Let's solve the first inequality at first. So,
−2(x + 4) + 10 < x − 7
-2x- 8 + 10 < x - 7 By distribution property.
-2x + 2 < x - 7 Adding the like terms.
-2x < x - 7 - 2 Subtract 2 from each sides.
-2x < x - 9 By simplifying.
-2x - x < -9 Subtract x from each sides.
-3x < -9
Since we are dividing by negative 3. So, sign of inequality will get change.
So, x>3
Now the next inequality is,
−2x + 9 > 3(x + 8)
-2x + 9 > 3x + 24
-2x > 3x + 24 - 9
-2x > 3x + 15
-2x - 3x > 15
-5x >15
So, x <-3
Hence, the correct choice is x > 3 or x < −3.
If arctan 4/3 = the tangent of that angle will be 4/3 , opposite 4 over adjacent 3
Now, you only have to take the sin of that angle it's opposite 4 over hypotenuse 5.
You will get that the answer is 4/5
hope this helps
Answer:
we conclude that:
If 4x - 6≠4, then 2x–5≠5 is the contrapositive of a conditional statement if 2x -5=5, then 4x-6=14.
Step-by-step explanation:
We know that the contrapositive of a conditional statement of the form "If p then q" is termed as "If ~q then ~p".
In other words, it is symbolically represented as:
' ~q ~p is the contrapositive of p q '
For example, the contrapositive of "If it is a rainy day, then they suspend the match" is "If they do not suspend the match, then it won't be a rainy day."
Given
p: 2x -5=5
q: 4x-6=14
As the contrapositive of a conditional statement of the form "If p then q" is termed as "If ~q then ~p
Thus, we conclude that:
If 4x - 6≠4, then 2x–5≠5 is the contrapositive of a conditional statement if 2x -5=5, then 4x-6=14.
9514 1404 393
Answer:
- 100 mL of 75% solution
- 150 mL of pure alcohol
Step-by-step explanation:
Let x represent the quantity (in mL) of pure alcohol needed for the mix. Then the amount of 75% needed is (250-x). The amount of alcohol in the mixture is ...
1.00x +0.75(250 -x) = 0.90(250)
0.25x +187.5 = 225 . . simplify
0.25x = 37.5 . . . . . . . . subtract 187.5
x = 150 . . . . . . . . . . . . . divide by 0.25
(250 -x) = 100 . . . . mL of 75% solution
You need 100 mL of the 75% solution and 150 mL of pure alcohol to obtain the desired mixture.
