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3 years ago

Is the expression below completely factored? If not, complete the factorization.

Mathematics

1 answer:

Ket [755]3 years ago

6 0

Answer:

A) No, because the greatest common factor is 8y?, and the completely factored form is 8y2(4y2 - 6y + 3).

Step-by-step explanation:

Considering the expression

4y(8y3 – 12y2 + 6y)

From the elements in the parenthesis, 2 and y can still be factored out such that what will be left of each element

8y3/2y = 4y2

12y2/2y = 6y

6y/2y = 3

Hence

4y(8y3 – 12y2 + 6y) = 4y*2y(4y2 - 6y +3)

= 8y2(4y2 - 6y + 3)

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8x+3y=4 <br> -7x+5y=-34 <br><br> Elimination using multiplication

irga5000 [103]

Answer:

x= 2 and y = -4

Step-by-step explanation:

8x + 3y = 4 ---------------------------------(1)

-7x + 5y = -34 -----------------------------(2)

Multiply through equation (1) by 5 and multiply through equation(2) by 3

40x + 15y = 20 ----------------------------(3)

-21x + 15y =-102----------------------------(4)

Subtract equation (4) from equation (3)

61x = 122

Divide both-side of the equation by 61

61x/61 = 122/61

(At the left-hand side of the equation 61 will cancel-out 61 leaving us with just x, while at the left-hand side of the equation 122 will be divided by 61)

x = 122/61

x=2

Substitute x= 2 into equation (1)

8x + 3y = 4

8(2) + 3y = 4

16 + 3y = 4

Subtract 16 from both-side of the equation

16-16 + 3y = 4-16

3y = -12

Divide both-side of the equation by 3

3y/3 = -12/3

y = -4

x= 2 and y = -4

4 0

3 years ago

Read 2 more answers

X = ? y = ? 16 45 degrees

mezya [45]

Let's put more details in the figure to better understand the problem:

Let's first recall the three main trigonometric functions:

$\text{ Sine }\theta\text{ = }\frac{\text{ Opposite Side}}{\text{ Hypotenuse}}$ $\text{ Cosine }\theta\text{ = }\frac{\text{ Adjacent Side}}{\text{ Hypotenuse}}$ $\text{ Tangent }\theta\text{ = }\frac{\text{ Opposite Side}}{\text{ Adjacent Side}}$

For x, we will be using the Cosine Function:

$\text{ Cosine }\theta\text{ = }\frac{\text{ Adjacent Side}}{\text{ Hypotenuse}}$ $Cosine(45^{\circ})\text{ = }\frac{\text{ x}}{\text{ 1}6}$ $(16)Cosine(45^{\circ})\text{ = x}$ $(16)(\frac{1}{\sqrt[]{2}})\text{ = x}$ $\text{ }\frac{16}{\sqrt[]{2}}\text{ x }\frac{\sqrt[]{2}}{\sqrt[]{2}}\text{ = }\frac{16\sqrt[]{2}}{2}$ $\text{ 8}\sqrt[]{2}\text{ = x}$

Therefore, x = 8√2.

For y, we will be using the Sine Function.

$\text{ Sine }\theta\text{ = }\frac{\text{ Opposite Side}}{\text{ Hypotenuse}}$ $\text{ Sine }(45^{\circ})\text{ = }\frac{\text{ y}}{\text{ 1}6}$ $\text{ (16)Sine }(45^{\circ})\text{ = y}$ $\text{ (16)(}\frac{1}{\sqrt[]{2}})\text{ = y}$ $\text{ }\frac{16}{\sqrt[]{2}}\text{ x }\frac{\sqrt[]{2}}{\sqrt[]{2}}\text{ = }\frac{16\sqrt[]{2}}{2}$ $\text{ 8}\sqrt[]{2}\text{ = y}$

Therefore, y = 8√2.

5 0

1 year ago

Please help solve the inequality.

gulaghasi [49]

Answer:

Are there two you're asking for?

#2: x ≥ 9

#3: x > -2

Step-by-step explanation:

#2 Work:

x - 13 ≥ -4

Step 1: Add 13 to both sides

x - 13 + 13 ≥ -4 + 13

Add -4 and 13 to get 9.

x ≥ 9

#3 Work:

x/2 > -1

Multiply both sides by 2. Since 2 is positive, the inequality direction remains the same

x/2 * 2 > -1 * 2

x > -2

5 0

2 years ago

HELP ASAP!!<br> What is the unit rate for the situation in terms of centimeter/minute?

vesna_86 [32]

The unit rate is 5cm per 1min

5:1

4 0

3 years ago

Two friends sold many pieces of furniture and made $1550 during their garage sale. They had fifteen more $10 bills than $50 b

Novosadov [1.4K]

Answer:

The number of $ 10 bills is 37, the number of $ 20 is 6 and the number of $ 50 bills is 22.

Step-by-step explanation:

Let n₁ = number of $ 10 bills,

Let n₂ = number of $ 20 bills and

Let n₃ = number of $ 50 bills

Given that 10n₁ + 20n₂ + 50n₃ = 1550 (1)

Also, since we have fifteen more $10 bills than $50 bills, n₁ = n₃ + 15 (2)

and we have 4 more than three times as many $20 bills as $50 bills. n₃ = 3n₂ + 4. (3)

substituting equations (2) and (3) into (1), we have

10(n₃ + 15) + 20n₂ + 50n₃ = 1550

expanding the bracket, we have

10n₃ + 150 + 20n₂ + 50n₃ = 1550

collecting like terms, we have

60n₃ + 150 + 20n₂ = 1550

inserting equation (3), we have

60(3n₂ + 4) + 150 + 20n₂ = 1550

expanding the bracket, we have

180n₂ + 240 + 150 + 20n₂ = 1550

collecting like terms, we have

200n₂ + 390 = 1550

subtracting 390 from both sides, we have

200n₂ = 1550 - 390

200n₂ = 1160

dividing both sides by 200, we have

n₂ = 1160/200

n₂ = 5.8

n₂ ≅ 6 since it cannot be a fraction.

Substituting this into (3), we have

n₃ = 3n₂ + 4 = 3(6) + 4 = 18 + 4 = 22

substituting n₃ into (2), we have

n₁ = n₃ + 15 = 22 + 15 = 37

So, the number of $ 10 bills is 37, the number of $ 20 is 6 and the number of $ 50 bills is 22.

3 0

3 years ago