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3 years ago

8

Solve the compound inequality and give your answer in interval notation

1 answer:

frutty [35]3 years ago

7 0

Answer:

(-∞, -8) U [3, ∞)

Step-by-step explanation:

4x - 4 < -36 OR -2x -1 ≤ -7

4x < -32 OR -2x ≤ -6

x < -8 OR x ≥ 3 *divide by a negative, switch inequality

(-∞, -8) U [3, ∞)

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If h:k = 2:5, x:y=3:4 and 2h+x:k+2y = 1:2, find the ratio h-x: k-y.

fenix001 [56]

Given:

$h:k=2:5,x:y=3:4,2h+x:k+2y=1:2$

To find:

$h-x:k-y$

Solution:

We have, $h:k=2:5$ and $x:y=3:4$ .

Let the values of h and k are 2a and 5a respectively.

Let the values of x and y are 3b and 4b respectively.

We have,

$2h+x:k+2y=1:2$

It can be written as

$\dfrac{2h+x}{k+2y}=\dfrac{1}{2}$

$\dfrac{2(2a)+(3b)}{5a+2(4b)}=\dfrac{1}{2}$

$\dfrac{4a+3b}{5a+8b}=\dfrac{1}{2}$

$2(4a+3b)=1(5a+8b)$

On further simplification, we get

$8a+6b=5a+8b$

$8a-5a=8b-6b$

$3a=2b$

$a=\dfrac{2b}{3}$

Now,

$h-x:k-y=\dfrac{h-x}{k-y}$

$h-x:k-y=\dfrac{2-3b}{5a-4b}$

$h-x:k-y=\dfrac{2\times \dfrac{2b}{3}-3b}{5\times \dfrac{2b}{3}-4b}$

$h-x:k-y=\dfrac{\dfrac{4b}{3}-3b}{\dfrac{10b}{3}-4b}$

On further simplification, we get

$h-x:k-y=\dfrac{\dfrac{4b-9b}{3}}{\dfrac{10b-12b}{3}}$

$h-x:k-y=\dfrac{-5b}{-2b}$

$h-x:k-y=\dfrac{5}{2}$

$h-x:k-y=5:2$

Therefore, the ratio $h-x:k-y$ is $5:2$ .

8 0

3 years ago

0.25 (y-4)+0.07=0.22y-0.05 (60)

Georgia [21]

First, let's use distributive property and expand this equation:

<span>0.25 (y-4)+0.07=0.22y-0.05 (60)
</span>0.25y - 1 + 0.07= 0.22y - 3

Now, isolate the values of y and solve!

0.25y - 1 + 0.07= 0.22y - 3
0.25y - 0.22y = 1 - 0.07 - 3
0.03y = -2.07
y = -69

Hope this helps!
Message me if you have any questions :)

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katen-ka-za [31]

Answer:

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-(28.62-27.56)
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