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inna [77]
2 years ago
9

The expression on (3+i)(4+5i) can be written in form a+bi, where a and b are integers. What are the values of a and b? (Show you

r work please)
Mathematics
1 answer:
gregori [183]2 years ago
8 0

(3 + i)(4 + 5i) \\ 12 + 15i + 4i + 5 {i }^{2}  \\ 12 + 19i - 5 \\ 7 + 19i

Therefore, a is 7 aka real part and b is 19 which is imaginary part.

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The formula F = ma shows the relationship between force, mass, and acceleration. Solve this formula for a.
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2 years ago
Y=-1/3x^2-4x-5 in vertex form
grigory [225]

Answer:

Y=-\frac{1}{3}(x+6)^2+7   [Vertex form]

Step-by-step explanation:

Given function:

Y=-\frac{1}{3}x^2-4x-5

We need to find the vertex form which is.,

y=a(x-h)^2+k

where (h,k) represents the co-ordinates of vertex.

We apply completing square method to do so.

We have  

Y=-\frac{1}{3}x^2-4x-5

First of all we make sure that the leading co-efficient is =1.

In order to make the leading co-efficient is =1, we multiply each term with -3.

-3\times Y=-3\times\frac{1}{3}x^2-(-3)\times4x-(-3)\times 5

-3Y=x^2+12x+15

Isolating x^2 and x terms on one side.

Subtracting both sides by 15.

-3Y-15=x^2+12x-15-15

-3Y-15=x^2+12x

In order to make the right side a perfect square trinomial, we will take half of the co-efficient of x term, square it and add it both sides side.  

square of half of the co-efficient of x term = (\frac{1}{2}\times 12)^2=(6)^2=36

Adding 36 to both sides.

-3Y-15+36=x^2+12x+36

-3Y+21=x^2+12x+36

Since x^2+12x+36 is a perfect square of (x+6), so, we can write as:

-3Y+21=(x+6)^2

Subtracting 21 to both sides:

-3Y+21-21=(x+6)^2-21

-3Y=(x+6)^2-21

Dividing both sides by -3.

\frac{-3Y}{-3}=\frac{(x+6)^2}{-3}-\frac{21}{-3}

Y=-\frac{1}{3}(x+6)^2+7   [Vertex form]

8 0
3 years ago
Plz help!!!! (click on the pic)
goblinko [34]

Answer:

x^2+8x

Step-by-step explanation:

instructions included above :)

7 0
3 years ago
I WILL GIVE BRAINLEST!!! (6 points!)
vlada-n [284]

Answer:

OPTION A: 2x + 3y = 5

Step-by-step explanation:

The product of slopes of two perpendicular lines is -1.

We rewrite the given equation as follows:

2y = 3x + 2

⇒ y = $ \frac{3}{2}x + 1 $

The general equation of the line is: y = mx + c, where 'm' is the slope of the line.

Here, m = $ \frac{3}{2} $.

Therefore, the slope of the line perpendicular to the line given = $ \frac{-2}{3} $ because $ \frac{3}{2} \times \frac{-2}{3} = -1 $.

To determine the equation of the line passing through the given point and a slope we use the Slope - One - point formula which is:

                                  y - y₁ = m(x - x₁)

The point is: (x₁, y₁) = (-2, 3)

Therefore, the equation is:

y - 3 = $ \frac{-2}{3} $(x + 2) $

⇒ 3y - 9 = -2(x + 2)

⇒ 3y - 9 = -2x - 4

⇒ 2x + 3y = 5 is the required equation.

6 0
3 years ago
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