An equation for the volume of the prism as a function of the height is Volume = h³ + 2h² - 15h.
- We are given a rectangular prism.
- A rectangular prism is no different than a cuboid.
- Let the height of the rectangular prism be "h".
- The length of the rectangular prism is "h-3".
- The width of the rectangular prism is "h+5".
- The volume of the rectangular prism is the same as that of the cuboid.
- The volume of the rectangular prism is the product of its length, its width, and its height.
- The volume of the rectangular prism is (h - 3)*(h + 5)*h.
- An equation for the volume of the prism as a function of the height is :
- Volume = (h - 3)*(h + 5)*h
- Volume = (h² + 2h - 15)*h
- Volume = h³ + 2h² - 15h
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The solutions of the equations are x = 1 and y = 2
The system of equations are
4x + 3y = 10
-4x + 5y = 6
Here we have to use the elimination method. Eliminate the x term and find the value of y term
Add both equation
3y + 5y = 10 +6
Add the like terms
8y = 16
y = 16 / 8
Divide the terms
y = 2
Substitute the value of x in the first equation
4x + 3y = 10
4x + 3×2 = 10
Multiply the terms
4x + 6 = 10
4x = 10 - 6
4x = 4
x = 4 / 4
Divide the terms
x = 1
Hence, the solutions of the equations are x = 1 and y = 2
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Answer: 24
Step-by-step explanation:
The ratio of sandcastles to kites was 3 to 5 so if 15 kites were spotted that meant that the 5 was multiplied by 3 so then we multiply the 3 by 3. Now there are 9 sandcastles and 15 kites so now we add 9 to 15 to figure out how many items were seen in all. Nine added to 15 equals 24 which means that 24 items were seen in total.
<span>In addition to linear, quadratic, rational, and radical functions, there are exponential functions. Exponential functions have the form f(x) = <span>bx</span>, where b > 0 and b ≠ 1. Just as in any exponential expression, b is called the base and x is called the exponent.</span>
<span>An example of an exponential function is the growth of bacteria. Some bacteria double every hour. If you start with 1 bacterium and it doubles every hour, you will have 2x bacteria after x hours. This can be written as f(x) = 2x.</span>
<span>Before you start, f(0) = 2<span>0 </span>= 1</span>
<span>After 1 hour f(1) = 21 = 2</span>
<span>In 2 hours f(2) = 22 = 4</span>
<span>In 3 hours f(3) = 23 = 8</span>
and so on.
<span>With the definition f(x) = <span>bx</span> and the restrictions that b > 0 and that b ≠ 1, the domain of an exponential function is the set of all real numbers. The range is the set of all positive real numbers. The following graph shows f(x) = 2x.</span>
<span> </span>
Answer:
The circumference is the distance around the circle, similar to the perimeter of a polygon.
Step-by-step explanation:
The term "circumference" is often used to refer to the once-around length of any circular or roughly-circular object. One can refer to the circumference of an ellipse or of one's head, for example.
