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3 years ago

7

James has 3 hats, 2 pairs of shorts, and 5 shirts to chose from. If he wears exactly 1 of each item, how many different combinat

ions (1 hat, 1 shirt, and 1 pair of shorts) can he choose to wear?

1 answer:

Art [367]3 years ago

6 0

Yes he can! 3+2+5=10‍♀️

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Estimate the product. Solve using an area model and the standard algorithm. Remember to express your products in standard form.

snow_tiger [21]

Answer:

Step-by-step explanation:

Using the area model and standard algorithm, we have:

332 (tenths)

<u> × 21 </u>

332

<u> 664 </u>

<u> 6972 </u> tenths = 697.2

<u />

30 + 3 tenths

1 300 32 332

20 600 64 664

33.2 × 21 =<u> 30 </u> × <u> 1 </u> = <u> 30 </u>

8 0

2 years ago

Factor completely. <br> <img src="https://tex.z-dn.net/?f=x%5E%7B8%7D-%5Cfrac%7B1%7D%7B81%7D" id="TexFormula1" title="x^{8}-\fra

Eduardwww [97]

We have 3⁴ = 81, so we can factorize this as a difference of squares twice:

$x^8 - \dfrac1{81} = \left(x^2\right)^4 - \left(\dfrac13\right)^4 \\\\ x^8 - \dfrac1{81} = \left(\left(x^2\right)^2 - \left(\dfrac13\right)^2\right) \left(\left(x^2\right)^2 + \left(\dfrac13\right)^2\right) \\\\ x^8 - \dfrac1{81} = \left(x^2 - \dfrac13\right) \left(x^2 + \dfrac13\right) \left(\left(x^2\right)^2 + \left(\dfrac13\right)^2\right) \\\\ x^8 - \dfrac1{81} = \left(x^2 - \dfrac13\right) \left(x^2 + \dfrac13\right) \left(x^4 + \dfrac19\right)$

Depending on the precise definition of "completely" in this context, you can go a bit further and factorize $x^2-\frac13$ as yet another difference of squares:

$x^2 - \dfrac13 = x^2 - \left(\dfrac1{\sqrt3}\right)^2 = \left(x-\dfrac1{\sqrt3}\right)\left(x+\dfrac1{\sqrt3}\right)$

And if you're working over the field of complex numbers, you can go even further. For instance,

$x^4 + \dfrac19 = \left(x^2\right)^2 - \left(i\dfrac13\right)^2 = \left(x^2 - i\dfrac13\right) \left(x^2 + i\dfrac13\right)$

But I think you'd be fine stopping at the first result,

$x^8 - \dfrac1{81} = \boxed{\left(x^2 - \dfrac13\right) \left(x^2 + \dfrac13\right) \left(x^4 + \dfrac19\right)}$

6 0

2 years ago

Find the total surface area of this triangular prism.<br> 30 cm<br> 18 cm<br> 7 cm<br> 24 cm

Inessa05 [86]

Answer: <em>936 cm²</em>

Step-by-step explanation:

<em>A = (18 × 24 × 0.5) × 2 + (18 + 30 +24) × 7 = 936 (cm²)</em>

5 0

2 years ago

HELPPPPP ME OUUTTTTTTT!!!!

klemol [59]

Answer:

20 degrees

Step-by-step explanation:

we can consider 33 to be the radius of a circle.

31 would then be the cos of the angle in that circle.

the regular cos function is defined for the standard circle with radius 1. so, that would be multiplied by 33 for this circle here.

31 = cos(?) × 33

cos(?) = 31/33 = 0.9393...

? = 20.05 ≈ 20 degrees

5 0

2 years ago

What is the measure of angle c

irakobra [83]

Answer:

? wouldn't it be obtuse

Step-by-step explanation:

6 0

2 years ago