MATHEMATICS HIGH SCHOOL

Add and subtract functions

Answers

Answer 1

Answer:

Answer: $3x^2+5x+3$

Step-by-step explanation:

For this exercise you need to remember the multiplication of signs:

$(+)(+)=+\n(-)(-)=+\n(-)(+)=-\n(+)(-)=-$

You know that the function f(x) is:

$f(x)=5x+3$

And the function g(x) is:

$g(x)=3x^2$

Then to find $(f+g)(x)$ you need to add the function f(x) and the function g(x) by adding (or combining) the like terms, you get that the sum is the following:

$(f+g)(x)=(5x+3)+(3x^2)$

$(f+g)(x)=5x+3+3x^2\n\n(f+g)(x)=3x^2+5x+3$

As you can notice, when you add the functions given in the exercise, you get a Quadratic function, which is a function whose highest exponent is 2 and has this form:

$f(x) = ax^2 + bx + c$

Where "a", "b", and "c" are numbers ( $a\neq 0$ )

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Find sin(7pie/4) using exact values

Answers

$sin( ( 7\pi )/(4) )=-sin(2 \pi - ( 7\pi )/(4) )=-sin ( \pi )/(4) =- (1)/( √(2) )$

How do you simplify radical expressions
81 1/4

Answers

$81^(1)/(4)=\sqrt[4]{81}=\sqrt[4]{3^4}=3\n\n-----------------------\n\n81^(1)/(4)=\left(3^4\right)^(1)/(4)=3^{4\cdot(1)/(4)}=3^1=3$

you mean convert 81^(1/4) into a radical expression?

which equations represent the line that is parallel to 3x − 4y = 7 and passes through the point (−4, −2)? Check all that apply. y = –x + 1 3x − 4y = −4 4x − 3y = −3 y – 2 = –(x – 4) y + 2 = (x + 4)

Answers

Answer:

$\text{The equation represent the line that is parallel to 3x - 4y = 7 and passes through the point (-4, -2) is 3x-4y=-4}$

Step-by-step explanation:

Given the equation 3x - 4y = 7

we have to find the equation which represent the line that is parallel to 3x - 4y = 7 and passes through the point (-4, -2)

As parallel lines have same slope therefore we find the slope of given line

$3x-4y=7$

$4y=3x-7$

$y=(3)/(4)x-(7)/(4)$

Comparing above equation with general equation y=mx+c, where m is slope

⇒ $m=(3)/(4)$

$\text{The equation of line having slope }(3)/(4)\text{ and passing through the point (-4,-2) is}$

$y-y'=m(x-x')$

$y-(-2)=(3)/(4)(x-(-4))$

$y+2=(3)/(4)(x+4)$

$4y+8=3x+12$

$3x-4y=-4$

which is required equation.

Option 2 is correct.

Solve for X in y=12x-5

Answers

$y=12x-5\n\n12x-5=y\ \ \ \ /+5\n\n12x-5+5=y+5\n\n12x=y+5\ \ \ \ /:12\n\nx=(y+5)/(12)\n\nx=(y)/(12)+(5)/(12)\n\nx=(1)/(12)y+(5)/(12)$

A closed container has 6.08 ⋅ 1023 atoms of a gas. Each atom of the gas weighs 1.67 ⋅ 10–24 grams. Which of the following shows and explains the approximate total mass, in grams, of all the atoms of the gas in the container?