Mr karki divided a sum of Rs 1,80,000 between his son and daughter in the ratio of 4:5 find the sum obtained by eachof them.
​

The simplified form of the given fraction is, 2/3.

What is greatest common factor?

The largest gap between the two integers is considered to be the biggest common factor. Firstly, make a list of each number's prime factors to determine its largest common factor. The ages of 18 and 24 have one 2 and one 3. The GCF of 18 and 24 is obtained by multiplying them, therefore 2 * 3 = 6.

Consider, the given fraction [tex]\frac{48}{72}[/tex]

The divisors of 48 are, 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.

The divisors of 72 are, 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.

So, from above the greatest common factor of 48 and 72 is 24.

Therefore,

[tex]\frac{48}{72} = \frac{24(2)}{24(3)} = \frac{2}{3}[/tex]

Therefore, the simplified form of the given fraction is, 2/3.

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Answer: 0

Step-by-step explanation:

Since y is 2, and it’s being multiplied by 4, you have 8 - 8 which =0

Y=2

4(2) - 8

8-8

0

Answer:

0

Step-by-step explanation:

4y - 8

Given that,

y = 2

To find the value of given expression, replace y with 2 and solve the expression.

Let us solve it now.

4y - 8

4 × 2 - 8

8 - 8

0

The two positive numbers are 5 , 5.

Given:

Product of two positive numbers = 25

sum of these number is minimum.

Let a and b be the two positive numbers.

a*b = 25

b = 25/a

sum s = a+b

= a + 25/a

apply derivation on both sides.

ds/da = 1 - 25/[tex]a^{2}[/tex]= 0.

1 = 25/[tex]a^{2}[/tex]

a = [tex]\sqrt{25}[/tex]

a = 5 , -5

since given are positive numbers so 5 is considered.

b = 25/5

b = 5

Therefore the two positive numbers are 5 , 5.

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Answer:

488

Step-by-step explanation:

2(20x8) + 2(20x3)+2(8x3)

Assuming the "x" is not a variable.

The answer is 488

However, if "x" is a variable. The equation would be

40x^8 + 56x^3

Answer:

488

Step-by-step explanation:

using BODMAS

METHOD 1.

[tex]2(20 \times 8) + 2(20 \times 3 + 2(8 \times 3) \\ = 2(160) + 2(60) + 2(24) = \\ = 320 + 120 + 48 \\ = 448[/tex]

METHOD 2.

[tex]2(20 \times 8) + 2(2 \times 3) + 2(8 \times 3) \\ = 2(160) + 2(60) + 2(24) \\ = 2(160 + 60 + 24) \\ = 2 \times 244 \\ =488[/tex]

The annual percentage rate of depreciation of the number of rhinos represented by the statistics is approximately 6.41 %

The rate of depreciation is the rate at which the number or value of an item reduces within each specified period.

The initial number of black rhinos in 1970 = 60,500

The number of black rhinos remaining in 2011 = 4,000

The annual rate of depreciation can be found using the formula;

Where;

FV = The future value = 4,000

PV = The present value = 60,500

r = The annual depreciation rate

n = The number of years

[tex]4,000 = 60,500 \times \left(1+\dfrac{r}{100} \right)^{(2011-1970)}=60,500 \times \left(1+\dfrac{r}{100} \right)^{41}[/tex]

[tex]\left(1+\dfrac{r}{100} \right)^{41} = \dfrac{4000}{60500} = \dfrac{8}{121}[/tex]

[tex]r = 100\times \left(\sqrt[41]{ \dfrac{8}{121}} - 1\right) \approx -6.41[/tex]

The annual rate of depreciation is approximately 6.41%

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If a line's angle with the x-axis is then, that line's slope will be tanα, and the new road's slope will be tan(0) = 0.

D Street is depicted as a vertical line with a 90° angle of inclination in the accompanying figure. In other words, D Street has an infinite slope.

The new road will therefore have 0° of inclination if it is perpendicular to D street because if they are perpendicular and D street is vertical, the new road is level and has 0° of inclination.

A horizontal line now has zero slopes.

The new road has a zero slope as a result.

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Using Simplification , all the equations that are equivalent to (6x+2)/3 = 2 - (3x+14)  are (6x+2)/3 = -3x - 12 and  6x + 2 = -9x - 36 , the correct option is  (a) and (d) .

