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3 years ago

Given the following exponential function, identify whether the change represents

Mathematics

1 answer:

mart [117]3 years ago

5 0

Answer:

it is a decay, it's value drops by 4%

Step-by-step explanation:

0.96 is less than 1 so it is a decay function.

1-0.96 = 0.04 so it drops at the rate of 4%

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Question 14 of 25What is the complete factorization of the polynomial below?x³+x² + 4x+4O A. (x-1)(x+2)(x+2)B. (x + 1)(x + 2)(x

mote1985 [20]

GIVEN:

We are given the following polynomial;

$x^3+x^2+4x+4$

Required;

We are required to factorize this polynomial completely.

Step-by-step explanation;

To factorize this polynomial, we start by grouping;

$(x^3+x^2)+(4x+4)$

We now take the common factor in each group;

$\begin{gathered} x^2(x+1)+4(x+1) \\ \\ (x^2+4)(x+1) \end{gathered}$

Next, we factorize the first parenthesis. To do this we set the equation equal to zero and solve for x as follows;

$\begin{gathered} x^2+4=0 \\ \\ Subtract\text{ }4\text{ }from\text{ }both\text{ }sides: \\ \\ x^2=-4 \\ \\ Take\text{ }the\text{ }square\text{ }root\text{ }of\text{ }both\text{ }sides: \\ \\ x=\pm\sqrt{-4} \\ \\ x=(\pm\sqrt{-1}\times\sqrt{4}) \\ \\ x=\pm2i \end{gathered}$

Therefore, the factors of the other parenthesis are;

$(x+2i)(x-2i)$

Therefore, the complete factorization of the polynomial is;

ANSWER:

$(x+1)(x+2i)(x-2i)$

Option C is the correct answer.

4 0

1 year ago

Write the equation of the line that is the perpendicular bisector of the segment with endpoints (4, 1) and (2, -5)

Sedbober [7]

Answer: $\bold{y=-\dfrac{1}{3}x-1}$

<u>Step-by-step explanation:</u>

(4, 1) & (2, -5)

First, find the slope (m) and then the perpendicular (opposite reciprocal) slope:

$m=\dfrac{y_2-y_1}{x_2-x_1}\\\\\\m=\dfrac{-5-1}{2-4} = \dfrac{-6}{-2}=3\quad \rightarrow \quad m_{\perp}=-\dfrac{1}{3}\\$

Next, find the midpoint of (4, 1) and (2, -5):

$Midpoint=\bigg(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\bigg)\\\\\\.\qquad \qquad=\bigg(\dfrac{4+2}{2},\dfrac{1-5}{2}\bigg)\\\\\\.\qquad \qquad=\bigg(\dfrac{6}{2},\dfrac{-4}{2}\bigg)\\\\\\.\qquad \qquad=(3, -2)$

Lastly, input the perpendicular slope and the midpoint into the Point-Slope formula to find the equation of the line:

$y - y_1 = m_{\perp}(x - x_1)\\\\y - (-2) = -\dfrac{1}{3}(x - 3)\\\\y + 2=-\dfrac{1}{3}x +1\\\\y =-\dfrac{1}{3}x - 1\\$

6 0

3 years ago

Liana can see that the measure of Angle L and Angle M form a straight line. Since Liana knows that a straight line has an angle

cricket20 [7]

Answer:

150 degrees

Step-by-step explanation:

Let's start off by looking at what we are working with in this specific problem:

We can see that we are looking at 2 angles, angle L and angle M, that add up to a total of 180 degrees (aka a straight line)

Now that we know that, we also have to keep is mind that angle L + angle M = 180 degrees.

Now that we've got all of that out of the way, let's set up a simple algebraic equation:

angle L + angle M = 180

We also know that angle L is 30 degrees so let's add it into the equation we have just created:

30 + angle M = 180

We now know that 30 plus angle M (whatever it might be) is equal to 180 so in order to solve this problem we have to do some simple subtraction.

180 - 30 = angle M

Now we are left with:

150 degrees = angle M

4 0

3 years ago

Sierra left $17.75 as a tip for a waiter. This was 20% of the bill before the tip. How much was her total bill before the tip

iris [78.8K]

Answer:

$31.95 Before tip.

Step-by-step explanation:

I believe you should just add 17.75+80%=31.95

4 0

2 years ago

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Nady [450]

Answer:

Okay, hello to you too.

5 0

3 years ago

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