Ask question

Ask question

All categories

3 years ago

15

if a 25 ft rope is cut into two sections with one section four times as long as the other section, how long is the shorter piece

?

2 answers:

Ganezh [65]3 years ago

4 0

Total length of rope = 25 feet

Let us say one part of the rope is x, then the other part will be 25-x.

We are given that one section of the rope is four times as long as the other.

So let us make an equation using this information,

$x=4(25-x)$

$x=100-4x$

$5x=100$

x=20

So one part is 20 feet and the second part is 25-20= 5 feet.

Answer: The shorter part of the rope is 5 feet long.

grin007 [14]3 years ago

3 0

3.125 ft long or 3.13 ft long

You might be interested in

A sample of 80 high school senlors, 45% of which are female, were surveyed as to whether or not they are employed

fgiga [73]

Answer:

33 boys

Step-by-step explanation:

Since 45% of the participants were female and there were a total of 80 students, 36 of the 80 students were female. That means that 44 of the students were male.

25% of 44 is 11. So there are 11 boys that are not employed. From there you can just subtract 44 - 11 and get 33.

33 boys are employed

3 0

3 years ago

Read 2 more answers

Find two consecutive odd integers whose sum is 116 (and please have steps) thank you

matrenka [14]

It's 57 and 59
Call (n) is the first odd interger => the second odd interger is (n+2)
=> n + (n + 2) = 116
=> n + n + 2 = 116
=> 2n = 114
=> n = 57
First odd interger is 57 and the second odd interger is 59 .
Sorry my English so bad =)))

6 0

4 years ago

The compound interest on a sum of money in

Yakvenalex [24]

Answer:

The difference between the principal and the compound interest in three years is Rs 17,994

Step-by-step explanation:

The compound interest is given according to the following formula;

$C.I. = P \cdot \left ( 1 + \dfrac{r}{n} \right ) ^{n\cdot t} - P$

The given amount of the compound after 2 years = Rs 5,460

The given amount of the compound after 4 years = Rs 12,066.60

Therefore, we have;

$5,460 = P \cdot \left ( 1 + \dfrac{r}{100} \right ) ^{2} - P$ ...(1)

$12,066.60 = P \cdot \left ( 1 + \dfrac{r}{100} \right ) ^{4} - P$ ...(2)

Dividing equation (2) by (1), we have;

$\dfrac{12,066.60}{5,460} = \dfrac{P \cdot \left ( \left ( 1 + \dfrac{r}{100} \right ) ^{4} - 1\right )}{P \cdot \left (\left ( 1 + \dfrac{r}{100} \right ) ^{2} -1 \right ) } =\dfrac{\left ( 1 + \dfrac{r}{100} \right ) ^{4} - 1}{\left ( 1 + \dfrac{r}{100} \right ) ^{2} -1 }$

$Let \ \left ( 1 + \dfrac{r}{100} \right ) ^{2} = x, we \ get;$

$\dfrac{12,066.60}{5,460} =\dfrac{\left ( 1 + \dfrac{r}{100} \right ) ^{4} - 1}{\left ( 1 + \dfrac{r}{100} \right ) ^{2} -1 } = \dfrac{x^2 - 1}{x - 1}$

∴ 12,066.60 × (x - 1) = 5,460 × (x² - 1) = 5,460 × (x - 1) ×(x + 1)

∴ 12,066.60 × (x - 1)/(x - 1) = 5,460 × (x + 1)

12,066.60/5,460 = x + 1

x = 12,066.60/5,460 - 1 = 1.21 = 121/100

x = 121/100

$\left ( 1 + \dfrac{r}{100} \right ) ^{2} = x = \dfrac{121}{100}$

$1 + \dfrac{r}{100} =\sqrt{ \dfrac{121}{100}} = \dfrac{11}{10}$

We get

$\dfrac{12,066.60}{5,460} =\dfrac{221}{100}$

$\therefore \dfrac{12,066.60}{5,460} =\dfrac{221}{100} = \left ( 1 + \dfrac{r}{100} \right ) ^{2}$

$1 + \dfrac{r}{100} = \sqrt{ \dfrac{221}{100} } = \dfrac{\sqrt{221} }{10}$

$\dfrac{r}{100} = \dfrac{\sqrt{221} }{10} - 1$

$\dfrac{r}{100} = \dfrac{11}{10} - 1 = \dfrac{1}{10} = 0.1$

r = 100 × 0.1 = 10%

r = 10%

Therefore, we have;

$5,460 = P \cdot \left ( 1 + \dfrac{r}{100} \right ) ^{2} - P = P \times \left ( 1 + 0.1\right ) ^{2} - P$

$5,460 = P \times \left ( 1 + 0.1\right ) ^{2} - P = P \times \left (\left ( 1 + 0.1\right ) ^{2} - 1\right) = P \times \dfrac{21}{100}$

$P = \dfrac{100}{21} \times 5,460 = 26,000$

The principal = Rs. 26,000

The compound interest in 3 years is therefore;

$CI_3 = 26,000 \times \left ( 1 + \dfrac{10}{100} \right ) ^{3} - 26,000= 8606$

The difference, 'd', between the principal and the compound interest in three years, is given as follows;

d = P - CI₃

d = 26,600 - 8606 = 17994

The difference between the principal and the compound interest in three years, d = Rs 17,994.

5 0

3 years ago

Which of the following is the minimum value of the equation y = 3x2 - 4x - 2?

natka813 [3]

Answer: 3x

Step-by-step explanation:

*Remember BIDMAS*

b- brackets i- Indices (exponents) d- division m- multiplication a- addition s- subtraction

(*Reminder* exponents can be written on a keyboard like 2 squared is 2^2)

you need to follow these steps to be able to solve any equation

if there is no brackets like yours then add to make it easier

3x^2 - 4x - 2 = (3x^2) - 4x - 2

From the steps I showed you indices is first so 3x multiplied by 3x is 9x

now there is nothing left except for subtraction so solve from left to right always so 9x - 4x - 2 is 5x then 5x - 2 is 3x, x doesn’t change or gets subtracted.

i hope it helped :)

3 0

3 years ago

Three ratios that are equivalent to 16;12

lukranit [14]

Step-by-step explanation:

Touch and hold a clip to pin it. Unpinned clips will be deleted after 1 hour.Touch and hold a clip to pin it. Unpinned clips will be deleted after 1 hour.Touch and hold a clip to pin it. Unpinned clips will be deleted after 1 hour.Touch and hold a clip to pin it. Unpinned clips will be deleted after 1 hour.Touch and hold a clip to pin it. Unpinned clips will be deleted after 1 hour.

7 0

3 years ago