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NemiM [27]
3 years ago
9

How does anyone know how to prove parallel lines, especially when there are two pairs of them?

Mathematics
1 answer:
Maurinko [17]3 years ago
6 0

Answer:

Step-by-step explanation:

If two lines are cut by a transversal so that any pair of alternate interior angles are congruent, then the lines are parallel. If two lines are cut by a transversal so that any pair of corresponding angles are congruent, then the lines are parallel. You can use these converses to decide whether two lines are parallel.

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Solve the equation: -6p + 14 and 3p - 2
sleet_krkn [62]

Answer:

p = 16/9

Step-by-step explanation:

-6p+14=3p-2\qquad\text{subtract 14 from both sides}\\\\-6p=3p-16\qquad\text{subtract 3p from both sides}\\\\-9p=-16\qquad\text{divide both sides by (-9)}\\\\\boxed{p=\dfrac{16}{9}\to p=1\dfrac{7}{9}}

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Suppose 4-year-olds in a certain country average 3 hours a day unsupervised and that most of the unsupervised children live in r
natta225 [31]

Answer:

D)the time (in hours) a 4-year-old spends unsupervised per day

Step-by-step explanation:

Given that 4-year-olds in a certain country average 3 hours a day unsupervised and that most of the unsupervised children live in rural areas, considered safe

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P(X

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3 years ago
Whats the decimal equivalent of 16%
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Answer:

0.16

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A worker is to construct an open rectangular box with a square base and a volume of 196196 ft cubedft3. If material for the bott
Archy [21]

Answer:

Therefore the dimensions of the box is 7 ft by 7 ft by 4 ft.

Therefore the minimum cost to manufacture the box is $12936.

Step-by-step explanation:

Given the volume of the open box is 196 cube ft.

Let the one side of the base of the box be x.

Since the base of the box is square in shape.

The other side of the base is also x.

The area of the base of the box = x² square ft

Let the height of the box be h.

The volume of the box is = Area of the base× height

                                          =(x²×h) cube ft.

                                           =x²h cube ft.

According to the problem,

x²h=196

\Rightarrow h=\frac{196}{x^2}

The material cost for the bottom is $88 per square ft and the material cost for the sides $77  per square ft.

The material cost for the bottom of the box = $(88×x²)

                                                                         =$88x²

The area sides = 2(length+width)height

                       =2(x+x)h

                      =4xh square ft.

The material cost for the sides of the box =$(77×4xh)

                                                                    =$308 xh

Total cost to make the box is =$(88x²+308 xh)

∴C=88x²+308 xh    [ C is in dollar]

Now putting h=\frac{196}{x^2}

C=88x^2+308x\times \frac{196}{x^2}

\Rightarrow C=88x^2+ \frac{60368}{x}

Differentiating with respect to x

C'=176x- \frac{60368}{x^2}

Again differentiating with respect to x

C''=176+ \frac{120736}{x^3}

Now to find the minimum cost, we set C'=0

\therefore 176x- \frac{60368}{x^2}=0

\Rightarrow 176x= \frac{60368}{x^2}

\Rightarrow x^3= \frac{60368}{176}

\Rightarrow x^3=343

\Rightarrow x=7

Now, C''|_{x=7}=176+ \frac{120736}{7^3}>0

Therefore at x=7, the manufacturing cost will be minimum.

The height of the box is h=\frac{196}{7^2} = 4ft

Therefore the dimensions of the box is 7 ft by 7 ft by 4 ft.

The manufacturing cost is C=88.7^2+ \frac{60368}{7}   [ putting x=7]

                                             =$12936

Therefore the minimum cost to manufacture the box is $12936.

4 0
3 years ago
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