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3 years ago

Solve the equation log3(x+24)+log3 x=4

Mathematics

1 answer:

fredd [130]3 years ago

7 0

Log_3(x(x + 24) = 4

log_3(x^2 + 24x) = 4

3^4 = (x^2 + 24x)

81 = x^2 + 24x

x^2 + 24x - 81 = 0

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A mirror is 24 inches high and 28 inches wide. The center of the mirror will hang 514 feet from the floor on a wall that is 8 fe

Vanyuwa [196]

The distance from the top of the mirror to the ceiling once the mirror is hung on the wall is 21 inches

The dimension of the mirror is given as:

$Height = 24\ in$

$Width = 28\ in$

From the center of the mirror to the floor of the wall, the distance is:

$Distance =5\frac14\ ft$

So, the distance to the top of the mirror will be:

$Top = 5\frac 14\ ft + \frac 12 \times Height$

Substitute 24 for height

$Top = 5\frac 14\ ft+ \frac 12 \times 24\ in$

$Top = 5\frac 14\ ft+ 12 \ in$

Convert feet to inches

$Top = 5\frac 14\times 12\ in+ 12 \ in$

$Top = 63\ in+ 12 \ in$

$Top = 75 \ in$

The distance from the top of the mirror to the ceiling is the difference between the height of the wall and 75 inches.

So, we have:

$Distance = 8\ ft - 75\ in$

Convert feet to inches

$Distance = 8\times 12\ in - 75\ in$

$Distance = 96\ in - 75\ in$

$Distance = 21\ in$

Hence, the distance is 21 inches

Read more about lengths at:

brainly.com/question/10545161

3 0

2 years ago

14. Thomas is building a fence around his

Black_prince [1.1K]

Answer:

18 meters

Step-by-step explanation:

4 cm = 6m

2cm = 3m

6x3=18

Please <3 my Answer B )

4 0

2 years ago

Read 2 more answers

PLEASE HELP!!! THANK YOU!!!

notka56 [123]

Answer:

A. 4%

Step-by-step explanation:

remember that there are 52 weeks in a year, so multiply 1000 by each answer, then multiply what you get by 52 to see if it is either below 2000 or just above 2000, and you'll see how i got 4%.

3 0

3 years ago

A ship leaves port at noon and has a bearing of S29oW. The ship sails at 20 knots. How many nautical miles south and how many na

ira [324]

Answer:

Approximately $58.2\; \text{nautical miles}$ (assuming that the bearing is ${\rm S$29^{\circ}$W}$ .)

Step-by-step explanation:

Let $v$ denote the speed of the ship, and let $t$ denote the duration of the trip. The magnitude of the displacement of this ship would be $v\, t$ .

Refer to the diagram attached. The direction ${\rm S$29^{\circ}$W}$ means $29^{\circ}$ west of south. Thus, start with the south direction and turn towards west (clockwise) by $29^{\circ}$ to find the direction of the displacement of the ship.

The hypothenuse of the right triangle in this diagram represents the displacement of the ship, with a length of $v\, t$ . The dashed horizontal line segment represents the distance that the ship has travelled to the west (which this question is asking for.) The angle opposite to that line segment is exactly $29^{\circ}$ .

Since the hypotenuse is of length $v\, t$ , the dashed line segment opposite to the $\theta = 29^{\circ}$ vertex would have a length of:

$\begin{aligned}& \text{opposite (to $\theta$)} \\ =\; & \text{hypotenuse} \times \frac{\text{opposite (to $\theta$)}}{\text{hypotenuse}} \\ =\; & \text{hypotenuse} \times \sin (\theta) \\ =\; & v\, t \, \sin(\theta) \\ =\; & v\, t\, \sin(29^{\circ})\end{aligned}$ .

Substitute in $\begin{aligned} v &= 20\; \frac{\text{nautical mile}}{\text{hour}}\end{aligned}$ and $t = 6\; \text{hour}$ :

$\begin{aligned} & v\, t\, \sin(29^{\circ}) \\ =\; & 20\; \frac{\text{nautical mile}}{\text{hour}} \times 6\; \text{hour} \times \sin(29^{\circ}) \\ \approx\; & 58.2\; \text{nautical mile}\end{aligned}$ .

7 0

2 years ago

How can you Express 3 3/8 as a fraction ?

Solnce55 [7]

Answer:

You mean improper fraction?

3 x 8 = 24

24 + 3 = 27

27/8

3 0

3 years ago