Write the linear equation in slope intercept form.4x+y=1

Mathematics

1 answer:

geniusboy [140]2 years ago

8 0

Answer: y=-4x+1

Step-by-step explanation:

The slope-intercept form of a line is y=mx+b. Therefore, y needs to be on one side of the equation, and the x term and constant need to be on the other. Rearrange the equation to make this true:

4x+y=1

(4x+y)-4x=1-4x

y=1-4x

y=-4x+1

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1. If a polynomial of Degree 4 has an imaginary zero at -2i and a real zero at 5, how many imaginary zeros does it have?

Vadim26 [7]

Answer:

Complex roots for polynomials equations will always come in conjugate pairs. Since 1-2i is a root, 1+2i will also be a root. (Just switch the sign of the imaginary part to its opposite.)

Step-by-step explanation:

So far we have 1-2i and 1+2i as roots. We need two more to make a 4th degree polynomial.

x=1 with multiplicity of 2 means that we count the root twice when we write down the polynomial: (x - 1)(x - 1) = (x - 1)2

Putting it all together, we can construct our polynomial of degree 4 as

y = f(x) = (x - 1)(x - 1)[x - (1-2i)][x - (1+2i)]

Multiply the factors (FOIL):

[x - (1-2i)][x - (1+2i)] =

x2 - (1+2i)x - (1-2i)x + (1-2i)(1+2i) =

x2 - x - 2ix - x + 2ix + (1 + 2i - 2i + 4) =

x2 - 2x + 5

(x - 1)(x - 1) = x2 - x - x + 1 = x2 - 2x + 1

Now multiply the two underlined expressions:

y = (x2 - 2x + 5)(x2 - 2x + 1)

= x4 - 2x3 + 5x2 - 2x3 + 4x2 - 10x + x2 - 2x + 5 by multiplying term by term

= x4 - 4x3 + 10x2 -12x + 5 by collecting like terms.

4 0

2 years ago

A survey showed that 77% of adults need correction (eyeglasses, contacts, surgery, etc.) for their eyesight. If 22 adults are

Sveta_85 [38]

Answer:

The probability that no more than more than 11 of them need correction for their eyesight is 0.00512

No, 11 is not a significantly low low number of adults requiring eyesight correction .

Step-by-step explanation:

A survey showed that 77% of adults need correction for their eyesight.

If 22 adults are randomly selected, find the probability that no more than more than 11 of them need correction for their eyesight.

n =22

p = 0.77

q = 1-p = 1- 0.77=0.23

We are supposed to find $P(x\leq 11)$

$P(x\leq 11)=P(x=1)+P(x=2)+P(x=3)+.....+P(x=11)$

Formula : $P(x=r)=^nC_r p^r q^{n-r}$

$P(x\leq 11)=^{22}C_1 (0.77)^1 (0.23)^{22-1}+^{22}C_2 (0.77)^2 (0.23)^{22-2}+^{22}C_3 (0.77)^1 (0.23)^{22-3}+.....+^{22}C_{11} (0.77)^1 (0.23)^{22-11}$