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2 years ago

If a polynomial function f(x) has roots 4 – 13i and 5, what must be a factor of f(x)?

Mathematics

1 answer:

Morgarella [4.7K]2 years ago

7 0

The factor of f(x) is (x-(4-13i))

If a polynomial function f(x) has roots 4 – 13i and 5

One of the complex roots is 4-13i

If we have one complex root then there should be one more complex root.

<h3>What is the complex root?</h3>

complex roots come in pairs like (a+ib) and (a-ib)

so another complex root for 4-13i is 4+13i

If 'a' is a root then the factor is (x-a)

4+13i is a root

So the factor is (x-(4-13i))

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There are 8 fish in a fish tank<br> 2 drowned and three died, how many fish are left in the tank?

MakcuM [25]

Answer: 8

Step-by-step explanation:

Fish cannot drown

Three died but they are still in the tank

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3 years ago

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Dan buys a car for £2200.

KatRina [158]

Answer:

The worth of the car after 6 years is £2,134.82

Step-by-step explanation:

The amount at which Dan buys the car, PV = £2200

The rate at which the car depreciates, r = -0.5%

The car's worth, 'FV', in 6 years is given as follows;

$FV = PV \cdot \left ( 1 + \dfrac{r}{100} \right )^n$

Where;

r = The depreciation rate (negative) = -0.5%

FV = The future value of the asset

PV = The present value pf the asset = £2200

n = The number of years (depreciating) = 6

By plugging in the values, we get;

$FV = 2200 \times \left ( 1 + \dfrac{-0.5}{100} \right )^6 \approx 2,134.82$

The amount the car will be worth which is its future value, FV after 6 years is FV ≈ £2,134.82 (after rounding to the nearest penny (hundredth))

8 0

3 years ago

Segment AB is tangent to T at B. What is the radius of T?

juin [17]

The value of the radius of T is 28 units

<h3>How to determine the value of the radius of T</h3>

From the question, we understand that:

Segment AB is tangent to T at B

This means that

<ABT = 90

So, we have a right triangle

Let the radius of the triangle be r

By the Pythagoras theorem, we have

AT^2 = AB^2 + VT^2

This gives

(25 + r)^2 = 45^2 + r^2

Open the bracket

625 + 50r + r^2 = 2025 + r^2

Subtract r^2 from both sides of the equation

625 + 50r = 2025

Subtract 625 from both sides of the equation

50r = 1400

Divide both sides by 50

r = 28

Hence, the value of the radius of T is 28 units

Read more about tangent at:

brainly.com/question/17040970

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2 years ago

If x = 7 and y = 10, what is the value of the expression xy - ( y + 2) ?

Katena32 [7]

You times 7×10-(10+2) And making it C 58
Hope that helped

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4 years ago

Read 2 more answers

The U.S. Energy Information Administration (US EIA) reported that the average price for a gallon of regular gasoline is $2.94. T

Anit [1.1K]

Answer:

a) 25

b) 67

c) 97

Step-by-step explanation:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1-0.95}{2} = 0.025$

Now, we have to find z in the Ztable as such z has a pvalue of $1-\alpha$ .

So it is z with a pvalue of $1-0.025 = 0.975$ , so $z = 1.96$

Now, find the margin of error M as such

$M = z*\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample. In this problem, $\sigma = 0.25$

(a) The desired margin of error is $0.10.

This is n when M = 0.1. So

$M = z*\frac{\sigma}{\sqrt{n}}$

$0.1 = 1.96*\frac{0.25}{\sqrt{n}}$

$0.1\sqrt{n} = 1.96*0.25$

$\sqrt{n} = \frac{19.6*0.25}{0.1}$

$(\sqrt{n})^{2} = (\frac{19.6*0.25}{0.1})^{2}$

$n = 24.01$

Rounding up to the nearest whole number, 25.

(b) The desired margin of error is $0.06.

This is n when M = 0.06. So

$M = z*\frac{\sigma}{\sqrt{n}}$

$0.06 = 1.96*\frac{0.25}{\sqrt{n}}$

$0.06\sqrt{n} = 1.96*0.25$

$\sqrt{n} = \frac{19.6*0.25}{0.06}$

$(\sqrt{n})^{2} = (\frac{19.6*0.25}{0.06})^{2}$

$n = 66.7$

Rounding up, 67

(c) The desired margin of error is $0.05.

This is n when M = 0.05. So

$M = z*\frac{\sigma}{\sqrt{n}}$

$0.05 = 1.96*\frac{0.25}{\sqrt{n}}$

$0.05\sqrt{n} = 1.96*0.25$

$\sqrt{n} = \frac{19.6*0.25}{0.05}$

$(\sqrt{n})^{2} = (\frac{19.6*0.25}{0.05})^{2}$

$n = 96.04$

Rounding up, 97

8 0

3 years ago