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larisa [96]
3 years ago
9

find the surface area of a rectangular prism with a height of 6 inches, a width of 7 inches and the length of 13 inches

Mathematics
2 answers:
vredina [299]3 years ago
6 0

Answer:

We know, Surface area of a rectangular prism = 2(wl + hl + hw)

area = 2(7*13 + 6*13 + 7*6)

area = 2(91+78+42)

area = 2(211)

area = 422 in²

So, your final answer is 422 in²

Hope this helps!

kozerog [31]3 years ago
5 0

The answer is 546. all variables have to be multiplied to get the answer

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Rationalize the denominator of sqrt -49 over (7 - 2i) - (4 + 9i)
zubka84 [21]
\sqrt{ \frac{-49}{(7-2i)-(4+9i) } } 


This one is quite the deal, but we can begin by distributing the negative on the denominator and getting rid of the parenthesis:

\frac{ \sqrt{-49}}{7-2i-4-9i}

See how the denominator now is more a simplification of like terms, with this I mean that you operate the numbers with an "i" together and the ones that do not have an "i" together as well. Namely, the 7 and the -4, the -2i with the -9i.
Therefore having the result: 

\frac{ \sqrt{-49} }{3-11i}

Now, the \sqrt{-49} must be respresented as an imaginary number, and using the multiplication of radicals, we can simplify it to \sqrt{49}  \sqrt{-1}
This means that we get the result 7i for the numerator.

\frac{7i}{3-11i}

In order to rationalize this fraction even further, we have to remember an identity from the previous algebra classes, namely: x^2 - y^2 =(x+y)(x-y)
The difference of squares allows us to remove the imaginary part of this fraction, leaving us with a real number, hopefully, on the denominator.

\frac{7i (3+11i)}{(3-11i)(3+11i)}

See, all I did there was multiply both numerator and denominator with (3+11i) so I could complete the difference of squares.
See how (3-11i)(3+11i)= 3^2 -(11i)^2 therefore, we can finally write:

\frac{7i(3+11i)}{3^2 - (11i)^2 }

I'll let you take it from here, all you have to do is simplify it further.
The simplification is quite straightforward, the numerator distributed the 7i. Namely the product 7i(3+11i) = 21i+77i^2.
You should know from your classes that i^2 = -1, thefore the numerator simplifies to -77+21i
You can do it as a curious thing, but simplifying yields the result:
\frac{-77+21i}{130}
7 0
3 years ago
The numerator of the given fraction is 4 less than the denominator. If 5 is added to both numerator and denominator, the resulti
Sholpan [36]

Answer:

5/9

Step-by-step explanation:

Let the denominator be x and numerator be y.

Given, numerator is 4 less than denominator

=> y = x - 4 ...(1)

When 5 is added to both:

Numerator = y + 5 , and, denominator = x + 5

Now their ratio is 5/7.

=> (y + 5)/(x + 5) = 5/7

=> 7(y + 5) = 5(x + 5)

=> 7y + 35 = 5x + 25

=> 7y - 5x = 25 - 35

=> 7(x - 4) - 5x = -10 {y=x-4}

=> 7x - 28 - 5x = -10

=> 2x = 18

=> x = 9

Thus,

Fraction is y/x = (x-4)/x = (9-4)/9 = 5/9

4 0
2 years ago
What is the slope of a line passing through (-3,-4) and (3,4)
svp [43]

Answer:

4/3

Step-by-step explanation:

you use slope formula

8 0
3 years ago
Read 2 more answers
What multiplies to 16 and adds to 18?
KonstantinChe [14]


The number 8 is a multiple of 16,   2 x 8 = 16  . And the number 8 + 10 = 18

So, I would think it's 8.

Hope I was able to help you. :-)

8 0
3 years ago
Read 2 more answers
✨PLEASE HELP✨ DUE SOON
mestny [16]
Hey :) it’s (2,5) it’s C !!
6 0
3 years ago
Read 2 more answers
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