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3 years ago

Help me ASAP PLEASE thanks Please show work Random answers will be moderated

Mathematics

1 answer:

Readme [11.4K]3 years ago

4 0

He's wrong. Both equations refer to the same line, that's why he saw only one line. The solution to the system is the set of real numbers.

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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

2 years ago

For the love of God, please answer this.<br> thanks, W.

Andrew [12]

The equation of the perpendicular line will be y = (4/3)x.

<h3>What is a linear equation?</h3>

A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

Then the equation of the perpendicular line will be given as

y = - (1 / m)x + c

The equation of line is y = -3/4 x + 1.

Then the equation of the perpendicular line will be

y = 4/3 x + c

The equation is passing through (9, 12), then we have

12 = 4/3 (9) + c

12 = 12 + c

c = 0

Then the equation of the perpendicular line will be y = (4/3)x.

More about the linear equation link is given below.

brainly.com/question/11897796

#SPJ1

8 0

1 year ago

The relationship between a bacteria population p, in thousands, and time d, in days, since it was measured to be 1,000 can be re

Assoli18 [71]

d = log₂p represents a logarithmic function, The expression log₂(10) tells us when the population reaches 10,000 and the equation 7 = log₂(128) tells us that the population reaches 128,000 in 7 days.

<h3>What is an exponential function?</h3>

An exponential function is in the form:

y = abˣ

Where a is the initial value of y and b is the multiplication factor.

Let p represent the bacteria population in thousand after d days.

Since each day, the bacteria population grows by a factor of 2, hence:

$p=2^d$

Hence, d = log₂p represents a logarithmic function

The expression log₂(10) tells us when the population reaches 10,000 and the equation 7 = log₂(128) tells us that the population reaches 128,000 in 7 days.

Find out more on exponential function at: brainly.com/question/12940982

8 0

2 years ago

A collection of dimes and quarters is worth $10.45. There are 70 coins in all. Find how many of each there are

Advocard [28]

There are 47 dimes and 23 quarters.

Step-by-step explanation:

Total amount = $10.45 = 10.45*100 = 1045 cents

Total coins = 70

1 dime = 10 cents

1 quarter = 25 cents

Let,

Dimes = x

Quarters = y

According to given statement;

x+y=70 Eqn 1

10x+25y=1045 Eqn 2

Multiplying Eqn 1 by 10;

$10(x+y=70)\\10x+10y=700\ \ \ Eqn\ 3$

Subtracting Eqn 3 from Eqn 2

$(10x+25y)-(10x+10y)=1045-700\\10x+25y-10x-10y=345\\15y=345$

Dividing both sides by 15;

$\frac{15y}{15}=\frac{345}{15}\\y=23$

Putting y=23 in Eqn 1

$x+23=70\\x=70-23\\x=47$

There are 47 dimes and 23 quarters.

Keywords: linear equations, subtraction

Learn more about linear equations at:

#LearnwithBrainly

6 0

2 years ago

We are having trouble with question 7

Verdich [7]

First off, you can multiply a 2-digit number by 2 and just add 0 to the product. For instance: 12 x 20

Number line: two jumps of number 12.

So : 12 x 2 = 24

Finally, 12 x 20 = 240

Hope this helped.

4 0

3 years ago