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Montano1993 [528]
3 years ago
11

GCF OF 16 20 and 24 .....

Mathematics
2 answers:
diamong [38]3 years ago
6 0

Answer:4

Step-by-step explanation:

16: 1,2,4,16

20:1,2,4,5,10,20

24: 1,2,3,4,6,8,12,24

The greatest common factor is four

Gemiola [76]3 years ago
3 0

Answer:

the gcf of 16, 20, and 14 is 4

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3 years ago
Which set of lengths might be used to represent the sides of a right triangle?
UNO [17]

Answer:

Step-by-step explanation:

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3 0
3 years ago
A box designer has been charged with the task of determining the surface area of various open boxes (no lid) that can be constru
Viktor [21]

Answer:

1) S = 2\cdot w\cdot l - 8\cdot x^{2}, 2) The domain of S is 0 \leq x \leq \frac{\sqrt{w\cdot l}}{2}. The range of S is 0 \leq S \leq 2\cdot w \cdot l, 3) S = 176\,in^{2}, 4) x \approx 4.528\,in, 5) S = 164.830\,in^{2}

Step-by-step explanation:

1) The function of the box is:

S = 2\cdot (w - 2\cdot x)\cdot x + 2\cdot (l-2\cdot x)\cdot x +(w-2\cdot x)\cdot (l-2\cdot x)

S = 2\cdot w\cdot x - 4\cdot x^{2} + 2\cdot l\cdot x - 4\cdot x^{2} + w\cdot l -2\cdot (l + w)\cdot x + l\cdot w

S = 2\cdot (w+l)\cdot x - 8\cdpt x^{2} + 2\cdot w \cdot l - 2\cdot (l+w)\cdot x

S = 2\cdot w\cdot l - 8\cdot x^{2}

2) The maximum cutout is:

2\cdot w \cdot l - 8\cdot x^{2} = 0

w\cdot l - 4\cdot x^{2} = 0

4\cdot x^{2} = w\cdot l

x = \frac{\sqrt{w\cdot l}}{2}

The domain of S is 0 \leq x \leq \frac{\sqrt{w\cdot l}}{2}. The range of S is 0 \leq S \leq 2\cdot w \cdot l

3) The surface area when a 1'' x 1'' square is cut out is:

S = 2\cdot (8\,in)\cdot (11.5\,in)-8\cdot (1\,in)^{2}

S = 176\,in^{2}

4) The size is found by solving the following second-order polynomial:

20\,in^{2} = 2 \cdot (8\,in)\cdot (11.5\,in)-8\cdot x^{2}

20\,in^{2} = 184\,in^{2} - 8\cdot x^{2}

8\cdot x^{2} - 164\,in^{2} = 0

x \approx 4.528\,in

5) The equation of the box volume is:

V = (w-2\cdot x)\cdot (l-2\cdot x) \cdot x

V = [w\cdot l -2\cdot (w+l)\cdot x + 4\cdot x^{2}]\cdot x

V = w\cdot l \cdot x - 2\cdot (w+l)\cdot x^{2} + 4\cdot x^{3}

V = (8\,in)\cdot (11.5\,in)\cdot x - 2\cdot (19.5\,in)\cdot x^{2} + 4\cdot x^{3}

V = (92\,in^{2})\cdot x - (39\,in)\cdot x^{2} + 4\cdot x^{3}

The first derivative of the function is:

V' = 92\,in^{2} - (78\,in)\cdot x + 12\cdot x^{2}

The critical points are determined by equalizing the derivative to zero:

12\cdot x^{2}-(78\,in)\cdot x + 92\,in^{2} = 0

x_{1} \approx 4.952\,in

x_{2}\approx 1.548\,in

The second derivative is found afterwards:

V'' = 24\cdot x - 78\,in

After evaluating each critical point, it follows that x_{1} is an absolute minimum and x_{2} is an absolute maximum. Hence, the value of the cutoff so that volume is maximized is:

x \approx 1.548\,in

The surface area of the box is:

S = 2\cdot (8\,in)\cdot (11.5\,in)-8\cdot (1.548\,in)^{2}

S = 164.830\,in^{2}

4 0
3 years ago
4x + 5y = 3<br>kx + 15y = 9 find k<br>​
9966 [12]

Answer:

12

Step-by-step explanation:

4x + 5y = 3 ................ (i)

kx + 15y = 9................(ii)

Dividing eqn (ii) by 3, we get,

k/3 x + 5y = 3.............(iii)

Subtracting eqn (iii) by eqn (i), we get,

-4x - k/3 x = 0

or, -(4 - k/3 )x = 0

or, 4 - k/3 = 0/x

or, 4 - k/3 = 0

or, 4 = k/3

or, k = 4*3

:. k = 12 (Ans)

6 0
3 years ago
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kenny6666 [7]

Answer:

what percent of 60 is 45, = 45/60 = x/100 = 75%,  16 is 20% of what number = 16/x = 20/100 = 80 not 75,  12.6 is 28%of what number = 45

Step-by-step explanation:

just trust me this would be to long to put on this space but if you have any queztions on why I ordered it this way just ask me.

5 0
2 years ago
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