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snow_lady [41]
3 years ago
10

Solve the equation below: ln x- ln 5= -1

Mathematics
1 answer:
Anastaziya [24]3 years ago
4 0

Answer:

x = 5/e

Step-by-step explanation:

ln x- ln 5= -1

We know that ln a - ln b = ln (a/b)

ln x- ln 5= -1

ln(x/5) = -1

Raise each side to the power of e

e^ ln(x/5) = e^-1

We know that e^-1 = 1/e

x/5 = 1/e

Multiply each side by 5

x/5 *5 = 1/e * 5

x = 5/e

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The Amount of sales tax on a new car varies directly to the purchase price of the car. On a 25,000 car, sales tax is 1,750. What
Gekata [30.6K]

Answer:

50,000

Step-by-step explanation:

1st car had $1,750 tax

2nd car has $3,500 tax

1750(2) = 3500

 

so your tax doubled so the price must be doubled.

The car is $50,000

Algebraically using direct variation:

 

t = kp    where t=tax, p = purchase price, 

             and k is constant of variation

 

1750 = 25000k

k = 1750/25000

k = 0.07

 

Your equation is:  t = 0.07p

3500 = 0.07p

p = 3500/0.07

p = $50,000

6 0
2 years ago
Find the equation of the line passing through point (4,2) and perpendicular to AB
Setler [38]

Answer:

a. -⅓

b. 3

c. y = 3x - 10

Step-by-step explanation:

a. Gradient of line AB:

A(1, 3), B(7, 1)

Gradient = \frac{y_2 - y_1}{x_2 - x_1} = \frac{1 - 3}{7 - 1} = \frac{-2}{6} = -\frac{1}{3}

Gradient (m) = -⅓

b. The of the line that is perpendicular to line AB would be the negative reciprocal of the gradient of line AB.

Thus, the negative reciprocal of -⅓ = 3

Gradient of the line perpendicular to line AB = 3

c. Equation of the line that passes through (4, 2) and is perpendicular to line AB:

We can write the equation using the point-slope form equation, y - b = m(x - a), where,

(a, b) represents a point on the line, and,

m = gradient/slope

We know that the gradient/slope (m) = 3

Also, a point, (a, b) = (4, 2).

Therefore, substitute a = 4, b = 2, and m = 3 into y - b = m(x - a)

Thus:

y - 2 = 3(x - 4)

y - 2 = 3x - 12

Add 2 to both sides

y = 3x - 12 + 2

y = 3x - 10

5 0
2 years ago
Find the quotient. (12x 2 - 10x -12) ÷ (3x + 2)
MAXImum [283]
I'm attaching the solution.. feel free to ask if you have questions.. I basically did long division.  Hope this helps.

5 0
2 years ago
Mind giving me help on this?? :0
sergey [27]

Answer:

no

Step-by-step explanation:

8 0
2 years ago
Quick!!
Ira Lisetskai [31]

Answer:

c) three

-----------------------------------------------------------------------------------------------------------------

Step-by-step:

The tetrahedron is a triangular pyramid with equilateral triangles on each face.

3 0
2 years ago
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