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3 years ago

10

The inequality -x - 6<0

1 answer:

dmitriy555 [2]3 years ago

8 0

Answer:

-x <6+0=x<6

Step-by-step explanation:

you first need to collect the like terms together and work out the question

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Find the solution set of this inequality|10x+20| ≤10

Pavlova-9 [17]

Answer:

solution is

[-3,-1]

Step-by-step explanation:

we are given

$|10x+20|\leq 10$

Firstly, we will find critical values

so, let's assume it is equal

$|10x+20|= 10$

now, we can break absolute sign

For $|10x+20|= -(10x+20)$ :

$-(10x+20)= 10$

we can solve for x

$-10x-20= 10$

Add both sides by 20

$-10x-20+20= 10+20$

$-10x= 30$

Divide both sides by -10

and we get

$x=-3$

For $|10x+20|= (10x+20)$ :

$(10x+20)= 10$

we can solve for x

$10x+20= 10$

Subtract both sides by 20

$10x+20-20= 10-20$

$10x= -10$

Divide both sides by 10

and we get

$x=-1$

so, critical values are

$x=-3$

$x=-1$

now, we can draw a number line and locate these values

and then we can check inequality on each intervals

For $(-\infty,-3)$ :

We can select any random value from this interval and plug that in inequality

and we get

we can plug x=-5

$|10\times -5+20|\leq 10$

$|-50+20|\leq 10$

$30\leq 10$

so, this is FALSE

For $[-3,-1]$ :

We can select any random value from this interval and plug that in inequality

and we get

we can plug x=-2

$|10\times -2+20|\leq 10$

$|-20+20|\leq 10$

$0\leq 10$

so, this is TRUE

For $(-1,\infty)$ :

We can select any random value from this interval and plug that in inequality

and we get

we can plug x=0

$|10\times 0+20|\leq 10$

$|0+20|\leq 10$

$20\leq 10$

so, this is FALSE

so, solution is

[-3,-1]

7 0

3 years ago

4trig review please help me

egoroff_w [7]

Answer:

$4 \sqrt{3}$

4 0

3 years ago

If the lateral area of a right rectangular prism is 384 cm^2, its length twice its width, and its height is twice its length, fi

Katen [24]

Width = w
Length = 2w
Height = 4w
$w \times 2w = 384 \\ {2w}^{2} = 384 \\ {w}^{2} = 192 \\ w = 13.86cm$
Width = 13.86cm

Hope this helps. - M

7 0

3 years ago

Find the distance between (4,-2) & (-1,3)

AleksAgata [21]

Step-by-step explanation:

Use Pythagorean theorem here. To find the height, find the difference of the 2 y's. To find the length, find the difference between the 2 x's.

Length = x2 - x1

Height = y2 - y1

√length^2 + height^2 = distance

√5^2 + 5^2 = √50 = 7.07

8 0

3 years ago

Farmer Jack needs 1,800 square feet of garden space to have enough corn for a year. His garden space is currently 10 5?6 feet by

sergey [27]

Answer:

$1,605\ ft^{2}$

Step-by-step explanation:

step 1

Find the area of the garden space

First convert mixed number to an improper fraction

$10\frac{5}{6}\ ft=\frac{10*6+5}{6}=\frac{65}{6}\ ft$

$A=\frac{65}{6}*18=195\ ft^{2}$

step 2

Find how much more land Farmer Jack needs to plant the rest of his corn

$1,800\ ft^{2}-195\ ft^{2}=1,605\ ft^{2}$

4 0

3 years ago