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3 years ago

Factor the expression completely. 625x4 - 256y4

Mathematics

1 answer:

scoundrel [369]3 years ago

5 0

Answer:

(625 • (x4)) - 28y4

54x4 - 28y4 3.1 Factoring: 625x4-256y4

Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)

Proof : (A+B) • (A-B) =

A2 - AB + BA - B2 =

A2 - AB + AB - B2 =

A2 - B2Note : AB = BA is the commutative property of multiplication.

Note : - AB + AB equals zero and is therefore eliminated from the expression.

Check : 625 is the square of 25

Check : 256 is the square of 16

Check : x4 is the square of x2

Check : y4 is the square of y2

Factorization is : (25x2 + 16y2) • (25x2 - 16y2) 3.2 Factoring: 25x2 - 16y2

Check : 25 is the square of 5

Check : 16 is the square of 4

Check : x2 is the square of x1

Check : y2 is the square of y1

Factorization is : (5x + 4y) • (5x - 4y)this is the answer: (25x2 + 16y2) •(5x + 4y) • (5x - 4y)

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Kim scored 33 points at her basketball game game with a combination of 2-point shots and 3-point shots. If she made a total of 1

Rudik [331]

Answer:

(12, 3)

Step-by-step explanation:

write the equation:

if x = number of 2 point shots

and y = number of 3 point shots

2x + 3y = 33

write another equation with the total baskets

x + y = 15

plug them both into desmos and find the solution

(12, 3)

she made 12 2-point shots and 3 3-point shots

3 0

3 years ago

Read 2 more answers

Solve the equation, and check the solutions (√x+3)+6=3.

larisa86 [58]

Answer:

The equation has no solution.

Step-by-step explanation:

Hi there!

First, let´s write the equation:

(√x + 3) + 6 = 3

To solve the equation, let´s subtract 6 to both sides of the equation:

√x + 3 = -3

subtract 3 to both sides of the equation:

√x = -6 (the square root of any number can´t be negative, but let´s solve it anyway and then check the solution).

Square both sides of the equation:

x = 36

Now, let´s check the solution:

(√x + 3) + 6 = 3

x = 36

(√36 + 3) + 6 = 3

(6 + 3) + 6 = 3

9 + 6 = 3

15 ≠ 3

Then, the equation has no solution.

Have a nice day!

6 0

2 years ago

Find the measures of the interior

Ainat [17]

Answer:

Angle 1 = 108°

Angle 2 = 72°

Angle 3 = 120°

Angle 4 = 96°

Angle 5 = 144°

Step-by-step explanation:

We need to find the measures of the interior angles in a pentagon if the measure of each consecutive angle is in the ratio 9:6:10:8:12.

Let x be the common ratio

So, we can write:

Angle 1 = 9x

Angle 2 = 6x

Angle 3 = 10x

Angle 4 = 8x

Angle 5 = 12x

We know that the sum of all angles of pentagon = 540

So, adding all angles and equal them to 540, we can find value of x

$9x+6x+10x+8x+12x=540\\45x=540\\x=\frac{540}{45}\\x=12$

So, we get the value of x: x=12

Now, calculating the angles by putting x=12:

Angle 1 = 9x = 9(12) = 108°

Angle 2 = 6x = 6(12) = 72°

Angle 3 = 10x = 10(12) = 120°

Angle 4 = 8x = 8(12) = 96°

Angle 5 = 12x= 12(12) = 144°

6 0

3 years ago

You have a coupon for an additional 25% off the price of any sale item at a store. The store has put a watercolor kit on sale fo

telo118 [61]

Final price=original price*(100%- discount 1)(100%-discount 2)
original price=$40
discount 1=25%⇒ 100 - discount 1=100%-25%=75%=75/100=0.75
discount 2=15%⇒ 100 - discount 2=100%-12%=85%=85/100=0.85

original price=$40(0.75)(0.85)=$25.5

Answer: $25.5

4 0

3 years ago

2.4x-9 < 1.8x+6 solve the inequality

nasty-shy [4]

Answer:

x<25

Step-by-step explanation:

Let's solve your inequality step-by-step.

2.4x−9<1.8x+6

Step 1: Subtract 1.8x from both sides.

2.4x−9−1.8x<1.8x+6−1.8x

0.6x−9<6

Step 2: Add 9 to both sides.

0.6x−9+9<6+9

0.6x<15

Step 3: Divide both sides by 0.6

0.6x/0.6 < 15/0.6

x<25

8 0

3 years ago