The expression x3 – 64 can be written as (x)3 – (4)3. What is the factorization of x3 – 64?

a3 – b3 = (a – b)(a2 + ab + b2)

A. (x – 4)(x2 + 4x + 8)
B. (x – 4)(x2 + 4x + 16)
C. (x – 64)(x2 + 64x + 16)
D. (x – 64)(x2 + 64x + 4,096)

Answer:

The image if the point is (-7, -9)

Step-by-step explanation:

∵ The given point is (9, -7)

∴ x = 9 and y = -7

∵ The given point is rotated 270° counterclockwise about the origin

→ By using the third rule above

∴ The image of the point is (y, -x)

→ That mean change the sign of x-coordinate, then switch them

∵ x = 9 and y = -7

∴ The image if the point is (-7, -9)

Answer:

You already know how to simplify an expression like

7

(

4

x

+

3

)

, right? Just use the distributive property to multiply 7 times 4x and then 7 times 3. This gives you an answer of

28

x

+

21

. Pretty simple. But - What if you have something like this:

(

4

x

+

6

)

(

x

+

2

)

? That's where we use the FOIL method. FOIL means First, Outside, Inside, Last. That's not too hard to remember if you say it in your head a few times.

You use FOIL to multiply the terms inside the parenthesis in a specific order: first, outside, inside, last. Here's how to solve

(

4

x

+

6

)

(

x

+

2

)

:

First - multiply the first term in each set of parenthesis:

First

4

x

∗

x

=

4

x

2

Outside - multiply the two terms on the outside:

Outside

4

x

∗

2

=

8

x

Inside - multiply both of the inside terms:

Inside

6

∗

x

=

6

x

Last - multiply the last term in each set of parenthesis:

Last

6

∗

2

=

12

Now just add everything together to get

4

x

2

+

14

x

+

12

. This method only works easily with two binomials. To multiply something complicated like

(

4

x

+

6

)

(

5

x

−

3

)

(

15

−

x

)

, just do FOIL on two of the binomials and then distribute the answer onto the remaining binomial.

Here are some more examples of FOIL multiplication:

Example:

Multiply the following:

(

6

x

+

1

)

(

2

x

+

9

)

Solution:

Just follow the letters in FOIL:

First:

6

x

∗

2

x

=

12

x

2

Outside:

6

x

∗

9

=

54

x

.

Inside:

1

∗

2

x

=

2

x

.

Last:

1

∗

9

=

9

.

Sum it all up and you get:

12

x

2

+

56

x

+

9

.

Example:

Multiply the following:

(

2

x

−

5

)

(

x

−

4

)

Solution:

Just follow the letters in FOIL:

First:

2

x

∗

x

=

2

x

2

Outside:

2

x

∗

(

−

4

)

=

−

8

x

Inside:

−

5

∗

x

=

−

5

x

Last:

(

−

5

)

∗

(

−

4

)

=

20

Sum it all up and you get:

(

2

x

2

−

13

x

+

20

)

.

The FOIL method is not too difficult to learn once you remember what it stands for. Just repeat first, outside, inside, last and you'll remember it. Other than that, it's just a matter of multiplying each of those steps and adding everything together. Even if the numbers are really ugly with fractions and negative signs and such just follow the steps and the method will work.

Step-by-step explanation

Answer:

[tex]\displaystyle x = 25.2[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Step-by-step explanation:

Step 1: Define

[tex]\displaystyle \frac{7}{8} = \frac{x}{28.8}[/tex]

Step 2: Solve for x

To show the converse of the Pythagorean theorem using side lengths chosen from 5 cm, 9 cm, 12 cm, and 13 cm  the procedure that can be used is : C. Knowing that 52 + 122 = 132, draw the 5 cm side and the 12 cm side with a right angle between them. The 13 cm side will fit to

form a right triangle.

In Option C, we are given the lengths 5 cm, 9 cm, 12 cm, and 13 cm. The converse of the Pythagorean theorem states that if the square of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.

In this case, we have 52 + 122 = 132, which satisfies the condition for a right triangle according to the Pythagorean theorem.

By drawing the 5 cm side and the 12 cm side with a right angle between them, we can see that the 13 cm side will fit perfectly to form a right triangle. This demonstrates the converse of the Pythagorean theorem.

Option C is the correct procedure to show the converse of the Pythagorean theorem using the given side lengths.

For more such questions on Pythagorean theorem

https://brainly.com/question/343682

#SPJ8

Answer:

34

Step-by-step explanation:

Answer:

x=34

Step-by-step explanation:

2x=x+34

-x   -x

x=34

TADA! :D

Answer:

Choice 2 and 4 should be the answer

Step-by-step explanation:

For choice 2: both started away from home and finished at home.

For choice 4, Peter is farther away from home than Camilla, but they reached home at the same time which proves that Peter is faster.

Domain is basically an input while Range is an output. Domain is the set of all x-values while Range is the set of y-values.

[tex]\large \boxed {domain} = > \large \boxed{range}[/tex]

From input to output. That means from if we substitute domain in the equation, we would get range.

