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3 years ago

How to express each of the following pairs of

Mathematics

1 answer:

vichka [17]3 years ago

7 0

Answer:

a) 3<x<8

b) -4<x<-2

c) -6<x<5

d) -21/4 < x-8/3

e) 0<x<7

Step-by-step explanation:

Given the following inequalities

a) x > 3, 2x - 3 < 15

Solve 2x - 3 < 15

2x < 15+3

2x<18

x<18/2

x<8

Combine x>3 and x<8

If x>3, then 3<x

On combining, we have:

3<x<8

b) For the inequalities 25 > 1 - 6x, 1 > 3x + 7

25 > 1 - 6x

25-1>-6x

24>-6x

Divide through by -6:

24/-6 > -6x/-6

-4 <x

For the inequality 1 > 3x + 7

1-7>3x

-6>3x

-6/3 > 3x/3

-2 > x

x < -2

Combining both results i.e -4 <x and x < -2, we will have:

-4<x<-2

c) For the inequalities 2x - 7<3< 27 + 4x

On splitting:

2x - 7<3 and 3< 27 + 4x

2x < 3+7

2x<10

x<5

Also for 3< 27 + 4x

3-27<4x

-24<4x

-24/4 < 4x/4

-6<x

Combining both solutions i.e x<5 and -6<x will give;

-6<x<5

d) For the inequalities 3x + 8 <0 < 21 + 4x

3x + 8 <0

3x < -8

x < -8/3

Also for 0 < 21 + 4x

0-21<4x

-21<4x

-21/4 < 4x/4

-21/4 < x

Combining -21/4 < x and x < -8/3 will give;

-21/4 < x-8/3

e) For the inequalities 5x - 36 < -1 < 2x – 1

Split:

5x - 36 < -1

5x < -1+36

5x<35

5x/5 < 35/5

x < 7

For the expression -1 < 2x – 1

-1+1 < 2x

0 < 2x

0<x

Combining both inequalities 0<x and x < 7 will give:

0<x<7

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2 years ago

The vertex of the parabola below is at the point (4, -1). Which of the equations below could be the one for this parabola?

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However, this is not the only possible equation. There could be multiple values for a, in front of the parentheses, that we don't know about from the information we are given.

We can also write this equation in standard form (y=ax²+bx+c). First write the squared binomial as the product of two binomials:
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Multiply the binomials:
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3 years ago

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dolphi86 [110]

Answer:

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Step-by-step explanation:

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add the equations

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plug in x for one of the equations

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