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lakkis [162]
2 years ago
7

Can someone get this? Ive been trying and cant get it

Mathematics
1 answer:
Dmitry [639]2 years ago
6 0

<u>Given</u><u> </u><u>:</u><u>-</u>

  • The roots of the function are 5 and -3 .

<u>To</u><u> </u><u>Find</u><u> </u><u>:</u><u>-</u>

  • The Quadratic function .

<u>Answer</u><u> </u><u>:</u><u>-</u>

The roots of the function are 5 and -3 . In general we can write the Quadratic function with roots π and ∆ as ,

\sf\longrightarrow f(x) = ( x - π )(x-∆)

So on using this we have ,

\sf\longrightarrow f(x) = ( x -5)( x -(-3))

\sf\longrightarrow f(x) = (x-5)(x+3)

\sf\longrightarrow f(x) = x(x-5)+3(x-5)

\sf\longrightarrow f(x) = x² -5x +3x -15

\sf\longrightarrow f(x) = x² -2x -15

<u>Hence </u><u>the</u><u> required</u><u> </u><u>answer</u><u> </u><u>is </u><u>x²</u><u> </u><u>-2x </u><u>-</u><u>1</u><u>5</u><u>.</u>

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Using the Factor Theorem, which of the polynomial functions has the zeros 2, radical 3 , and negative radical 3 ?
Alja [10]

Using the factor theorem, it is found that the polynomial is:

f(x) = x^3 - 2x^2 - 3x + 6

Given by the first option

---------------------------

Given a polynomial f(x), this polynomial has roots x_{1}, x_{2}, x_{n} using the factor theorem it can be written as: a(x - x_{1})*(x - x_{2})*...*(x-x_n), in which a is the leading coefficient.

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In this question:

  • x_1 = 2
  • x_2 = \sqrt{3}
  • x_3 = -\sqrt{3}
  • By the options, leading coefficient a = 1

Thus:

f(x) = (x - 2)(x - \sqrt{3})(x + \sqrt{3})

f(x) = (x - 2)(x^2 - 3)

f(x) = x^3 -2x^2 - 3x + 6

Which is the polynomial.

A similar problem is given that: brainly.com/question/4786502

5 0
2 years ago
Find the domain of the rational expression: x-3/2x-8
miss Akunina [59]

Answer:

\huge\boxed{x\neq4\to x\in\mathbb{R}\backslash\{4\}}

Step-by-step explanation:

\dfrac{x-3}{2x-8}

We know: the denominator must be different than 0.

Therefore

2x-8\neq0        <em>add 8 to both sides</em>

2x-8+8\neq0+8

2x\neq8             <em>divide both sides by 2</em>

\dfrac{2x}{2}=\dfrac{8}{2}\\\\x\neq4

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3 years ago
How do I do this problem
STatiana [176]

Answer:

shape one would have to move 8 units to the right and 5 units down and then flip

i hope this helped you to understand more

Step-by-step explanation:

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3 years ago
Find the circumference of the circle. Then, find the length of each bolded arc. Use appropriate notation
Vaselesa [24]

Answer:

\text{1) }\\\text{Circumference: }24\pi \text{ m}},\\\text{Length of bolded arc: }18\pi \text{ m}\\\\\text{3)}\\\text{Circumference. }4\pi \text{ mi},\\\text{Length of bolded arc: }  \frac{3\pi}{2}\text{ mi}

Step-by-step explanation:

The circumference of a circle with radius r is given by C=2\pi r. The length of an arc is makes up part of this circumference, and is directly proportion to the central angle of the arc. Since there are 360 degrees in a circle, the length of an arc with central angle \theta^{\circ} is equal to 2\pi r\cdot \frac{\theta}{360}.

Formulas at a glance:

  • Circumference of a circle with radius r: C=2\pi r
  • Length of an arc with central angle \theta^{\circ}: \ell_{arc}=2\pi r\cdot \frac{\theta}{360}

<u>Question 1:</u>

The radius of the circle is 12 m. Therefore, the circumference is:

C=2\pi r,\\C=2(\pi)(12)=\boxed{24\pi\text{ m}}

The measure of the central angle of the bolded arc is 270 degrees. Therefore, the measure of the bolded arc is equal to:

\ell_{arc}=24\pi \cdot \frac{270}{360},\\\\\ell_{arc}=24\pi \cdot \frac{3}{4},\\\\\ell_{arc}=\boxed{18\pi\text{ m}}

<u>Question 2:</u>

In the circle shown, the radius is marked as 2 miles. Substituting r=2 into our circumference formula, we get:

C=2(\pi)(2),\\C=\boxed{4\pi\text{ mi}}

The measure of the central angle of the bolded arc is 135 degrees. Its length must then be:

\ell_{arc}=4\pi \cdot \frac{135}{360},\\\ell_{arc}=1.5\pi=\boxed{\frac{3\pi}{2}\text{ mi}}

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Answer:

$100 is less than or equal to x

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