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3 years ago

Find the area of a square when all sides are 6 and 1/2 inches. Thank you!

Mathematics

1 answer:

erastovalidia [21]3 years ago

8 0

The answer is 42.25!! hope it helps!!

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1. Let a be a positive real number. In Part (1) of Theorem 3.25, we proved that for each real number x, jxj < a if and only i

krek1111 [17]

Answer:

(a)

if $x \geq 0$ then $x \geq a$ and if x<0 then $-x > a$

(b)

That is straightforward from what you showed on theorem 3.25

(c)

Following the same ideas from (a) x>a or -x > a.

Step-by-step explanation:

Remember how we define the absolute value of a number.

(a)

In general

$|x| = x \,\,\,\text{if} \,\,\,\, x \geq 0 \\|x| = -x \,\,\,\text{if} \,\,\,\, x < 0$

Therefore if $|x| \geq a$ you have two cases, if $x \geq 0$ then $x \geq a$ and if x<0 then $-x > a$

(b)

That is straightforward from what you showed on theorem 3.25

(c)

Following the same ideas from (a) x>a or -x > a.

8 0

3 years ago

I am thinking of a number x. what algebraic expression represents 7 less than three times this number?

sammy [17]

Step-by-step explanation:

Answer: 3x-7

Explanation: x times 3

(3x)

subtracted by 7

(3x-7)

Is this what you are looking for?

8 0

3 years ago

(X^4)-(45x^2)+324 what are the zeroes? And how many turning points?

dmitriy555 [2]

Zeroes:

We must solve

$x^4-45x^2+324=0$

To do so, we define the auxiliary variable $t=x^2$ . The equation becomes

$t^2-45t+324=0$

The quadratic formula yields the solutions

$t=9,\quad t=36$

Substituting back $t=x^2$ gives

$x^2=9 \iff x=\pm 3,\quad x^2=36 \iff x=\pm 6$

So, the zeroes are -6, -3, 3, 6.

Turning points:

Turning points are points where a function stops being increasing to become decreasing, or vice versa. Since functions are increasing when their first derivative is positive and decreasing when it's negative, turning points are points where the first derivative is zero.

We have

$f(x)=x^4-45x^2+324 \implies f'(x)=4x^3-90x$