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oksano4ka [1.4K]
3 years ago
9

Solve and graph the absolute value inequality: |2x + 4| > 8. number line with open circles on negative 6 and 2, shading in be

tween. number line with closed circles on negative 6 and 2, shading going in the opposite directions. number line with open circles on negative 6 and 2, shading going in the opposite directions. number line with open circles on negative 2 and 2, shading going in the opposite directions.
Mathematics
1 answer:
Klio2033 [76]3 years ago
6 0
|2x+4| > 8 breaks down into two inequalities: 2x+4 > 8 or 2x+4 < -8

Solving <span> 2x+4 > 8 leads to...
</span><span>2x+4 > 8
</span><span>2x+4-4 > 8-4
</span>2x > 4
2x/2 > 4/2
x > 2

Solving <span>2x+4 < -8 leads to...
</span><span>2x+4 < -8
</span><span>2x+4-4 < -8-4
</span>2x < -12
2x/2 < -12/2
x < -6

So either x > 2 or x < -6

You'll have 2 open circles at 2 and -6 on the number line. The shaded region will be the region to the left of -6 and to the right of 2. Basically everything but in between -6 and 2
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10 points
marishachu [46]

Answer:

150+12x=630

Step-by-step explanation:

The x represents the amount of months and it is multiplied by 12 because each month costs 12$. 150 have to be paid up front and this added to the monthly fee is equal to 630$

3 0
3 years ago
15 points!!! GEOMETRY help please!!<br> Questions attached!
dolphi86 [110]
3. Look at the picture.

We have the right angle triangle. We know the sum of measures of angles in triangle is equal 180°. Therefore:

x^o+90^o+43^o=180^o\\\\x^o+133^o=180^o\ \ \ |-133^o\\\\x^o=47^o

Answer:\ \boxed{47^o}

4.
Look at the picture.

Use Pythagorean theorem:

x^2+14^2=(10+x)^2\\\\x^2+196=10^2+2\cdot10\cdot x+x^2\ \ \ \ |-x^2\\\\196=100+20x\ \ \ |-100\\\\20x=96\ \ \ |:20\\\\x=4.8

Used:\ (a+b)^2=a^2+2ab+b^2

Answer:\ \boxed{4.8\ units}

5.
TRUE: 1; 2; 4

6.
We find a slope of the line OP:

m=\dfrac{y_2-y_1}{x_2-x_1}\\\\O(2;\ 6)\to x_1=2;\ y_1=6\\\\P(4;\ 3)\to x_2=4;\ y_2=3\\\\m=\dfrac{3-6}{4-2}=\dfrac{-3}{2}

We have: OP:\ y=-\dfrac{3}{2}x+b

Now, we must find the slope of the line perpendicular to the line OP.
We know:

k:y=m_1x+b;\ l:y=m_2x+c\\\\k\ \perp\ l\iff m_1m_2=-1

therefore

-\dfrac{3}{2}m_2=-1\ \ \ |\cdot\left(-\dfrac{2}{3}\right)\\\\m_2=\dfrac{2}{3}

So. We have the answer! :)

Answer:\ \boxed{y=\dfrac{2}{3}x+\dfrac{1}{3}}

6 0
2 years ago
PLEASE HELP!!!!!!!!!!!! WILL GIVE CORRECT ANSWER BRAINLIEST!!!!!!!!!
Korolek [52]

Answer:22.75

Step-by-step explanation:

8 0
3 years ago
Santana went for a hike on the 21 mile South Boundary Trail. If she can hike2 miles
Katena32 [7]

Answer:

It will take santana 630 minutes or 10.5 hours to complete the 21 miles.

Step-by-step explanation:

<h3>\frac{2}{60\\} \frac{21}{y}  y is what you are trying to find multiple her miles by the number of minutes and then divided by how many miles in  60 min. </h3><h3 /><h3 /><h3> </h3>
5 0
3 years ago
Please help....this is difficult for me to figure out..
Nitella [24]

Answer:

z would be 0.4 !

Step-by-step explanation:

Hope this helps :)))

6 0
3 years ago
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