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2 years ago

Special Right Triangles

Mathematics

1 answer:

Leokris [45]2 years ago

7 0

Answer:

first option

Step-by-step explanation:

Using the sine/ cosine ratios in the right triangle and the exact values

sin30° = $\frac{1}{2}$ , cos30° = $\frac{\sqrt{3} }{2}$

sin30° = $\frac{opposite}{hypotenuse}$ = $\frac{x}{32}$ = $\frac{1}{2}$ ( cross- multiply )

2x = 32 ( divide both sides by 2 )

x = 16

----------------------------------------------------------

cos30° = $\frac{adjacent}{hypotenuse}$ = $\frac{y}{32}$ = $\frac{\sqrt{3} }{2}$ ( cross- multiply )

2y = 32 $\sqrt{3}$ ( divide both sides by 2 )

y = 16 $\sqrt{3}$

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Calculator

Sedaia [141]

Check the picture below.

so let's find the lengths of those two sides in red, since are the length and width of the rectangle.

$\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-6}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{-3}~,~\stackrel{y_2}{6})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d = \sqrt{[-3-(-6)]^2+[6-3]^2}\implies d=\sqrt{(-3+6)^2+(6-3)^2} \\\\\\ d=\sqrt{9+9}\implies \boxed{d=\sqrt{18}} \\\\[-0.35em] ~\dotfill$

$\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-6}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{-2}~,~\stackrel{y_2}{-1})~\hfill d=\sqrt{[-2-(-6)]^2+[-1-3]^2} \\\\\\ d=\sqrt{(-2+6)^2+(-1-3)^2}\implies d=\sqrt{16+16}\implies \boxed{d=\sqrt{32}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{area of the rectangle}}{(\sqrt{18})(\sqrt{32})}\implies \sqrt{18\cdot 32}\implies \sqrt{576}\implies 24$

7 0

3 years ago

Can someone solve and explain it to me please

lys-0071 [83]

Answer is C) 6

36 + 3(4x - 9) = 6(2x + 1)

36 + 12x - 27 = 12x + 6

12x - 12x = 6 - 9

0 ≠ -3

No solution

3 0

3 years ago

Answer 7, 8, 9, 10. <br> I am giving out a 5- star rating! and marking u brainy if its right!

UNO [17]

7. Four and 7 tenths
8. Twenty two and eighty nine hundredths
9. Forty Five and Three hundred Twenty Nine Thousandths
10.Twenty seven hundredths

3 0

3 years ago

For f(x) = 4x2 + 13x + 10, find all values of a for which f(a) = 7.

sammy [17]

Answer:

0.84

Step-by-step explanation:

4x2+13a+10=7

13a=7-10-8

13a=-11

a=-11:13

a=0.84

4 0

3 years ago

Let f be a differentiable function such that f(3)=15, f(6)=3, f ' (3)= -8, and f ' (6)= -2. The function g is differentiable and

Ray Of Light [21]

Answer:

A. $g'(3)=-\frac{1}{2}$

Step-by-step explanation:

We have been given that f be a differentiable function such that $f(3)=15$ , $f(6)=3$ , $f'(3)= -8$ , and $f'(6)= -2$ . The function g is differentiable and $g(x)= f^{-1} (x)$ for all x.