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BigorU [14]
2 years ago
5

A curve has equation y=2x^2-3x Find the set of values of x for which y>9

Mathematics
1 answer:
zavuch27 [327]2 years ago
6 0

Good morning ☕️

Answer:

<h2>(-∞ , -3/2)∪(3 , +∞)</h2>

Step-by-step explanation:

Here we have to solve this inequality 2x² - 3x - 9 > 0 for x.

In order to solve this inequality we need to factorize the expression at first:

2x² - 3x - 9 = 2x² - 3x - 3x + 3x - 9

                  = 2x² + 3x - (6x + 9)

                 = x(2x + 3) - 3(2x + 3)

                 = (2x + 3)(x - 3)

check the attached picture

conclusion:

the set of values of x for which y>9 is :

(-∞ , -3/2)∪(3 , +∞)

___________________

:)

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b. Sixty-five pounds of candy was divided into four different boxes. The second box contained twice the amount of the first box.
Ainat [17]

First box = 14 pounds

Second box = 2x = 28 pounds

Third Box = x+2= 16 pounds

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<u>Step-by-step explanation:</u>

Here we have , Sixty-five pounds of candy was divided into four different boxes. The second box contained twice the amount of the first box. The third box contained two more pounds than the first box. The last box contained one-fourth the amount in the second box. We need to find How much candy was in each box. Let's find out:

We have a total of 65 pounds of candy ! Let in first box we have x pounds so , second box contained twice the amount of the first box i.e.

⇒ 2x

The third box contained two more pounds than the first box i.e.

⇒ x+2

The last box contained one-fourth the amount in the second box i.e.

⇒ (\frac{1}{4})2x = \frac{x}{4}

Therefore , Sum of pounds of candy are :

⇒ \frac{x}{2} +x+2+2x+x=65

⇒ \frac{x}{2} +4x=63

⇒ \frac{9x}{2}=63

⇒ x=63(\frac{2}{9} )

⇒ x=14

Therefore , Candy in each box is :

First box = 14 pounds

Second box = 2x = 28 pounds

Third Box = x+2= 16 pounds

Fourth box = x/2 = 7 pounds

8 0
3 years ago
If y varies directly as x, and y =6 when x =10, find x when y=18
bonufazy [111]

Answer:

X=30

Step-by-step explanation:

y=kx

6=10k

k=0.6

y=0.6x

18=0.6x

X=18/0.6

x=30

7 0
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