the denominator of a fraction is 2 more than its numerator.when both the numerator and the denominator are increased by 3,the fraction is increased by 3/20.Find the original fraction given that both the numerator and denominator are positive integers

Answers

Answer 1

Answer:  3/5

Step-by-step explanation:

[tex]\dfrac{a}{a+2}+\dfrac{3}{20}=\dfrac{a+3}{(a+2)+3}\\\\\\\dfrac{a}{a+2}\bigg(\dfrac{20}{20}\bigg)+\dfrac{3}{20}\bigg(\dfrac{a+2}{a+2}\bigg)=\dfrac{a+3}{a+5}\\\\\\\dfrac{23a+6}{20(a+2)}=\dfrac{a+3}{a+5}\\\\\\(23a+6)(a+5)=20(a+2)(a+3)\\\\\\23a^2+121a+30=20a^2+100a+120\\\\\\3a^2+21a-90=0\\\\\\a^2+7a-30=0\\\\\\(a+10)(a-3)=0\\\\\\a=-10\quad a=3[/tex]

Since "a" is a positive integer, disregard a = -10

So the only valid answer is a=3   →  a+2=5

[tex]\dfrac{a}{a+2}=\large\boxed{\dfrac{3}{5}}[/tex]


Related Questions

need help asap!!! WILL GIVE THE MOST BRAINIEST TO WHOEVER ANSWERS IT RIGHT PUT THE ANSWER IN A BOX

Answers

Answer:

36PI

113.04

Step-by-step explanation:

4/3*PI*R^3=V

4/3*PI*27=V

36*PI=V

113.04

BRAINLIEST PLS

              -ZYLYNN JADE

Answer:

113.10 (to the nearest hundredth)

Step-by-step explanation:

just google volume of a sphere

Pqrs is a rhombus. Find x, y and z. Justify your finding.

Answers

Answer:

x = 4, y = 2√21, z = 10

Step-by-step explanation:

Since all sides of a rhombus are congruent, z = SR = 10. Since the diagonals of a rhombus bisect each other, x = PO = 4. Using Pythagorean Theorem (look at ΔPSO, we know that PS = 10 and PO = 4), y = 2√21.

how to do this question plz ​

Answers

Answer:

adult = £7 and child = £2

Step-by-step explanation:

let a represent adult ticket and c child ticket, then

2a + 3c = 20 → (1)

a + 4c = 15 → (2)

Multiply (2) by - 2 and add to (1) to eliminate a

- 2a - 8c = - 30 → (3)

Add (1) and (3) term by term

- 5c = - 10 ( divide both sides by - 5 )

c = 2

Substitute c = 2 into either of the 2 equations and solve for a

Substituting into (1)

2a + 3(2) = 20

2a + 6 = 20 ( subtract 6 from both sides )

2a = 14 ( divide both sides by 2 )

a = 7

Cost of adult ticket is £7 and child ticket is £2

please help i will give out brainliest

Answers

Answer:

6, 0, 10

b

Step-by-step explanation:

(2x + 3)(5x2 - 2x - 1) = Ax3 + Bx2 + Cx + D. What are the values of B and C?

Answers

Answer:

B = 11; C = -8

Step-by-step explanation:

When simplified I get 10x^3 + 11x^2 - 8x - 3

PLEASE HELP - Find the area of a regular octagon with a side length of 5 cm. Round to the nearest tenth. (Please explain in full detail the process, im trying to learn how to do these) thank you!!

Answers

Answer:

120.7

Step-by-step explanation:

The formula for finding the area of a regular octagon is: A = 2(1+[tex]\sqrt{2}[/tex])[tex]a^{2}[/tex].

Using the formula I got 120.7(rounded).

The area of the regular octagon with a side length of 5 cm is approximately 120.7cm².

We have,

To find the area of a regular octagon with a side length of 5 cm, you can use the following formula:

Area = 2 * (1 + √2) * (Side Length)²

Plugging in the values:

Area = 2 * (1 + √2) * (5 cm)² ≈ 120.7 cm²

Therefore,

The area of the regular octagon with a side length of 5 cm is approximately 120.7cm².

Learn more about octagons here:

https://brainly.com/question/30182906

#SPJ4

What decimal represents the shaded part in the picture?

Answers

Answer:

40/100 = 0.4

your welcome

find the y-intercept of the function: f(×)=(×+10)/(×-5)​

Answers

Answer:

(-10,0)

Step-by-step explanation:

Hello

this is (-10,0) point

because f(-10)=0

hope this helps

the y intercept is (0,-2) and the x intercept is (-10,0)

Need help again ?!???

