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vova2212 [387]
2 years ago
6

A quadratic function with zeroes 1 and -9

Mathematics
2 answers:
baherus [9]2 years ago
8 0

Answer:

(x-1)(x+9) or x^2 + 8x-9, if you simplify.

Step-by-step explanation:

Len [333]2 years ago
5 0

Step-by-step explanation:

By Factor theorem, (x - 1) and (x + 9) are factors of the function.

=> (x - 1)(x + 9) = x² + 8x - 9 is one such function.

You might be interested in
why do we need imaginary numbers?explain how can we expand (a+ib)^5. finally provide the expanded solution of (a+ib)^5.(write a
zheka24 [161]

Answer:

a. We need imaginary numbers to be able to solve equations which have the square-root of a negative number as part of the solution.

b. (a + ib)⁵ = a⁵ + 5ia⁴b - 10a³b² - 10ia²b³ + 5ab⁴ + ib⁵

Step-by-step explanation:

a. Why do we need imaginary numbers?

We need imaginary numbers to be able to solve equations which have the square-root of a negative number as part of the solution. For example, the equation of the form x² + 2x + 1 = 0 has the solution (x - 1)(x + 1) = 0 , x = 1 twice. The equation x² + 1 = 0 has the solution x² = -1 ⇒ x = √-1. Since we cannot find the square-root of a negative number, the identity i = √-1 was developed to be the solution to the problem of solving quadratic equations which have the square-root of a negative number.

b. Expand (a + ib)⁵

(a + ib)⁵ =  (a + ib)(a + ib)⁴ = (a + ib)(a + ib)²(a + ib)²

(a + ib)² = (a + ib)(a + ib) = a² + 2iab + (ib)² = a² + 2iab - b²

(a + ib)²(a + ib)² = (a² + 2iab - b²)(a² + 2iab - b²)

= a⁴ + 2ia³b - a²b² + 2ia³b + (2iab)² - 2iab³ - a²b² - 2iab³ + b⁴

= a⁴ + 2ia³b - a²b² + 2ia³b - 4a²b² - 2iab³ - a²b² - 2iab³ + b⁴

collecting like terms, we have

= a⁴ + 2ia³b + 2ia³b - a²b² - 4a²b² - a²b² - 2iab³  - 2iab³ + b⁴

= a⁴ + 4ia³b - 6a²b² - 4iab³ + b⁴

(a + ib)(a + ib)⁴ = (a + ib)(a⁴ + 4ia³b - 6a²b² - 4iab³ + b⁴)

= a⁵ + 4ia⁴b - 6a³b² - 4ia²b³ + ab⁴ + ia⁴b + 4i²a³b² - 6ia²b³ - 4i²ab⁴ + ib⁵

= a⁵ + 4ia⁴b - 6a³b² - 4ia²b³ + ab⁴ + ia⁴b - 4a³b² - 6ia²b³ + 4ab⁴ + ib⁵

collecting like terms, we have

= a⁵ + 4ia⁴b + ia⁴b - 6a³b² - 4a³b² - 4ia²b³ - 6ia²b³ + ab⁴ + 4ab⁴ + ib⁵

= a⁵ + 5ia⁴b - 10a³b² - 10ia²b³ + 5ab⁴ + ib⁵

So, (a + ib)⁵ = a⁵ + 5ia⁴b - 10a³b² - 10ia²b³ + 5ab⁴ + ib⁵

5 0
3 years ago
The parallelogram shown below has an area of 35 units2.
sleet_krkn [62]
The height is 5 becuase if the area is 35 that means the length is 7 so you would divide and get 5
6 0
3 years ago
In a quiz-based program, there are three teams A, B and C. There is a total of five rounds in a game; 20 marks are given for eac
9966 [12]

From the given scenarios, the positions of winning of each team is; Team C came first, Team A came second and Team B came third

<h3>How to find probability of winning?</h3>

From the question, we can derive the following;

Marks gained by team A = 3 × 20 = 60 marks

Marks deducted = 2 × 10 = 20 marks

Hence;

Total marks for Team A = 60 - 20 = 40 marks

Marks gained by team B = 2 × 20 = 40 marks

Marks deducted = 2 × 10 = 20 marks

Hence, total marks of team B = 40 - 20 = 20 marks

Marks gained by team C = 3 × 20 = 60 marks

Marks deducted = 1 × 10 = 10 marks

Hence,  total marks of team C = 60 - 10 = 50 marks

Thus, we can conclude that;

Team C came first, Team A came second and Team B came third

Read more about Probability of winning at; brainly.com/question/24756209

#SPJ1

7 0
2 years ago
(-2x-1)^2=0 How to solve brackets, please help
malfutka [58]
Not quite sure what you mean by brackets, but you can get the solution to this equation in a few steps:

<span>(-2x - 1)</span>² <span>= 0  ... square root both sides to eliminate the squared binomial
</span>√(-2x - 1)² = √0  ... simplify; the square is canceled out and the root of 0 brings you back to 0
-2x - 1 = 0  ... solve like a two-step equation
-2x = 1
x = -1/2 is your x-value.
3 0
3 years ago
Read 2 more answers
What is the equation of the line that passes through (-3, -1) and has a slope of 2/5? Put your answer in slope-intercept form.
Zanzabum
Hi there!

The general formula of A line in slope-intercept form is the following:
y = mx + n

In this formula m represents the slope of the line. Therefore, we can conclude that m = 2/5.
y =  \frac{2}{5} x + n

We also know that the line passes through the point (-3, -1) and we can therefore substitute this coordinate into the formula of the line.
x = -3 and y = -1

- 1 =  \frac{2}{5}  \times  - 3 + n

Multiply first.
- 1 =  -  1\frac{1}{5}  + n

And finally add 1 1/5 to both sides of the equation.
\frac{1}{5}  = n

We can now switch sides.
n =  \frac{1}{5}

Now we've found our value of n, which we can substitute into the formula of our line. Hence, in slope-intercept form, we find the following:
y =  \frac{2}{5}  x  +  \frac{1}{5}

7 0
3 years ago
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