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8_murik_8 [283]
3 years ago
12

Katy's measured the growth of a plant seedling. The seedling grew 1/3 inch by the end of the first week. The seedling grew 5/6 i

nch by the end of the second week. About how much did the seedling grow in the fist 2 weeks?
Mathematics
2 answers:
Vikki [24]3 years ago
8 0
In the given problem it is already given that the seedling grew by 1/3 inch in the first week and 5/6 inch in the second week. Then it would not be a problem to find the total length of growth of the seedling.
The length up to which the seedling grew in 2 weeks = (1/3) + (5/6)
                                                                                     = (2 + 5)/6
                                                                                     = 7/6 inch
So the seedling grew by 7/6 inches in two weeks. I hope that this answer is what you were looking for. You can solve such problems in the future by following the method that is applied for solving this problem.
ddd [48]3 years ago
5 0
1/3 + 5/6 = 2/6 + 5/6 = 7/6
It grew by 7/6 or 1 1/6 inches by the first 2 weeks.
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2 tan 30°<br>II<br>1 + tan- 300​
shusha [124]

Question:

\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}

Answer:

\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}= sin(60^{\circ})

Step-by-step explanation:

Given

\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}

Required

Simplify

In trigonometry:

tan(30^{\circ}) = \frac{1}{\sqrt{3}}

So, the expression becomes:

\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})} = \frac{2 * \frac{1}{\sqrt{3}}}{1 + (\frac{1}{\sqrt{3}})^2}

Simplify the denominator

\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})} = \frac{2 * \frac{1}{\sqrt{3}}}{1 + \frac{1}{3}}

\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})} = \frac{\frac{2}{\sqrt{3}}}{1 + \frac{1}{3}}

\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})} = \frac{\frac{2}{\sqrt{3}}}{ \frac{3+1}{3}}

\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})} = \frac{\frac{2}{\sqrt{3}}}{ \frac{4}{3}}

Express the fraction as:

\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}= \frac{2}{\sqrt 3} / \frac{4}{3}

\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})} = \frac{2}{\sqrt 3} * \frac{3}{4}

\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})} = \frac{1}{\sqrt 3} * \frac{3}{2}

\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})} = \frac{3}{2\sqrt 3}

Rationalize

\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})} = \frac{3}{2\sqrt 3} * \frac{\sqrt{3}}{\sqrt{3}}

\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})} = \frac{3\sqrt{3}}{2* 3}

\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})} = \frac{\sqrt{3}}{2}

In trigonometry:

sin(60^{\circ}) =  \frac{\sqrt{3}}{2}

Hence:

\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}= sin(60^{\circ})

3 0
3 years ago
IPod Touch 64 GB<br> On Sale For $299.99<br> Originally $349.99<br> _______% Savings
liubo4ka [24]

Answer:

14.286% savings

Step-by-step explanation:

299.99 / 349.99 = 0.8571..

1-0.8571= 14.286

3 0
3 years ago
There are 4,000 books in the town's library. Of these 2,600 are fiction. Write a percent equation that you can use to find the p
defon

Answer:

x = (2600/4000) × 100%

x = 0.65 × 100%

x = 65%

Step-by-step explanation:

The percentage equation that can be used to find the percent of books that are fiction can only be found where the number of fiction books is known and the total number of books available is known as well.

Given;

Number of fiction books = 2,600

Number of books = 4,000

let the percent of books that are fiction be x

x = (2600/4000) × 100%

x = 0.65 × 100%

x = 65%

5 0
3 years ago
On a certain hot​ summer's day, 340 people used the public swimming pool. The daily prices are $1.25 for children and $2.25 for
UkoKoshka [18]

Answer:

Number of children = x = 88

Number of Adults = y = 252

Step-by-step explanation:

Let us represent:

Number of children = x

Number of Adults = y

On a certain hot​ summer's day, 340 people used the public swimming pool.

Hence:

x + y = 340..... Equation 1

x = 340 - y

The daily prices are $1.25 for children and $2.25 for adults. The receipts for admission totaled $677.00.

$1.25 × x + $2.25 × y =$ 677

1.25x + 2.25y = 677..... Equation 2

Let us substitute: 340 - y for x in Equation 2

1.25(340 - y) + 2.25y = 677

= 425 - 1.25y + 2.25y = 677

Collect like terms

- 1.25y + 2.25y = 677 - 425

1y = 252

y = 252

Solving for x

x = 340 - y

x = 340 - 252

x = 88

Therefore the number of children and adults that swam at the public pool that​ day are: 88 children and 252 Adults.e

3 0
3 years ago
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NARA [144]
I will get you started.

Car Problem:

10,750(0.059) = 634.25

Year 1:

10,750 - 634.25 = 10,115.75

The price of the car after year one at 0.059 is $10,115.75.

Continue the same pattern for the remaining 9 years.

Population Problem:

17, 724(0.02) = 354.48

For Year 1:

17,724 + 354.48 = 18,078.48

Continue the same pattern for the remaining 18 years. Use your calculator.
7 0
3 years ago
Read 2 more answers
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