Answers

Answer:

11.47

Step-by-step explanation:

Use SohCahToa. In this problem, you are given the hypotenuse and you are trying to solve for the adjacent side so it will be cosine. (cosine = [tex]\frac{adjacent}{hypotenuse}[/tex])

1. set up the equation

cos55 = [tex]\frac{x}{20}[/tex]

2. Multiply both sides by 20 to solve for x

20 · cos55 = 11.47

Answer:

11.47

Solution,

From the figure,

[tex]cos \: 55 = \frac{PQ}{PR} [/tex]

[tex]cos \: 55 = \frac{PQ}{20} [/tex]

[tex]PQ = 20 \: cos \: 55[/tex]

[tex]PQ= 11.472[/tex]

[tex]PQ= 11 .47[/tex]

Hope this helps...

Good luck on your assignment...

The mean length of 4 childrens' big finger is 14cm. The mean length of 9 adults' big finger is 16.1cm. What is the mean length (rounded to 2 DP) of these 13 people's big finger?

Answers

Answer:

The mean length of the 13 people's big finger is 15.45 cm

Step-by-step explanation:

Given;

mean length of 4 childrens' big finger, x' = 14cm

mean length of 9 adults' big finger is 16.1cm, x'' = 16.1cm

Let the total length of the 4 childrens' big finger = t

[tex]x' = \frac{t}{n} \\\\x' = \frac{t}{4}\\\\t = 4x'\\\\t = 4 *14\\\\t = 56 \ cm[/tex]

Let the total length of the 9 adults' big finger = T

[tex]x'' = \frac{T}{N} \\\\x'' = \frac{T}{9}\\\\T = 9x''\\\\T = 9*16.1\\\\T = 144.9 \ cm[/tex]

The total length of the 13 people's big finger = t + T

                                                                           = 56 + 144.9

                                                                            =200.9 cm

The mean length of these 13 people's big finger;

x''' = (200.9) / 13

x''' = 15.4539 cm

x''' = 15.45 cm (2 DP)

Therefore, the mean length of the 13 people's big finger is 15.45 cm

Factor (x^2-1x)(-4x+4), with work shown

Answers

Answer:

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

Step-by-step explanation:

refer the attachment

Purple paint requires an exact mixture of blue and red. The ratio of blue paint to red paint is 2:5. Marissa needs 35 cups of purple paint to paint a wall. How much of each color would be needed to make a total of 35 cups of perfect purple paint?

Answers

Answer:

achievements

Step-by-step explanation:

exact value of :7 1/2 - 1 5/8 +(1 3/8 × 2 7/11 )​

Answers

Answer:

261/44

Step-by-step explanation:

hope this helps. :)

Answer:

9 1/2

Step-by-step explanation:

7 1/2 - 1 5/8 + (1 3/8 × 2 7/11)​ =

= 7 4/8 - 1 5/8 + 11/8 * 29/11

= 6 12/8 - 1 5/8 + 29/8

= 5 7/8 + 3 5/8

= 8 12/8

= 8 + 8/8 + 4/8

= 9 1/2

. Write an example problem that includes a compound event. b. List all of the outcomes of the sample space of the compound event.

Answers

Answer:

living organism

Step-by-step explanation:

soil particals and decad crops living organism

PLEASE. NEED HELP. Find the sum.

Answers

Distribute the sum:

[tex]\displaystyle\sum_{i=1}^{24}(3i-2)=3\sum_{i=1}^{24}i-2\sum_{i=1}^{24}1[/tex]

Use the following formulas:

[tex]\displaystyle\sum_{i=1}^n1=n[/tex]

[tex]\displaystyle\sum_{i=1}^ni=\dfrac{n(n+1)}2[/tex]

[tex]\implies\displaystyle\sum_{i=1}^{24}(3i-2)=3\cdot\frac{24\cdot25}2-2\cdot24=\boxed{852}[/tex]

In case you don't know where those formulas came from:

The first one is obvious; you're just adding n copies of 1, so 1 + 1 + ... + 1 = n.

The second can be proved in this way: let S be the sum 1 + 2 + 3 + ... + n. Rearrange it as S = n + (n - 1) + (n - 2) + ... + 1. Then 2S = (n + 1) + (n + 1) + (n + 1) + ... + (n + 1), or n copies of n + 1. So 2S = n(n + 1). Divide both sides by 2 and we're done.

13 points, please answer!

Which shows the dilation with a possible scale factor of 1/2?

Answers

Answer:

Option B

Step-by-step explanation:

With a scale factor of 1/2, the dilated shape should be smaller because of the scale factor, So in Option B the dilated shape is smaller than the real one.

