

ANSWER:

x=\frac{5+5i\sqrt[]{5}}{3},x=\frac{5-5i\sqrt[]{5}}{3}

3 0
1 year ago
To rent a certain meeting room, a college charges a reservation fee of $ 46 and an additional fee of $ 6.40 per hour. The chemis
lisabon 2012 [21]

Answer:

Up to 5 hours

Step-by-step explanation:

<u>Given:</u>

  • One off fee = $46
  • Hourly rent = $6.4 / hr
  • Amount limitation= $78

<u>Equation to reflect the condition:</u>

  • 78 = 46 + 6.4t
  • 6.4t = 78 - 46
  • 6.4t = 32
  • t = 32/6.4
  • t = 5 hours max

So, the meeting room can be rented for up to 5 hours with $78

8 0
2 years ago
Help please, and explain.
Korvikt [17]

Answer: 2x + y

<u>Step-by-step explanation:</u>

logₐ(3) = x

logₐ(5) = y

logₐ(45) = logₐ(3²· 5)

             = logₐ(3)² + logₐ(5)

             = 2 logₐ(3) + logₐ(5)

             = 2     x      +   y        <em>substituted given values (stated above)</em>


4 0
3 years ago
Read 2 more answers
how man 1/3 inch cubes does it take to fill a box with width 2 2/3 inches,lenght 3 1/3 inches and height 2 1/3
galben [10]

idk anymore ;-; please WELP ME

3 0
3 years ago
Two sides of an isosceles triangle measure 3 inches and 7 inches. Which could be the length of the third side?
slamgirl [31]

Answer:

7

Step-by-step explanation:

6 0
2 years ago
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