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3 years ago

Find the value of c so that the polynomial p(x) is divisible by (x-3). p(x) =-x^3+cx^2-4x+3. c=?

Mathematics

1 answer:

Vilka [71]3 years ago

4 0

Answer:

$\boxed{\textsf {The value of c is $\sf \dfrac{-14}{3}$. }}$

Step-by-step explanation:

A polynomial is given to us . We need to find the value of c so that it is divisible by (x-3 ) .The given polynomial to us is ,

$\sf \implies p(x)=- x^3+cx^2-4x+3$

And the factor is ,

$\sf \implies g(x) = x + 3$

Now , according to factor theorem , p(x) will be divisible by g(x) if p(-3) = 0

$\sf \implies p(x)= - x^3+cx^2-4x+3 \\\\\implies\sf p(-3) = 0 \\\\\sf\implies -(-3)^3+c(-3)^2-4(-3)+3 = 0 \\\\\sf\implies 27 + 9c +12+3=0 \\\\\sf\implies 9c +42=0 \\\\\sf\implies 9c = (-42) \\\\\sf\implies c = \dfrac{-42}{9}\\\\\sf\implies \boxed{\pink{\sf c = \dfrac{-14}{3}}}$

<h3><u>Hence </u><u>the </u><u>value </u><u>of </u><u>c </u><u>is </u><u>(</u><u>-</u><u>1</u><u>4</u><u>)</u><u>/</u><u>3</u><u> </u><u>.</u></h3>

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A translation does not maintain congruency.<br> A. True<br> B. False

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Answer: True.

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2 years ago

Relations and Functions, please help with these 3 questions asap. I will give brainliest! Only answer if you know how to do this

gladu [14]

<h2> Question # 1</h2>

Part A) Is the relation a function? Explain.

A function relates each element of a set with exactly one element of another set.

Important things for a relationship to be a function:

Every element in X is related to some element in Y.

A function cannot have one-to-many relationship.

A function must contain single valued, means it is not having one-to-many relation

Considering the points on coordinate plane

(-4, 2), (-3, 0), (-2, -1), (0, 2), (2, -3), (3, 3)

If we carefully observe, we determine that relation

relates each element of a set with exactly one element of another set

is single-valued, means It is not giving back 2 or more results for the same input. In other words, it is not having one-to-many relation.

It is in fact, having many to one. For example, the pairs (0, 2) and (-4, 2) is having many- to-one relationship.

So, from the above observation, it is clear that the relationship is a function.

Part B) What is the domain of the relation?

Considering the points on coordinate plane

(-4, 2)

(-3, 0)

(-2, -1)

(0, 2)

(2, -3)

(3, 3)

Also we know that domain of the relation is the set of all the x-values of an ordered pairs.

So, the domain of the relation: {-4, -3, -2, 0, 2, 3}

Part C) What is the range of the relation?

Considering the points on coordinate plane

(-4, 2)

(-3, 0)

(-2, -1)

(0, 2)

(2, -3)

(3, 3)

As we know that the range of a relationship is the set of all the y-values of an ordered pair.

So, the range of the relationship will be: { -3, -1, 0, 2, 3}

<em>Note:</em>

The duplicated entries in the domain and range are written only once.
Also, the domain and range can be written in ascending order.

Part D) What is the value of y when x = 2? Explain

Considering the points on coordinate plane

(-4, 2)

(-3, 0)

(-2, -1)

(0, 2)

(2, -3)

(3, 3)

From the given points on the coordinate plane, it is clear that when the value of x = 2, then the value of y = -3

Therefore, the value of y is -2 when x = 2

<h2> Question # 2</h2>

Considering the points on coordinate plane

(-4, -1), (-2, 1), (0, -3), (2, 3), (4, -2)

If we bring a point, let say (2, 4), and graphed on the coordinate system, then the relation will no longer be function.

The reason is that the induction of the point (2, 4) would violate the definition of a relation to be a function.

Observe that (2, 4) and (2, 3) will make the relation having one-to-many relationship as (2, 4) and (2, 3) is giving 2 outputs i.e. y = 4, and y = 3 for a single input i.e. x = 2.

Therefore, the induction of the point (2, 4), when graphed, makes the relation not a function.

<h2> Question # 3</h2>

Part A)

$f\left(x\right)\:=\:|x\:-\:3|\:-\:2$ ; $x = -5$

The attached figure a shows the graph for the function

$f\left(x\right)\:=\:|x\:-\:3|\:-\:2$

In the attached figure a, the graph represents an absolute value relationship as the absolute value of a number is never negative.

Evaluate the function for x = -5

$f\left(x\right)\:=\:|x\:-\:3|\:-\:2$

$|\left-5\right\:-\:3|\:-\:2....[A]$

Solving

$\left|-5-3\right|$

$\mathrm{Subtract\:the\:numbers:}\:-5-3=-8$

$=\left|-8\right|$

$\mathrm{Apply\:absolute\:rule}:\quad \left|-a\right|=a$

$\left|-8\right|=8$

So,

$\left|-5-3\right|=8$

Equation [A] becomes

$\:|-5\:-\:3|\:-\:2\:=8\:-\:2\:$ ∵ $\left|-5-3\right|=8$

$=6$

Therefore,

the value of $f\left(x\right)\:=\:|x\:-\:3|\:-\:2$ at $x = -5$ will be 6.

i.e. $f(x)=6$

<h2 />

Part B)

$g\left(x\right)=1.5x;\:x=0.2$

The attached figure b shows the graph for the function

$g\left(x\right)=1.5x$

In the attached figure b, the graph shows that the function represents a linear relationship as the graph is a straight line.

Evaluate the function for x = 0.2

$g\left(x\right)=1.5x$

Putting x = 0.2

$g\left(x\right)=1.5\left(0.2\right)$

$1.5\left(0.2\right)=0.3$

$g\left(x\right)=0.3$

So,

the value of $g\left(x\right)=1.5x$ at $x = 0.2$ will be 0.3.

i.e. $g\left(x\right)=0.3$

Part C)

$p\left(x\right)\:=\:|7\:-\:2x|;\:x\:=\:-3$

As the absolute value of a number will be never negative.

The attached figure c shows the graph for the function

$p\left(x\right)\:=\:|7\:-\:2x|$

In the attached figure c, the graph represents an absolute value relationship as the absolute value of a number is never negative.

Evaluate the function for x = -3

$p\left(x\right)\:=\:|7\:-\:2x|$

Solving

$\left|7-2x\right|$

$\left|7-2\left(-3\right)\right|$

$=\left|7+6\right|$

$=\left|13\right|$

$\mathrm{Apply\:absolute\:rule}:\quad \left|a\right|=a,\:a\ge 0$

$=13$

So,

$\left|7-2x\right|=13$

So,

the value of $p\left(x\right)\:=\:|7\:-\:2x|$ at $x = -3$ will be 13.

i.e $p\left(x\right)\:=13$

Keywords: function, relation

Learn more about functions from brainly.com/question/2335371

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3 0

4 years ago

A radius of a circle is perpendicular to a chord if and only if it

NNADVOKAT [17]

Answer:C

Step-by-step explanation:

6 0

3 years ago

I got no clue how to do this.

melisa1 [442]

Answer:

Step-by-step explanation:

Just to keep the computer happy by not having to figure out rounding answers that involve square roots and other problem numbers. I've chosen numbers that should work out evenly. And you should be able to draw the trapezoid.

Givens

H = 14

a = 23

b = 25

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Formula

Area = (a + b)*h/2

Solution

Area = (23 + 25)*14/2

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Note if a + b = 48 any values for a and b will work.

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