What is the following sum?

The value of log subscript 625 baseline 5 is 1/4.

The logarithmic function is an inverse function to exponentiation.

Rewrite as an equation.

[tex]\rm log_{625}{(5)} = x[/tex]

Rewrite log625 (5) = x in exponential form using the definition of a logarithm.

If x and b are positive real numbers and b does not equal 1, then log(x) = y is equivalent to b^y = x.

[tex]\rm 625^x=5[/tex]

Create expressions in the equation that all have equal bases.

[tex]\rm (5^4)^x=5^1\\\\5^{4x}=5^1\\\\4x=1\\\\x=\dfrac{1}{4}[/tex]

Hence, the value of log subscript 625 baseline 5 is 1/4.

To know more about the log function click the link given below.

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Answer:

1/4

Step-by-step explanation:

Work Shown:

(540 grams sugar)/(5 liter soda) = (x grams sugar)/(3 liter soda)

540/5 = x/3

540*3 = 5*x

1620 = 5x

5x = 1620

x = 1620/5

x = 324

3 liters of soda has 324 grams of sugar

Answer:

24% and 38%

Step-by-step explanation:

Answer:

24% and 38%

Step-by-step explanation:

Answer:

B = 50

Step-by-step explanation:

[tex]\frac{5}{10} =\frac{b}{100}[/tex]   do butterfly multiplication

[tex]5*100=500[/tex]

[tex]10*b=10b[/tex]

[tex]\frac{10b}{10}=\frac{500}{10}[/tex]

B = 50

Answer:

10

Step-by-step explanation:

see in the attached picture...

Answer:

11,232km/h

Step-by-step explanation:

You have 3120m/s and want kilometers per hour. There are 1000m in 1km, and 3600sec in 1h:

[tex] \frac{3120}{1} \frac{m}{s} \times \frac{1}{1000} \frac{km}{m} \times \frac{3600}{1} \frac{s}{h} [/tex]

Meters cancel. Seconds cancel. This leaves kilometers per hour:

[tex] \frac{3120 \times 3600}{1000} \frac{km}{h} = 11232 \frac{km}{h} [/tex]

Let the distance be x

Answer:

[tex]c=325m[/tex]

Step-by-step explanation:

Hope this helps

Answer:

Step-by-step explanation:

