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3 years ago

Write a polynomial function in it's factored form with zeros 5, -1, and 2

Mathematics

1 answer:

Zina [86]3 years ago

8 0

Answer:

$(x-5)(x+1)(x-2)$

Step-by-step explanation:

well as a general case we have

when we say that

$x=y$ it gives zero moving the y to the other side we have

$x-y=0$

so in our case

$\longrightarrow x-5=0\\\\\rightarrow x-(-1)=0\\\\\longrightarrow x+1=0\\\\\longrightarrow x-2=0$

just multiply the ones that have $\longrightarrow$

and get

$(x-5)(x+1)(x-2)=0$

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Explain what the differences between an arithmetic and geometric sequence are? IN FULL SENTENCES. *

jek_recluse [69]

Answer:

An arithmetic sequence has a constant difference between each term. ... A geometric sequence has a constant ratio (multiplier) between each term. An example is: 2,4,8,16,32,… So to find the next term in the sequence we would multiply the previous term by 2.

Step-by-step explanation:

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3 years ago

Consider a single spin of the spinner. Which events are mutually exclusive? Select two options.

kozerog [31]

Answer:

There is no option in the question given.

However, In logic and probability theory, two events are mutually exclusive or disjoint if they cannot both occur at the same time. A clear example is the set of outcomes of a single coin toss, which can result in either heads or tails, but not both.

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3 years ago

Read 2 more answers

Part 4: Use the information provided to write the vertex formula of each parabola.

sergey [27]

Answer: 1. x = (y - 2)² + 8

$\bold{2.\quad x=-\dfrac{1}{2}(y-10)^2}+1$

3. y = 2(x +9)² + 7

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

Notes: Vertex form is: y =a(x - h)² + k or x =a(y - k)² + h

(h, k) is the vertex
point of vertex is midpoint of focus and directrix: $\dfrac{focus+directrix}{2}$

$\bullet\quad a=\dfrac{1}{4p}$

p is the distance from the vertex to the focus

$focus = \bigg(\dfrac{-31}{4},2\bigg)\qquad directrix: x=\dfrac{-33}{4}\\\\\text{Since directrix is x, then the x-value of the vertex is:}\\\\\dfrac{focus+directrix}{2}=\dfrac{\frac{-31}{4}+\frac{-33}{4}}{2}=\dfrac{\frac{-64}{4}}{2}=\dfrac{-16}{2}=-8\\\\\text{The y-value of the vertex is given by the focus as: 2}\\\\\text{vertex (h, k)}=(-8,2)$

Now let's find the a-value:

$p=focus-vertex\\\\p=\dfrac{-31}{4}-\dfrac{-32}{4}=\dfrac{1}{4}\\\\\\a=\dfrac{1}{4p}=\dfrac{1}{4(\frac{1}{4})}=\dfrac{1}{1}=1$

Now, plug in a = 1 and (h, k) = (-8, 2) into the equation x =a(y - k)² + h

x = (y - 2)² + 8

***************************************************************************************

$focus = \bigg(\dfrac{1}{2},10\bigg)\qquad directrix: x=\dfrac{3}{2}\\\\\text{Since directrix is x, then the x-value of the vertex is:}\\\\\dfrac{focus+directrix}{2}=\dfrac{\frac{1}{2}+\frac{3}{2}}{2}=\dfrac{\frac{4}{2}}{2}=\dfrac{2}{2}=1\\\\\text{The y-value of the vertex is given by the focus as: 10}\\\\\text{vertex (h, k)}=(1,10)$

Now let's find the a-value:

$p=focus-vertex\\\\p=\dfrac{1}{2}-\dfrac{2}{2}=\dfrac{-1}{2}\\\\\\a=\dfrac{1}{4p}=\dfrac{1}{4(\frac{-1}{2})}=\dfrac{1}{-2}=-\dfrac{1}{2}$

Now, plug in a = -1/2 and (h, k) = (1, 10) into the equation x =a(y - k)² + h

$\bold{x=-\dfrac{1}{2}(y-10)^2}+1$

***************************************************************************************

$focus = \bigg(-9,\dfrac{57}{8}\bigg)\qquad directrix: y=\dfrac{55}{8}\\\\\text{Since directrix is y, then the y-value of the vertex is:}\\\\\dfrac{focus+directrix}{2}=\dfrac{\frac{57}{8}+\frac{55}{8}}{2}=\dfrac{\frac{112}{8}}{2}=\dfrac{14}{2}=7\\\\\text{The x-value of the vertex is given by the focus as: -9}\\\\\text{vertex (h, k)}=(-9,7)$

Now let's find the a-value:

$p=focus-vertex\\\\p=\dfrac{57}{8}-\dfrac{56}{8}=\dfrac{1}{8}\\\\\\a=\dfrac{1}{4p}=\dfrac{1}{4(\frac{1}{8})}=\dfrac{1}{\frac{1}{2}}=2$

Now, plug in a = 2 and (h, k) = (-9, 7) into the equation y =a(x - h)² + k

y = 2(x +9)² + 7

4 0

3 years ago

PLEASE HELP MEEEEEEEEEEEEEEEEEEEEEE

DedPeter [7]

Answer:

Step-by-step explanation:

8 0

3 years ago

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Write an algebraic expression that represents<br> the following phrase:<br> The product of 8 and 12

Ainat [17]

Answer:

$8*12$

Step-by-step explanation:

First, the problem asks for an expression; this means that there should be no equal sign. Also, the keyword "product" means that both the terms must be multiplied. So, $8*12$ is the final expression; this equals 96.

6 0

3 years ago