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The set A satisfying the given inequality is A = (-, -10].
Following are some facts which are true for an inequality relation:
- Equal numbers can be added or subtracted from both sides of an inequality without affecting the inequality sign.
- The Inequality sign is unchanged if both sides are multiplied or divided by a positive number, but when multiplied or divided by a negative number the inequality sign is reversed.
Since y ∈ B, -2 ≤ y ≤ 7. So,
The set {-x | inequality (1) holds ∀ y ∈ B} is [10, ) i.e.
10 ≤ -x ≤ .
Multiplying -1 throughout gives
-10 ≥ x ≥ -.
x, thus, lies in the range A = (-, -10}.
Learn more about the inequality here.
Disclaimer: The question was incomplete. Please find the full content below.
<h3>Question </h3>Find the set A such that for x ∈ A
∀y ∈ B = {y ∈ R | -2 ≤ y ≤ 7}.
#SPJ4
No rounding is necessary to answer the question.
We can subtract the (linear) density of the second box from that of the first to see which box is heavier per unit height.
This value is obviously less than zero, so ...
... the box of magazines has the greater mass per unit height.
_____
The question didn't ask for the mass per height, and we didn't compute it. All we did was make a conversion to comparable units. The units we ended up with are mixed English and metric units, but that doesn't matter for the purpose of comparison.
Since all we're really interested in is <em>the sign of the difference</em> of mass/height, we don't even need to actually compute that difference. We just need to do enough computation to be able to tell whether the sign is positive or negative.
g(x) = (1/4)x^2 . correct option C) .
<u>Step-by-step explanation:</u>
Here we have , and we need to find g(x) from the graph . Let's find out:
We have , . From the graph we can see that g(x) is passing through point (2,1 ) . Let's substitute this point in all of the four options !
A . g(x) = (1/4x)^2
Putting (2,1) in equation g(x) = (x/4)^2 , we get :
⇒
⇒
Hence , wrong equation !
B . g(x) = 4x^2
Putting (2,1) in equation g(x) = 4x^2 , we get :
⇒
⇒
Hence , wrong equation !
C . g(x) = (1/4)x^2
Putting (2,1) in equation g(x) = (1/4)x^2 , we get :
⇒
⇒
Hence , right equation !
D . g(x) = (1/2)x^2
Putting (2,1) in equation g(x) = (1/2)x^2 , we get :
⇒
⇒
Hence , wrong equation !
Therefore , g(x) = (1/4)x^2 . correct option C) .
We are given this inequality,
We will follow these steps to solve it:
Step 1:
First let us bring 10 to the left side.
10 is in addition on right, so we apply opposite operation of addition that is subtracting 10 from left side, we get
Step 2:
Next we have to eliminate -4 which is in multiplication with x on the right side.
So applying opposite operation of multiplication that is dividing both sides by -4.
We have to consider here that when we divide or multiply with a negative the sign of inequality reverses, that is ≥ becomes ≤ and vice versa.
x≥4
Answer is last option x≥4.