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vlabodo [156]
3 years ago
5

3^n+4=27^2n solve using common bases?

Mathematics
1 answer:
pickupchik [31]3 years ago
7 0
\bf 3^{n+4}=27^{2n}\qquad 27=3^3\qquad thus
\\\\
3^{n+4}=(3^3)^{2n}\implies 3^{n+4}=3^{3\cdot 2n}\implies 3^{n+4}=3^{6n}
\\\\
\textit{same bases, thus the exponent must be the same}
\\\\
n+4=6n

pretty sure you'd know what "n" is
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Sam can mow a lawn in 40 minutes. Vanessa can mow the same lawn in 60 minutes. How long does it take for both Sam and Vanessa to
xxMikexx [17]

Answer:

As a reduced fraction: \frac{120}{5} minutes, which is 24 minutes

Step-by-step explanation:

Sam's speed is 1 lawn in 40 minutes. Vanessa's speed is 1 lawn in 60 minutes. If they both work together, the total speed is:

\frac{1}{40}+\frac{1}{60}=\frac{1(3)}{40(3)}+\frac{1(2)}{60(2)}=\frac{3}{120}+\frac{2}{120}=\frac{5}{120}

Which means that the total speed would be 5 lawns in 120 minutes. To find the time it would take to mow one lawn at that speed, we need to invert that speed so we get minutes per lawn:

\frac{120}{5}=24minutes

5 0
4 years ago
Amber borrows $1,450 from the bank. If she repays the loan in 3 years, the annual interest rate is 5%, compounded annually. Howe
Step2247 [10]
The answer is $126 the asked for 20 charaters so
3 0
3 years ago
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RSB [31]
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5 0
3 years ago
Bentley had $25 to spend on 5 paintbrushes for his art class. After buying them, Bentley had $5 left. How much did each of the p
scZoUnD [109]

Answer:

$4

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6 0
3 years ago
Determine if y varies directly with x. Give the constant of variation, when appropriate. (picture below)
maxonik [38]

Based on the given variation, y does not vary directly with x and the constant of variation are 8, 3.2 and 1.25 respectively.

<h3>Variation</h3>

y = k × x

where,

k = constant of proportionality

y = -40

x = -5

y = k × x

-40 = k × -5

-40 = -5k

k = -40/-5

k = 8

when,

y = 8 and x = 2.5

y = k × x

8 = k × 2.5

8 = 2.5k

k = 8/2.5

k = 3.2

when,

y = 5 and x = 4

y = k × x

5 = k × 4

5 = 4k

k = 5/4

k = 1.25

Learn more about variation:

brainly.com/question/6499629

#SPJ1

5 0
2 years ago
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