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2 years ago

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Alexis Brian and Carli collect graphic novels, Brian has 5 more graphic novels then Alexis and Carli has twice as many as Alexis

. Define a variable and write an expression to represent the total number of graphic novels for the three people

1 answer:

kkurt [141]2 years ago

4 0

According to Google, a Variable is <span>any factor, trait, or condition that can exist in differing amounts or types. If you type in variable in the Google search bar, it will give you the definition in a little box at the very top of the page :).
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Х- а<br>x-b<br>If f(x) = b.x-a÷b-a + a.x-b÷a - b<br>Prove that: f (a) + f(b) = f (a + b)

GenaCL600 [577]

Given:

Consider the given function:

$f(x)=\dfrac{b\cdot(x-a)}{b-a}+\dfrac{a\cdot(x-b)}{a-b}$

To prove:

$f(a)+f(b)=f(a+b)$

Solution:

We have,

$f(x)=\dfrac{b\cdot(x-a)}{b-a}+\dfrac{a\cdot (x-b)}{a-b}$

Substituting $x=a$ , we get

$f(a)=\dfrac{b\cdot(a-a)}{b-a}+\dfrac{a\cdot (a-b)}{a-b}$

$f(a)=\dfrac{b\cdot 0}{b-a}+\dfrac{a}{1}$

$f(a)=0+a$

$f(a)=a$

Substituting $x=b$ , we get

$f(b)=\dfrac{b\cdot(b-a)}{b-a}+\dfrac{a\cdot (b-b)}{a-b}$

$f(b)=\dfrac{b}{1}+\dfrac{a\cdot 0}{a-b}$

$f(b)=b+0$

$f(b)=b$

Substituting $x=a+b$ , we get

$f(a+b)=\dfrac{b\cdot(a+b-a)}{b-a}+\dfrac{a\cdot (a+b-b)}{a-b}$

$f(a+b)=\dfrac{b\cdot (b)}{b-a}+\dfrac{a\cdot (a)}{-(b-a)}$

$f(a+b)=\dfrac{b^2}{b-a}-\dfrac{a^2}{b-a}$

$f(a+b)=\dfrac{b^2-a^2}{b-a}$

Using the algebraic formula, we get

$f(a+b)=\dfrac{(b-a)(b+a)}{b-a}$ $[\because b^2-a^2=(b-a)(b+a)]$

$f(a+b)=b+a$

$f(a+b)=a+b$ [Commutative property of addition]

Now,

$LHS=f(a)+f(b)$

$LHS=a+b$

$LHS=f(a+b)$

$LHS=RHS$

Hence proved.

5 0

1 year ago

Find the difference and simplify the following<br> expressions.<br> (n – 8) – (2n + 2)

blagie [28]

Answer:

-n-10

Step-by-step explanation:

(n-8)-(2n+2)

n-8-(2n+2)

n-8-2n-2

-n-8-2

-n-10

4 0

2 years ago

In 2012, a competition sponsored 301 sporting events. This was 256 more events than there were in an 1896 competition. How many

Vika [28.1K]

There were 54 sporting events in the year 1896 hosted by the competition

What is the function to determine the number of events in 1896?

The fact that events which are 301 sporting events in 2012 are 256 more than that of the events in 1896, means that the number of events in 1896 is 256 less than that of 2012

number of events in 1896=number of events in 2012-256

number of events in 2012=310

number of events in 1896=310-256

number of events in 1896=54 events

Find out more about more about number operations on:brainly.com/question/4344214

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4 0

8 months ago

Please answer this question!

Reil [10]

The answer is D, 2,500

5 0

2 years ago

100 points ! and I will mark me Brainliest

Romashka [77]

Answer:

it ARBY'S

Step-by-step explanation:

7 0

2 years ago

Read 2 more answers