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3 years ago

9 is the difference between two numbers, and their sum is 31. Find the numbers.

Mathematics

1 answer:

algol [13]3 years ago

4 0

Answer:

The first number is 20, the second one is 11

Step-by-step explanation:

Let the first number be x and the second number be y

Since it says "9 is the difference between two numbers", the first equation will be x-y=9

It also says that "their sum is 31". That means the second equation will be x+y=31

here are the two equations:

x-y=9

x+y=31

You can solve this any way you like, but I'll show elimination

add the two equations

x-y=9

x+y=31

2x=40

divide by 2

x=20

Substitute 20 as x in one of the equations

20+y=31

subtract 20 from both sides

y=11

That means the two numbers are 20 and 11

Hope this helps!

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A polynomial f (x) and one or more of its zeros are given.

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Answer:

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3 years ago

What perfect swuare lies between 120 and 130

Natalka [10]

Answer:

the perfect squares between 120 and 300 are the squares of numbers from 11 to 17. Clearly, these are 7 in number.

Step-by-step explanation:

5 0

3 years ago

Simplifying rational expressions <br> x^2-16/x^2+6x+8 = x-4/x+2<br> x^2-x-6/x^2-3x-10 = x-3/x-5

enot [183]

$\dfrac{x^2-16}{x^2+6x+8}$

Decompose the numerator and denominator into multipliers

To simplify the numerator we use the formula of difference of squares

$x^2-y^2=(x-y)(x+y)$

$x^2-16=(x-4)(x+4)$

To decompose the denominator into multipliers solve the square equation

$x^2+6x+8=0\\D=6^2-4*8=4=2^2\\x_1=\dfrac{-6+2}{2} =-2\\x_2=\dfrac{-6-2}{2} =-4$

Formula for factoring a square equation

$(x-x_1)(x-x_2)$

Substituting the found roots of the equation into the formula

$(x-(-2))(x-(-4))=(x+2)(x+4)$

After simplifying the numerator and denominator we get a fraction

$\dfrac{(x-4)(x+4)}{(x+2)(x+4)}=\dfrac{x-4}{x+2}$ , so

$\dfrac{x^2-16}{x^2+6x+8}=\dfrac{(x-4)(x+4)}{(x+2)(x+4)}=\dfrac{x-4}{x+2}$

$\dfrac{x^2-x-6}{x^2-3x-10}$

Decompose the numerator and denominator into multipliers

To decompose the numerator into multipliers solve the square equation

$x^2-x-6=0\\D=(-1)^2-4*(-6)=25=5^2\\x_1=\dfrac{1+5}{2} =3\\x_2=\dfrac{1-5}{2} =-2$

Formula for factoring a square equation

$(x-x_1)(x-x_2)$

Substituting the found roots of the equation into the formula

$(x-3)(x-(-2))=(x-3)(x+2)$

To decompose the denominator into multipliers solve the square equation

$x^2-3x-10=0\\D=(-3)^2-4*(-10)=49=7^2\\x_1=\dfrac{3+7}{2} =5\\x_2=\dfrac{3-7}{2} =-2$

Formula for factoring a square equation

$(x-x_1)(x-x_2)$

Substituting the found roots of the equation into the formula

$(x-5)(x-(-(-2))=(x-5)(x+2)$

After simplifying the numerator and denominator we get a fraction

$\dfrac{(x-3)(x+2)}{(x-5)(x+2)}=\dfrac{x-3}{x-5}$ , so

$\dfrac{x^2-x-6}{x^2-3x-10}=\dfrac{(x-3)(x+2)}{(x-5)(x+2)}=\dfrac{x-3}{x-5}$

Hello from Russia:^)

6 0

3 years ago

The graph shows two functions, f(x) and g(x).

timofeeve [1]

The graph shows two functions, f(x) and g(x). So point (-2,2) is on h(x)

<h3>What is graph?</h3>

A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

In the question, we have two functions f(x)=x²-2 and g(x)=x²+2 by adding the function we will get the combined function.

So the graph i attached is showing the two functions and their relation to each other.

So we can see from the graph that the function is varying from the coordinates (-2,2)

Hence graph shows two functions, f(x) and g(x). So point (-2,2) is on h(x)

To know more about graph follow

brainly.com/question/25020119

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2 years ago

5. Find the equation of the line in slope-intercept form.<br> a. (1,-6) and (-7, 2)

boyakko [2]

Step-by-step explanation:

y=1x-(-6)

y=-7x-2

follow and label y and x inside the equation

make sure you draw a graph to help you find the intercept form.

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2 years ago