Solve the inequality 4x<-12

. If α and β are the roots of

Lostsunrise [7]

Answer:

$18x^2+85x+18 = 0$

Step-by-step explanation:

Given Equation is

=> $2x^2+7x-9=0$

Comparing it with $ax^2+bx+c = 0$ , we get

=> a = 2, b = 7 and c = -9

So,

Sum of roots = α+β = $-\frac{b}{a}$

α+β = -7/2

Product of roots = αβ = c/a

αβ = -9/2

Now, Finding the equation whose roots are:

α/β ,β/α

Sum of Roots = $\frac{\alpha }{\beta } + \frac{\beta }{\alpha }$

Sum of Roots = $\frac{\alpha^2+\beta^2 }{\alpha \beta }$

Sum of Roots = $\frac{(\alpha+\beta )^2-2\alpha\beta }{\alpha\beta }$

Sum of roots = $(\frac{-7}{2} )^2-2(\frac{-9}{2} ) / \frac{-9}{2}$

Sum of roots = $\frac{49}{4} + 9 /\frac{-9}{2}$

Sum of Roots = $\frac{49+36}{4} / \frac{-9}{2}$

Sum of roots = $\frac{85}{4} * \frac{2}{-9}$

Sum of roots = S = $-\frac{85}{18}$

Product of Roots = $\frac{\alpha }{\beta } \frac{\beta }{\alpha }$

Product of Roots = P = 1

The Quadratic Equation is:

=> $x^2-Sx+P = 0$

=> $x^2 - (-\frac{85}{18} )x+1 = 0$

=> $x^2 + \frac{85}{18}x + 1 = 0$

=> $18x^2+85x+18 = 0$

This is the required quadratic equation.

5 0

3 years ago

Read 2 more answers

PLEASE I NEWD HELP ON THIS

Zarrin [17]

Answer:

5. Inequality form: n ≥ 3

Interval notation: [3, ∞)

6. Inequality form: x < 4

Interval notation: (- ∞, 4)

11. Inequality form: x > 50

Interval notation: (50, ∞)

12. Inequality form: y $\geq$ 8

Interval notation: [8, ∞)

15. Inequality form: z < 8

Interval notation: (- ∞, 8)

16. Inequality form: y $\geq$ 4

Interval notation: [4, ∞)

Step-by-step explanation:

I tried to graph them as best as I could, I hope this helps!

7 0

3 years ago

Dr. E. Quation says the Infant Mortality Rate of Korea shown by the expression; 7(m + 3) - 2. Is equal to his criminal success r

GarryVolchara [31]

Answer:

The infant mortality rate in Korea based on equality provided is:

1.8

Step-by-step explanation:

Since the text mentions that the infant mortality rate in Korea is equal to the criminal success rate, the two expressions must equalize and clear the variable m, which is the rate in each of the expressions:

7 (m + 3) - 2 = 8m + 17.2
7m + 21 - 2 = 8m + 17.2
7m + 19 = 8m + 17.2
19 - 17.2 = 8m - 7m
1.8 = m

As you can see, once the equality of the expressions is solved, a rate of 1.8 is obtained.

6 0

3 years ago

A carton has a length of 2 2/3 feet, width of 1 1/3 feet, and a height of 1 1/2. What is the volume of the carton? A( 4 cubic fe

notsponge [240]

Answer:

The volume of the carton is 5 1/3 cubic feet

Step-by-step explanation:

A carton has a length of 2 2/3 feet, width of 1 1/3 feet, and a height of 1 1/2.

The dimensions can be rewritten as

Length of carton =2 2/3 = 8/3 converting to improper fraction).

width of 1 1/3 feet = 4/3 feet

and a height of 1 1/2= 3/2 ,feet

volume of the carton = length of the carton × width of the carton × height of the carton

Volume of carton = 8/3 ×4/3 × 3/2

= 96/18 cubic feet

Converting to mixed fractions, we have

96/18= 5 1/3 cubic feet

8 0

3 years ago

Ten cards numbered 1 through 10 are mixed together and then one card is drawn. Find the probability of each event. Write each an

liraira [26]

Answer:

2/5, 0.4, 40%

7/10, 0.7, 70%

1/2, 0.5, 50%

4/5, 0.8, 80%

3/5, 0.6, 60%

3/10, 0.3 ; 30%

Step-by-step explanation:

Sample space = (1, 2, 3, 4, 5, 6, 7, 8, 9, 10)

P(less Than 5) :

Required = (1, 2, 3, 4) = 4 observations

P(less than 5) = 4 / 10 = 2 / 5 = 0.4 = 40%

Greater than 3) = (4, 5,6,7,8,9,10) = 7 observations

P greater Than 3) = 7/10 = 0.7 = 70%

Odd = (1,3,5,7,9) = 5

P(odd) = 5 / 10 = 1/2 = 0.5 = 50%

(even) = (2,4,6,8,10) = 5

P(even) = 5 / 10 = 1/2 = 0.5 = 50%

Not a multiple of 4 = (1,2, 3,5,6,7,9,10) = 8

P(not A multiple of 4) = 8/10 = 4/5 = 0.8 = 80%

not 5, 6, 7, or 8 = (1,2,2,4,9,10).= 6

P(not 5, 6, 7, or 8) = 6 / 10 = 3/5 = 0.6 = 60%

Divisible by 3 = (3, 6, 9) = 3

P(divisible by 3). = 3/10 = 0.3 = 30%

4 0

2 years ago