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Softa [21]
2 years ago
10

What are the roots of this equation?

Mathematics
1 answer:
Katyanochek1 [597]2 years ago
4 0

Answer:

x = 2 ± (i)√5  (Answer b)

Step-by-step explanation:

x²-4x+9=0 can be solved in a variety of ways; the first two that come to mind that are also appropriate are (1) completing the square and (2) using the quadratic formula.

Completing the square is fast here:

Rewrite x²-4x+9=0 as   x²-4x                    +9=0

Identify the coefficient of the x term:  it is -4

Take half of that, obtaining -2

Square this result, obtaining 4

Add 4 to   x²-4x                    +9=0, in the blank space in the middle, and then subtract 4:      x²-4x +4          -4         +9=0

Rewrite           x²-4x +4 as the square of a binomial:

                          (x - 2)² - 4 + 9  = 0  →    (x - 2)²  = -5

Take the square root of both sides:       x - 2  = ±√(-5)  =  ± (i)√5

Then x = 2 ± (i)√5

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7
natulia [17]

Answer:

diagonal = = 12.8 inches (to the nearest tenth of an inch)

Step-by-step explanation:

As shown in the diagram attached to this solution:

Let the Length of the rectangular board = a

Let the width = b

Let the diagonal = d

where:

a = 10 inches

b = 8 inches

d = ?

Triangle ABC in the diagram is a right-angled triangle, therefore, applying Pythagoras theorem:

(hypotenuse)² = (Adjacent)² + (Opposite)²

d² = 10² + 8²

d² = 100 + 64

d² = 164

∴ d = √(164)

d = 12.806 inches

d = 12.8 inches (to the nearest tenth of an inch)

<em>N:B Rounding off to the nearest tenth of an inch is the same as rounding off to 1 decimal place.</em>

3 0
3 years ago
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SashulF [63]
Misha would combine 3x-2x and-8-7
5 0
3 years ago
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T.J. invests $8,100 in an account
QveST [7]

Answer:

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Step-by-step explanation:

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6 0
2 years ago
A basic cellular phone plan costs $4 per month for 70 calling minutes. Additional time costs $0.10 per minute. The formula C= 4+
Harrizon [31]

Answer:

For a monthly cost of at least $7 and at most $8, you can have between 100 and 110 calling minutes.

Step-by-step explanation:

The problem states that the monthly cost of a celular plan is modeled by the following function:

C(x) = 4 + 0.10(x-70)

In which C(x) is the monthly cost and x is the number of calling minutes.

How many calling minutes are needed for a monthly cost of at least $7?

This can be solved by the following inequality:

C(x) \geq 7

4 + 0.10(x - 70) \geq 7

4 + 0.10x - 7 \geq 7

0.10x \geq 10

x \geq \frac{10}{0.1}

x \geq 100

For a monthly cost of at least $7, you need to have at least 100 calling minutes.

How many calling minutes are needed for a monthly cost of at most 8:

C(x) \leq 8

4 + 0.10(x - 70) \leq 8

4 + 0.10x - 7 \leq 8

0.10x \leq 11

x \leq \frac{11}{0.1}

x \leq 110

For a monthly cost of at most $8, you need to have at most 110 calling minutes.

For a monthly cost of at least $7 and at most $8, you can have between 100 and 110 calling minutes.

8 0
3 years ago
Evaluate the expression without using a calculator 8 4/3
artcher [175]

Answer: 128/3

Step-by-step explanation: maybe

6 0
3 years ago
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