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2 years ago

Please help! I’ll mark as brainliest

Mathematics

1 answer:

Talja [164]2 years ago

7 0

Answer:

see below

Step-by-step explanation:

domain is all x values for which a graph has
and range is all y values for which a graph has

domain in this case is -4<x<4. The range is -3<= x <= 3

Function is increasing when slope of the line is positive, function is decreasing when slope of the line is negative.

When 2 lines meet and there is an edge like at (-1,3) there is no increase of decrease of the function. If you are in calculus, this is because the derivative of the function will not be valid at those points. If you are not in calculus, then don't pay attention to the derivative stuff.

Function is increasing on interval -4<x<-1 and 2<x<4
Function is decreasing on interval -1<x<2

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Solve for x: 4 over x plus 4 over quantity x squared minus 9 equals 3 over quantity x minus 3. (2 points) Select one: a. x = -4

Kay [80]

Answer:

Step-by-step explanation:

$\dfrac{4}{x}+\dfrac{4}{x^2-9}=\dfrac{3}{x-3}$

Domain:

$x\neq0\ \wedge\ x^2-9\neq0\ \wedge\ x-3\neq0\\\\x\neq0\ \wedge\ x\neq\pm3$

solution:

$\dfrac{4}{x}+\dfrac{4}{x^2-3^2}=\dfrac{3}{x-3}$

use (a - b)(a + b) = a² - b²

$\dfrac{4}{x}+\dfrac{4}{(x-3)(x+3)}=\dfrac{3}{x-3}$

multiply both sides by (x - 3) ≠ 0

$\dfrac{4(x-3)}{x}+\dfrac{4(x-3)}{(x-3)(x+3)}=\dfrac{3(x-3)}{x-3}$

cancel (x - 3)

$\dfrac{4(x-3)}{x}+\dfrac{4}{x+3}=3$

subtract $\frac{4(x-3)}{x}$ from both sides

$\dfrac{4}{x+3}=3-\dfrac{4(x-3)}{x}\\\\\dfrac{4}{x+3}=\dfrac{3x}{x}-\dfrac{(4)(x)+(4)(-3)}{x}\\\\\dfrac{4}{x+3}=\dfrac{3x-\bigg(4x-12\bigg)}{x}\\\\\dfrac{4}{x+3}=\dfrac{3x-4x-(-12)}{x}\\\\\dfrac{4}{x+3}=\dfrac{-x+12}{x}$

cross multiply

$(4)(x)=(x+3)(-x+12)$

use FOIL

$4x=(x)(-x)+(x)(12)+(3)(-x)+(3)(12)\\\\4x=-x^2+12x-3x+36$

subtract 4x from both sides

$0=-x^2+12x-3x+36-4x$

combine like terms

$0=-x^2+(12x-3x-4x)+36\\\\0=-x^2+5x+36$

change the signs

$x^2-5x-36=0\\\\x^2-9x+4x-36=0\\\\x(x-9)+4(x-9)=0\\\\(x-9)(x+4)=0$

The product is 0 if one of the factors is 0. Therefore:

$x-9=0\ \vee\ x+4=0$

$x-9=0$ add 9 to both sides

$x=9\in D$

$x+4=0$ subtract 4 from both sides

$x=-4\in D$

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3 years ago

Nine less than one forth of a number is 6

snow_lady [41]

Answer:

$x = 60$

Step-by-step explanation:

Step 1: Convert into an equation

Nine less than one forth of a number is 6

$1/4x - 9 = 6$

Step 2: Add 9 to both sides

$1/4x - 9 = 6$

$1/4x - 9 + 9= 6+ 9$

$1/4x = 15$

Step 3: Multiply both sides by 4

$1/4x * 4 = 15 * 4$

$x = 60$

Answer: $x = 60$

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2 years ago

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sdas [7]

Answer:

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Step-by-step explanation:

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3 years ago

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Simplify (5x^2 -3x+3) - (x^2+2x-1).

Natali [406]

Eliminate parenthesis by using the distribution property

= 5x² -3x +3 - x² - 2x +1

Group similar terms

= (5-1)*x² + (-3 -2)*x + (3+1)

Then sum everything:

= 4x² -5x +4

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3 years ago

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If mr. douty goes to the store and purchases 5 equally priced items for a total of $172.45, how much did each item cost individu

natima [27]

Answer:

$34.49

Step-by-step explanation:

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In this case it is...

172.45/5

=34.49

So the price of each item is approx. $34.49

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