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Yuri [45]
3 years ago
5

Solve with interval notation Solve: 5 | x − 2 | + 4 > 8

Mathematics
1 answer:
Gnesinka [82]3 years ago
5 0

Answer:

x<6/5, x>14/5

Step-by-step explanation:

Steps

$5\left|x-2\right|+4>8$

$\mathrm{Subtract\:}4\mathrm{\:from\:both\:sides}$

$5\left|x-2\right|+4-4>8-4$

$\mathrm{Simplify}$

$5\left|x-2\right|>4$

$\mathrm{Divide\:both\:sides\:by\:}5$

$\frac{5\left|x-2\right|}{5}>\frac{4}{5}$

$\mathrm{Simplify}$

$\left|x-2\right|>\frac{4}{5}$

$\mathrm{Apply\:absolute\:rule}:\quad\mathrm{If}\:|u|\:>\:a,\:a>0\:\mathrm{then}\:u\:<\:-a\:\quad\mathrm{or}\quad\:u\:>\:a$

$x-2<-\frac{4}{5}\quad\mathrm{or}\quad\:x-2>\frac{4}{5}$

Show Steps

$x-2<-\frac{4}{5}\quad:\quad x<\frac{6}{5}$

Show Steps

$x-2>\frac{4}{5}\quad:\quad x>\frac{14}{5}$

$\mathrm{Combine\:the\:intervals}$

$x<\frac{6}{5}\quad\mathrm{or}\quad\:x>\frac{14}{5}$

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Setler [38]

Answer:

-15x + 30

Step-by-step explanation:

-3(5x -10)

-15x + 30

7 0
2 years ago
Write the solution as an inequality -10x&gt;250
jeyben [28]

Answer:

(X<-25) or -oo, -25

Step-by-step explanation:

because max is -25

3 0
3 years ago
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Find the exact values of all three trigonometric functions for each angle.
My name is Ann [436]

Answer:

Sin (270º)= -1

Cos (270º) = 0

Tan (270º) = -∞

Sin (330º) = -0.5

Cos (330º) = \frac{\sqrt{3} }{2} = 0.8660

Tan (330º) = - \frac{\sqrt{3} }{3} \\ = -0.57735

Step-by-step explanation:

3 0
3 years ago
A cylinder has volume 45 pie and radius 3. What is its height?
liraira [26]

Answer:

5 units

Step-by-step explanation:

The <u>volume of the cylinder</u> is the area of the circle multiplied by it's height. Therefore, the volume of the cylinder is πr² × h, which when simplified, gives us πr²h. Let's substitute the volume and the radius in the formula to find the height.

⇒ πr²h = Volume of cylinder

⇒ (π)(3²)(h) = 45π

Now, simplify the equation to evaluate the area of the cylinder.

⇒ (π)(3²)(h)/(3²)(π) = 45π/(3²)(π)

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7 0
2 years ago
BRAINLIESTTT ASAP!! PLEASE HELP ME :)
Andrej [43]

Answer:

2017.

Step-by-step explanation:

The equation for the future sale of motorcycles

= 5.75(1.16)^t  where t is in years

For cars it is

3.5(1.25)^t

3.5(1.25)^t > 5.75(1.16)^t

(1.25)^t > (5.75/3.5) 1.16^t

t ln 1.25 > ln 1.64286 + t ln 1.16

t ln 1.25 -  t ln 1.16 > ln 1.64286

t (ln 1.25 - ln 1.16) > ln 1.64286

t > ln 1.64286 / (ln1.25 - ln 1.16)

t > 6.64 .

So the answer is in the year 2017.

4 0
3 years ago
Read 2 more answers
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