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2 years ago

What are the solutions of the equation (x – 3)2 + 2(x – 3) -8 = 0? Use u substitution to solve.

Mathematics

1 answer:

Andrej [43]2 years ago

6 0

Answer:

x = -1 and x = 5

Step-by-step explanation:

<em>What are the solutions of the equation (x – 3)² + 2(x – 3) -8 = 0? Use u substitution to solve.</em>

<em />

(x – 3)² + 2(x – 3) -8 = 0 -------------------------------------------------------(1)

To solve this problem, we will follow the steps below;

let u = x-3

we will replace x-3 by u in the given equation:

(x – 3)² + 2(x – 3) -8 = 0

u² + 2u -8 = 0 ----------------------------------------------------------- --------------(2)

We will now solve the above quadratic equation

find two numbers such that its product gives -8 and its sum gives 2

The two numbers are 4 and -2

That is; 4×-2 = -8 and 4+(-2) = 2

we will replace 2u by (4u -2u) in equation (2)

u² + 2u -8 = 0

u² + 4u - 2u -8 = 0

u(u+4) -2(u+4) = 0

(u+4)(u-2) = 0

Either u + 4 = 0

u = -4

u-2 = 0

u = 2

Either u = -4 or u = 2

But u = x-3

x = u +3

when u = -4

x = u + 3

x = -4 + 3

x=-1

when u = 2

x = u + 3

x = 2 + 3

x=5

Therefore, x = -1 and x =5

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ikadub [295]

Answer:

508.8 seconds

Step-by-step explanation:

The most accurate determination mathematically is to assume that Lola will maintain an average of 5.3 seconds per signature as she signs all 96 invitations.

Therefore, multiply the time it takes her to sign each invitation (5.3 seconds) by the total number of invitations there are (96 invitations) to get the projected total amount of time that it will take Lola to sign all 96 invitations: $96\cdot 5.3=\boxed{508.8\text{ seconds}}$

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2 years ago

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What is the value of the expression i 0 × i 1 × i 2 × i 3 × i 4?

astraxan [27]

ANSWER

The value of the expression is
$- 1$

EXPLANATION

Method 1: Rewrite as product of
${i}^{2}$

The expression given to us is,

${i}^{0} \times {i}^{1} \times {i}^{2} \times {i}^{3} \times {i}^{4}$

We use the fact that
${i}^{2} = - 1$
to simplify the above expression.

${i}^{0} \times {i}^{1} \times {i}^{2} \times {i}^{3} \times {i}^{4} = {i}^{0} \times {i}^{1} \times {i}^{3} \times {i}^{2} \times {i}^{4}$

This implies,

${i}^{0} \times {i}^{1} \times {i}^{2} \times {i}^{3} \times {i}^{4} = {i}^{0} \times {i}^{2} \times {i}^{2} \times {i}^{2} \times {i}^{2} \times {i}^{2}$

We substitute to obtain,

${i}^{0} \times {i}^{1} \times {i}^{2} \times {i}^{3} \times {i}^{4} = 1\times - 1 \times - 1 \times - 1\times - 1 \times - 1$

${i}^{0} \times {i}^{1} \times {i}^{2} \times {i}^{3} \times {i}^{4} = 1\times 1 \times 1 \times - 1 = - 1$

Method 2: Use indices to solve.

${i}^{0} \times {i}^{1} \times {i}^{2} \times {i}^{3} \times {i}^{4} = {i}^{0 + 1 + 2 + 3 + 4}$

This implies that,

${i}^{0} \times {i}^{1} \times {i}^{2} \times {i}^{3} \times {i}^{4} = {i}^{10}$

${i}^{0} \times {i}^{1} \times {i}^{2} \times {i}^{3} \times {i}^{4} = ( {{i}^{2}} )^{5}$

${i}^{0} \times {i}^{1} \times {i}^{2} \times {i}^{3} \times {i}^{4} = ( - 1 )^{5} = - 1$

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Answer:

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