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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

Mathematics

1 answer:

STALIN [3.7K]3 years ago

6 0

Answer:

c=4

Step-by-step explanation:

If polynomial p(x) is divisible by (x-3), then x=3 is zero of p(x).

p(x) =-x^3+cx^2-4x+3

0=p(3)=-3^3 +c*3^2 - 4*3+3

0=-27+9c-12+3

0=-27-9+9c

0=-36+9c

36=9c

c=36/9

c=4

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Your vacation cabin on the lake has three rooms. The bathroom is 12' X 6', the bedroom is 14' X 18' and the great room is 20' X

GarryVolchara [31]

Answer: $9240\ ft^3$

Step-by-step explanation:

Given

Dimension of the bathroom is $12'\times 16'$

Dimension of the bedroom is $14'\times 18$

Dimension of the great room is $20'\times 30'$

Height of the ceiling is $h=10'$

Total area of the cabin

$\Rightarrow A=12\times6+14\times 18+20\times 30\\\Rightarrow A=72+252+600\\\Rightarrow A=924\ ft^2$

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2 years ago

Emmanuel sections off a part of the backyard of his house to build the rectangular stone patio for his grill. The length of the

liq [111]

Answer: x + 3feet

Step-by-step explanation:

From the question, Emmanuel sections a part of his house backyard in order to build the rectangular stone patio for his grill. We are told that the length of the base is going to be 3 feet more than the width and the width has been defined as x.

Since the length of the base will be 3 feet more than the width and the width is x. Therefore, the length will be:

Length = x + 3feet

5 0

3 years ago

Approximate <img src="https://tex.z-dn.net/?f=-8%20%2B%5Csqrt%7B20%7D" id="TexFormula1" title="-8 +\sqrt{20}" alt="-8 +\sqrt{20}

alisha [4.7K]

The value of the radical expression -8 + √20 when expanded and solved is -3.6, based on the given parameters

<h3>What are equivalent expressions?</h3>

Equivalent expressions are different expressions that have equal values when evaluated and compared

<h3>How to approximate the radical expression?</h3>

The expression is given as:

-8 + √20

The above expression is a radical expression

So, we start by doing the following

Express 20 as 5 * 4

-8 + √20 = -8 + √(5 * 4)

Split the radical expression √(5 * 4)

-8 + √20 = -8 + √5 * √4

Evaluate the square root of 4 i.e. √4 = 2

-8 + √20 = -8 + √5 * 2

This gives

-8 + √20 = -8 + 2√5

Evaluate the square root of 5

-8 + √20 = -8 + 2 * 2.2

Evaluate the product of 2 and 2.2

-8 + √20 = -8 + 4.4

Evaluate the difference

-8 + √20 = -3.6

Based on the given parameters, the value of the radical expression -8 + √20 when expanded and solved is -3.6

So, the complete equation is:

-8 + √20 = -3.6