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4 years ago

After multiplying each side of the equation by the LCD and simplify , the resulting equation is

Mathematics

2 answers:

emmasim [6.3K]4 years ago

4 0

Answer:

option c

Step-by-step explanation:

Aleks04 [339]4 years ago

3 0

least common denominator (LCD)
The number that results from calculating the lowest common multiple of the denominators of those same fractions is called the lowest common denominator of two or more fractions.
For this case:
((x ^ 2-x-6) / (x ^ 2)) = ((x-6) / (2x)) + ((2x + 12) / (x))
LCD = x ^ 2
Multiplying both sides by LCD
x ^ 2 ((x ^ 2-x-6) / (x ^ 2)) = x ^ 2 (((x-6) / (2x)) + ((2x + 12) / (x)))
Simplifying
(x ^ 2-x-6) = ((x ^ 2-6x) / (2)) + (2x ^ 2 + 12x))
(2x ^ 2-2x-12) = ((x ^ 2-6x) + (4x ^ 2 + 24x))
(2x ^ 2-2x-12) = (5x ^ 2 + 18x)
3x ^ 2 + 20x + 12 = 0
the answer is
3x ^ 2 + 20x + 12 = 0

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4 years ago

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Blizzard [7]

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3 years ago

V(t), left parenthesis, t, right parenthesis models the number of visitors in a park as a function of the outside temperature t

Kruka [31]

Answer:

The number of visitors increases at the same rate over both intervals

Step-by-step explanation:

The unit rate at which the number of visitors in the park increases over a given temperature interval is called the average rate of change, or ARCARCA, R, C.

To find the average rate of change of a function over an interval, we need to take the total change in the function value over the interval and divide it by the length of the interval.

Hint #22 / 3

We are asked to compare the rates at which the number of visitors increases over the interval between an outside temperature of 181818 degrees Celsius and 202020 degrees Celsius, and over the interval between an outside temperature of 202020 degrees Celsius and 272727 degrees Celsius. These correspond to the domain intervals [18,20][18,20]open bracket, 18, comma, 20, close bracket and [20,27][20,27]open bracket, 20, comma, 27, close bracket.

Let's calculate the average rate of change of VVV over those intervals:

ARC_{[18,20]}ARC

[18,20]

A, R, C, start subscript, open bracket, 18, comma, 20, close bracket, end subscript ARC_{[20,27]}ARC

[20,27]

A, R, C, start subscript, open bracket, 20, comma, 27, close bracket, end subscript

\begin{aligned} \dfrac{V(20)-V(18)}{20-18}&=\dfrac{18-10}{2}\\\\&=\dfrac{8}{2}\\\\&=4\end{aligned}\quad

20−18

V(20)−V(18)

18−10

\begin{aligned} \dfrac{V(27)-V(20)}{27-20}&=\dfrac{46-18}{7}\\\\&=\dfrac{28}{7}\\\\&=4\end{aligned}

27−20

V(27)−V(20)

46−18

Hint #33 / 3

The average rate of change over the interval [18,20][18,20]open bracket, 18, comma, 20, close bracket is the same as the average rate of change over the interval [20,27][20,27]open bracket, 20, comma, 27, close bracket.

Therefore, the number of visitors increases at the same rate over both intervals.

7 0

3 years ago

Write an equation for the line passing through the given point and having the given slope.

Nadusha1986 [10]

Answer: The equation, in "slope-intercept form" ; is:

________________________________________________

→ " y = x + 4 " .

________________________________________________

Step-by-step explanation:

________________________________________________

Use the formula for linear equations; written in "point-slope format" ;

which is:

y − y₁ = m( x − x₁ ) ;

We are given the slope, "m" ; has a value of: "1 " ;

that is; " m = 2 " .

________________________________________________

We are given the coordinates to 1 (one) point on the line; in which the coordinates are in the form of :

" ( x₁ , y₁ ) " ;

→ that given point is: "(10, 6)" ;

in which: x₁ = 10 ;

y₁ = 6 .

→ Given: The slope, "m" equals "1" ; ________________________________________________

Let's plug our known values into the formula:

→ " y − y₁ = m( x − x₁ ) " ;

_______________________________________________

→ As follows:

→ " y − 10 = 1(x − 6) ;

______________________________________________

Now, focus on the "right-hand side of the equation" ;

→ 1(x − 6) = ? ; Simplify.

______________________________________________

Note the "distributive property" of multiplication:

→ a(b + c) = ab + ac ;

As such: " 1(x − 6) = (1*x) + (1 * -6) " ;

= 1x + (-6) ;

= x − 6 ;

[Note that: " 1 x = 1 * x = x " ;

[Note that " + (-6) " = " ( " − 6 " ) .] ;

→ {since: "Adding a negative" is the same as:

"subtracting a positive."} ;

________________________________________________

Now, let us bring down the "left-hand side of the equation" ; &

rewrite the entire equation; as follows:

________________________________________________

→ " y − 10 = x − 6 " ;

________________________________________________

Note: We want to rewrite the equation in "slope-intercept form" ;

that is; " y = mx + b " ;

in which: "y" ; stands alone as a single variable on the "left-hand side" of the equation; with "no coefficients" [except for the "implied coefficient" of " 1 "} ;

"m" is the coefficient of "x" ;

and the "slope of the line" ;

Note that "m" may be a "fraction or decimal" ; and may be "positive or negative.

If the slope is "1" ; (that is "1 over 1" ; or: " $\frac1}{1}$ " ;

then, " m = 1 " ; and we can write " 1x " as simply "x" ; since the implied coefficient is "1" ;

→ since " 1" , multiplied by any value {in our case, any value for "x"} , equals that same value.

________________________________________________

"b" refers to the "y-intercept" of the graph of the equation;

that is; the "y-value" of the point at which the graphed line of the equation crosses the "y-axis" ;

that is, the "y-value" of the coordinates of the point at which the graphed line of the equation crosses the "y-axis" ;

that is, the ["y-value" of the] y-intercept" .

Note that the value of "b" may be positive or negative, and may be a decimal or fraction.

If the value for "b" is negative, the equation can be written in the form:

" y = mx - b " ;

{since: " y = mx + (-b) " is a bit tedious .}

If the y-intercept is "0" ; (i.e. the line crosses the y-axis at the origin, at point: " (0,0) " ;

then we simply write the equation as: "y = mx " ;

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So; we have: → " y − 10 = x − 6 " ;

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→ We want to rewrite our equation in slope-intercept form,

that is; " y = mx + b " ; as explained above.

We can add "10" to each side of the equation ; to isolation the "y" on the "left-hand side" of the equation:

→ " y − 10 + 10 = x − 6 + 10 " ;

to get:

→ " y = x + 4 " ;

________________________________________________

→ which is our answer.

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Note: This answer: " y = x + 4 " ;

→ is written in the "slope-intercept format";

→ " y = mx + b " ;

in which: "y" is isolated as a single variable on the "left-hand side of the equation" ;

The slope of the equation is "1" ; or an implied value of "1" ;

that is; " m = 1 " ;

"b = 4 " ;

→ {that is; the "y-value" of the "y-intercept" — "(0, 4)" — of the graph of the equation is: "4 ".} .

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Hope this answer is helpful!

Best wishes to you in your academic pursuits

— and within the "Brainly" community!

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6 0

3 years ago

Write an equation in slope-intercept form of the line that passes through the given point and is perpendicular to the graph of t

Setler79 [48]

Answer:

y = -2x - 1

Step-by-step explanation:

y = -2x + b

3 = -2(-2) + b

3 = 4 + b

-1 = b

y = -2x - 1

6 0

3 years ago