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3 years ago

Solve the following equation and show all the steps to solving.

1 answer:

8 0

$\bf \cfrac{x}{x-2}+\cfrac{x-1}{x+1}=-1\impliedby LCD\to (x-2)(x+1)\\\\
-------------------------------\\\\
\cfrac{x(x+1)+(x-1)(x-2)}{(x-2)(x+1)}=-1
\\\\\\
x^2+x+x^2-3x+2=-1(x-2)(x+1)
\\\\\\
2x^2-2x+2=-1(x^2-x-2)\implies 2x^2-2x+2=-x^2+x+2
\\\\\\
3x^2-3x=0\implies 3x(x-1)=0\implies 
\begin{cases}
3x=0\implies &x=0\\
x-1=0\implies &x=1
\end{cases}$

You might be interested in

Describe the error(s) that occurred and show the correct solution.

RideAnS [48]

Answer:

$-x^{2}+4x$

Step-by-step explanation:

we have

$(x^{2}+x)-(2x^{2} -3x)$

step 1

Eliminate the parenthesis

$x^{2}+x-2x^{2} +3x$

The symbol of the term 3x is incorrect, must be positive instead of negative

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

Group terms that contain the same variable

$(x^{2}-2x^{2})+(x+3x)$

Combine like terms

$-x^{2}+4x$

6 0

3 years ago

30 Points please help!! Please explain too!

sergiy2304 [10]

Initial: 200 feet = opp. side
Angle = 17.31, adj. Side = a
So tan (17.31) = opp. Side / adj. Side
tan (17.31) = 200 / a
--> a = 200/tan17.31 = 641.73
When stopped: adj. Still = a
Opp. Side still = 200, angle = 46.41
tan46.41 = 200 / a
--> a = 200/tan46.41 = 190.39
Now subtract those two distances to get the distance traveled from initial to when it stopped:
641.73 - 190.39 = 451.34 feet

3 0

3 years ago

Write the cubic polynomial function f(x)in expanded form with zeros −6,−5,and −1, given that f(0)=60

RSB [31]

Answer:

$f(x)=2x^{3}+24x^{2}+82x+60$

Step-by-step explanation:

we know that

The roots of the polynomial are the values of x when the value of the polynomial f(x) is equal to zero

The roots of the polynomial function are

x=-6 -----> (x+6)=0

x=-5 -----> (x+5)=0

x=-1 -----> (x+1)=0

The equation of the cubic polynomial is

$f(x)=a(x+6)(x+5)(x+1)$

where

a is the leading coefficient

Remember that

f(0)=60

That means ------> For x=0 the value of f(x) is equal to 60

substitute the value of x and the value of y in the function and solve for a

$60=a(0+6)(0+5)(0+1)$

$60=a(6)(5)(1)$

$60=30a$

$a=2$

$f(x)=2(x+6)(x+5)(x+1)$

Applying the distributive property

Convert to expanded form

$f(x)=2(x+6)(x+5)(x+1)\\\\f(x)=2(x+6)(x^{2}+x+5x+5)\\\\f(x)=2(x+6)(x^{2}+6x+5)\\\\f(x)=2(x^{3}+6x^{2}+5x+6x^{2}+36x+30)\\\\f(x)=2x^{3}+24x^{2}+82x+60$

3 0

3 years ago

Sue's Sushi placed two orders with its fish supplier. One order was for 11 pounds of salmon and 6 pounds of tuna; the order tota

lidiya [134]

Hi there

One pound of salmon will cost $13, and one pound of tuna will cost $8.

Here's why.

X will be the cost of pound of salmon, and y will be the cost of a pound of tuna.
| 15x+8y=259
| 12x+6y-204

6y = 204-12x
y=34-2x

15x+8(34-2x)=259
272-259=16x-15x
x=13

y=34-2*13
y=34-26
y=8

So, again...
1lb Salmon : $13
1lb Tuna : $8

3 0

3 years ago

An arithmetic sequence has a first term of 4 and a common difference of 3. What is the 20th term

tino4ka555 [31]

Answer:

Step-by-step explanation:

aₙ = a₁ + (n - 1)d

aₙ = 4 + (20 - 1)3

aₙ = 4 + (19)3

aₙ = 4 + 57

aₙ = 61

8 0

2 years ago