Answer: 1/2(m<TUV)= m<TUW
Step-by-step explanation: If you divide TUV by 2 then you would get 28 degrees which would be The < TUW
<h3>Answer:</h3>
B) 10 pounds
<h3>Explanation:</h3>
Let x represent the amount of 70¢ candy to be added. The value of the mixture can be written as ...
... 90×30 + 70x = 85×(30+x) . . . . . where 30+x is the total weight of the mix
... 2700 +70x = 2550 +85x
... 150 = 15x . . . . . . add -70x-2550
... 10 = x . . . . . . . . . divide by the coefficient of x
10 pounds of candy at 70¢/lb must be added.
Answer:
x = 1 or x = -5
Step-by-step explanation:
We are given;
- The quadratic equation, x² + 4x - 13 = -8
We are required to solve the equation using the completing square method.
To do this, we use the following steps;
Step 1: We make sure the coefficient of x² is one
x² + 4x - 13 = -8
Step 2: Combine the like terms (take the constant term to the other side)
x² + 4x - 13 = -8
x² + 4x = -8 + 13
we get
x² + 4x = 5
Step 3: We add the square of half the coefficient of x on both sides of the equation
Coefficient of x = 4
Half of coefficient of x = 2
Square of half the coefficient of x = 2² (4)
We get;
x² + 4x + (2²) = 5 + (2²)
Step 4: Put x and 2 under one square and the solve the other side of the equation.
We get
(x + 2)² = 5 + 4
(x + 2)² = 9
Step 5: Get the square root on both sides of the equation;
(x + 2)² = 9
√(x + 2)² = ±√9
(x + 2)= ±3
Therefore;
x+2 = + 3 or x + 2 = -3
Thus, x = 1 or -5
The solution of the equation is x = 1 or x = -5
Answer:
the rate at which the height of the box is decreasing is -0.0593 cm/s
Step-by-step explanation:
Given the data in the question;
Constant Volume of a rectangular box with a square base = 500 cm³
area of the base increases at a rate of 6 cm²/sec
so change in the area of the base with respect to time dA/dt = 6 cm²/sec
each side of the base is 15 cm long
so Area of the base = 15 cm × 15 cm = 225 cm²
the rate at which the height of the box is decreasing = ?
Now,
V = Ah
dv/dt = 0 ⇒ Adh/dt + hdA/DT = 0
⇒ dh/dt = -hdA/dt / A
we substitute
dh/dt = [ -( 500 / 225 ) × 6 ] / 225
dh/dt = [ -(2.22222 × 6) ] / 225
dh/dt = [ -13.3333 ] / 225
dh/dt = -0.0593 cm/s
Therefore, the rate at which the height of the box is decreasing is -0.0593 cm/s
Answer:
54
Step-by-step explanation:
90+36= 126
180-126= 54
