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3 years ago

A method to prove statements using properties that justify each step.

Mathematics

1 answer:

vesna_86 [32]3 years ago

6 0

Answer:

A two column proof is a method to prove statements using properties that justify each step. The properties are called reasons.

Step-by-step explanation:

hope dis helps!

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The sum of twice a number and three is 21. find the number

Alisiya [41]

Answer:

sum of twice a number and three is 21

2x + 3 = 21

x = 9

7 0

4 years ago

Money deposited $8000 into an account 6 years ago. The account earned simple interest at a yearly rate. So far the total interes

matrenka [14]

Answer:

2.5%

Step-by-step explanation:

interest = principal * rate * time

1200 = 8000r6

1200 = 48000r

r = 0.025

Rate for account is 2.5%

4 0

4 years ago

Suppose you deposit $1200 into a savings account that compounds interest continuously at 3.9%. You left your money in the accoun

kodGreya [7K]

Answer: you would have $1772 at the end of 10 years.

Step-by-step explanation:

The formula for continuously compounded interest is

A = P x e (r x t)

Where

A represents the future value of the investment after t years.

P represents the present value or initial amount invested

r represents the interest rate

t represents the time in years for which the investment was made.

e is the mathematical constant approximated as 2.7183.

From the information given,

P = $1200

r = 3.9% = 3.9/100 = 0.039

t = 10 years

Therefore,

A = 1200 x 2.7183^(0.039 x 10)

A = 1200 x 2.7183^(0.39)

A = $1772 to the nearest dollar

4 0

4 years ago

How many pounds of chocolate worth $1.5 a pound must be mixed with 10 pounds of chocolate worth 60 cents a pound to produce a mi

Mashcka [7]

Answer:

$8\ pounds$

Step-by-step explanation:

Let

x-----> amount of pounds of chocolate worth $1.5

we know that

$1.5x+0.60(10)=1(x+10)$

$1.5x+6=x+10$

$1.5x-x=10-6$

$0.5x=4$

$x=8\ pounds$

8 0

3 years ago

Read 2 more answers

A restaurant owner was experimenting with the taste of her homestyle lemon drink. She started with 60 litres of water. She remov

Burka [1]

Answer:

ratio of pure lemon juice to water in the homestyle lemon drink is 5 : 19.

Step-by-step explanation:

In order to solve the final ratio of lemon juice to water, let us start by determining the initial ratio of pure lemon juice to water in the first mix. This is done as follows:

Total volume of mixture = 60 liters

initial volume of water = 60 liters

initial volume of lemon juice = 0 liters

1) She removed 15 liters of the water and replaced it with 15 liters of pure lemon juice.

Volume of water = 60 - 15 = 45 liters

Volume of lemon juice = 15 liters

$\therefore \frac{15}{60}\ = \frac{1}{4}\ of\ the\ first\ mix\ is\ lemon\ juice\\\frac{45}{60}\ = \frac{3}{4}\ of\ the\ first\ mix\ is\ pure\ water$

2) She removed 10 liters of the new mixture

Let us convert this amount removed into ratio:

$lemon\ juice\ = \frac{1}{4}\ \times 10 = \frac{10}{4} = \frac{5}{2}\ liters.\\ \therefore the\ owner\ removes\ \frac{5}{2}\ liters\ of\ pure\ lemon\ juice\\pure\ water\ = \frac{3}{4}\ \times 10 = \frac{30}{4} = \frac{15}{2}\ liters\\ \therefore\ the\ owner\ removes\ \frac{15}{2}\ liters\ of\ water\ from\ the\ first\ mix.$

New volumes of water and lemon juice after removing the 10 liters of mixture is calculated as follows:

$lemon\ juice\ = 15 - \frac{5}{2} = \frac{30-5}{2} = \frac{25}{2}\ liters\ of\ lemon\ juice\\pure\ water\ = 45 - \frac{15}{2} = \frac{90-15}{2} = \frac{75}{2}\ liters\ of\ pure\ water$

3) and replaced it with 10 liters of water.

$New\ volume\ of\ water\ = 10 + \frac{75}{2} = \frac{20+ 75}{2} = \frac{95}{2}\ liters$

The final ratio of lemon juice to water:

$\frac{25}{2} : \frac{95}{2}\\= 25 : 95\\= 5 : 19$

Therefore, the final ratio of pure lemon juice to water in the homestyle lemon drink is 5 : 19.

4 0

3 years ago

A method to prove statements using properties that justify each step.​

A method to prove statements using properties that justify each step.