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2 years ago

What is the value of f(7.5) when f(x)=2x+7

Mathematics

1 answer:

Ivan2 years ago

6 0

Hey there!!

Given :

$f ( x ) = 2x + 7$

Find f ( 7.5 )

Now, we will need to substitute the value of 7.5 in place of x

$f(7.5) = 2(7.5) + 7$

$f(7.5) = 15 + 7$

$f(7.5) = 22$

Hope my answer helps!

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There are 3 islands A,B,C. Island B is east of island A, 8 miles away. Island C is northeast of A, 5 miles away and northwest of

Nostrana [21]

Answer:

The bearing needed to navigate from island B to island C is approximately 38.213º.

Step-by-step explanation:

The geometrical diagram representing the statement is introduced below as attachment, and from Trigonometry we determine that bearing needed to navigate from island B to C by the Cosine Law:

$AC^{2} = AB^{2}+BC^{2}-2\cdot AB\cdot BC\cdot \cos \theta$ (1)

Where:

$AC$ - The distance from A to C, measured in miles.

$AB$ - The distance from A to B, measured in miles.

$BC$ - The distance from B to C, measured in miles.

$\theta$ - Bearing from island B to island C, measured in sexagesimal degrees.

Then, we clear the bearing angle within the equation:

$AC^{2}-AB^{2}-BC^{2}=-2\cdot AB\cdot BC\cdot \cos \theta$

$\cos \theta = \frac{BC^{2}+AB^{2}-AC^{2}}{2\cdot AB\cdot BC}$

$\theta = \cos^{-1}\left(\frac{BC^{2}+AB^{2}-AC^{2}}{2\cdot AB\cdot BC} \right)$ (2)

If we know that $BC = 7\,mi$ , $AB = 8\,mi$ , $AC = 5\,mi$ , then the bearing from island B to island C:

$\theta = \cos^{-1}\left[\frac{(7\mi)^{2}+(8\,mi)^{2}-(5\,mi)^{2}}{2\cdot (8\,mi)\cdot (7\,mi)} \right]$

$\theta \approx 38.213^{\circ}$

The bearing needed to navigate from island B to island C is approximately 38.213º.

8 0

2 years ago

Tell whether the given value is a solution of the inequality

kipiarov [429]

Answer:

Yes it is, because...

Step-by-step explanation:

This is an inequality, so you can treat it as an algebraic expression.

The first step is to multiple both sides by 2, to get rid of the 2 on the left side.
Your equation will now look like this:
y >= 2y - 22

The next step is to get all the y variables to one side, now that its a lot more simplified. Subtract 2y from both sides to get:
-y >= -22

Finally, cancel out the negative on both sides of the equation to get the y as a positive y, all by itself. This will get you:
y <= 22

REMINDER: when you divide by a negative number, such as in this case dividing by -1 on both sides, the inequality sign will flip!

y = 18 works because it is less than 22. (: