Answer:
C. x<18
Step-by-step explanation:
If you substituted the inequalities with 5, the logical one is x<18.
Especially since 5 is less than 18, it isn;t greater than or less than 2,9, or 42.
Answer:
Equilateral triangle implies each angle is 60 degree.
And any median is the altitude.
So, NT perpendicular LM, where T is the midpoint of [ML];
We use the Pythagorean Theorem in right triangle NTL ( NT = h; NL = a;
LT = a / 2 );
h² = a² - (a/2)² = a² - a²/4 = 4a²/4 - a²/4 = 3a²/4
;
It follows that
h = √(3a²/4) = a√3/2 ≈ 0,866*a;
But, a = 8;
h ≈ 0,866 * 8 ≈ 6,928;
Step-by-step explanation:
Answer:
7.5 ft³/min
Step-by-step explanation:
Let x be the depth below the surface of the water. The height, h of the water is thus h = 10 - x.
Now, the volume of water V = Ah where A = area of isosceles base of trough = 1/2bh' where b = base of triangle = 4 ft and h' = height of triangle = 1 ft. So, A = 1/2 × 4 ft × 1 ft = 2 ft²
So, V = Ah = 2h = 2(10 - x)
The rate of change of volume is thus
dV/dt = d[2(10 - x)]/dt = -2dx/dt
Since dV/dt = 15 ft³/min,
dx/dt = -(dV/dt)/2 = -15 ft³/min ÷ 2 = -7.5 ft³/min
Since the height of the water is h = 10 - x, the rate at which the water level is rising is dh/dt = d[10 - x]/dt
= -dx/dt
= -(-7.5 ft³/min)
= 7.5 ft³/min
And the height at this point when x = 8 inches = 8 in × 1 ft/12 in = 0.67 ft is h = (10 - 0.67) ft = 9.33 ft
Answer: x=1/2
she was wrong, it's supposed to be
Step-by-step explanation: 8(x−3)+7=2x(4−17)
Step 1: Simplify both sides of the equation.
8(x−3)+7=2x(4−17)
(8)(x)+(8)(−3)+7=2x(4−17)(Distribute)
8x+−24+7=−26x
(8x)+(−24+7)=−26x(Combine Like Terms)
8x+−17=−26x
8x−17=−26x
Step 2: Add 26x to both sides.
8x−17+26x=−26x+26x
34x−17=0
Step 3: Add 17 to both sides.
34x−17+17=0+17
34x=17
Step 4: Divide both sides by 34.
34x/34=17/34 x=1/2
