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Naddika [18.5K]

2 years ago

9

A college writing seminar increased its size by 50% from the first to the second day. If the total number of students in the sem

inar on the second day was 15 how many students were in the class on the first day

2 answers:

slava [35]2 years ago

7 0

10 students on the first day

Cerrena [4.2K]2 years ago

7 0

20000 is the correct answer

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A rectangle is 7/8 feet wide and 1 3/5 feet long<br>what is the area of the rectangle!<br><br>help!

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area= 7/8×8/5 = 7/5 =1.4 sq feet

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Dhruv is 24 years older than Sanjay.10 years back Dhruv’s age was five times the age of Sanjay. Find their ages.

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2 years ago

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A passenger train traveled 100 miles in the same amount of time it took a freight train to travel 80 miles. The rate of the frei

andreev551 [17]

Answer:

The passenger train traveled at a speed of 25 miles/hour

Step-by-step explanation:

In this question, we are asked to calculate the rate at which a particular passenger train is traveling.

We use the information in the question to answer as follows;

Firstly, we identify that they traveled at the same time but their distances are different. This means that their speed must be different also.

Mathematically, we know that time can be calculated as distance/ time.

Let us say the speed at which the passenger train traveled is x miles per hour. This means that the speed of the freight train which was 5 miles per hour slower would be (x-5) miles per hour.

We know their times are equal;

Hence;

100/x = 80/(x-5)

We cross multiply

100(x-5) = 80x

100x -500 = 80x

100x-80x = 500

20x = 500

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6 0

3 years ago

Help fast, please

pshichka [43]

ANSWER

1.

$log_{4}(3x) = log_{4}(3) + log_{4}(x)$

2.

$log_{3}( \frac{27}{x} ) = 3 - log_{3}(x)$

3.

$log_{4}( {x}^{5} ) = 5 log_{4}(x)$

EXPLANATION

1. The given logarithmic expression is

$log_{4}(3x)$

Use the product rule:

$log_{a}(mn) = log_{a}(m) + log_{a}(n)$

We apply this rule to obtain:

$log_{4}(3x) = log_{4}(3) + log_{4}(x)$

2. The given logarithmic expression is

$log_{3}( \frac{27}{x} )$

We apply the quotient rule:

$log_{a}( \frac{m}{n} ) = log_{a}(m) - log_{a}(n)$

This implies that;

$log_{3}( \frac{27}{x} ) = log_{3}(27) - log_{3}(x)$

We simplify to get;

$log_{3}( \frac{27}{x} ) = log_{3}( {3}^{3} ) - log_{3}(x)$

Apply the power rule:

$log_{a}( {m}^{n} ) = n log_{a}(m)$

$log_{3}( \frac{27}{x} ) = 3 log_{3}( {3}) - log_{3}(x)$

simplify;

$log_{3}( \frac{27}{x} ) = 3 (1) - log_{3}(x)$

$log_{3}( \frac{27}{x} ) = 3 - log_{3}(x)$

3. The given logarithmic expression is;

$log_{4}( {x}^{5} )$

Apply the power rule of logarithms.

$log_{a}( {m}^{n} ) = n log_{a}(m)$

This implies that,

$log_{4}( {x}^{5} ) = 5 log_{4}(x) .$

8 0

2 years ago