Mathematics: 1. three times a number increased by four is less than -62. 2. the quotient of a number and -5 increased by one is at most 7. 3. the quotient of a number and 3 minus two is at least -12. 4. the product of -2 and a number minus six is greater than -18

1. three times a number increased by four is less

ashmarie69

19.09.2022

$\text{11) }x\approx 9.44,\\\text{12) }x\approx 7.88,\\\text{13) }x\approx 15.79,$

Step-by-step explanation:

In a right triangle only, the sine of an angle is equal to the angle's opposite side divided by the hypotenuse of the triangle. (o/h)

The cosine of the angle is equal to the angle's adjacent side divided by the hypotenuse of the triangle. (a/h)

The tangent of the angle is equal to angle's opposite side divided by the adjacent side. (o/a)

*In all three of these problems, we will be using sine, since we are given the angle's opposite side and the hypotenuse. (o/h)

11) Using the reference above, we have the following equation:

$\sin 19^{\circ}=\frac{x}{29},\\x=29\sin 19^{\circ},\\x\approx \boxed{9.44}$

12) Using the reference above, we have the following equation:

$\sin 21^{\circ}=\frac{x}{22},\\x=22\sin 21^{\circ},\\x\approx \boxed{7.88}$

13) Using the reference above, we have the following equation:

$\sin 33^{\circ}=\frac{x}{29},\\x=29\sin 33^{\circ},\\x\approx \boxed{15.79}$

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