MATHEMATICS HIGH SCHOOL

The sum of two numbers is 100, their difference is 56, what are the two numbers?

Answers

Answer 1

Answer:

$\large\bf{\underline{\underline{\mathfrak{Question}:}}}$

The sum of two numbers is 100, their difference is 56, what are the two numbers?

$\large\bf{\underline{\underline{\mathfrak{Solution}:}}}$

Let'sassume that,

$:{\Longrightarrow{\small{\rm{The\:one\:number\:=a}}}}$

$:{\Longrightarrow{\small{\rm{The\:other\:number\:=b}}}}$

Now,accordingto thequestion,

$:{\Longrightarrow{\small{\rm{a+b=100\:\:....(i)}}}}$

$:{\Longrightarrow{\small{\rm{a-b=56\:\:....(ii)}}}}$

Here, substitution method must be applied.

Now,use the first equation

$:{\Longrightarrow{\small{\rm{a+b=100}}}}$

$:{\Longrightarrow{\small{\rm{a=100-b}\:\:....(iii)}}}$

Putthevalueofequation(iii)inequation(ii)

$:{\Longrightarrow{\small{\rm{a-b=56}}}}$

$:{\Longrightarrow{\small{\rm{100-b-b=56}}}}$

$:{\Longrightarrow{\small{\rm{100-2b=56}}}}$

$:{\Longrightarrow{\small{\rm{2b=56-100}}}}$

$:{\Longrightarrow{\small{\rm{2b=-44}}}}$

$:{\Longrightarrow{\small{\rm{b=(-44)/(-2)}}}}$

$:{\Longrightarrow{\small{\rm{b=\frac{\cancel{-44}}{\cancel{-2}}}}}}$

$:{\Longrightarrow{\small{\rm{b=(22)/(1)}}}}$

${\therefore{\small{\rm{b=22}}}}$

Now,putthisvalueinequation(iii)forgettingtheanswer.

$:{\Longrightarrow{\small{\rm{a=100-22}}}}$

${\therefore{\small{\rm{a=78}}}}$

For verification:

Put the value of a and b in the equation (i)and(ii)

Wehave,

$:{\Longrightarrow{\small{\rm{a=78}}}}$

$:{\Longrightarrow{\small{\rm{b=22}}}}$

Incase1:

$:{\Longrightarrow{\small{\rm{78+22=100}}}}$

$:{\Longrightarrow{\small{\rm{100=100}}}}$

$:{\Longrightarrow{\small{\rm{L.H.S=R.H.S}}}}$

Incase2:

$:{\Longrightarrow{\small{\rm{78-22=56}}}}$

$:{\Longrightarrow{\small{\rm{56=56}}}}$

$:{\Longrightarrow{\small{\rm{L.H.S=R.H.S}}}}$

Hence,verified!

Answer 2

Answer:

Answer: X = 78 and Y = 22.

Step-by-step explanation:

Let's call the two numbers X and Y. We are given two pieces of information:

1. The sum of the two numbers is 100, so we can write this as an equation: X + Y = 100.

2. The difference between the two numbers is 56, which can also be written as an equation: X - Y = 56.

Now, you have a system of two equations with two variables:

1. X + Y = 100

2. X - Y = 56

You can solve this system of equations by adding the two equations together to eliminate the Y variable:

(X + Y) + (X - Y) = 100 + 56

This simplifies to:

2X = 156

Now, divide both sides by 2 to solve for X:

2X / 2 = 156 / 2

X = 78

Now that you know the value of X, you can substitute it into one of the original equations to find the value of Y. Let's use the first equation:

X + Y = 100

78 + Y = 100

Subtract 78 from both sides:

Y = 100 - 78

Y = 22

So, the two numbers are X = 78 and Y = 22.

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Sama has $12. She buys a book for $9. How much money does Sama now have? (1 F
$

Answers

the answer is that you have $3 left

20,612,439 scientific notation

Answers

The scientific notation of the population is $2.0*10^(7)$ .

It is required to find the solution.

What is Scientific notation?

Scientific notation is a way of writing very large or very small numbers. A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10. Scientific Notation is the expression of a number n in the form a∗10b. where a is an integer such that 1≤|a|<10. and b is an integer too.

Given :

The given number is

20,612,439

in scientific notation is

$2.0*10^(7)$

Move the decimal point so that there is seven non-zero digit to the left.

Hence, the scientific notation of the population is $2.0*10^(7)$ .

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Answer:

2.0612439 x 10 to the 7th power

Step-by-step explanation:

Which of the following functions has the largest value when x = 3?c(x) = 3x2 + 5x + 22
j(x) = 12x
a(x) = 9x

All the functions are equal at x = 3.
c(x)
j(x)
a(x)

Answers

Answer:

c(3) is the largest

Step-by-step explanation:

For positive values of x, j(x) > a(x), so the comparison is between c(x) and j(x).

Without evaluating the functions, you can subtract 5x from them to get ...

c'(x) = c(x) -5x = 3x² +22

j'(x) = j(x) -5x = 7x

Now the question is whether c'(3) is larger than j'(3). The latter is ...

j'(3) = 7·3 = 21

Since c'(3) has an added constant of 22 and x² will be positive, we know that ...

c(3) > j(3) > a(3)

The function with the largest value at x=3 is c(x).

_____

You can, of course, simply evaluate the functions:

c(3) = (3·3 +5)·3 +22 = 14·3 +22 = 42 +22 = 64
j(3) = 12·3 = 36
a(3) = 9·3 = 27

c(3) > j(3) > a(3) . . . . . . . c(3) is the largest

Answer:

It’s D

Step-by-step explanation:

a(x)

Solve each equation by finding all roots x^4-16=0

Answers

${ x }^( 4 )-16=0\n \n { x }^( 4 )=16\n \n x=\pm \sqrt [ 4 ]{ 16 } \n \n \therefore \quad x=\pm 2$

add both sides by 16
so you'll have x^4 =16
take the 4th root of both sides and you'll get x= 2

Freddy reads an equal number of pages of a book every week. The graph below shows the number of pages of the book left to read, y, after x weeks:Which equation best models the relationship between x and y?

y = −5x + 40
y = −40x + 280
y = −40x + 200
y = −5x + 200

Answers

Wow, the only thing i can think of is that it gives you y and x, so you're basically plugging in the other numbers. So y = 200 and x = 5, and if you were to plug those numbers into each equation they give you, you would come up with 15, 80, 0, and 175. But you're trying to get y to equal 200, so the closest one is c. I'm sorry that's the only thing i can come up with. The rest just aren't close.

The linear equation that best models the relationship between x and y is y = -40x + 200.

What is the graph of a linear equation?

The graph of a linear equation is a straight line graph and the function of a linear equation assumes a slope-intercept form y = mx + b

where;

Slope = m
y-intercept = b

The slope = rise/run

From the graph, we need to rise 200 units to the origin and run 5 units to the horizontal positive axis.

So,

Slope = -200/5
Slope = -40

The y-intercept is the region at which the line cuts the vertical axis.

y-intercept = (0,200)

Now, putting it all together and using the slope-intercept form, the equation that best models the relationship between x and y is:

y = -40x + 200

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If T(n) = 6n + 2 what is the 3rd term

Answers

To find the 3rd term, just replace the 'n' with 3.

Therefore:

t(3) = 6(3) + 2
t(3) = 18 + 2
t(3) = 20.

The 3rd term is 20.

T(n)=6n+2 T3=6(3)+2 T3=20

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