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Brums [2.3K]
3 years ago
8

Show that 5x^2 + 2x - 3 < 0 can be written in the form | x + 1/5 | < 4/5

Mathematics
1 answer:
Sliva [168]3 years ago
8 0

Step-by-step explanation:

First let solve the inequality

5 {x}^{2}  + 2x - 3 < 0

Factor by grouping

5 {x}^{2}  + 5x - 3x - 3 < 0

5x(x + 1) - 3(x + 1)

So the factor are

(5x - 3)(x + 1)

So the factor are

x =  \frac{3}{5}

and

x =  - 1

Solutions to a quadratic can be represented by a absolute value equation because remeber quadratics

creates 2 roots and/or double roots.

The inequality

|x - b|   <  c

works as

b is the midpoint between 2 roots. And c is the

|x + b|  = c

We know that the midpoint between both roots is-1/5.

so

|x - ( -  \frac{1}{5} )|  < c

|x +  \frac{1}{5} |  < c

Let use roots 3/5

| \frac{3}{5}  +  \frac{1}{5} |  =  \frac{4}{5}

-1 works as well.

| - 1 +  \frac{1}{5} |  =   |   -   \frac{4}{5} |  =  \frac{4}{5}

So the absolute value equation is

|x +  \frac{1}{5} |  <  \frac{4}{5}

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If x+y=9, and 8(x+3y)= 120, what is the value of x-y
Triss [41]

Answer:

3

Explanation:

Apply Multiplicative Distribution Law:

{x + y =9

{8x + 24y = 120

Reduce the greatest common factor on both sides of the equation.

{x + y = 9

{x + 3y = 15

Subtract the two equations: x + y - (x +3y) = 9 - 15

Remove paranthesis: x + y - x - 3y = 9 - 15

Cancel the unknown variables: y - 3y = 9 - 15

Combine like terms: -2y=9 - 15

Calculate the sum or difference: -2y = -6

Reduce the greatest common factor on both sides of the equation: y =3

Substitute one unknown quantity into the elimination: x + 3 = 9

Rearrange unknown terms to the left side of the equation: x = 9 - 3

Calculate the sum or difference: x = 6

Write the solution set of equations: {x = 6

                                                           {y = 3

Substitute: 6 - 3

Calculate the sum or difference: 3

Answer: 3

6 0
3 years ago
In the city, the dust and between the library and the police station is 3 miles less than twice the distance between the police
alina1380 [7]

Answer:

7 miles

Step-by-step explanation:

Let's call the distance between the library and police station x. Then, the distance between the police station and fire station would be 3 less than twice x. Twice means multiply by 2 so twice x is 2 * x = 2x and 3 less than means that you subtract 3 so 3 less than 2x is 2x - 3. Now, we know that x = 5 so all we have to do now is substitute x = 5 into 2x - 3, therefore, the answer is 2 * 5 - 3 = 7 miles.

4 0
3 years ago
Owning a small and successful business isn't easy! There is a monthly cost of shipping
galben [10]

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8 0
4 years ago
Mrs Lim packs 35 big and small bags of candies for her pupils. Each big bag contains 12 candies and each small bag contains 7 ca
Anastasy [175]

Answer:

there are 11 big-bags and 24 small-bags.

Step-by-step explanation:

there are x big-bags and y small-bags.

so now we can know:

(1) x + y = 35

(2) 12x + 7y = 300

in (1),we can do like this:

both left and right x7

then (x + y)x7 = 35 x 7

then 7x + 7y = 35 x 7  

then 7x + 7y = 245

now,

(1)7x + 7y =245

(2)12x + 7y = 300

we can both left and right do this: (2) - (1)

then

(12x + 7y) - (7x + 7y) = 300 -245

then

12x + 7y - 7x - 7y = 300 -245

then

12x - 7x +7y - 7y =300 -245

then

5x =55

then

5x ÷ 5 = 55 ÷ 5

then

x = 11

because

x + y =35;x=11

so

11 + y =35

11+ y -11 = 35 -11

then

y = 24

now we know:there are 11 big-bags and 24 small-bags.

3 0
3 years ago
Explain and show your work, please.
ArbitrLikvidat [17]
It is given that aiden has purchased a 2 lb package, a 3 lb package, and a 4 lb package
The first step is to add these packages together
2+3+4 is 9
each turkey burger needs 1/3 lb of turkey, which also means that every pound of turkey aiden has can make 3 turkey burgers

Aiden has 9 pounds of turkey, so he can make 27 turkey burgers (3*9)

Hope this helped! If you still need help I can answer in comments
5 0
3 years ago
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