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mihalych1998 [28]
3 years ago
9

Write the equation of a line with y-intercept of 5 and a slope of 3 forths.

Mathematics
1 answer:
STALIN [3.7K]3 years ago
4 0
Isnt it y= 3/4 + 5....
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we want to build a box with square base of side x and height and in such a way that the volume is 128 cubic inches. If we know t
sergij07 [2.7K]

Answer:

4 in × 4 in × 8 in or  

6.47 in × 6.47 in × 3.06 in

Step-by-step explanation:

Data:

(1)                  V = 128 in³

(2)                  l = w = x

(3) 4(l + w + h) = 64 in  (There are 12 edges)

Calculation:

The formula for the volume of the box is

(4)                 V = lwh

(5)              128 = x²h          Substituted (1) and (2) into (4)

(6)                  h = 128/x²     Divided each side by x²

          l + w +h = 16            Divided (1) by 4

          x + x + h = 16           Substituted (2) into 6

(7)          2x + h = 16           Combined like terms

     2x + 128/x² = 16           Substituted (6) into (7)

        2x³ + 128 = 16x²        Multiplied each side by x²

2x³ - 16x²+ 128 = 0            Subtracted 16x² from each side

    x³ - 8x² + 64 = 0           Divided each side by 2

According to the Rational Zeros theorem, a rational root must be a positive or negative factor of 64.

The possible factors are ±1, ±2, ±4, ±8, ±16, ±32, ± 64.

After a little trial-and-error with synthetic division (start in the middle and work down) we find that x = 4 is a zero.              

4|1   -8     0   64

 <u>|      4  -16  -64 </u>

   1  -4  -16      0

So, the cubic equation factors into (x - 4)(x² - 4x + 16) = 0

We can use the quadratic formula to find that the roots of the quadratic are

x = 2 - 2√5 and x = 2+ 2√5

We reject the negative value and find that there are two solutions to the problem.

x = 4 in and x = 2 + 2√5 ≈ 6.472 in

Case 1. x = 4 in

h = 128/x² = 128/4² = 128/16 = 8 in

The dimensions of the box are 4 in × 4 in × 8 in

Also, 4(l + w + h) = 4( 4 + 4 + 8) = 4 × 16 =  64 in

Case 2. x = 6.472 in

h = 128/x² = 128/6.472² = 128/41.89 = 3.056 in

The dimensions of the box are 6.47 in × 6.47 in × 3.06 in

Also, 4(l + w + h) = 4( 6.47 + 6.47 + 3.06) = 4 × 16.00 =  64 in

The two solutions are

(a) 4 in       × 4 in      × 8 in

(b) 6.47 in × 6.47 in × 3.06 in    

7 0
3 years ago
16 increased by twice a number is -24
wlad13 [49]
X-the number

16 + 2x = -24    |subtract 16 from both sides

2x = -40      |divide both sides by 2

<u>x = -20</u>

Answer: <em>The number is -24</em>
8 0
3 years ago
2 (x-3) + 3 = 6x - 5​
anygoal [31]

Answer:

x = \frac{1}{2}

Step-by-step explanation:

2x-6+3=6x-5

2x-3=6x-5

2x-6x=-5+3

-4x=-2

x=.5or 1/2

5 0
3 years ago
hiker is climbing down a valley. He stops for a water break 4 times. Between each break, he descends 15 meters. How many meters
sergij07 [2.7K]
The word in the problem that indicates is a negative number is “descend”
8 0
3 years ago
Read 2 more answers
A football coach is trying to decide: When a team is ahead late in the game,
brilliants [131]

Answer:

I play football and my coach will do this: Play a "prevent* defense that guards against long gains but makes short

gains easier.

Step-by-step explanation:

8 0
2 years ago
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