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AfilCa [17]
3 years ago
7

5.Solve:

Mathematics
1 answer:
lara31 [8.8K]3 years ago
8 0

Answer:

C) x=2 y=-1 z=3

Step-by-step explanation:

2x + y - z = 0

2(2) + (-1) - (3) = 0

0 = 0

x - y + z =6

2 - (-1) + 3 = 6

6 = 6

x + 2y + z = 3

2 + 2(-1) + 3 = 3

3 = 3

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Simplify: 12÷12(4−6)<br> A. 2<br> B. -2<br> C. 1<br> D. - 0.5
Marina86 [1]
12÷(-24)
-1/2
-0.5

hope this helps u
6 0
3 years ago
Read 2 more answers
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
2 years ago
The net of a pyramid is shown below. The surface area of the solid is ____ square inches.
Effectus [21]
Area of a triangle= bh/2b=4in h=8in8x4/2=16in
there are 4 triangles
4x16=64
area of a rectangle=bh
4x4=16
64+16=80in^2
5 0
3 years ago
Read 2 more answers
The yellow rose taxi service charges $1.75 per passenger and $2.25 per mile for a ride . How much will the yellow rose taxi serv
Ann [662]

Answer:

$40.50 for the miles and 1.75 x P (passangers)

Step-by-step explanation:

Since $2.25 is the fee for miles, 2.25 x 18 = $40.50

and since it depends on the group, ima say its probably 3, the passenger fee would be $5.25

that would add up to about $45.75

but if there is a different amount of passengers, just multiply it by $1.75 then add it to $40.50!

5 0
3 years ago
a garden is 18 feet 3 inches long and 10 feet 8 inches wide. the amount of fencing needed to enclose the garden is Need help and
Anna [14]

Answer:

\boxed{57ft 10in}

Step-by-step explanation:

<em>Hey there!</em>

Well if the length is 18 and 3 inches we need to find the sum of both lengths,

18ft 3in + 18ft 3in = 36ft 6in

Width- 10ft 8in + 10ft 8in = 20ft 16 in -> 21ft 4in

l + w = 57ft 10in

<em>Hope this helps :)</em>

5 0
3 years ago
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