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3 years ago

1. How do I solve equations with like terms?

Mathematics

2 answers:

Gre4nikov [31]3 years ago

5 0

Combine like terms first

distribute it and then combine like terms

hoa [83]3 years ago

4 0

Answer:

Step-by-step explanation:

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If f(x)=ax+b/x and f(1)=1 and f(2)=5, what is the value of A and B?

LUCKY_DIMON [66]

Answer:

$\huge\boxed{a=9 ; b = -8}$

Step-by-step explanation:

$f(x) = \frac{ax+b}{x}$

Putting x = 1

=> $f(1) = \frac{a(1)+b}{1}$

Given that f(1) = 1

=> $1 = a + b$

=> $a+b = 1$ -------------------(1)

Now,

Putting x = 2

=> $f(2) = \frac{a(2)+b}{2}$

Given that f(2) = 5

=> $5 = \frac{2a+b}{2}$

=> $2a+b = 5*2$

=> $2a+b = 10$ ----------------(2)

Subtracting (2) from (1)

$a+b-(2a+b) = 1-10\\a+b-2a-b = -9\\a-2a = -9\\-a = -9\\a = 9$

For b , Put a = 9 in equation (1)

$9+b = 1\\Subtracting \ both \ sides \ by \ 9\\b = 1-9\\b = -8$

5 0

3 years ago

How does the graph of f(x) = (x − 1)2 relate to the basic function f(x) = x2?

Nadya [2.5K]

Answer:

Both functions are multiplied by 2.

Step-by-step explanation:

6 0

3 years ago

Prove the formula for (d/dx)(cos−1(x)) by the same method as for (d/dx)(sin−1(x)). Let y = cos−1(x). Then cos(y) = and 0 ≤ y ≤ π

gtnhenbr [62]

Answer:

$\frac{d(cos^{-1}x )}{dx} = \frac{-1}{\sqrt{1-x^2} }$

Step-by-step explanation:

Given the differential (d/dx)(cos−1(x)), to find the equivalent formula we will differentiate the inverse function using chain rule as shown below;

let;

$y = cos^{-1} x \\\\taking \ cos\ of\ both\ sides\\\\cosy = cos(cos^{-1} x)\\\\cosy = x\\\\x = cosy\\\\\frac{dx}{dy} = -siny\\$

$\frac{dy}{dx} = \frac{-1}{sin y} \\\\from\ trigonometry\ identity,\ sin^{2} x+cos^{2}x = 1\\sinx = \sqrt{1-cos^{2} x}$

Therefore;

$\frac{dy}{dx} = \frac{-1}{\sqrt{1-cos^{2}y } }$

Since x = cos y from the above substitute;

$\frac{dy}{dx} = \frac{-1}{\sqrt{1-x^{2}} }$

Hence, $\frac{d(cos^{-1}x )}{dx} = \frac{-1}{\sqrt{1-x^2} }$ gives the required proof

5 0

4 years ago

What is 23 + 23 - 789

Alex Ar [27]

Answer:

743

Step-by-step explanation:

23+23=46

789-46=743

4 0

3 years ago

Read 2 more answers

What is the equation of the line that passes through the points (-1, 7) and (2, 10) in Standard Form?

Usimov [2.4K]

bearing in mind that standard form for a linear equation means

• all coefficients must be integers, no fractions

• only the constant on the right-hand-side

• all variables on the left-hand-side, sorted

• "x" must not have a negative coefficient

$\bf (\stackrel{x_1}{-1}~,~\stackrel{y_1}{7})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{10}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{10-7}{2-(-1)}\implies \cfrac{3}{2+1}\implies \cfrac{3}{3}\implies 1$

$\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-7=1[x-(-1)]\implies y-7=x+1 \\\\\\ y=x+8\implies \boxed{-x+y=8}\implies \stackrel{\textit{standard form}}{x-y=-8}$

just to point something out, is none of the options, however -x + y = 8, is one, though improper.

3 0

3 years ago