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Arisa [49]
3 years ago
5

Plzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz

Mathematics
2 answers:
statuscvo [17]3 years ago
8 0

9514 1404 393

Answer:

  (a)  x = (3 -ln(3))/5 ≈ 0.819722457734

  (b)  y = 10

Step-by-step explanation:

(a) Taking the natural log of both sides, we have ...

  2x +1 = ln(3) +4 -3x

  5x = ln(3) +3 . . . . . . . . add 3x-1

  x = (ln(3) +3)/5 ≈ 0.820

__

(b) Assuming "lg" means "log", the logarithm to base 10, we have ...

  log(y -6) +log(y +15) = 2

  (y -6)(y +15) = 100 . . . . . . . taking antilogs

  y^2 -9x -190 = 0 . . . . . . . . eliminate parentheses, subtract 100

  (y -19)(y +10) = 0 . . . . . . . . factor

The values of y that make these factors zero are -19 and 10. We know from the first term that (y-6) > 0, so y > 6. That means y = -19 is an extraneous solution.

The solution is ...

  y = 10

__

When solving equations using a graphing calculator, it often works well to define a function f(x) such that the solution is f(x) = 0, the x-intercept(s). That form is easily obtained by subtracting the right side of the equation from both sides of the equation. In part (a) here, that is ...

  f(x) = e^(2x+1) -3e^(4-3x)

3241004551 [841]3 years ago
3 0

Answer:

Step-by-step explanation:

e^(2x + 1) = 3e^(4 - 3x)

e^(2x + 1) = e^3(4-  3x)

lne^ (2x + 1) =ln e^3(4-  3x)

2x + 1 = 3*(4 - 3x)

2x + 1 = 12 - 9x

11x + 1 = 12

11x = 12 - 1

11x = 11

x = 1

====================

I've never worked with binary logs but I'll give this my best shot. If someone comes along and gives you a different answer, use it.

lg(y-6) + lg(y + 15) = 2

lg (y - 6)(y + 15) = 2

inverse (y - 6)(y + 15) = 2^2

(y - 6)(y + 15) = 4

y^2 + 9y - 90 - 4 = 0

y^2 + 9y - 94 = 0

y = 6.19

y = -15,19

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<span>Based in the information given in the problem, you must apply the The Angle Bisector Theorem. Let's call the triangle: "ABC"; the internal bisector of the angle that divides its opposite side: "AP"; and "x": the longest and shortest possible lengths of the third side of the triangle.

 If BP= 6 cm and CP= 5 cm, we have:

 BP/CP = AB/AC

 We don't know if second side of the triangle (6.9 centimeters long) is AB or AC, so:

 1. If AB = 6.9 cm and AC = x:
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6 0
3 years ago
Naty bought a dress for $24.95 and a skirt for $14.95.
FrozenT [24]

Answer:

Total items = $39.90

Sales tax amount = $3.7905

Total cost = $43.691

The clerk's error is using 9.5 as sales tax amount instead of finding 9.5% of the total items

Step-by-step explanation:

Dress = $24.95

Skirt = $14.95

steps the clerk completed.

Step 1: 24.95 + 14.95 = 39.90

Step 2: 39.90 +9.5 = 49.40

Correct steps:

Total items = dress + skirt

= $24.95 + $14.95

= $39.90

Sales tax = 9.5%

Sales tax amount = 9.5% of total

= 9.5/100 × $39.90

= 0.095 × 39.90

= $3.7905

Total cost = Total + sales tax amount

= $39.90 + $3.7905

= $43.6905

To the nearest hundredth

= $43.691

Sales tax is the amount of money imposed by government on the sales of some items

Total cost is the cost of all items including sales tax

7 0
3 years ago
Expand and simplify . 5(3m+6n)-4(11m-8n) PLEASE HELP. BEST ANSWER RECIEVES A BRIANLIEST​
Lynna [10]

Answer:

-29m+62n

Step-by-step explanation:

5 (3m+6n)-4 (11m-8m)

15m+30n-44m+30n

15m-44m +32n+30n

-29m +62n

4 0
3 years ago
13.50 ÷ 1.25 = 10.8, but can you explain why?
harkovskaia [24]

135/100÷125/100

135/100×100/125

100cancel 100,it remains 135/125

135/÷5/125÷5

27/25=10.8

7 0
3 years ago
i am greater than one-fourth but less than four tenths . i am a decimal rounded to the hundreds place. what number am i
artcher [175]
(0.25,0.40). Written in interval notation. It can be any number greater than 1/4 but less that 4/10. 
3 0
3 years ago
Read 2 more answers
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