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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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Parallel / Perpendicular Practice

deff fn [24]

The slope and intercept form is the form of the straight line equation that includes the value of the slope of the line

Neither
║
Neither
⊥
║
Neither
Neither
Neither

Reason:

The slope and intercept form is the form y = m·x + c

Where;

m = The slope

Two equations are parallel if their slopes are equal

Two equations are perpendicular if the relationship between their slopes, m₁, and m₂ are; $m_1 = -\dfrac{1}{m_2}$

1. The given equations are in the slope and intercept form

$\ y = 3 \cdot x + 1$

The slope, m₁ = 3

$y = \dfrac{1}{3} \cdot x + 1$

The slope, m₂ = $\dfrac{1}{3}$

Therefore, the equations are neither parallel or perpendicular

Neither

2. y = 5·x - 3

10·x - 2·y = 7

The second equation can be rewritten in the slope and intercept form as follows;

$y = 5 \cdot x -\dfrac{7}{2}$

Therefore, the two equations are parallel

3. The given equations are;

-2·x - 4·y = -8

-2·x + 4·y = -8

The given equations in slope and intercept form are;

$y = 2 -\dfrac{1}{2} \cdot x$

Slope, m₁ = $-\dfrac{1}{2}$

$y = \dfrac{1}{2} \cdot x - 2$

Slope, m₂ = $\dfrac{1}{2}$

The slopes

Therefore, m₁ ≠ m₂

$m_1 \neq -\dfrac{1}{m_2}$

The lines are Neither parallel nor perpendicular

Neither

4. The given equations are;

2·y - x = 2

$y = \dfrac{1}{2} \cdot x +1$

m₁ = $\dfrac{1}{2}$

y = -2·x + 4

m₂ = -2

Therefore;

$m_1 \neq -\dfrac{1}{m_2}$

Therefore, the lines are perpendicular

5. The given equations are;

4·y = 3·x + 12

-3·x + 4·y = 2

Which gives;

First equation, $y = \dfrac{3}{4} \cdot x + 3$

Second equation, $y = \dfrac{3}{4} \cdot x + \dfrac{1}{2}$

Therefore, m₁ = m₂, the lines are parallel

6. The given equations are;

8·x - 4·y = 16

Which gives; y = 2·x - 4

5·y - 10 = 3, therefore, y = $\dfrac{13}{5}$

Therefore, the two equations are neither parallel nor perpendicular

Neither

7. The equations are;

2·x + 6·y = -3

Which gives $y = -\dfrac{1}{3} \cdot x - \dfrac{1}{2}$

12·y = 4·x + 20

Which gives

$y = \dfrac{1}{3} \cdot x + \dfrac{5}{3}$

m₁ ≠ m₂

$m_1 \neq -\dfrac{1}{m_2}$

Neither

8. 2·x - 5·y = -3

Which gives; $y = \dfrac{2}{5} \cdot x +\dfrac{3}{5}$

5·x + 27 = 6

$x = -\dfrac{21}{5}$

Therefore, the slopes are not equal, or perpendicular, the correct option is Neither

Learn more here:

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6 0

3 years ago

Thanks if u help ✨:)

faltersainse [42]

Answer:

D.mode

Step-by-step explanation:

4 0

3 years ago

. The cost of 2 pizzas and 1 burger is ₹ 450. Write a linear equation for this situation and draw its graph.

Akimi4 [234]

Answer:

The linear equation is;

Y = 450 - 2·X

Please find the included graph

Step-by-step explanation:

Whereby we have the following relation;

The cost of 1 pizza = X

The cost of 1 burger = Y

Hence;

450 = Y + 2·X

Which gives;

Y = 450 - 2·X

The linear equation for the situation is therefore as presented above

The graph of the linear equation can be plotted using the assumed data as follows;

Y, X

1, 448

2, 446

3, 444

4, 442

5, 440

6, 438

7, 436

8, 434

9, 432

10, 430

11, 428

12, 426

13, 424

14, 422

15, 420

16, 418

8 0

3 years ago

Geomtry plz help me 15 pointz

nikitadnepr [17]

Answer:

m∠R=76°

Step-by-step explanation:

∠STR=∠RST=(2x+2)° (base angles of isos triangle)

2(2x+2)+(3x+1)=180 (angle sum of triangle)

4x+4+3x+1=180

7x+5=180

7x=180-5

=175

x=175÷7

=25

Hence, m∠R = (3x+1)°

= [3(25)+1]°

= (75+1)°

= 76°

7 0

3 years ago

Read 2 more answers

Select the correct answer from each drop-down menu. Right triangle ABC is represented with the right angle at vertex B. Base BC

Svetradugi [14.3K]

By using trigonometric relations, we will see that:

AC = 15.6 in

AB = 8.4 in.

<h3>How to get the measures of the other two sides of the right triangle?</h3>

Here we have the right triangle where:

B = 90°

C = 40°

BC = 10 in.

Notice that is the adjacent cathetus to the angle C, then we can use the two relations:

sin(a) = (adjacent cathetus)/(hypotenuse).
tan(a) = (opposite cathetus)/(adjacent cathetus).

Where:

hypotenuse = AC
opposite cathetus = AB.

Then we will have:

sin(40°) = 10in/AC.

AC = 10in/sin(40°) = 15.6 in

tan(40°) = AB/10in

tan(40°)*10in = AB = 8.4 in.

So we can conclude that for the given right triangle we have:

AC = 15.6 in

AB = 8.4 in.

If you want to learn more about right triangles:

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6 0

2 years ago