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tankabanditka [31]

3 years ago

7

You have a board of wood that measures 9 3/4 feet. You cut a piece off the board measuring 2 15/16 feet and then another piece m

easuring 4 3/8 feet. You now need a piece that is 2 1/2 feet long. You say your remaining board of wood is long enough. Is this reasonable?

1 answer:

denpristay [2]3 years ago

7 0

No u only have 2 7/16

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Luna is buying food for a dinner party. She is going to buy 2 key lime pies that cost $8.99 each. Shrimp costs $8.50 a pound. Sh

spin [16.1K]

Answer:

x=45- 2*8.99/8.50

x~3.18

3 lbs of shrimp

3 0

3 years ago

Determine consecutive integer values of x between which each real zero is located.

frozen [14]

Answer:

1. x = -2 or x = sqrt(6) - 2 or x = -2 - sqrt(6)

2. x = -2.10947 or x = -0.484343 or x = 1.67884 or x = 2.91497

Step-by-step explanation:

Solve for x:

x^3 + 6 x^2 + 6 x - 4 = 0

The left hand side factors into a product with two terms:

(x + 2) (x^2 + 4 x - 2) = 0

Split into two equations:

x + 2 = 0 or x^2 + 4 x - 2 = 0

Subtract 2 from both sides:

x = -2 or x^2 + 4 x - 2 = 0

Add 2 to both sides:

x = -2 or x^2 + 4 x = 2

Add 4 to both sides:

x = -2 or x^2 + 4 x + 4 = 6

Write the left hand side as a square:

x = -2 or (x + 2)^2 = 6

Take the square root of both sides:

x = -2 or x + 2 = sqrt(6) or x + 2 = -sqrt(6)

Subtract 2 from both sides:

x = -2 or x = sqrt(6) - 2 or x + 2 = -sqrt(6)

Subtract 2 from both sides:

Answer: x = -2 or x = sqrt(6) - 2 or x = -2 - sqrt(6)

_________________________________________

Solve for x:

x^4 - 2 x^3 - 6 x^2 + 8 x + 5 = 0

Eliminate the cubic term by substituting y = x - 1/2:

5 + 8 (y + 1/2) - 6 (y + 1/2)^2 - 2 (y + 1/2)^3 + (y + 1/2)^4 = 0

Expand out terms of the left hand side:

y^4 - (15 y^2)/2 + y + 117/16 = 0

Subtract -3/2 sqrt(13) y^2 - (15 y^2)/2 + y from both sides:

y^4 + (3 sqrt(13) y^2)/2 + 117/16 = (3 sqrt(13) y^2)/2 + (15 y^2)/2 - y

y^4 + (3 sqrt(13) y^2)/2 + 117/16 = (y^2 + (3 sqrt(13))/4)^2:

(y^2 + (3 sqrt(13))/4)^2 = (3 sqrt(13) y^2)/2 + (15 y^2)/2 - y

Add 2 (y^2 + (3 sqrt(13))/4) λ + λ^2 to both sides:

(y^2 + (3 sqrt(13))/4)^2 + 2 λ (y^2 + (3 sqrt(13))/4) + λ^2 = -y + (3 sqrt(13) y^2)/2 + (15 y^2)/2 + 2 λ (y^2 + (3 sqrt(13))/4) + λ^2

(y^2 + (3 sqrt(13))/4)^2 + 2 λ (y^2 + (3 sqrt(13))/4) + λ^2 = (y^2 + (3 sqrt(13))/4 + λ)^2:

(y^2 + (3 sqrt(13))/4 + λ)^2 = -y + (3 sqrt(13) y^2)/2 + (15 y^2)/2 + 2 λ (y^2 + (3 sqrt(13))/4) + λ^2

-y + (3 sqrt(13) y^2)/2 + (15 y^2)/2 + 2 λ (y^2 + (3 sqrt(13))/4) + λ^2 = (2 λ + 15/2 + (3 sqrt(13))/2) y^2 - y + (3 sqrt(13) λ)/2 + λ^2:

(y^2 + (3 sqrt(13))/4 + λ)^2 = y^2 (2 λ + 15/2 + (3 sqrt(13))/2) - y + (3 sqrt(13) λ)/2 + λ^2

Complete the square on the right hand side:

(y^2 + (3 sqrt(13))/4 + λ)^2 = (y sqrt(2 λ + 15/2 + (3 sqrt(13))/2) - 1/(2 sqrt(2 λ + 15/2 + (3 sqrt(13))/2)))^2 + (4 (2 λ + 15/2 + (3 sqrt(13))/2) (λ^2 + (3 sqrt(13) λ)/2) - 1)/(4 (2 λ + 15/2 + (3 sqrt(13))/2))

To express the right hand side as a square, find a value of λ such that the last term is 0.

This means 4 (2 λ + 15/2 + (3 sqrt(13))/2) (λ^2 + (3 sqrt(13) λ)/2) - 1 = 8 λ^3 + 18 sqrt(13) λ^2 + 30 λ^2 + 45 sqrt(13) λ + 117 λ - 1 = 0.

Thus the root λ = 1/4 (-3 sqrt(13) - 5) + (2 2^(2/3) (i sqrt(3) + 1))/(i sqrt(183) - 29)^(1/3) + ((-i sqrt(3) + 1) (i sqrt(183) - 29)^(1/3))/(2 2^(2/3)) allows the right hand side to be expressed as a square.

