Which rule describes rotating 90° counterclockwise?

The range of f(x) = 7 4x is all positive real numbers. true or false

Rudik [331]

Range of f(x) = 7 + 4x is all positive real numbers.

5 0

3 years ago

The ratio 8.4 to 4.4

Mnenie [13.5K]

Ratios can be written in multiple ways such as

a:b
a to b
a/b

So we can write yours in those three ways:

8.4:4.4
8.4 to 4.4
8.4/4.4

5 0

3 years ago

a plane flies 5.0km due north from a point O and then 6.0km on a bearing of 060° the pilot then changes course on a bearing of 1

Virty [35]

The plane flies a distance of approximately 10.536 kilometers in straight line and with a bearing of approximately 035°.

A plane that travels a distance $r$ , in kilometers, with a bearing of $\theta$ sexagesimal degrees can be represented in standard position by means of the following expression:

$\vec r = r\cdot (\sin\theta, \cos \theta)$ (1)

We can obtain the resulting vector ( $\vec R$ ) by the principle of superposition:

$\vec R = \Sigma_{i=1}^{n} [r_{i}\cdot (\sin \theta_{i}, \cos \theta_{i})]$ (2)

If we know that $r_{1} = 5\,km$ , $\theta_{1} = 0^{\circ}$ , $r_{2} = 6\,km$ , $\theta_{2} = 60^{\circ}$ , $r_{3} = 4\,km$ and $\theta_{3} = 120^{\circ}$ , then the resulting vector is:

$\vec R = 5\cdot (\sin 0^{\circ}, \cos 0^{\circ}) + 6\cdot (\sin 60^{\circ}, \cos 60^{\circ}) + 4\cdot (\sin 120^{\circ}, \cos 120^{\circ})$

$\vec R = (5\sqrt{3}, 6) \,[km]$

The magnitude of the resultant is found by Pythagorean theorem:

$\|\vec R\| = \sqrt{R_{x}^{2}+R_{y}^{2}}$

And the bearing is determined by the following inverse trigonometric relationship:

$\theta_{R} = \tan^{-1} \left(\frac{R_{y}}{R_{x}}\right)$ (3)

If we know that $R_{x} = 5\sqrt{3}\,km$ and $R_{y} = 6\,km$ , then the magnitude and the bearing of the resultant is:

$\|\vec R\| = \sqrt{(5\sqrt{3})^{2}+6^{2}}$

$\|\vec R\| \approx 10.536\,km$

$\theta_{R} = \tan^{-1} \left(\frac{6}{5\sqrt{3}} \right)$

$\theta_{R} \approx 34.715^{\circ}$

The plane flies a distance of approximately 10.536 kilometers in straight line and with a bearing of approximately 035°.

To learn more on vectors, we kindly invite to check this verified question: brainly.com/question/21925479

6 0

2 years ago

What is 7%tax of something that costs 2.99

KonstantinChe [14]

For this case we can make the following rule of three:
2.99 ----------> 100%
x --------------> 7%
From here, we clear the value of x.
We have then:
 $x = (7/100) * (2.99)
$
 Rewriting the expression we have:
 $x = (0.07) * (2.99)

x = 0.2093 $$ 
Answer:
The sales taxes are:
x = 0.2093 $

3 0

3 years ago

Read 2 more answers

53x458/12+758-8= +30=

natta225 [31]

Answer

2802.833

Step-by-step explanation:

3 0

2 years ago

Read 2 more answers