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Sonja [21]
3 years ago
11

13(10 + 2) could be used to simplify which of the following problems?

Mathematics
1 answer:
Veseljchak [2.6K]3 years ago
6 0
Well first you need to show the rest of the problems before i can truely help you sorry.
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Simplify (1-√3)(⅓+√3) leaving your answer in the form p+q√3​
Mars2501 [29]

Answer:

\frac{-8 +2\sqrt{3} }{3}

Step-by-step explanation:

When working with surds we need to take note of the roots present there.

To expand this equation we can do it the following way noting that √3 X √3 = 3

<em></em>

<em>Expanding (1-√3)(⅓+√3)</em>

1 X 1/3 = 1/3

1 X √3 = √3

-√3 X 1/3 =-√3/3

√3 X √3 = 3

hence, expanding the equation, we have

1/3 + √3 -√3/3 + 3

We can simply group the like terms and add them up.

[1/3 +3] +[√3-√3/3]

10/3 + \frac{2\sqrt{3} }{3}

= \frac{-8 +2\sqrt{3} }{3}

8 0
3 years ago
Evaluate tan ( cos^-1 ( 1/8 ) ) , giving your answer as an exact value (no decimals)
vekshin1

\bf cos^{-1}\left( \cfrac{1}{8} \right)=\theta \qquad \qquad cos(\theta )=\cfrac{\stackrel{adjacent}{1}}{\stackrel{hypotenuse}{8}}\impliedby \textit{let's find the \underline{opposite}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2-a^2}=b \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ \pm\sqrt{8^2-1^1}=b\implies \pm\sqrt{63}=b ~\hfill tan(\theta )=\cfrac{\stackrel{opposite}{\pm\sqrt{63}}}{\stackrel{adjacent}{1}} \\\\\\ ~\hspace{34em}


\bf \stackrel{\textit{keeping in mind that}}{tan\left(cos^{-1}\left( \frac{1}{8} \right) \right)}\implies tan(\theta )

5 0
3 years ago
I need a word problem for this system of equation y=-80x+300. and I also need to explain the initial value and discuss the rate
photoshop1234 [79]

Answer:

15\4

Step-by-step explanation:

7 0
3 years ago
Stephanie rdes her bike 2 miles to the post office, and then another 50 yards to the train station. How many yards long was her
mestny [16]
There are 1,760 yards in a mile.

Multiply 1,760 by 2 = 3,520

Add 50 to 3,520 = 3,570

Stephanie's trip was 3,570 yards long.
7 0
3 years ago
Find the volume and surface area of this triangular prism. 12 cm 13 cm 18 cm and 5 cm ​
Ipatiy [6.2K]
⇒ s = a+b+c2=5+12+132 a + b + c 2 = 5 + 12 + 13 2 = 15 cm.
Area of the base = √s(s−a)(s−b)(s−c)
= √15×10×3×2 15 × 10 × 3 × 2 cm2 = 30 cm2
3 0
2 years ago
Read 2 more answers
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