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3 years ago

A rectangle has an area of 30 m² and a perimeter of 34 m. What are the dimensions of the rectangle?

1 answer:

7 0

Length is l
width is w
l*w = 30
2l + 2w = 34

You can simplify the second equation to l + w = 17

Factors of 30:
30*1
15*2
10*3
6*5

Try adding each of these factors together, to find out which equals 17

30 + 1 = 31
15 + 2 = 17
10 + 3 = 13
6 + 5 = 11

So the dimensions of the rectangle are 15m * 2m

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7.60. When Paul crossed the finish line of a 60-meter race, he was ahead of Robert by 10 meters and ahead of Sam by 20 meters. S

Lelechka [254]

Answer:

The number of meters Robert will beat Sam is 12 meters.

Step-by-step explanation:

Given:

When Paul crossed the finish line of a 60-meter race, he was ahead of Robert by 10 meters and ahead of Sam by 20 meters. Suppose Robert and Sam continue to race to the finish line without changing their rates of speed.

Find:

the number of meters by which Robert will beat Sam

Step 1 of 1

When Paul finishes, Robert has run 60-10=50 meters and Sam has run 60-20=40 meters.

Therefore, when Robert and Sam run for the same amount of time, Sam covers $\frac{40}{50}=\frac{4}{5}$ of the distance that Robert covers. So, while Robert runs the final 10 meters of the race, Sam runs $\frac{4}{5} \cdot 10=8$ meters.

This means Robert's lead over Sam increases by 2 more meters, and he beats Sam by 10+2=12 meters.

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2 years ago

The quotient of a number and 2 is equal to 50

Vadim26 [7]

I think it’s 25....Yeah I’m pretty sure it’s 25

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3 years ago

The first, third and thirteenth terms of an arithmetic sequence are the first 3 terms of a geometric sequence. If the first term

Salsk061 [2.6K]

Answer:

The first three terms of the geometry sequence would be $1$ , $5$ , and $25$ .

The sum of the first seven terms of the geometric sequence would be $127$ .

Step-by-step explanation:

Let $d$ denote the common difference of the arithmetic sequence.

Let $a_1$ denote the first term of the arithmetic sequence. The expression for the $n$ th term of this sequence (where $n\!$ is a positive whole number) would be $(a_1 + (n - 1)\, d)$ .

The question states that the first term of this arithmetic sequence is $a_1 = 1$ . Hence:

The third term of this arithmetic sequence would be $a_1 + (3 - 1)\, d = 1 + 2\, d$ .
The thirteenth term of would be $a_1 + (13 - 1)\, d = 1 + 12\, d$ .

The common ratio of a geometric sequence is ratio between consecutive terms of that sequence. Let $r$ denote the ratio of the geometric sequence in this question.

Ratio between the second term and the first term of the geometric sequence:

$\displaystyle r = \frac{1 + 2\, d}{1} = 1 + 2\, d$ .

Ratio between the third term and the second term of the geometric sequence:

$\displaystyle r = \frac{1 + 12\, d}{1 + 2\, d}$ .

Both $(1 + 2\, d)$ and $\left(\displaystyle \frac{1 + 12\, d}{1 + 2\, d}\right)$ are expressions for $r$ , the common ratio of this geometric sequence. Hence, equate these two expressions and solve for $d$ , the common difference of this arithmetic sequence.

$\displaystyle 1 + 2\, d = \frac{1 + 12\, d}{1 + 2\, d}$ .

$(1 + 2\, d)^{2} = 1 + 12\, d$ .

$d = 2$ .

Hence, the first term, the third term, and the thirteenth term of the arithmetic sequence would be $1$ , $(1 + (3 - 1) \times 2) = 5$ , and $(1 + (13 - 1) \times 2) = 25$ , respectively.

These three terms ( $1$ , $5$ , and $25$ , respectively) would correspond to the first three terms of the geometric sequence. Hence, the common ratio of this geometric sequence would be $r = 25 /5 = 5$ .

Let $a_1$ and $r$ denote the first term and the common ratio of a geometric sequence. The sum of the first $n$ terms would be:

$\displaystyle \frac{a_1 \, \left(1 - r^{n}\right)}{1 - r}$ .

For the geometric sequence in this question, $a_1 = 1$ and $r = 25 / 5 = 5$ .

Hence, the sum of the first $n = 7$ terms of this geometric sequence would be:

$\begin{aligned} & \frac{a_1 \, \left(1 - r^{n}\right)}{1 - r}\\ &= \frac{1 \times \left(1 - 2^{7}\right)}{1 - 2} \\ &= \frac{(1 - 128)}{(-1)} = 127 \end{aligned}$ .

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3 years ago

How to convert 18 gallons/1 hour to cups and minutes

Ne4ueva [31]

So there are 2 things you need to convert, the first is the gallons to cups and the second is the hours to minutes. so I like to set it up with numerators and denominators and then multiply the ratios. All same terms will cross out and be opposite of each other.

(18 gal/1 hour) x (1 hour / 60 minutes), now we have (0.3 gallons/1 minute) we just have to change gallons to cups

(0.3 gallons/ 1 minute) x (4 quarts/1 gallon) x (2 pints/1 quart) x (2 cups/1 pint)

this comes out 4.8 cups/1 minute

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3 years ago

What would be the answer to writing the equations included in the same set of related facts as 6×8=48

larisa [96]

Included in the same facts

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3 years ago