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Rufina [12.5K]
3 years ago
7

Subtract: 3.8 - 2.923. Explain in your own words how you would solve this, in detail, from start to finish.

Mathematics
1 answer:
Cerrena [4.2K]3 years ago
4 0

Given:

The expression is 3.8 - 2.923.

To find:

The subtraction.

Solution:

We have,

3.8-2.923

It can be written as

3.800-2.923

Now,

3 . 8 0 0

-2 . 9 2 3

-----------------

0 . 8 8 7

-----------------

So, 3.800-2.923=0.887

Therefore, the value of 3.800-2.923 is 0.887.

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To find the upper and lower bounds we have to add 5 to 32 AND subtract 5 from 32 to get 37 and 27 respectively.

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Solve (x + 3)2 + (x + 3) – 2 = 0. Let u = Rewrite the equation in terms of u. (u2 + 3) + u – 2 = 0 u2 + u – 2 = 0 (u2 + 9) + u –
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Answer:

The solutions of the original equation are x=-5 and x=-2

Step-by-step explanation:

we have

(x+3)^2+(x+3)-2=0

Let

u=(x+3)

Rewrite the equation

(u)^2+(u)-2=0

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u^2+u=2

u^2+u+1/4=2+1/4

u^2+u+1/4=9/4

rewrite as perfect squares

(u+1/2)^2=9/4

square root both sides

(u+1/2)=\pm\frac{3}{2}

u=(-1/2)\pm\frac{3}{2}

u=(-1/2)+\frac{3}{2}=1

u=(-1/2)-\frac{3}{2}=-2

the solutions are

u=-2,u=1

<em>Alternative Method</em>

The formula to solve a quadratic equation of the form

ax^{2} +bx+c=0

is equal to

x=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}

in this problem we have

(u)^2+(u)-2=0

so

a=1\\b=1\\c=-2

substitute in the formula

u=\frac{-1\pm\sqrt{1^{2}-4(1)(-2)}} {2(1)}

u=\frac{-1\pm\sqrt{9}} {2}

u=\frac{-1\pm3} {2}

u=\frac{-1+3} {2}=1

u=\frac{-1-3} {2}=-2

the solutions are

u=-2,u=1

<em>Find the solutions of  the original equation</em>

For u=-2

-2=(x+3) ----> x=-2-3=-5

For u=1

1=(x+3) ----> x=1-3=-2

therefore

The solutions of the original equation are

x=-5 and x=-2

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Answer: 40%

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