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2 years ago

Peter wants to cut a rectangle of size 6x7 into squares with integer sides. What is the smallest number of squares he can get

Mathematics

1 answer:

Semmy [17]2 years ago

5 0

He can cut 5 squares, by making 1 4 × 4, 2 3 × 3 and 2 2 × 2 squares.

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Jocelyn is considering taking out one of the two following loans. Loan H is a three-year loan with a principal of $5,650 and an

Alexus [3.1K]

<span>c.<span>Loan I's monthly payment will be $11.88 smaller than Loan H's.</span></span>

7 0

1 year ago

Read 2 more answers

The first term of a finite geometric series is 6 and the last term is 4374. The sum of all the term os 6558. find the common rat

Oliga [24]

A geometric series is written as $ar^n$ , where $a$ is the first term of the series and $r$ is the common ratio.

In other words, to compute the next term in the series you have to multiply the previous one by $r$ .

Since we know that the first time is 6 (but we don't know the common ratio), the first terms are

$6, 6r, 6r^2, 6r^3, 6r^4, 6r^5, \ldots$ .

Let's use the other information, since the last term is $4374 > 6$ , we know that $r>1$ , otherwise the terms would be bigger and bigger.

The information about the sum tells us that

$\displaystyle \sum_{i=0}^n 6r^i = 6\sum_{i=0}^n r^i = 6558$

We have a formula to compute the sum of the powers of a certain variable, namely

$\displaystyle \sum_{i=0}^n r^i = \cfrac{r^{n+1}-1}{r-1}$

So, the equation becomes

$6\cfrac{r^{n+1}-1}{r-1} = 6558$

The only integer solution to this expression is $n=6, r=3$ .

If you want to check the result, we have

$6+6*3+6*3^2+6*3^3+6*3^4+6*3^5+6*3^6 = 6558$

and the last term is

$6*3^6 = 4374$

7 0

1 year ago

How do you this question? Please help.

dangina [55]

N - Nicholes money
M - Marys money

(1) N + M = 4800 ⇒ N = 4800 - M
(2) N - 800 = M - 2/5M ⇒ N - 800 = 3/5M

subtitute (1) to (2)

4800 - M - 800 = 3/5M
4000 - M = 3/5M
-M - 3/5M = -4000
-8/5M = -4000 |multiply both sides by (-5/8)
M = 2500

subtitute the value of M to (1)

N = 4800 - 2500
N = 2300

Answer: Mary had at first $2500. (Nichole: $2300).

5 0

1 year ago

A new parking lot is being built for a medical office. The expression representing the number of parking spots in the new lot is

docker41 [41]

Answer:

111 spots

Step-by-step explanation:

Let y denote the total number of parking spots expressed as:

$y=\frac{15x}{4}-9\\\\$