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GenaCL600 [577]
3 years ago
9

Find the product of -43, 7, and -21

Mathematics
2 answers:
Flauer [41]3 years ago
7 0
6321
-43 times 7 is -301
-301 times -21 is 6321. The answer is positive because the 2 negative signs cancel each-other out.
aivan3 [116]3 years ago
6 0
(-43) x 7 x (-21) = 6,321
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kari74 [83]

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Which of the following is the correct factorization of the polynomial below?<br> x3 + 14x2 + 49x
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For this case we must factor the following polynomial:

x ^ 3 + 14x ^ 2 + 49x\\

We can take common factor x:

x(x ^ 2+ 14x + 49)

To factor the expression within the parenthesis, we must find two numbers that when multiplied give 49 and when added together, 14 are obtained. These are: 7 and 7.

7*7=49,7+7=14

Thus, the expression is factored as:

x(x + 7)(x +7)

Answer:

x (x + 7) ^ 2

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Here is a picture of a cube, and the net of this cube.<br><br>What is the surface area of this cube?
Murljashka [212]

Answer:

726

Step-by-step explanation:

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√13

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2 years ago
You have 100 cm of string which can be cut in one place (or not cut at all) and then formed into a circle and a square (or just
Ne4ueva [31]

Answer:

44cm for minimum area and 0 for maximum area (circle)

Step-by-step explanation:

Let's C be the circumference of the circle and S be the circumference of the square. If we cut the string into 2 pieces the total circumferences would be the string length 100cm.

S + C  = 100 or S = 100 - C

The side of square is S/4 and radius of the circle is \frac{C}{2\pi}

So the area of the square is

A_S = \frac{S^2}{4^2} = \frac{S^2}{16}

A_C = \pi\frac{C^2}{(2\pi)^2} = \frac{C^2}{4\pi}

Therefore the total area is

A = A_S + A_C = \frac{S^2}{16} + \frac{C^2}{4\pi}

We can substitute 100 - C for S

A = \frac{(100 - C)^2}{16} + \frac{C^2}{4\pi}

A = \frac{100^2 - 200C + C^2}{16} + \frac{C^2}{4\pi}

A = 625 -12.5C + \frac{C^2}{16} + \frac{C^2}{4\pi}

A = 625 -12.5C + C^2(\frac{1}{16} + \frac{1}{4\pi})

To find the maximum and minimum of this, we can take the first derivative and set that to 0

A^{'} = -12.5 + 2C(\frac{1}{16} + \frac{1}{4\pi}) = 0

C(\frac{1}{8} + \frac{1}{2\pi}) = 12.5

C \approx 44 cm

If we take the 2nd derivative:

A^{''} = \frac{1}{8} + \frac{1}{2\pi} > 0

We can see that this is positive, so our cut at 44 cm would yield the minimum area.

The maximum area would be where you not cut anything and use the total string length to use for either square or circle

if C = 100 then A_C = \frac{C^2}{4\pi} = \frac{100^2}{4\pi} = 795.77 cm^2

if S = 100 then A_S = \frac{S^2}{16} = \frac{100^2}{16} = 625 cm^2

So to yield maximum area, you should not cut at all and use the whole string to form a circle

4 0
4 years ago
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