Using properties of logarithms in excersises 13-18, use the properties of logarithms o write the logarithm in terms of log3(5) and log3(7) log3 (21/5)

9514 1404 393

Answer:

  86.6 inches

Step-by-step explanation:

The side length of an equilateral triangle is 2/√3 times the altitude. So, the perimeter is ...

  P = 3s = 3(25)(2/√3) = 50√3 ≈ 86.6 . . . . inches

Answer:

That's your answer. Let me know if you need an explanation.

Answer:

[tex] A(\triangle ABC) = 7.2\: units^2 [/tex]

Step-by-step explanation:

C = (0, 7)

Since, point A lies in y-axis, so it's x coordinate will be zero. Line y = 2x + 1 passes through point A.

Therefore, plug x = 0 in y = 2x +1, we find:

y = 2*0 + 1 = 0 + 1 = 1

Hence, coordinates of point A are (0, 1).

Now, by distance formula:

[tex] AC= \sqrt{(0-0)^2 +(7-1)^2} [/tex]

[tex] AC= \sqrt{(0)^2 +(6)^2 }[/tex]

[tex] AC= \sqrt{0 +36 }[/tex]

[tex] AC= \sqrt{36 }[/tex]

[tex] AC= 6\: units[/tex]

Length of perpendicular CB dropped from point C (0, 7) to line y = 2x + 1 or 2x - y + 1 = 0 can be obtained as given below:

[tex] CB =\frac{|2\times 0+(-1)\times 7+1|}{\sqrt {2^2 +(-1)^2} } [/tex]

[tex] CB =\frac{|0-7+1|}{\sqrt {4 +1} } [/tex]

[tex] CB =\frac{|-6|}{\sqrt {5} } [/tex]

[tex] CB =\frac{6}{2.24} [/tex]

[tex] CB =2.68\: units [/tex]

By Pythagoras Theorem:

[tex] AB=\sqrt{AC^2 - CB^2} [/tex]

[tex] AB=\sqrt{6^2 - (2.68)^2} [/tex]

[tex] AB=\sqrt{36 - 7.18} [/tex]

[tex] AB=\sqrt{28.82} [/tex]

[tex] AB=5.36842621\: units [/tex]

[tex] AB\approx 5.37\: units [/tex]

[tex] A(\triangle ABC) = \frac{1}{2} \times AB\times CB[/tex]

[tex] A(\triangle ABC) = \frac{1}{2} \times 5.37\times 2.68[/tex]

[tex] A(\triangle ABC) = \frac{1}{2} \times 14.3916[/tex]

[tex] A(\triangle ABC) = 7.1958[/tex]

[tex] A(\triangle ABC) = 7.2\: units^2 [/tex]

Hope it be correct.

Answer:

3/5

Step-by-step explanation:

0.6 = 6/10 = 3/5

Answer:

50 cents per apple

Step-by-step explanation:

to find the unit price you have to divide the total cost by number of apples

6.00÷12=0.5

Answer:

the coordinates are (3,3)

Step-by-step explanation:

hope I helped!!

Answer:

2s+3b=154

s=2b

solving: s= 44, b= 22

Step-by-step explanation:

s=number of sundaes sold

b=number of banana splits sold

2s+3b=154

s=2b

to solve:

substitute s=2b into the first equation

2(2b)+3b=154

4b+3b=154

7b=154

divide both sides by 7

7b/7=154/7

b=22

s=44

Answer:   Slope = -32

Explanation:

The given equation is in y = mx+b form

m = -32 is the slope

b = -9/38 is the y intercept

Answer:

slope: -32

Step-by-step explanation:

Use the slope-intercept form to find the slope and y-intercept.

Slope:  − 32

y-intercept:  ( 0 , − 9/ 38 )

Answer:

45 degrees

Step-by-step explanation:

A straight angle is equal to 180, so subtract 135 from 180

Answer:

45

Step-by-step explanation:

Answer:

y = -1/2 x - 3

Step-by-step explanation:

Use the coordinates from the graph:

(-6, 0) and (0, -3)

Slope m = -3-0/0-(-6)

m = -3/6

m = -1/2

The y-intercept is -3 (point where the line meet the y intercept)

Substitute unto the expression y = mx+c

y = -1/2 x - 3

Hence the required equation is y = -1/2 x - 3

Step-by-step explanation:

748 ≠ 712 so 534 + 214 only = 748 not 712

Answer: I think that it is  62

Step-by-step explanation:

77 minus 15= 62

tell me if its right.

hope this helps

Answer:

Step-by-step explanation:

The probability of getting one even and one odd is the sum of probability of getting even and of getting odd and even. Since there are 3 even or odd on each die out of six numbers you have

P(EO)(3/6)(3/6)=1/4 and P(OE)=(3/6)(3/6)=1/4 so 1/4+1/4= 1/2

or you can find the probability of getting two odds or two evens and subtract that from 1

P(EE)=(3/6)(3/6)=1/4, P(OO)=(3/6)(3/6)=1/4

P(EO)=1-1/4-1/4=1/2

Answer:

$10

Step-by-step explanation:

Per capita means per person, so divide the GDP by the number of people.

$100/10 = $10

Answer:

4 m/s

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]\frac{146}{\pi}\\ \\ \text{Pi is irrational and cannot be expressed as a ratio of two integers.}\\ \\ \frac{146}{\pi}\approx 46.47[/tex]

Answer:

46 degrees for both b and c

Step-by-step explanation:

the vertical angles postulate means that the opposite angle must be the same, so 134*2=268

since all angles must be 360, subtract 268, which is 92

using the vertical angles again, b and c are the same, and the sum must be 92

92 divided by 2 is 46

Answer:

She has $5

Step-by-step explanation:

Answer:

x=24 ,y=156 ,z=24

Step-by-step explanation:

using linear pair 180 degrees

Answer:

25.6%

Step-by-step explanation:

Purchase price = $250 / share

Jan - feb : 38% decrease

(100 - 38)% * 250 = $155

February - March : 20% increase

(100 + 20)% * $155

120% * $155 = $186

Percentage decrease from January to March :

[(250 - 186) / 250] * 100%

(64 / 250) * 100%

0.256 * 100%

25.6%

Answer:

mia

Step-by-step explanation:

mia: 10/6 per minute

shawn: 5/4 per minute

common denominator is 12, multiply by 2 and 3

20/12 lap per minute mia

15/12 laps per minute shawn

20 > 15

Complete Question

On a map, 90 miles is represented by 3 inches. A measure of 1/2 inch on the map would represent miles.

Answer:

15 miles

Step-by-step explanation:

From the above question,

3 inches = 90 miles

1/2 inch = x miles

Cross Multiply

3 inches × x miles = 90 miles × 1/2 inch

x miles = 90 miles × 1/2 inch/3 inches

x miles = 15 miles

Therefore, a measure of 1/2 inch on the map would represent 15 miles

b. -10 each time

c. The height of the slide/ the height at the top of the slide

d. 6 seconds. when Kirk is on the ground ( 0 feet off the ground), 6 seconds have past. You can see this in the point (6,0)

Answer:

Can I please help you? i need you to translate this to english for my effort

Step-by-step explanation:

Answer:

24,282,000 visitors (total)

Step-by-step explanation:

Add these two counts together:

8 306 000

15 976 000

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

24 282 000 total number of visitors

Answer:

Add the number of France visitors and Australia visitors and you will get...

Step-by-step explanation:

24,282,000 visitors