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3 years ago

If f(x) = x/2 - 3 and g(x) = 3x^2 + x - 6, find (f+g)(x)

Mathematics

1 answer:

drek231 [11]3 years ago

5 0

$(f+g)(x) = f(x) +g(x)$

$(f+g)(x) = \left(\dfrac{x}{2}-3\right)+\left(3x^2+x-6\right)$

$(f+g)(x) =3x^2 +\dfrac{3x}{2}-9$

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I just need no. a please help me to prove this.

OleMash [197]

Answer: see proof below

<u>Step-by-step explanation:</u>

Given: A + B + C = π and cos A = cos B · cos C

scratchwork:

A + B + C = π

A = π - (B + C)

cos A = cos [π - (B + C)] Apply cos

= - cos (B + C) Simplify

= -(cos B · cos C - sin B · sin C) Sum Identity

= sin B · sin C - cos B · cos C Simplify

cos B · cos C = sin B · sin C - cos B · cos C Substitution

2cos B · cos C = sin B · sin C Addition

$2=\dfrac{\sin B\cdot \sin C}{\cos B \cdot \cos C}$ Division

2 = tan B · tan C

$\text{Use the Sum Identity:}\quad \tan(B+C)=\dfrac{\tan B+\tan C}{1-\tan B\cdot \tan C}$

<u>Proof LHS → RHS</u>

Given: A + B + C = π

Subtraction: A = π - (B + C)

Apply tan: tan A = tan(π - (B + C))

Simplify: = - tan (B + C)

$\text{Sum Identity:}\qquad \qquad \qquad =-\bigg(\dfrac{\tan B+\tan C}{1-\tan B\cdot \tan C}\bigg)$

Substitution: = -(tan B + tan C)/(1 - 2)

Simplify: = -(tan B + tan C)/-1

= tan B + tan C

LHS = RHS: tan B + tan C = tan B + tan C $\checkmark$

5 0

3 years ago

X^2 + 5x - 24 = 0 How do I solve by factoring

tiny-mole [99]

Answer:

x = -8 or x = 3

Step-by-step explanation:

To factor ax² + bx + c, use AC method.

a times c is 1 × -24 = -24.

Factors of ac (-24) that add up to b (5) are 8 and -3.

Divide by a and reduce: 8/1 and -3/1.

Therefore, the factors are x + 8 and x − 3.

x² + 5x − 24 = 0

(x + 8) (x − 3) = 0

x = -8 or 3

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3 years ago

Whenever a,x,y are positive integers, which of the following expressions is equivalent to x^ay^a

lilavasa [31]

Answer:

${(xy)}^{a}$

Step-by-step explanation:

when the exponent is equal, we can put the x and y together in a bracket and a as the Exponent of xy.

Hope I get your question~

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3 years ago

F(x)=4x4−5x3−2x+6 and g(x)=3x3−4x2−2x+1 . What is f(x)+g(x) ?

igomit [66]

4*4-5*3-2x+6= -x-7/2 slope = 2

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3 years ago

A bag of numbered lottery balls contains the numbers 1 through 40. What is the probability that a randomly selected ball will be

MA_775_DIABLO [31]

Answer:

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So we look for all the multiples of 13 not over 40

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So it will be 3/40

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