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2 years ago

The sales tax rate is

Mathematics

1 answer:

ruslelena [56]2 years ago

7 0

The price will be $25.30

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How to solve these two problems ？

puteri [66]

8) $\theta$ is -0.896 radians

9) length of arc is 41.91 cm

Solution:

Given that,

$tan\ \theta = \frac{-5}{4}$

$\theta$ is in quadrant 4

To find: $\theta$

From given,

$tan\ \theta = \frac{-5}{4}\\\\\theta = tan^{-1} \frac{-5}{4}\\\\\theta = tan^{-1} (-1.25)\\\\\theta = -51.34$

Thus value of $\theta$ is -51.34 degrees

Convert degrees to radians

$-51.34\ degree = -51.34 \times \frac{ \pi }{180}\ radian\\\\-51.34\ degree = -0.896\ radian$

Thus $\theta$ is -0.896 radians

From given,

radius = 15.4 cm

$\theta = \frac{13 \pi }{15}$

The length of arc when angle in radians is:

$arc\ length = r \times \theta\\\\arc\ length = 15.4 \times \frac{ 13 \pi }{15}\\\\arc\ length = 15.4 \times 2.721\\\\arc\ length = 41.91$

Thus length of arc is 41.91 cm

4 0

2 years ago

Find the distance between the points given. (-3, 2) and (9, -3)

g100num [7]

The distance will be given by the equation;
D= $\sqrt{( x_{1} - x_{2} )^{2} +( y_{1} - y_{2} )^{2} }$
D= $\sqrt{ (-3-9)^{2}+( 2--3)^{2} }$
D= $\sqrt{ (-12)^{2} + (5)^{2} }$
D= $\sqrt{169}$
D=13 units

8 0

3 years ago

Lionel plays trumpet for a minimum of 45 minutes on the days that he practices. If x is the number of days that Lionel practices

Angelina_Jolie [31]

Answer:

The inequality is $0.75x\geq y$

Step-by-step explanation:

Given : Lionel plays trumpet for a minimum of 45 minutes on the days that he practices. If x is the number of days that Lionel practices and y is the total number of hours he spends practicing.

To find : Which inequality represents this situation?

Solution : He plays trumpet for a minimum of 45 minutes

$45 \text{minutes}=\frac{45}{60}=\frac{3}{4}=0.75\text{hours}$