[tex]f(x) = 4x + 2 \\ f(0) = 4(0) + 2 = 0 + 2 = 2 \\ f(3) = 4(3) + 2 = 12 + 2 = 14 \\ f(6) = 4(6) + 2 = 24 + 2 = 26[/tex]

We input the value of x that are given and we get the value of f(x) which is the output at the specified domain.

[tex] \large \boxed{2, 14, 26}[/tex]

Answer:

The mass of the 2.5 kilograms mass in grams is 2,500 grams.

Answer:

192 in 2. multiply all of the numbers together

Step-by-step explanation:

6x4x8=192

Answer:

the answer will be a because its on top of it

Answer:

E, I hope this helps :D

Answer:

1/4 of ur pens

Step-by-step explanation:

Answer:

x-intercept: -1/7

y-intercept: 1/4

Step-by-step explanation:

change equation into standard form:  7x - 4y = -1

set 'x' to zero and solve for y:  0 - 4y = -1

                                                        y = 1/4

set 'y' to zero and solve for x:  7x - 0 = -1

                                                        x = -1/7

Answer:

The length of the first piece is 0.51 m

The length of the second piece is 0.31 m

The length of the third piece is 0.28 m

Step-by-step explanation:

The question is a simultaneous equation with word problem

The total length of the wood = 0.9 m

The number of pieces the wood is cut into = 3

The length of the first piece = 0.2 m + The length of the second piece

The length of the third piece = The length of the second piece - 0.23 m

Let "y" represent the length of the second piece, let "x" represent the length of the first piece, and let "z" represent the length of the third piece, we have;

x = 0.2 + y...(1)

z = y - 0.23...(2)

x + y + z = 0.9...(3)

Therefore, by substitution, we have;

0.2 + y + y + y - 0.23 = 0.9

3·y - 0.03 = 0.9

3·y = 0.9 + 0.03 = 0.93

y = 0.93/3 = 0.31

y = 0.31

The length of the second piece = y = 0.31 m

From equation (1), we have;

x = 0.2 + y = 0.2 + 0.31 = 0.51

x = 0.51

The length of the first piece = x = 0.51 m

From equation (2), we have;

z = y - 0.23

z = 0.51 - 0.23 = 0.28

z = 0.28

The length of the third piece = z = 0.28 m.

Answer:

It means that it requires 2268 to manufacture 63 chairs, (because it costs 36 to manufacture one chair).

Step-by-step explanation:

Answer:

false, true and false

Step-by-step explanation:

Answer:

The smallest angle is the angle shown by 3x - 17 which ends up being 49°.

Step-by-step explanation:

The angles of a triangle add up to 180 degrees. We can write an equation and solve for x.

75 + (2x + 12) + (3x - 17) = 180

~Combine like terms

70 + 5x = 180

~Subtract 70 to both sides

5x = 110

~Divide 5 to both sides

x = 22

Using what we found for x, solve for the missing angles.

2x + 12

2(22) + 12

44 + 12

66

3x - 17

3(22) - 17

66 - 17

49

Best of Luck!

Answer:

160

Step-by-step explanation:

the length betwenn side to side woukd be 160

Answer:

The answer is 100

Step-by-step explanation:

a² + b² = c²

80²+60²=c²

6,400+1,200=c²

√6,400=√c²

subtract 1,200 - 6,400= 5,200

c2=72.1

Answer:

47/24

Step-by-step explanation:

24x1 = 24

24+23 = 47

47/24

Answer:

47/24

Step-by-step explanation:

just add 24 to the 23 and you'll get your answer.

Answer:

B. [tex]y= \left \{ {{x^{2}+4,\,x< 2 } \atop {-x+4,\,x \ge 2}} \right.[/tex]

Step-by-step explanation:

The piecewise function consists in two functions:

(i) A vertical parabola directed in the +x direction and centered at [tex]V(x,y) = (0, 4)[/tex] for all [tex]x \in (-\infty, 2)[/tex]. That is:

[tex]y = x^{2}+4[/tex], [tex]x < 2[/tex]

(ii) A line with negative slope for all [tex]x \in [2, +\infty)[/tex].

[tex]y = -x+4[/tex], [tex]x \ge 2[/tex]

The correct answer is B.

Answer:

h = 24 cm

Step-by-step explanation:

By using the similar triangle property in the given triangles,

Since, ΔBCD ~ ΔBAE

Their corresponding sides will be in the same ratio,

[tex]\frac{BC}{BA}= \frac{CD}{AE}= \frac{BD}{BE}=\frac{a}{h}[/tex]

[tex]\frac{CD}{AE}=\frac{a}{h}[/tex]

[tex]\frac{10}{20}=\frac{(36-h)}{h}[/tex]

10h = 20(36 - h)

10h = 720 - 20h

30h = 720

h = 24 cm

Therefore, height h = 24 cm is the answer.

Answer:

24

Step-by-step explanation:

I took the test

Answer

y=4

y=2x-1

Step-by-step explanation:

Y is the vertical axis

Answer:

[tex]y=1/3x[/tex]

Step-by-step explanation:

It's positive, and it goes up once for every three times it goes to the right.

Answer:

The value for X is 25

Step-by-step explanation:

I hope this helps you out!