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2 years ago

11

In(x-4) + ln (x+3) = ln18

1 answer:

stellarik [79]2 years ago

3 0

Answer:

The value of x is 6 , - 5

Step-by-step explanation:

Given as ;

log(x - 4) + log(x + 3) = log 18

<u>From log property </u>

I.e log m + log n = log ( m × n)

So, log(x - 4) + log(x + 3) = log 18

or, log {(x - 4) × (x + 3)} = log 18

Or, (x - 4) × (x + 3) = 18

Or, x² + 3 x - 4 x - 12 = 18

Or, x² - x -12 - 18 = 0

or, x² - x - 30 = 0

Or, x² - 6 x + 5 x - 30 = 0

or, x ( x - 6 ) + 5 ( x - 6 ) = 0

or, ( x - 6 ) ( x + 5 ) = 0

So, the value of x is 6 , - 5

Hence the value of x is 6 , - 5 Answer

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Lindsey bought a picnic basket originally priced at $40 but on sale for 50% off. After 10% sales tax, what was the total cost?

MaRussiya [10]

Answer:

$30

Step-by-step explanation:

Given data

Origianal price= $40

discount= 50%

Tax= 10%

Let us find the amount of the discount and tax

Discount

=50/100*40

=0.5*40

=$20

Tax

=10/100*40

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Hence the total cost is

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7 1

2 years ago

Read 2 more answers

The lengths of the sides of triangle PQR are consecutive even integers. The perimeter of triangle PQR is 42 cm. What is the leng

Yuri [45]

Answer:

16 cm

Step-by-step explanation:

Let the three consecutive even integers representing the sides of the triangle PQR be x, (x +2) and (x + 4).

Since, perimeter of triangle PQR = 42 cm

$\therefore \: x + (x + 2) + (x + 4) = 42 \\ 3x + 6 = 42 \\ 3x = 42 - 6 \\ 3x = 36 \\ x = \frac{36}{3} \\ x = 12 \\ \\ \because \: longest \: side = x + 4 \\ \therefore \: longest \: side = 12 + 4 \\ \red{ \bold{ \therefore \: longest \: side = 16 \: cm}} \\$

6 0

1 year ago

Arrange these functions from the greatest to the least value based on the average rate of change in the specified interval.Tiles

Ugo [173]

By definition, the average rate of change is given by:

$AVR = \frac{f(x2)-f(x1)}{x2-x1}$

We evaluate each of the functions in the given interval.

We have then:

For f (x) = x ^ 2 + 3x:

Evaluating for x = -2:

$f (-2) = (-2) ^ 2 + 3 (-2)\\f (-2) = 4 - 6\\f (-2) = - 2$

Evaluating for x = 3:

$f (3) = (3) ^ 2 + 3 (3)\\f (3) = 9 + 9\\f (3) = 18$

Then, the AVR is:

$AVR = \frac{18-(-2)}{3-(-2)}$

$AVR = \frac{18+2}{3+2}$

$AVR = \frac{20}{5}$

$AVR = 4$

For f (x) = 3x - 8:

Evaluating for x =4:

$f (4) = 3 (4) - 8\\f (4) = 12 - 8\\f (4) = 4$

Evaluating for x = 5:

$f (5) = 3 (5) - 8\\f (5) = 15 - 8\\f (5) = 7$

Then, the AVR is:

$AVR = \frac{7-4}{5-4}$

$AVR = \frac{3}{1}$

$AVR = 3$

For f (x) = x ^ 2 - 2x:

Evaluating for x = -3:

$f (-3) = (-3) ^ 2 - 2 (-3)\\f (-3) = 9 + 6\\f (-3) = 15$

Evaluating for x = 4:

$f (4) = (4) ^ 2 - 2 (4)\\f (4) = 16 - 8\\f (4) = 8$

Then, the AVR is:

$AVR = \frac{8-15}{4-(-3)}$

$AVR = \frac{-7}{4+3}$

$AVR = \frac{-7}{7}$

$AVR = -1$

For f (x) = x ^ 2 - 5:

Evaluating for x = -1:

$f (-1) = (-1) ^ 2 - 5\\f (-1) = 1 - 5\\f (-1) = - 4$

Evaluating for x = 1:

$f (1) = (1) ^ 2 - 5\\f (1) = 1 - 5\\f (1) = - 4$

Then, the AVR is:

$AVR = \frac{-4-(-4)}{1-(-1)}$

$AVR = \frac{-4+4}{1+1}$

$AVR = \frac{0}{2}$

$AVR = 0$

Answer:

from the greatest to the least value based on the average rate of change in the specified interval:

f(x) = x^2 + 3x interval: [-2, 3]

f(x) = 3x - 8 interval: [4, 5]

f(x) = x^2 - 5 interval: [-1, 1]

f(x) = x^2 - 2x interval: [-3, 4]

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Ari rents the bike for 4 hours, and Meg rents the scooter for 3 hours. What is the total cost of the rentals?

Rudiy27

Answer: it’s 66 I got it right

Step-by-step explanation:

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2 years ago

Kelly purchased 6 planters for a total of $18. She wants to purchase another 16 planters at the same unit price. How much will 1

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Answer:

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Step-by-step explanation:

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2 years ago