In the question ,

it is given that

the equation is (6x+2)/3 = 2 - (3x+14)

solving the brackets on the right side of the equation ,

(6x+2)/3 = 2 - 3x - 14

(6x+2)/3 = -3x - 12                     ....option(a)

On Cross Multiplying , we get

6x + 2 = 3(-3x - 12)

6x + 2 = -9x - 36                      ....option(d)

Therefore , all the equations that are equivalent to (6x+2)/3 = 2 - (3x+14)  are (6x+2)/3 = -3x - 12 and  6x + 2 = -9x - 36  .

The given question is incomplete , the complete question is

Using Simplification , Select all equations that are equivalent to

(6x+2)/3 = 2 - (3x+14)

(a) (6x+2)/3 = -3x-12

(b) (6x+2) = 2 - (3x+14)

(c) 2x + 2/3 = 2 - (3x+14)

(d) 6x+2 = -9x-36

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Answer: 4x + 29

Step-by-step explanation: add the like terms together.

Answer:

39 inches

Step-by-step explanation:

the triangle has all equal angles

this means it is equilateral and this also means all the sides are equal

so take 2 sides and set them equal to each other to find x

21 - x = x + 5

now solve

add x to both sides

21 = 2x + 5

subtract 5 to both sides

16 = 2x

divide everything by 2

8 = x

now flip it

x = 8

plug this is to one of the equations and multiply that by 3

8 + 5 = 13

13 * 3 = 39

that is the perimeter

The factored form of f(x) = x³ + 8x² - 23x - 30 is (x - 3)(x + 10)(x + 1).

We know that if x = a is one of the roots of a given polynomial x - a = 0 is a factor of the given polynomial.

To confirm if x - a = 0 is a factor of a polynomial we replace f(x) with f(a) and if the remainder is zero then it is confirmed that x - a = 0 is a factor.

Given a polynomial f(x) = x³ + 8x² - 23x - 30.

If f(3) = 0 then x - 3 is one of the factors of the polynomial f(x).

∴ f(x) = f₁(x)(x - 3), where f₁(x) is a quadratic equation we obtain it by long division or synthetic division.

f₁(x) = x² + 11x + 10.

Now, x² + 11x + 10 = 0.

x² + 10x + x + 10 = 0.

x(x +10) + 1(x + 10) = 0.

(x + 10)(x + 1) = 0.

x + 10 = 0 Or x = 1 = 0.

x = - 10 Or x = - 1.

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The algebraic expression of the mentioned statement will be 5x-3.

According to the question,

An unknown number is thought of, multiplied by 5, and then subtracted by 3 from the result.

Let the unknown number be taken as x.

If we have to write the statement mathematically by taking x as a variable, the algebraic expression will be,

x* (5), which is equal to 5x, (by taking the variable x and multiplying it with 5).

For the second step, the expression will be 5x -3, (by subtracting 3 from the previous result, that is, 5x).

Hence, algebraically the final statement will be 5x -3.

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The algebraic proof that 10+n²-(n - 2)² is always an even number is 2(5+(2n-2))

To show that this will always give an even number, we need to express in a form that it is 2 multiplied by some positive integer

Given: n is an integer greater than 1, prove 10+ n² - (n - 2)² algebraically

10+ n² - (n - 2)² = 10+ ( n² - (n - 2)² )      (factorize difference of two squares)

                     = 10+(n-(n-2))(n+(n-2))      

                     = 10+(n-n+2)(n+n-2)         (simplify)

                     = 10+(2)(2n-2)                  (factorize)

                     =  2(5+(2n-2))

Therefore, due to the factor of 2, the given expression is always even for integer n

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The distance between points  (-3,-4) and (2,8) is 13.

A right-angled triangle is a triangle, that has one of its interior angles equal to 90 degrees, or it follows Pythagoreans theorem.

The horizontal distance = 5

And the vertical distance = 12

The vertical and horizontal lines make a right angle when they meet,

To find distance between points, use Pythagoreans theorem,

(D)² = (5)²+(12)²

(D)² = 25 + 144

(D)² = 169

D = 13

The distance between points  (-3,-4) and (2,8) is 13.

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Answer:

no solution

Step-by-step explanation:

12=-4(-6x-3)

12=24x+12

0=24x

Answer:

  -1/11, +1/11

Step-by-step explanation:

You want the two square roots of 1/121.

A square root can be either positive or negative.

  [tex]\pm\sqrt{\dfrac{1}{121}}=\pm\dfrac{1}{\sqrt{121}}=\boxed{\pm\dfrac{1}{11}}[/tex]

__

Additional comment

The √ symbol generally means the principal square root, the positive root. To get the negative root, we precede the symbol with a minus sign. So, both square roots are identified as ±√( ).

