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3 years ago

A boat can hold 45 people.27more people can fit on the boat . how many people are on the boat now?

Mathematics

2 answers:

timurjin [86]3 years ago

7 0

There are 18 people on the boat

PilotLPTM [1.2K]3 years ago

3 0

Add them together its 72 but u said a boat can hold 45 people so I wouldn't say 72. I will need to know how many people were on the boat in the first place.

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An actor invests some money at 7%, and $24000 more than four times the amount at 8%. The total annual interest earned from the i

natita [175]

Answer:

$70,000 at 7%
$304,000 at 8%

Step-by-step explanation:

Given:

Total interest earned on two investments is $29,220.

An amount is invested at 7%.

$24,000 more than 4 times that amount is invested at 8%.

Find:

The amount invested at each rate.

Solution:

Our strategy will be to define a variable representing the amount invested at 7%, use that variable to write an expression for the amount invested at 8%, then write an equation for the total return on the investments.

Let x represent the amount invested at 7%. Then (24,000+4x) will be the amount invested at 8%. The total interest earned will be ...

interest on 7% account + interest on 8% account = total interest

0.07x + 0.08(24000+4x) = 29220

0.39x + 1920 = 29220 . . . . . . . . . . . simplify

0.39x = 27300 . . . . . . . . . . . . . . . . . .subtract 1920

x = 27300/0.39 = 70000 . . . . . . . . . divide by the coefficient of x

24,000 +4x = 24,000 +280,000 = 304,000 . . . . amount invested at 8%

He invested $70,000 at 7% and $304,000 at 8%.

Check

The answer must satisfy ...

7% interest + 8% interest = 29,220

0.07×70,000 +0.08×304,000 = 4,900 +24,320 = 29,220 . . . . as required

_____

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6 0

3 years ago

<img src="https://tex.z-dn.net/?f=5x-%20%5Cdfrac%7B%20%5Csqrt%7B%209%20%7B%20x%20%7D%5E%7B%202%20%7D%20-6x%2B1%20%5Cphantom%7B%5

Morgarella [4.7K]

Answer:

$=5x+1$ or $=5x-1$

Step-by-step explanation:

One is given the following equation:

$5x-\frac{\sqrt{9x^2-6x+1}}{1-3x}$

The problem asks one to simplify the expression, the first step in solving this equation is to factor the equation. Rewrite the numerator and denominator of the fraction as the product of two expressions. Remember the factoring patterns:

$(a-b)^2=a^2-2ab+b^2$

$=5x-\frac{\sqrt{9x^2-6x+1}}{1-3x}$

$=5x-\frac{\sqrt{(3x-1)^2}}{-(3x-1)}$

Now simplify the numerator. Remember, taking the square root of a squared value is the same as taking the absolute value of the expression,

$=5x-\frac{\sqrt{(3x-1)^2}}{1-3x}$

$=5x-\frac{|3x-1|}{-(3x-1)}$

Rewrite the expression without the absolute value sign in the numerator. Remember the general rule for removing the absolute value sign:

$|a-b|\\=a -b$ or $(-a-b) = b-a$

$=5x-\frac{|3x-1|}{-(3x-1)}$

$=5x-\frac{3x-1}{-(3x-1)}$ or $=5x-\frac{-(3x-1)}{-(3x-1)}$

Simplify both expressions, reduce by canceling out common terms in both the numerator and the denominator,

$=5x-\frac{3x-1}{-(3x-1)}$ or $=5x-\frac{-(3x-1)}{-(3x-1)}$

$=5x-(-1)$ or $=5x-(1)$

Simplify further by rewriting the expression without the parenthesis, remember to distribute the sign outside the parenthesis by the terms inside of the parenthesis; note that negative times negative equals positive.

$=5x-(-1)$ or $=5x-(1)$

$=5x+1$ or $=5x-1$

6 0

3 years ago

Math - Use unit conversion factor to convert the units.

nlexa [21]

Answer: 240 minutes, 20 cups, 4000 pounds

Step-by-step explanation:

Use the following conversions:

1 hour = 60 minutes

2 cups = 1 pint

2 pints = 1 quart

1 ton = 2000 pounds

$4\ hours\times \dfrac{60\ minutes}{1\ hour}=\large\boxed{240\ minutes}\\\\\\\\5\ quarts \times \dfrac{2\ pints}{1\ quart}\times \dfrac{2\ cups}{1\ pint}=\large\boxed{20\ cups}\\\\\\\\2\ tons\times \dfrac{2000\ pounds}{1\ ton}=\large\boxed{4000\ pounds}$