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3 years ago

Show all work to factor x4 − 10x2 + 9 completely.

Mathematics

2 answers:

AlekseyPX3 years ago

8 0

Step-by-step explanation:

Since both terms are perfect squares, factor using the difference of squares formula, a² - b² =(a+b)(a−b) where a=x and b=3.

(x+3)(x-3)(x+1)(x-1)

leva [86]3 years ago

6 0

Answer:

(x+1)(x-1)(x+3)(x-3)

Step-by-step explanation:

x4-10x^2+9

Group expression so that the coefficients of the x^2 terms add up to +9.

= x^4 -9x^2 - x^2+9

match coefficients in both groups

= x^4 -9x^2 - (x^2-9)

factor each group

= x^2 (x^2-9) - 1(x^2-9)

now factor out the common factor (x^2-9)

= (x^2-1)(x^2-9)

Finally, factor each quadratic factor

= (x+1)(x-1)(x+3)(x-3)

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Suppose that Stephen is the quality control supervisor for a food distribution company. A shipment containing many thousands of

OLga [1]

Answer:

probability that his sample will contain at least one damaged apple (P) = 0.7215

Step-by-step explanation:

Given:

Probability of damaged apples (p) = 12% = 0.12

number of samples (n) = 10

Consider,

x- number of apples damaged.

Using Binomial distribution formula:

P(x) = $(nCx) (P)^x (1-p)^(n-x)$

To find the probability that his sample will contain at least one damaged apple:

P(x≥1) = 1 - P(x<1)

= 1 - P(x=0)

= 1 - $10C_0 (0.12)^0 ( 1-0.12)^(10)$

P(x≥1) = 0.7215

4 0

3 years ago

The side lengths of the following right triangle 15,20 and 25, as shown below. The altitude from the right angle splits the hypo

kompoz [17]

Answer:

$h = 12$

$x = 9$

$y= 16$

Step-by-step explanation:

Given

The attached triangle

Required

Find h, x and y

Let the base of the triangle be 15.

So, the area is:

$A = \frac{1}{2} * 15 * 20$

$i.e\ height = 20$

$A = \frac{1}{2} * 300$

$A = 150$

Let the base of the triangle be 25.

So, the area is:

$A = \frac{1}{2} * 25 * h$

$i.e\ height = h$

$A = \frac{1}{2} * 25h$

Substitute $A = 150$

$\frac{1}{2}*25h = 150$

Solve for h

$h = \frac{150 *2}{25}$

$h = 6 *2$

$h = 12$

Considering the smallest triangle

$Hypotenuse = 15$

So:

$15^2 = h^2 + x^2$

$15^2 = 12^2 + x^2$

This gives:

$15^2 - 12^2 = x^2$

$81 = x^2$

Take square roots

$9 =x$

$x = 9$

Solving for y

$x + y = 25$

$y= 25 - x$

$y= 25 - 9$

$y= 16$

7 0

3 years ago

Somebody help me with this please .

erastova [34]

Step-by-step explanation:

12. Cos 60° = 8/c

0,5 = 8/c

0,5 c = 8

c = 16

D² = V16²-8²

= V256-64

=V192 = V16×12 = 4V12

= 4V4×3 = 8V3

13. Cos 30° = 6/b

V3/2 = 6/b

V3 b = 12

b = 12/V3

b/Sin B = a /sin A

b/Sin90° = 6/ sin 60°

b = 6

1 V3/2

b× V3 = 6

b = 6× 2/V3

= 12/V3

8 0

4 years ago

What is the equation of the line which includes points (1, 1) and (1, 5)?

Allisa [31]

Equation of the line that includes points (1, 1) and (1, 5) is a vertical line given by x = 1.

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3 years ago

pencils are sold in packages of 10 and erasers are sold in packages of 6 what is the least number of pencils and erasers you can

Keith_Richards [23]

6packs of pencils and 10packs of eraser's

6 0

4 years ago

Read 2 more answers