MATHEMATICS HIGH SCHOOL

One term of (x+y)^m is 31,824x^18y^11
What is the value of m ?

Answers

Answer 1

Answer:

Answer: The value of m is 29.

Step-by-step explanation:

Given that, One term of $(x+y)^m$ is $31,824x^(18)y^(11)$ ...(i)

We know that that (r+1)th term in $(a+b)^n$ is given by :-

$T_(r+1)=^nC_ra^(n-r)b^r$ ...(ii)

On comparing (i) with (ii) , we get

$a= x \text{ and } b= y \nn-r =18 \text{ and } r=11\nn=m$

i.e.

$m-r=18\Rightarow\ m-11=18\n\n\Rightarrow\ m=18+11=29$

Hence, the value of m is 29.

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Explain whether the figuers in b and d have the same area

Answers

b and d do have the same area d is just b facing the other way

An airline allows each passenger 33 kilograms of luggage. Carl has to lower the weight of his suitcase by 25% to stay within the limit. How much did the suitcase originally weigh?

Answers

Answer:

44 kg.

Step-by-step explanation:

The weight limit of the luggage = 33 kg

Let the original weight of the suitcase = x kg

Now, it has been given that Carl has to lower the weight of his suitcase by 25% to stay within the limit.

It means that if we decrease the original weight of the suitcase by 25% then it should be equal to 33 kg.

Thus, we have the equation

$x-0.25x=33$

Solve the equation

$0.75x=33\n\nx=(33)/(0.75)\n\nx=44$

Therefore, the original weight of the suitcase was 44 kg.

1- 0.25= 0.75 (multiplier)

33÷0.75=44

The suitcase originally weighed 44kg

Hope this helps!

A circular fountain has a radius of 9.4 feet find its diameter and circumference to the nearest tenth

Answers

Answer:

18.8 feet, 59.1 feet to the nearest tenth

Step-by-step explanation:

The diameter is the line drawn that divides the circle into two while the circumference is the perimeter of the circle. Both are a measure of the radius of the circle.

The diameter D = 2r where r is the radius of the circle

The circumference = 2Πr = ΠD where Π = 22/7

Given that the circular fountain has a radius of 9.4 feet

Its diameter = 2 × 9.4 feet = 18.8 feet

The circumference = 22/7 × 18.8 feet

=59.09 feet

≈ 59.1 feet to the nearest tenth

diameter = radius * 2
9.4 * 2 = 18.8
diameter is 18.8 feet
circumference = $\pi$ * diameter
c = 3.14 * 18.8
c = 59.032
circumference is 59 feet.

An ant has a mass of approximately 4 × 10–3 grams and an elephant has a mass of approximately 8 x 106 grams. How many times larger is the elephant's mass as compared to the ant's mass?

Answers

$2*10^(9)$ times larger is the elephant's mass as compared to the ant's mass.

Given that, the mass of an ant is approximately $4* 10^(-3)$ and the mass of an elephant is approximately $8*10^(6)$ .

We need to find how many times larger is the elephant's mass as compared to the ant's mass.

What is an equation?

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Let x be the number of times the elephant's mass is larger than an ant's mass.

So, x=The elephant's mass/An ant's mass= $(8*10^(6))/(4* 10^(-3))$