1) Option A is an enlargement

2) Option B is reduction

3) Option C is equality

what is teh surface area of a rectangular prism, if its length is 17 meters, its width is 2 meters and its height is 3 meters

Answers

Answer:

102m^2

Step-by-step explanation:

2x3x17=102m^2

can u pls mark brainliest :)

Answer:

182 m²

Step-by-step explanation:

The formula for surface area of a rectangular prism is;

Surface Area = 2(wl) + 2(lh) + 2(hw) where w is the width, l is the length and h is the height.

SA = 2(2 * 17)m² + 2(17 * 3)m² + 2(3 * 2)m²

     = 2(34)m² + 2(51)m² + 2(6)m²

     = 68 m²  + 102 m² + 12 m²

     = 182 m²

If (x+3) varies directly as y and x=3 when y=12, what is the value of x when y=8?

Answers

Answer:

x = 1.

Step-by-step explanation:

y = k(x + 3)

When x = 3 y = 12 so

12 = k(3 + 3)

6k = 12

k = 2.

So the relation is y = 2(x + 3)

When y is 8:

8 = 2(x + 3)

2x = 8 - 2*3 = 2

x = 1.

En una casa de empanadas hornean 1.200 por día. Si las cocinan en fuentes de 75 unidades, colocando siempre la mayor cantidad posible, ¿Cuántas fuentes preparan?

Answers

Answer:

16 unidades preparan simultáneamente 1200 empanadas por día.

Step-by-step explanation:

Si cada fuente tiene una capacidad de 75 empanadas por horneada y que la mayor cantidad posible ocurre cuando el volumen de producción se cocina simultáneamente, entonces el total de fuentes es la cantidad total de producción dividida por la capacidad de empanadas por fuente. Es decir:

[tex]x = \frac{1200\,emp}{75\,\frac{emp}{und} }[/tex]

[tex]x = 16\,unidades[/tex]

16 unidades preparan simultáneamente 1200 empanadas por día.

A chord cuts off a 120 degree arc. If the radius of the circle is 26 inches, find the
chord length

Answers

Answer:

26sqrt(3)

Step-by-step explanation:

You end up with two 30-60-90 triangles.

26/2 = 13

2 * 13 * sqrt(3) = 26sqrt(3)

Nash's Trading Post, LLC took a physical inventory on December 31 and determined that goods costing $208,000 were on hand. Not included in the physical count were $30,000 of goods purchased from Swifty Corporation, FOB, shipping point, and $23,500 of goods sold to Marigold Corp. For $30,000, FOB destination. Both the Swifty purchase and the Marigold sale were in transit at year-end.

Answers

Answer:

$261,500

Step-by-step explanation:

What amount should Nash report as its December 31 inventory?

Item                                                             Amount

Goods on hand as per physical count    $208,000

(+) Goods purchased from Swifty             $30,000

Corporation FOB shipping point    

(+) Goods sold to Marigold Corp               $23,500

FOB destination (at cost value)

Ending inventory                                        $261,500

Notes:

1) In case of FOB shipping point, the ownership of goods is transferred to the buyer when the goods are shipped and hence in the case of purchases from Swifty corporation, the goods should be included in the inventory of Nash's Trading Post as the goods are shipped and are in transit.

2) In case of FOB destination, the ownership of goods is transferred to the buyer when the goods reaches to the buyer, hence in the case of sales made to Marigold Corp, the goods are still in transit and the ownership is not transferred to Marigold Corp, hence Nash's Trading Post should included that goods in its inventory.

If 12^x = ^11√12, what value of x makes this equation true?

Answers

The root of a number is equivalent of being raised to its inverT

11 cubic root is = 1/11

X = 1/11

You have a prepaid bus pass that has $10 on it. Every time you ride the bus it costs you 50 cents. Assume that you cannot put anymore money on the card after it is used. Create an equation for the situation above.

Answers

Answer:

y = 10 - 0.5x for 0 ≤  x ≤ 20

Step-by-step explanation:

Initial value = (0,10)

final value = (20,0)

Cost per trip = debit of 0.50 = slope

equation : y = 10 - 0.5x for 0 <=  x <= 20

HELP IF YOU KNOW THIS PLEASEEEE

Answers

Answer:

63m

Step-by-step explanation:

Find the value of y.

Answers

197 degrees because 365 degrees minus “x”=168 equals 197
y is equal to 197 degrees

Use the given degree of confidence and sample data to construct interval for the population proportion. Of 369 randomly selected medical students, 23 said that they planned to work in a rural community. Construct a 95% confidence interval for the percentage of all medical students who plan to work in a rural community. (4.16%, 8.30%) (3.77%, 9.47%) (3.30%, 9.17%) (2.99%, 9.47%) (3.77%, 8.70%) In a poll of registered voters nationwide, 43% of those polled blamed of companies the most for the recent increase in gasoline prices. The margin of error at the 96% confidence level for this point estimate is 2.4%. Construct a 95% confidence level for the population proportion who blame oil companies for the recent increase in gasoline prices. (0.382, 0.478) (0.368, 0.492) (0.406, 0.477) (0.383, 0.477) Cannot be determined from the information given.

