Answer:x>7 or x ≤ -3
Solving the 1st inequality
-6x +14 < -28 --------------- (Collect like terms)
-6x < -28 - 14
-6x < - 42 -------------------- (Divide both sides by -6)
Note: If you decide an inequality expression by a negative value, the inequality sign changes)
-6x/-6 > -42/-6
x > 7
Solving the 2nd inequality
9x + 15 ≤ −12 ----------- (Collect like terms)
9x ≤ −12 - 15
9x ≤ −27 ------------------(Divide both sides by 9)
9
9x/9 ≤ −27/9
x ≤ -3
Bring both results together, we get
x>7 or x ≤ -3
The final result is complex (i.e. can't be combined together).
Step-by-step explanation:
In this question, you're trying to figure out what property is being represented.
Your answer would be the Distributive Property
This is your answer because as you can see, you are "distributing" the 2 to the variables inside the parenthesis.
When you distribute the number, you would be multiplying, in which in this case there is multiplication.
Therefore, Distributive property would be the correct answer.
The sides of a right triangle can always be expressed as:
h^2=x^2+y^2, where h is the length of the hypotenuse and x and y are the side lengths.
If we are to assume that "a" is a side length then 17 or "c" must be the hypotenuse so:
17^2=11^2+a^2
a^2=289-121
a^2=168
a=√168
a≈12.96 (to nearest hundredth)
Note we knew this assumption because of the answer choices, but technically, "a" COULD have been the hypotenuse without this implicit suggestion making:
a^2=17^2+11^2
a^2=410
a=√410
a≈20.25 (to the nearest hundredth)
Of course the above is not relevant to this particular question but be aware that you won't always be given answer choices to make the assumption of which side is the hypotenuse...
Answer:
1) x = 14°, y = 5°
2) x = 18.5°, y = 37°
Step-by-step explanation:
1) ∠AOC and ∠BOD are vertical angles, then ∠BOD = 25°
∠MOD = ∠MOB + ∠BOD = 90°
3x + 23° + 25° = 90°
3x = 90° - 23° - 25°
x = 42°/3
x = 14°
∠LOB = ∠LOM + ∠MOB = 90°
5y + 3x + 23° = 90°
5y = 90° - 23° - 3(14°)
y = 25°/5
y = 5°
2) ∠AOC and ∠BOD are vertical angles, then ∠BOD = 16°
∠EOB = ∠EOD + ∠DOB = 90°
2y + 16° = 90°
y = (90° - 16°)/2
y = 37°
∠DOF = ∠BOF + ∠DOB = 90°
4x + 16° = 90°
x = (90° - 16°)/4
x = 18.5°