[tex]\frac{a}{sinA}[/tex] = [tex]\frac{b}{sinB}[/tex] = [tex]\frac{c}{sinC}[/tex]

~~~~~~~~~~~~~~~~~

[tex]\frac{x}{sin41}[/tex] = [tex]\frac{4.5}{sin107}[/tex]

x = [tex]\frac{4.5sin41}{sin107}[/tex] ≈ 3.1 mi

[tex]\frac{y}{sin32}[/tex] = [tex]\frac{4.5}{sin107}[/tex]

y = [tex]\frac{4.5sin32}{sin107}[/tex] ≈ 2.5 mi

Ship A is 3.1 miles from the island.

Ship B is 2.5 miles from the island.

The value of tickets for rock concert is $120 and the value of tickets for soccer match is $40.

From the information, for five tickets for a rock concert and three tickets for a soccer match, they paid $720 and for two tickets for the same concert and six for the same soccer game, they paid $480.

Let the value of tickets for rock concert = x

Let the value of tickets for soccer match = y

Based on the information given, the equation will be:

5x + 3y = 720 .... i

2x + 6y = 480 ..... ii

Multiply equation i by 2

Multiply equation ii by 5

10x + 6y = 1440

10x + 30y = 2400

Subtract

24y = 960

y = 960 / 24

y = 40

Therefore, x will be:

5x + 3y = 720

5x + 3(40) = 720

5x + 120 = 720

5x = 720 - 120

5x = 600

Divide

x = 600 / 5

x = 120

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Complete question

For five tickets for a rock concert and three tickets for a soccer match, they paid $720 and for two tickets for the same concert and six for the same soccer game, they paid $480. What is the value of the ticket for each of the events?

Answer: n is 4

Step-by-step explanation: n-5= -1

Add 5 to both sides

n=-1+5

n=4

Step-by-step explanation:

5 Less than a number n 1. if you want 5 less than what you start with, you must take away 5

The diameter of the new rubber ball, to the nearest foot, must be D =  4.0 ft (in the case of the maximum cost).

Remember that for a sphere of diameter D, the surface area is:

A = 4*pi*(D/2)^2

In this case, the cost is $0.02 per square foot, and the company wants to expend (at maximum) $1 per ball, so first we need to solve:

$0.02*A = $1

A = $1/$0.02 = 50

So the surface of the ball must be 50 square feet.

Then we solve:

50ft^2 = 4*3.14*(D/2)^2

D = 2*√(50 ft^2/(4*3.14)) = 4.0 ft

If you want to learn more about spheres, you can read:

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Answer:

26

Step-by-step explanation:

complementary means same. so A and B are 26.

height = 24.4in

hope it helps...!!!

Answer:

24.4in.

Step-by-step explanation:

31.25 x 15.5 = 484.375

11818.75 / 484.375 = 24.4in.

Step-by-step explanation:

Angle W is the corresponds as to angle C

Answer:

q = 10

Step-by-step explanation:

[tex]\text{slope} =-3=\frac{q-4}{-7-(-5)} =\frac{q-4}{-2} \\\Longrightarrow -3=\frac{q-4}{-2} \\\Longrightarrow \left( -3\right) \times \left( -2\right) =q-4\\\Longrightarrow 6=q-4\\\Longrightarrow q=6+4\\\Longrightarrow q=10[/tex]

Answer:

250

Step-by-step explanation:

Answer:

$30,000

Step-by-step explanation:

1500 would be the remaining 5%. Simply double that, which gives you 3000, which is 10%. Adding the other 90% would make the answer be $30,000

Answer:

2925 dollars.

Step-by-step explanation:

1500 x 0.95 = 1425

1500 + 1425 = 2925

Answer:

Its the third one I think.

Step-by-step explanation:

I worked on it.

Answer:

c

Step-by-step explanation:

Answer:

PART ONE:

1.Most common sleep is: 8 1/2 hours of sleep.

2.There is a a outlinear in the data (6 1/2)

3. 10-6.5 = 3.5, So 3 1/2 hours diffence of sleep

4. 15 more people slept longer than 8 hours

Answer:

125 degrees

Step-by-step explanation:

5x=3x+50

5x-3x+50

2x=50

x=25

5x=25x5

   =125

Answer:

1 week

Step-by-step explanation:

Answer:

Step-by-step explanation:

This curved line is called a function.

What Function is it?

Nonlinear functions are curved lines, going through some of the axis.

Linear functions are straight lines, and it will forever go left and right.

The product of the two provided equations, obtained by multiplying each term of the first equation from the second one, is 6p³+29p²+22p-21.

To multiply the two equation, each term of the first equation is multiples from the second term.

         [tex]2p+ 7[/tex]

        [tex]3p^2 +4p-3[/tex]

The product of these two equations are,

[tex]P=(2p+7)\times (3p^2 +4p-3)\\P=6p^3+8p^2-6p+21p^2+28p-21[/tex]

Arrange the equation with the same power terms,

[tex]P=6p^3+8p^2+21p^2-6p+28p-21\\P=6p^3+29p^2+22p-21[/tex]

Hence, the product of the two provided equations, obtained by multiplying each term of the first equation from the second one, is 6p³+29p²+22p-21.

Learn more about the multiplication of two equation here;

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Answer:

x=12/17

Step-by-step explanation:

hope this helps

Answer:

I think it would be 4+10=14 and the bigger number is 10

Step-by-step explanation:

forgive me if I'm wrong

Answer:

Step-by-step explanation:

3a^2x^2 (x^5 -6x^3 - 8x)

= 3a^2x^2 * x^5 - 3a^2x^2 * 6x^3 - 3a^2x^2 * 8x

= 3a^2x^7 - 18a^2x^5 - 24a^2x^3.