8. 56 divided by 7 is 8, the simplest form of it
Let the side of the square base be x, and the height of the box be h.
<span>The material of the base is x^2, and the material of the four sides is 4xh. </span>
<span>4000 = hx^2 </span>
<span>h = 4000/x^2 </span>
<span>The total material is </span>
<span>M = x^2 + 4x(4000/x^2) = x^2 + 16000/x </span>
<span>Take the first derivative of M and set equal to 0. </span>
<span>M' = 2x - 16000/x^2 = 0 </span>
<span>Multiply by x^2: </span>
<span>2x^3 = 16000 </span>
<span>x^3 = 8000 </span>
<span>x = 20; h = 10; M = 1200</span>
Answer: Because the a-value is negative.
<u>Step-by-step explanation:</u>
The vertex form of a quadratic equation is: y = a(x - h)² + k where
- "a" is the vertical stretch
- -a is a reflection over the x-axis
- h is the horizontal shift (positive = right, negative = left)
- k is the vertical shift (positive = up, negative = down)
Given: g(x) = - (x + 1)² - 3
↓
a= -1
Since the a-value is negative, the parabola will be reflected over the x-axis which will change the curve from (U-shaped) to (∩-shaped).
A science test, which is worth 100 points, consists of 24 questions. Each question is worth either 3 points or 5 points. If x is the number of 3-point questions and y is the number of 5-point questions, the system shown represents this situation.
x + y = 24
3x + 5y = 100
What does the solution of this system indicate about the questions on the test?
The test contains 4 three-point questions and 20 five-point questions.
The test contains 10 three-point questions and 14 five-point questions.
The test contains 14 three-point questions and 10 five-point questions.
The test contains 20 three-point questions and 8 five-point questions.
Answer:
the value of x ? answer : 4
