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Delicious77 [7]

2 years ago

14

Find the length of side x in simplest radical form with a rational denominator.

1 answer:

alekssr [168]2 years ago

4 0

Answer:

$x = \frac{2*\sqrt{3}}{3}$

Step-by-step explanation:

Reference angle = 30°

Opposite side = x

Adjacent side = 2

Apply the tan trigonometric function, thus:

$tan (30) = \frac{opp}{adj}$

$tan (30) = \frac{x}{2}$

$2 * tan (30) = x$

$2 * \frac{1}{sqrt{3}} = x$ (tan 30 = 1/√3)

$\frac{2}{sqrt{3}} = x$

Rationalize

$\frac{2* \sqrt{3}}{sqrt{3} * \sqrt{3}} = x$

$\frac{2*\sqrt{3}}{3} = x$

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Maksim231197 [3]

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Help!<br> What is the cost of 50 shares of stock priced at $15.87.

lozanna [386]

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3 years ago

X2 - 4x + 3 = 0<br> lesser x =<br> greater x =<br> o

Levart [38]

Answer:

lesser x is 1

greater x is 3

Step-by-step explanation:

Here, we want to solve the equation so as to get the bigger and the lesser x values

We proceed as follows;

x^2 -4x + 3 = 0

x^2 - x-3x + 3 = 0

x(x-1) -3(x-1) = 0

(x-3)(x-1) = 0

x = 3

or x = 1

Greater x is 3

lesser x is 1

7 0

2 years ago

Od<br> 2<br> (<br> 2 7 1-3<br> 1 3 1-2<br> 6:1-6<br> b =<br> d =<br> IDONE

Lena [83]

Answer:

$a = \boxed{1},\: b=\boxed{0}\\\\c=\boxed{0},\: d=\boxed{1}$

Step-by-step explanation:

$\begin{bmatrix} 2 & 7\\\\1 & 3\end{bmatrix}\:\begin{bmatrix} -3 & 7\\\\1 & -2\end{bmatrix}=\begin{bmatrix} a & b\\\\c & d\end{bmatrix}$

Multiply both the matrices on left side, we find:

$\begin{bmatrix} 2(-3)+7(1) & 2(7)+7(-2)\\\\1(-3)+3(1) & 1(7)+3(-2)\end{bmatrix}=\begin{bmatrix} a & b\\\\c & d\end{bmatrix}$

$\rightarrow\begin{bmatrix} -6+7 & 14-14\\\\-3+3 & 7-6\end{bmatrix}=\begin{bmatrix} a & b\\\\c & d\end{bmatrix}$

$\rightarrow\begin{bmatrix} 1 & 0\\\\0 & 1\end{bmatrix}=\begin{bmatrix} a & b\\\\c & d\end{bmatrix}$

Comparing the corresponding elements of both the matrices on both sides, we find:

$a = \boxed{1},\: b=\boxed{0},\:c=\boxed{0},\: d=\boxed{1}$

7 0

2 years ago

Which ordered pairs are solutions to the inequality

Kipish [7]

Answer:

(1,-1)

(7,12)

(5,-3)

Step-by-step explanation:

we know that

If a ordered pair is a solution of the inequality, then the ordered pair must satisfy the inequality

we have

$y-2x \leq -3$

Verify each case

case 1) we have

(1,-1)

substitute the value of x and the value of y in the inequality and then compare the results

$-1-2(1) \leq -3$

$-3 \leq -3$ ----> is true

therefore

The ordered pair is a solution of the inequality

case 2) we have

(7,12)

substitute the value of x and the value of y in the inequality and then compare the results

$12-2(7) \leq -3$

$-12 \leq -3$ ----> is true

therefore

The ordered pair is a solution of the inequality

case 3) we have

(-6,-3)

substitute the value of x and the value of y in the inequality and then compare the results

$-3-2(-6) \leq -3$

$9 \leq -3$ ----> is not true

therefore

The ordered pair is not a solution of the inequality

case 4) we have

(0,-2)

substitute the value of x and the value of y in the inequality and then compare the results

$-2-2(0) \leq -3$

$-2 \leq -3$ ----> is not true

therefore

The ordered pair is not a solution of the inequality

case 5) we have

(5,-3)

substitute the value of x and the value of y in the inequality and then compare the results

$-3-2(5) \leq -3$

$-13 \leq -3$ ----> is true

therefore

The ordered pair is a solution of the inequality

6 0

2 years ago