Answer:We know that the dilation transformation of a figure either shrink or expand the original figure depending on the scale factor of the dilation.

As here we have scale factor=3>1.

Hence, the dilation  changes the original will expand the original figure.

Hence, each of the coordinate of a figure get multiplied by 3.

Hence, the co

ordinates of the image are given as:

i.e. A(0,0) → A'(0,0)

B(2,3) → B'(6,9)

C(1,-2) → C'(3,-6)

D(-3,-3) → D'(-9,-9)

Step-by-step explanation:

Answer:

gradient:

y2-y1/x2-x1

1-1/9-3

0/-6

= 0

Answer:

178 000

Step-by-step explanation:

178 383      8 is in the thousands place...if the number next to it (3) is ≥ 5 round it up by 1   o/w leave it alone

Answer:

178,000

Step-by-step explanation:

It's 178,000 because the number in front of the 8 in 178,383 was under five so the number dropped.

Alexi will not like the drink because the ratio of liquid to ice is 1/1.

Alexi likes her drink to have a liquid-to-ice ratio of about 1/3. A fast food restaurant put 16 ounces of ice in her 32-ounce cup. We need to find out if Alexi will like her drink or not, and if not, why not.

Let the ratio of the liquid to the ice in the drink be represented by the variable "R". The total volume of the cup is 32 ounces. The amount of ice in the cup is 16 ounces. So the amount of liquid in the drink is the difference between these two amounts. Hence, the amount of liquid in the cup is 32 - 16 = 16 ounces.

The ratio of the amount of liquid to the amount of ice in the drink is calculated below.

R = 16/16

R = 1/1

Hence, the ratio of the amount of liquid to the ice in the drink is 1/1. So, Alexi will not like her drink.

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The answer to the given question is <0.01.

What is confidence level?

The confidence level is the percentage of times we expect to get near to the same approximate if we run our experiment again or resample the population in the same way. The confidence level is the probability that the null hypothesis is true.

What is p-value?

P-value is the probability of getting the results you did, given that the null hypothesis is true.

When we are conducting a hypothesis testing and we determine the confidence level needed is 99%; then in order to reject the null hypothesis, the p-value needs to be below 0.01 (<0.01).

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Answer:

Can't be solved

Step-by-step explanation:

Using Pythagoras theorem,

H2= O2 + A2 (where, H= Hypotenuse,O=Opposite,A=Adjacent)

The hypotenuse,H=7feet long

If the opposite side of the triangle is 4 feet longer than the adjacent side, then;

O=A+4

while, A=A

,then using H^2= O^2 + A^2(The 2 are power,that is square)

7^2 = (A+4)^2 + A^2

49= (A+4)(A+4) + A^2

49=A^2 +4A+4A+16 + A^2

49=A^2+8A+16+A^2

(collect like terms)

49-16=A^2+A^2+8A

33=2A^2+8A

Then a quadratic equation,

2A^2+8A=33

2A^2+8A-33=0,

using (-b+/-√4ac) /2a

where b=8, a=2, c=-33

[-8 +/-√4*2*(-33) ]/2(2)

-8 +/-

Answer:

Step-by-step explanation:

y=2/3x+4

The density of the planet is 4.81 g/cm^3, and with this in mind, we assume that the planet is made of titanium or yttrium.

Density is defined as the quotient between mass and volume.

Here we know that the mass is:

9.43*10²⁷g

And the radius is 7.6x10^8cm, remember that the volume of a sphere of radius R is:

V = 3.14*(3/4)*R³

Then in this case the volume is:

V = 3.14*(3/4)*(9.43*10⁸ cm)³ = 1.96*10²⁷ cm³

Then the density is:

D = (9.43*10²⁷g)/(1.96*10²⁷ cm³) = 4.81 g/cm^3

For this density, we can assume that the planet is made of Titanium or Yttrium (or a combination of a lot of elements like most planets)

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Answer:

Step-by-step explanation:           The simplification form of the provided expression is 2y⁴/x⁴ option (A) 2y⁴/x⁴ is correct after applying the integer exponent properties.

What is an integer exponent?

In mathematics, integer exponents are exponents that should be integers. It may be a positive or negative number. In this situation, the positive integer exponents determine the number of times the base number should be multiplied by itself.

The question is incomplete.

The complete question is attached in the picture, please refer picture.

We have an expression:

Thus, the simplification form of the provided expression is 2y⁴/x⁴ option (A) 2y⁴/x⁴ is correct after applying the integer exponent properties.

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Answer:

35 square inches

Step-by-step explanation:

21x15=315

315/9=35

Therefore, the answer is 35 square inches