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alexira [117]
3 years ago
6

A rectangular box has the dimensions shown in the diagram. The volume of the box is given by the function V(x) = x^3 – 4x, where

x is the height in inches. What is the height of the box if the volume is 15 in.^3?
Mathematics
1 answer:
madreJ [45]3 years ago
4 0

Answer:

length, width, and height are (b+2), (b-2), (b+3)

Step-by-step explanation:

Doing what the problem statement tells you to do, you get ...

 (b^3 +3b^2) -(4b +12)

 = b^2(b +3) -4(b +3) . . . . . factor each pair of terms

 = (b^2 -4)(b +3) . . . . . . . . . write as a product

 = (b -2)(b +2)(b +3) . . . . . . use the factoring of the difference of squares

The three factors are (b-2), (b+2), and (b+3). We have no clue as to how to associate those with length, width, and height. We just know these are the dimensions of the box.

Step-by-step explanation:

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Write a quadratic equation in STANDARD FORM given the roots:<br> 1, 1/2
Zigmanuir [339]

Answer:

f(x) = 2x^2 - 3x + 1

Step-by-step explanation:

The root 1 is associated with the factor (x - 1).

The root 1/2 is associated with the factor (x - 1/2), which in turn is equivalent to (2x -1)

The quadratic in question is f(x) = (x - 1)(2x - 1).  To write this in standard form, perform the indicated multiplication:

f(x) = 2x^2 - 2x - x + 1, or f(x) = 2x^2 - 3x + 1

5 0
3 years ago
Which equation represents the line that passes through the points (-3, 7) and (9,-1)? oy--3x+5 o y=-x-7 o y=zx-7 oy - 12 2x+5​
olchik [2.2K]

Answer:

The answer is

<h2>y =  -  \frac{2}{3} x + 5</h2>

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

To find the equation we must first find the slope of the line.

So the slope of the line using points (-3, 7) and (9,-1) is

<h3>m =  \frac{ - 1 - 7}{9 + 3}  =  -  \frac{8}{12}  =  -  \frac{2}{3}</h3>

Now we use the formula

<h3>y - y1 = m(x - x1)</h3>

where

m is the slope

( x1 , y1) is any of the points given

So the equation of the line using point

( - 3 , 7) and slope - 2/3 is

<h3>y - 7 =  -  \frac{2}{3} (x + 3) \\ y - 7 =  -  \frac{2}{3} x - 2 \\ y =  -  \frac{2}{3} x - 2 + 7</h3>

We have the final answer as

<h3>y =  -  \frac{2}{3} x + 5</h3>

Hope this helps you

5 0
3 years ago
Read 2 more answers
Helppp math sucksss
Alex777 [14]

Answer:

H can't be a function.

Step-by-step explanation:

If x has more than one y then it doesn't pass the vertical line test and is not a function.

7 0
3 years ago
Someone please help!!!!!
Nadya [2.5K]

Answer:

144 people were originally at the party.

Step-by-step explanation:

18 boys is one fifth of the second boys population, so the second population is 18x9 = 162. The original population would be 162-18, which equals 144.

6 0
3 years ago
The sum of two numbers is 62, and their difference is 8. What are the numbers
Lemur [1.5K]
Sum of two numbers is 62?
Let's call the two numbers a and b

let's find two same numbers that would add up to 62: 31.
31 + 31 = 62

since it said the difference is 8, we have to add 4 to one number and subtract 4 from another.
31 - 4 = 27
31 + 4 = 35

Therefore, the two numbers following the given rules are 27 and 35
7 0
3 years ago
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