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3 years ago

Simplify the following expression -5(6 - 2i) +(3+ i)(2-3i)

Mathematics

1 answer:

Anuta_ua [19.1K]3 years ago

8 0

The answer will be -21+3i
Hope that helps have a nice day <3

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KIM [24]

Answer:

5 or 6

Step-by-step explanation:

7 0

3 years ago

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A ball is thrown up in the air, and it's height (in feet) as a function of time (in seconds) can be written as h(t) = -16t2 + 32

olga2289 [7]

Answer:

1) Using properties of the quadratic equation:

Here the height equation is:

h(t) = -16t^2 + 32t + 6

We can see that the leading coefficient is negative, this means that the arms of the graph will open downwards.

Then, the vertex of the quadratic equation will be the maximum.

Remember that for a general quadratic equation:

a*x^2 + b*x + c = y

the x-value of the vertex is:

x = -b/2a

Then in our case, the vertex is at:

t = -32/(2*-16) = 1

The maximum height will be the height equation evaluated in this time:

h(1) = -16*1^2 + 32*1 + 6 = 22

The maximum height is 22ft

2) Second method, using physics.

We know that an object reaches its maximum height when the velocity is equal to zero (the velocity equal to zero means that, at this point, the object stops going upwards).

If the height equation is:

h(t) = -16*t^2 + 32*t + 6

the velocity equation is the first derivation of h(t)

Remember that for a function f(x) = a*x^n

we have that:

df(x)/dx = n*a*x^(n-1)

Then:

v(t) = dh(t)/dt = 2*(-16)*t + 32 + 0

v(t) = -32*t + 32

Now we need to find the value of t such that the velocity is equal to zero:

v(t) = 0 = -32*t + 32

32*t = 32

t = 32/32 = 1

So the maximum height is at t = 1

(same as before)

Now we just need to evaluate the height equation in t = 1:

h(1) = -16*1^2 + 32*1 + 6 = 22

The maximum height is 22ft

4 0

3 years ago

Help with this one too, please.

OLEGan [10]

5 units left and 7 units up

5 0

3 years ago

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The difference between a and b is 10. The number a is 4 more than 3 times the number b. Which of the following pairs of equation

k0ka [10]

Answer:

D. a−b=10 a=3b+4

Step-by-step explanation:

Difference between a and b means to subtract b from a

We have,

a-b=10

a is 4 more than 3 times b

4 more than means to add 4

3 times b means to multiply b by 3

Therefore, a=3 times b + 4

a=3b+4

a - b=10; a=3b+4

4 0

4 years ago

What is the multiplicity of each of the roots of the graph of

pantera1 [17]

Answer:

The correct option is;

C. -3, multiplicity 2; -1, multiplicity 1; 1, multiplicity 1

Please find attached the required function graph

Step-by-step explanation:

To solve the equation f(x) = 2·x⁴ + 12·x³ + 16·x² -12·x - 18, by graphing the function, we have;

x ${}$ F(x)

-4 ${}$ 30

-3 ${}$ 0

-2 ${}$ 6

-1 ${}$ 0

0 ${}$ -18

1 ${}$ 0

2 ${}$ 150

The shape of a graph with multiplicity of 2

Given that the graph bounces of the horizontal axis at the y-intercept at point x = -3, the factor (x - 3) must be a quadratic of the form (x - 3)², thereby having a multiplicity of 2 in the solution which are;

x = 1, -1, and, giving

(x - 1)·(x + 1)·(x - 3)² = 0

Therefore, the correct option is -3, multiplicity 2; -1, multiplicity 1; 1 multiplicity 1.

3 0

3 years ago

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