(This value will be substituted later):

(y^2 + (3 sqrt(13))/4 + λ)^2 = (y sqrt(2 λ + 15/2 + (3 sqrt(13))/2) - 1/(2 sqrt(2 λ + 15/2 + (3 sqrt(13))/2)))^2

Take the square root of both sides:

y^2 + (3 sqrt(13))/4 + λ = y sqrt(2 λ + 15/2 + (3 sqrt(13))/2) - 1/(2 sqrt(2 λ + 15/2 + (3 sqrt(13))/2)) or y^2 + (3 sqrt(13))/4 + λ = -y sqrt(2 λ + 15/2 + (3 sqrt(13))/2) + 1/(2 sqrt(2 λ + 15/2 + (3 sqrt(13))/2))

Solve using the quadratic formula:

y = 1/4 (sqrt(2) sqrt(4 λ + 15 + 3 sqrt(13)) + sqrt(2) sqrt((108 - 24 sqrt(13) λ - 16 λ^2 - 4 sqrt(2) sqrt(4 λ + 15 + 3 sqrt(13)))/(4 λ + 15 + 3 sqrt(13)))) or y = 1/4 (sqrt(2) sqrt(4 λ + 15 + 3 sqrt(13)) - sqrt(2) sqrt((108 - 24 sqrt(13) λ - 16 λ^2 - 4 sqrt(2) sqrt(4 λ + 15 + 3 sqrt(13)))/(4 λ + 15 + 3 sqrt(13)))) or y = 1/4 (sqrt(2) sqrt((108 - 24 sqrt(13) λ - 16 λ^2 + 4 sqrt(2) sqrt(4 λ + 15 + 3 sqrt(13)))/(4 λ + 15 + 3 sqrt(13))) - sqrt(2) sqrt(4 λ + 15 + 3 sqrt(13))) or y = 1/4 (-sqrt(2) sqrt(4 λ + 15 + 3 sqrt(13)) - sqrt(2) sqrt((108 - 24 sqrt(13) λ - 16 λ^2 + 4 sqrt(2) sqrt(4 λ + 15 + 3 sqrt(13)))/(4 λ + 15 + 3 sqrt(13)))) where λ = 1/4 (-3 sqrt(13) - 5) + (2 2^(2/3) (i sqrt(3) + 1))/(i sqrt(183) - 29)^(1/3) + ((-i sqrt(3) + 1) (i sqrt(183) - 29)^(1/3))/(2 2^(2/3))

Substitute λ = 1/4 (-3 sqrt(13) - 5) + (2 2^(2/3) (i sqrt(3) + 1))/(i sqrt(183) - 29)^(1/3) + ((-i sqrt(3) + 1) (i sqrt(183) - 29)^(1/3))/(2 2^(2/3)) and approximate:

y = -2.60947 or y = -0.984343 or y = 1.17884 or y = 2.41497

Substitute back for y = x - 1/2:

x - 1/2 = -2.60947 or y = -0.984343 or y = 1.17884 or y = 2.41497

Add 1/2 to both sides:

x = -2.10947 or y = -0.984343 or y = 1.17884 or y = 2.41497

Substitute back for y = x - 1/2:

x = -2.10947 or x - 1/2 = -0.984343 or y = 1.17884 or y = 2.41497

Add 1/2 to both sides:

x = -2.10947 or x = -0.484343 or y = 1.17884 or y = 2.41497

Substitute back for y = x - 1/2:

x = -2.10947 or x = -0.484343 or x - 1/2 = 1.17884 or y = 2.41497

Add 1/2 to both sides:

x = -2.10947 or x = -0.484343 or x = 1.67884 or y = 2.41497

Substitute back for y = x - 1/2:

x = -2.10947 or x = -0.484343 or x = 1.67884 or x - 1/2 = 2.41497

Add 1/2 to both sides:

Answer: x = -2.10947 or x = -0.484343 or x = 1.67884 or x = 2.91497

8 0

3 years ago

Please help! i need to figure out this xD

Svetach [21]

The answer to this is D or at least that's what I got

6 0

3 years ago

How do how you cross cancel multiplying fractions

DENIUS [597]

It's easy once you spot the ones that can cross cancel!

Say we have the fractions 8/10 and 20/23. $\frac{8}{10} \frac{20}{23}$ (it's easier to see on top of each other)

If you look diagonally , so 8 and 23 and 10 and 20, you can see that 10 and 20 have a common factor. So we divide it by the highest common factor to reduce those numbers, making it easier to multiply. 10 and 20 can become 1 and 2, dividing by 10. So now we are left with 8/1 and 2/23, and now we multiply normally going across so 16/23.

This works going both diagonals and simplifying both, but in that case it would be easier to try and simplify the fractions before cross multiplying them.

Basically: look for those diagonals and if they can be divided down by the highest common factor, go for it to make it easier to multiply normally afterwards.

Hope I helped!

5 0

3 years ago

Complete the equation: x2 + 10x +__= (__)^2

Sliva [168]

Answer:

x2 + 10x +25 = (x+5)^2

Step-by-step explanation:

x^2 + 10x

To complete the square

Take the coefficient of x

10

Divide by 2

10/2 =5

Square it

5^2 =25

Add it

x2 + 10x +25

The coefficient of x divided by 2 is the factor we add to x inside the square

(x+5)^2

6 0

3 years ago

Read 2 more answers