What is |18x + 9| + 1 > 64 put into an interval notation and on a graph?

Mathematics

1 answer:

Gnoma [55]3 years ago

4 0

$\bf |18x+9| + 1 > 64\implies \pm(18x+9)+1>64 \\\\[-0.35em] ~\dotfill\\\\ +(18x+9)+1>64\implies 18x+10>64\implies 18x > 54 \\\\\\ x >\cfrac{54}{18}\implies \boxed{x > 3} \\\\[-0.35em] ~\dotfill\\\\ -(18x+9)+1>64\implies -18x-9+1>64\implies -18x-8>64 \\\\\\ -8>64+18x\implies -72 > 18x\implies \cfrac{-72}{18}=x\implies \boxed{-4>x}$

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From a radar station, the angle of elevation of an approaching airplane is 32.5 degree. The horizontal distance between the plan

denis23 [38]

Answer: 42.21 km

Step-by-step explanation:

We can solve this using trigonometry, since we have the following data:

$\theta=32.5\°$ is the the angle of elevation

$d=35.6 km$ is the horizontal distance between the plane and the radar station

$x$ is the hypotenuse of the right triangle formed between the radar station and the airplane

Now, the trigonometric function that will be used is <u>cosine</u>:

$cos\theta=\frac{d}{x}$ because $d$ is the adjacent side of the right triangle

$cos(32.5\°)=\frac{35.6 km}{x}$

Finding $x$ :

$x=\frac{35.6 km}{cos(32.5\°)}$

$x=42.21 km$

4 0

3 years ago

4/r=5/7solve for r. Help pls

antiseptic1488 [7]

Hello!

You first cross multiply

4 * 7 = 28

5 * r = 5 * r

r * 5 = 28

Divide both sides by 5

r = 28/5 = 5.6

The answer is 28/5 or 5.6

Hope this helps!

4 0

3 years ago

Read 2 more answers

(02.02 MC) Triangle ABC is shown. A is at negative 2, 1. B is at negative 1, 4. C is at negative 4, 5. If triangle ABC is reflec

Bezzdna [24]

Given:

The vertices of a triangle ABC are A(-2,1), B(-1,4) and C(-4,5).

Triangle ABC is reflected over the x‐axis, reflected over the y‐axis, and rotated 180 degrees.

To find:

The point B'.

Solution:

If a figure reflected over x-axis, then