Mathematics, 01.12.2019 06:31 kfull6027

The length of a rectangle is 6 units shorter than 1/4 of the width x. write an expression for the perimeter of the rectangle.

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Answers

$\bf \textit{perimeter of a rectangle}\\\\
P=2l+2w\quad 
\begin{cases}
l=length\\
w=width\\
-----\\
l=\frac{1}{4}w-6
\end{cases}\implies P=2\left( \frac{1}{4}w-6 \right)+2w
\\\\\\
P=\cfrac{1}{2}w-12+2w\implies P=\cfrac{w}{2}-12+2w\implies P=\cfrac{w-24+4w}{2}
\\\\\\
P=\cfrac{5w-24}{2}\implies P=\cfrac{5}{2}w-12$

Answer from: Quest

2 & 7

step-by-step explanation:

he climbs 300 ft/hr at a constant rate. the peak is at 1,500 ft.

when going up, he reaches 600 ft in 2 hours. remember, that he is going in a constant rate. divide 600 with 300:

600/300 = 2

assuming that he takes the same route back (meaning that it's a 1500 ft route back, you can solve.

note also that you are solving when he gets back to 600 ft after he reaches the peak.

first, find the amount of hours it takes to get up the peak. divide the total amount (1500), with the ft/her (300) to get the amount of hours (x):

1500/300 = x

x = 5

it takes jamie 5 hours to get up. now, he is returning down, and reaches 600 (his current destination). remember that he climbs at a constant 300 ft/hr. divide 600 with 300:

600/300 = x

x = 2

now add the two numbers together.

x = 5 + 2 = 7

jamie takes 7 hours to go up the mountain and reach his current position when descending.

(total amount/constant rate) = (time).

remember that it is a constant rate, so in total, when he gets back down the mountain, it will take the same amount of time as when he goes up. the total amount for the round trip is: 5 + 5 = 10.

Answer from: Quest

(a) common ratio in the given sequence is, 3

(b) $6.973568802 \times 10^9$ push ups will do kendall do on the 20th week

step-by-step explanation:

geometric sequence is a sequence of numbers that follows a pattern were the next term is found by multiplying by a constant called the common ratio(r)

(a)

given the sequence: 6 , 18 , 54 , 162 ,

this sequence is geometric sequence where each term is 3 times the previous term.

therefore,

common ratio(r) = 3.

(b)

a formula for nth term of geometric sequence is given by;

$a_n = a_1r^{n-1}$ , where r is the common ratio between the successive terms and $a_1$ is the first term,

to find how many push ups will kendall do on the 20th week.

here. n = 20th term.

in the given sequence first term $(a_1) = 6$

then;

$a_n = a_ 1 \cdot r^{n-1}$

$a_{20} = 6 \cdot 3^{20-1}$

simplify:

$a_{20} = 6.973568802 \times 10^9$

therefore, $6.973568802 \times 10^9$ push ups will do kendall do on the 20th week

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The length of a rectangle is 6 units shorter than 1/4 of the width x. write an expression for the pe...