Answers

Answer:

e)  (3.77%, 8.70%)

95% confidence interval for the percentage of all medical students who plan to work in a rural community

(3.83% , 8.69%)

95% confidence level for the population proportion who blame oil companies for the recent increase in gasoline prices

(0.406 , 0.454)

Step-by-step explanation:

Step(i):-

Given random sample size 'n' = 369

Sample proportion

                              [tex]p = \frac{x}{n} = \frac{23}{369} = 0.0623[/tex]

95% confidence intervals are determined by

[tex](p^{-} - Z_{0.05} \sqrt{\frac{p(1-p)}{n} } , p^{-} + Z_{0.05} \sqrt{\frac{p(1-p)}{n} })[/tex]

[tex](0.0623 - 1.96 \sqrt{\frac{0.0623(1-0.0623)}{369} } , 0.0623 + 1.96\sqrt{\frac{0.0623(1-0.0623)}{369} })[/tex]

(0.0623 - 0.0246 , 0.0623 + 0.0246)

(0.0383 , 0.0869)

(3.83% , 8.69%)

95% confidence interval for the percentage of all medical students who plan to work in a rural community

(3.83% , 8.69%)

Step(ii):-

Given 43% of those polled blamed of companies the most for the recent increase in gasoline prices

sample proportion 'p' = 0.43

Given Margin of error (M.E) = 0.024

95% confidence intervals are determined by

[tex](p^{-} - Z_{0.05} \sqrt{\frac{p(1-p)}{n} } , p^{-} + Z_{0.05} \sqrt{\frac{p(1-p)}{n} })[/tex]

[tex](0.43 - 0.024 } , 0.43 +0.024 )[/tex]

(0.406 , 0.454)

Final answer:-

95% confidence level for the population proportion who blame oil companies for the recent increase in gasoline prices

(0.406 , 0.454)

PLZ HELP ME!!!! I WILL GIVE BRAINLIEST!!!!!! 5 stars and a thanks!!!! 50 POINTS!!! Type out how you would explain the color blue to a blind person. The blind person has been blind ever since he was born. This is a real challenge question.

Answers

Answer:

As color is simply the kind of light reflected by surfaces(if the sun was green, many plants would die), color can be explained fairly simply to a blind person.  Each color represents a separate wavelength, and objects that reflect these wavelengths show up in various colors.  Thus simply state the following: The color blue is displayed by all objects that reflect wavelengths from 380 and 500 nanometers.

Hope it helps <3

p.s. I know this is supposed to be kind of philosophical, but I'm a nerd, so...

Evaluate the Following

Answers

Answer:

see explanation

Step-by-step explanation:

cscΘ = [tex]\frac{hypotenuse}{opposite}[/tex] = [tex]\frac{25}{7}[/tex]

secΘ = [tex]\frac{hypotenuse}{adjacent}[/tex] = [tex]\frac{25}{24}[/tex]

cotΘ = [tex]\frac{adjacent}{opposite}[/tex] = [tex]\frac{24}{7}[/tex]

The price (p), in cents, of a sweet is directly proportional to the mass (m) of the
sweet.
When the sweet cost 55 cents, the mass is 220 g. Find
(a) the equation connecting p and m.
(b) the mass, in grams, of a sweet which cost 540 cents,
(c) the cost of a sweet in cents, with a mass of 115 g

Answers

The equation for constant proportionality is:

a = k • b where k is the constant

Since we are given the letter variables, replace a and b.

p = k • m

Part (a)

We know p = 55 cents when m = 220g, insert those values in equation:

55 = k • 220

55/220 = k

k = 1/4

Therefore, equation connecting p and m is:

p = 1/4 • m

Part (b)

We know p = 540 and we know k ( constant term )

540 = 1/4 • m

540 x 4 = m

m = 2160g

Part (c)

We know m = 115g, k is constant and therefore remains 1/4

p = 1/4 x 115g = 28.75 cents

~Hoodini, hope this helps.

A student answered 12 out of 15 questions on an exam correctly.
a) What fraction of the 15 questions did the student answer correctly? Write your answer in
simplest terms.
b) What percent of the 15 questions did the student answer correctly?

Answers

Answer:

1. 4/5

2. 80%

Step-by-step explanation:

Other Questions
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