6. The area of a rectangular sheet of paper is 300 cm squared. The length is 5 cm more than the width

Mathematics

2 answers:

konstantin123 [22]3 years ago

8 0

Answer:

Step-by-step explanation:

width = x

length= x + 5

a) x + 5

b) x * (x+5) = 300

x^2 + 5x = 300

x^2 + 5x - 300 = 0

Δ = 25 + 1200 = 1225

width = (-5 + 35)/2 = 15 cm

lenght = 15 + 5 = 20 cm

murzikaleks [220]3 years ago

7 0

Answer:

a) length = x + 5

b) $x^{2}$ + 5x - 300 = 0

Step-by-step explanation:

x = width

x + 5 = length

(x)(x + 5) = 300

$x^{2}$ + 5x = 300

$x^{2}$ + 5x - 300 = 0

(x+20)(x-15)

x = -20 or x = 15 ( disregard the -20. measurements can't be negative)

width = 15

length = x+ 5 = 15+5 = 20

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Find k and help with the equation!

anzhelika [568]

<h3>Answer: k = 6+10x</h3>

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Work Shown:

$64*4^{5x}\\\\\left(2^6\right)*\left(2^{2}\right)^{5x}\\\\\left(2^6\right)*\left(2^{2*5x}\right)\\\\\left(2^6\right)*\left(2^{10x}\right)\\\\2^{6+10x}\\\\$

The result is in the form $2^k$ with k = 6+10x

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Explanation:

First we need to get everything as an exponential expression with a base 2.

We rewrite 64 as $2^6$ and 4 as $2^2$ in the second step.

In the third step, I used the rule $(a^b)^c = a^{b*c}$ which says to multiply the exponents together. That's how I went from $(2^2)^{5x}$ to $2^{2*5x}$ . Then the 2*5x in the exponent becomes 10x.