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2 years ago

Form a polynomial whose zeros and degree are given. Zeros: 2, multiplicity 1; 4, multiplicity 2; degree 3

Mathematics

1 answer:

jek_recluse [69]2 years ago

6 0

Answer:

If the polynomial is degree 3, then it is of the form y = Ax3 + Bx2 +Cx + D

And if the zeros are -2 with multiplicity of 1, then the factor is (x+2)1 = x+2

The other zero is -4 with multiplicity of 2, so it's factor is (x+4)2 = x2 +8x+16

So in general, if we let A = 1, then the polynomial is y = (x+2)(x+4)2 which multiplies out to

(x+2)(x2+8x+16) = x3 + 8x2 + 16x + 2x2 + 16x + 32

Combining like terms gives the polynomial:

y = x3 +10x2 + 32x + 32

If A is not 1, then y = A(x3 +10x2 + 32

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3 years ago

A teacher has a box of pens and pencils. There are 8 more pencils than pens. After the students take 1 pen and 5 pencils from th

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Let no. of pens be x.

Pens : x
Pencils: x+8

Total: 2x+8

Student takes 1 pen and 5 pencils.

Remainder: 2x+8 - 5 -1 = 2x+2
2x+2 = 26
2x= 24
x = 12 (original no. of pens)
x+ 8 = 20 (original no of pencils)

There are 12 pens at first and 20 pencils.
After 1 pen is taken, 11 pens are left.
After 5 pencils are taken, 20-5=15 pencils are left.

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3 years ago

Read 2 more answers

Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bars(s).

kirza4 [7]

Answer:

(a)23 (b)90 (c)3

Step-by-step explanation:

The equation for the line of best fit for this situation is given as

$y=\frac{3}{10}x+8$

where x=average temperature in degrees

y=average number of hot dogs she sold,

(a) The expected number of hot dogs sold when the temperature is 50° would be___hot dogs.

When x=50°

$y=\frac{3}{10}X50+8=15+8=23$

When the temperature is 50°, the expected number of hot dogs sold would be 23.

(b)If the vendor sold 35 hot dogs, the temperature is expected to be ___degrees.

If y=35

$35=\frac{3}{10}x+8\\35-8=\frac{3}{10}x\\27=\frac{3}{10}x$

Multiply both sides by 10/3

$27 X \frac{10}{3}= \frac{3}{10}x X \frac{10}{3}\\x=90^{0}$

If the vendor sold 35 hot dogs, the temperature is expected to be 90 degrees.

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3 years ago

You are carpeting a room in a house for your job. You have a boss that likes to play jokes, so instead of just giving you the di

forsale [732]

Answer:

$x^2-4x+3$

$63\ \text{sq. units}$

Step-by-step explanation:

l = Length = $\dfrac{x^2-x-6}{x-5}$

w = Width = $\dfrac{x^2-6x+5}{x+2}$

Area is given by

$A=lw\\\Rightarrow A=\dfrac{x^2-x-6}{x-5}\times\dfrac{x^2-6x+5}{x+2}\\\Rightarrow A=\dfrac{x^2-3x+2x-6}{x-5}\times\dfrac{x^2-5x-1x+5}{x+2}\\\Rightarrow A=\dfrac{(x-3)(x+2)}{x-5}\times\dfrac{(x-5)(x-1)}{x+2}\\\Rightarrow A=(x-3)(x-1)\\\Rightarrow A=x^2-4x+3$

Area of the room is $x^2-4x+3$ .

If $x=10$

Area of the room

$A=x^2-4x+3=10^2-4\times 10+3\\\Rightarrow A=63\ \text{sq. units}$

So, the amount of carpet needed would be $63\ \text{sq. units}$ .

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3 years ago

what are the x-intercepts of the graph of the function f(x) = x2 4x – 12? (–6, 0), (2,0) (–2, –16), (0, –12) (–6, 0), (–2, –16),

joja [24]

F(x) = x^2 + 4x - 12
x-intercepts are the values of x when y = 0
x^2 + 4x - 12 = 0
(x - 2)(x + 6) = 0
x - 2 = 0 or x + 6 = 0
x = 2 or x = -6
Therefore the x-intercepts are (-6, 0), (2, 0)

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3 years ago

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Form a polynomial whose zeros and degree are given. ​Zeros: 2​, multiplicity​ 1; 4​, multiplicity​ 2; degree 3

Form a polynomial whose zeros and degree are given. Zeros: 2, multiplicity 1; 4, multiplicity 2; degree 3