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3 years ago

Prove that the inequality (a+1)·(a+1)>(a−1)·(a−1) is not true for some values of a.

Mathematics

1 answer:

Effectus [21]3 years ago

7 0

Explanation:

Consider the case a = -1. Then the expression becomes ...

(-1+1)(-1+1) > (-1-1)(-1-1) . . . . test case

0·0 > (-2)(-2) . . . . . simplified a bit

0 > 4 . . . . . . . . NOT TRUE

_____

If we subtract the right side from both sides, the inequality becomes ...

(a+1)(a+1) -(a-1)(a-1) > 0

a² +2a +1 -(a² -2a +1) > 0

4a > 0

a > 0

The inequality is only true for positive values of "a". For a ≤ 0, the inequality will not be true.

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Need help for question 8 and 9. I need the equation that’s passes through the points!

dsp73

Answer:

Step-by-step explanation:

Question 8

Let the equation of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by,

y = mx + b

Here, m = slope and y-intercept = b

Since, m = $\frac{y_2-y_1}{x_2-x_1}$

For two points (1, 4) and (5, 8),

m = $\frac{8-4}{5-1}$

m = 1

Equation will be,

y = (1)x + b

y = x + b

Since, this line passes through (1, 4),

4 = 1 + b

b = 3

Therefore, equation of the line will be,

y = x + 3

Question 9

Let the equation is y = mx + b

m = $\frac{y_2-y_1}{x_2-x_1}$

For two points (2, 10) and (6, 4)

m = $\frac{10-4}{2-6}$

m = $-\frac{3}{2}$

By substituting the value of 'm' in the equation,

y = $-\frac{3}{2}x+b$

Since, this line passes through (2, 10)

10 = $-\frac{3}{2}(2)+b$

b = 10 + 2

b = 12

Therefore, equation of the line will be,

$y=-\frac{3}{2}x+12$

4 0

3 years ago

Which values of x and y will make this<br> quadrilateral a parallelogram?

Colt1911 [192]

Answer:

X = 6

y = 4

Step-by-step explanation:

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3 years ago

A grocery store owner is planning a display by stacking cans of soup in a pyramid. The top row of the stack will have 1 can, the

Artyom0805 [142]

Answer:

144?

Step-by-step explanation:

1+3+5+7+9+11 blah blah blah...

1+3+5+7+9+11+13+15+17+19+21+23 which gives 144.

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3 years ago

The volume of liquid in a beaker decreases at a rate of 3.25 mL/h. What is the change in the volume of the liquid in the beaker

luda_lava [24]

The volume of the beaker after is 6 hours is 19.5

8 0

4 years ago

Read 2 more answers

Determine the number of degrees in 8π/9 radians

snow_tiger [21]

Answer:

π radians=180°(basic definition) 8π9 radians=89⋅180∘=160∘

Hope this helps!! If so please mark brainliest and rate/heart to help my account if it did!!

6 0

4 years ago